Grad(E) #537

edinvay · 2026-01-09T16:03:33Z

DO NOT MERGE!

Currently, Mrchem is completely missing necessary infrastructure for a possibility of encoding non-SCF algorithms.
Therefore, the branch cannot be merged.

ilfreddy · 2026-01-19T11:59:09Z

Please change the content of the comments, especially those containing unacceptable language, or remove this pull request. And add a meaningful explanation about what this pull request is doing.

This commit consolidates the development of real-valued L2 and H1 inner products for OrbitalVector objects, implements gradient and preconditioning machinery, and resolves discrepancies caused by differing Laplacian conventions between MRCPP and MRChem. no control over SCF? I am about to modify the code added euclidian gradient added calculation of grad_E comments and small fixes grad can be computed now set convention R(- \Delta, \lambda) = (- \Delta - \lambda)^(-1) different conventions give the difference norm(grad_E - grad_E1) equaled approximately 10^(-6) removed some printing and added check of the convergence of A to 4 Fock matrix implemented preconditioning (without projection yet), TODO: project preconditioned grad_E

… check the correctness of MPI use

…vious commit 48d73b2

…t descent direction, skip preconditioning and then polak_ribiere momentum

… too low!? =========================================================================== Molecule --------------------------------------------------------------------------- Charge : 0 Multiplicity : 1 --------------------------------------------------------------------------- N Atom : x y z --------------------------------------------------------------------------- 0 N : -1.037000 0.000000 0.000000 1 N : 1.037000 0.000000 0.000000 --------------------------------------------------------------------------- Center of mass : 0.000000 0.000000 0.000000 =========================================================================== =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 2.645751e+00 -108.269858176166 -1.082699e+02 -------------------------------------- norm(grad_E1) = 3.366493e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.556167e-01 -------------------------------------- norm(preconditioned_grad_E) = 8.102398e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.090289e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 1.864618e+00 -------------------------------------- Candidate Energy: -1.088907e+02 1 1.440613e-01 -108.962388822011 -6.925306e-01 -------------------------------------- norm(grad_E1) = 8.705625e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.940525e-01 -------------------------------------- norm(preconditioned_grad_E) = 1.387195e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.386583e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 3.421696e-01 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.090336e+02 2 4.312143e-02 -108.989055109792 -2.666629e-02 -------------------------------------- norm(grad_E1) = 2.085578e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.047025e-01 -------------------------------------- norm(preconditioned_grad_E) = 4.596835e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.586699e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 1.082851e-01 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089864e+02 3 1.707873e-02 -108.992299615197 -3.244505e-03 -------------------------------------- norm(grad_E1) = 1.678439e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 6.986398e-02 -------------------------------------- norm(preconditioned_grad_E) = 2.020410e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.018604e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 5.198068e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Powell/guarded restart at iteration_index 4 (reason: powell) Candidate Energy: -1.089906e+02 4 7.687970e-03 -108.992930200435 -6.305852e-04 -------------------------------------- norm(grad_E1) = 5.095197e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.459597e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.085534e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.084000e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.448169e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089904e+02 5 4.018083e-03 -108.993096234392 -1.660340e-04 -------------------------------------- norm(grad_E1) = 5.151056e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.202816e-02 -------------------------------------- norm(preconditioned_grad_E) = 7.129098e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 7.121459e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.640985e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089924e+02 6 2.240271e-03 -108.993154249813 -5.801542e-05 -------------------------------------- norm(grad_E1) = 2.587876e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 7.206727e-03 -------------------------------------- norm(preconditioned_grad_E) = 5.640131e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.635313e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.133404e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089924e+02 7 1.400137e-03 -108.993179234465 -2.498465e-05 -------------------------------------- norm(grad_E1) = 1.954818e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.832087e-03 -------------------------------------- norm(preconditioned_grad_E) = 5.009678e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.007266e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 9.285995e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089929e+02 8 9.198816e-04 -108.993191385654 -1.215119e-05

Right now I tried a mixture of SCF and gradient descent and the convergence is super fast, even though I believe momentum is not used due to safeguards: previous_preconditioned_grad_E = preconditioned_grad_E; previous_grad_E = grad_E; previous_h1_inner_product_preconditioned_grad_E_grad_E = h1_inner_product_preconditioned_grad_E_grad_E; // Backtracking line search OrbitalVector Phi_backup = orbital::deep_copy(Phi_n); auto alpha_trial = alpha; int count = 0; while (true) { count += 1; // Retraction to Stiefel is Lowdin based: Phi_n = orbital::add(1.0, Phi_n, alpha_trial, direction); // Orthonormalization updates F_mat as a side effect?! orbital::orthonormalize(orb_prec, Phi_n, F_mat); // Compute Fock matrix and energy F.setup(orb_prec); //F_mat = F(Phi_candidate, Phi_candidate); E_n = F.trace(Phi_n, nucs); std::cout << "Candidate Energy: " << E_n.getTotalEnergy() << std::endl; break; } F.clear(); // Orthonormalize orbital::orthonormalize(orb_prec, Phi_np1, F_mat); // Compute orbital updates OrbitalVector dPhi_n = orbital::add(1.0, Phi_np1, -1.0, Phi_n); Phi_np1.clear(); kain.accelerate(orb_prec, Phi_n, dPhi_n); // Compute errors errors = orbital::get_norms(dPhi_n); err_o = errors.maxCoeff(); err_t = errors.norm(); json_cycle["mo_residual"] = err_t; // Update orbitals Phi_n = orbital::add(1.0, Phi_n, 1.0, dPhi_n); dPhi_n.clear(); orbital::orthonormalize(orb_prec, Phi_n, F_mat); // Compute Fock matrix and energy if (F.getReactionOperator() != nullptr) F.getReactionOperator()->updateMOResidual(err_t); F.setup(orb_prec); F_mat = F(Phi_n, Phi_n); E_n = F.trace(Phi_n, nucs); =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 1.000000e+00 -1.121259148073 -1.121259e+00 -------------------------------------- norm(grad_E1) = 7.719170e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.494689e-02 -------------------------------------- norm(preconditioned_grad_E) = 9.804705e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 9.804312e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.011383e-01 -------------------------------------- Candidate Energy: -1.133043e+00 1 3.792117e-03 -1.133123908006 -1.186476e-02 -------------------------------------- norm(grad_E1) = 1.917471e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.864444e-03 -------------------------------------- norm(preconditioned_grad_E) = 1.881873e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.881804e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 3.923942e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.133585e+00 2 3.867796e-04 -1.133586516442 -4.626084e-04 -------------------------------------- norm(grad_E1) = 5.582126e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.257129e-03 -------------------------------------- norm(preconditioned_grad_E) = 5.069788e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.069613e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.064044e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.133619e+00 3 9.951053e-05 -1.133619598704 -3.308226e-05 --------------------------------------------------------------------------- SCF converged in 3 iterations! =========================================================================== ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Calculation : Optimize ground state orbitals Method : Hartree-Fock Relativity : None Environment : None External fields : None Checkpointing : Off Max iterations : 100 KAIN solver : 2 Localization : Off Diagonalization : First two iterations Start precision : 1.00000e-05 Final precision : 1.00000e-05 Helmholtz precision : Dynamic Energy threshold : Off Orbital threshold : 1.00000e-04 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 1.414214e+00 -3.488804061639 -3.488804e+00 -------------------------------------- norm(grad_E1) = 1.754826e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.083659e-01 -------------------------------------- norm(preconditioned_grad_E) = 2.502909e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.499467e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 5.142178e-01 -------------------------------------- Candidate Energy: -3.569972e+00 1 9.265506e-03 -3.571745971143 -8.294191e-02 -------------------------------------- norm(grad_E1) = 6.052763e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.075909e-01 -------------------------------------- norm(preconditioned_grad_E) = 7.418470e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 7.402491e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 1.556673e-01 -------------------------------------- Polak-Ribière coefficient = 3.509740e-01 Powell/guarded restart at iteration_index 2 (reason: non-descent) Candidate Energy: -3.579551e+00 2 3.740434e-03 -3.579987286195 -8.241315e-03 -------------------------------------- norm(grad_E1) = 2.349168e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.357616e-02 -------------------------------------- norm(preconditioned_grad_E) = 2.794234e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.788182e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 5.978327e-02 -------------------------------------- Polak-Ribière coefficient = 5.071773e-01 Powell/guarded restart at iteration_index 3 (reason: non-descent) Candidate Energy: -3.581171e+00 3 1.767353e-03 -3.581256403291 -1.269117e-03 -------------------------------------- norm(grad_E1) = 1.091247e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.897994e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.204128e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.201640e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.680655e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -3.581492e+00 4 7.516380e-03 -3.581584173003 -3.277697e-04 -------------------------------------- norm(grad_E1) = 2.447794e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.682823e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.248966e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.247974e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 6.230738e-03 -------------------------------------- Polak-Ribière coefficient = 1.188284e-01 Candidate Energy: -3.581594e+00 5 3.773203e-03 -3.581573485709 1.068729e-05 -------------------------------------- norm(grad_E1) = 3.144394e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.504452e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.218417e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.213509e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 7.504617e-03 -------------------------------------- Polak-Ribière coefficient = 9.238694e-01 Candidate Energy: -3.581593e+00 6 1.727671e-03 -3.581594976597 -2.149089e-05 -------------------------------------- norm(grad_E1) = 1.172736e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.029809e-03 -------------------------------------- norm(preconditioned_grad_E) = 1.732954e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.732462e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 3.692733e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -3.581597e+00 7 8.498797e-05 -3.581597557830 -2.581233e-06 --------------------------------------------------------------------------- SCF converged in 7 iterations! =========================================================================== ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Calculation : Optimize ground state orbitals Method : Hartree-Fock Relativity : None Environment : None External fields : None Checkpointing : Off Max iterations : 100 KAIN solver : Off Localization : First two iterations Diagonalization : Off Start precision : 1.00000e-05 Final precision : 1.00000e-05 Helmholtz precision : Dynamic Energy threshold : Off Orbital threshold : 1.00000e-04 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 2.645751e+00 -108.270488550253 -1.082705e+02 -------------------------------------- norm(grad_E1) = 3.366493e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.553354e-01 -------------------------------------- norm(preconditioned_grad_E) = 8.096259e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.085628e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 1.864618e+00 -------------------------------------- Candidate Energy: -1.089529e+02 1 3.367737e-02 -108.962388975031 -6.919004e-01 -------------------------------------- norm(grad_E1) = 8.702999e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.940034e-01 -------------------------------------- norm(preconditioned_grad_E) = 1.366614e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.365918e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 3.421521e-01 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089884e+02 2 8.127645e-03 -108.989055314844 -2.666634e-02 -------------------------------------- norm(grad_E1) = 2.085843e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.046874e-01 -------------------------------------- norm(preconditioned_grad_E) = 4.622894e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.613665e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 1.082957e-01 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089922e+02 3 3.984630e-03 -108.992299858263 -3.244543e-03 -------------------------------------- norm(grad_E1) = 1.679433e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 6.987745e-02 -------------------------------------- norm(preconditioned_grad_E) = 2.018051e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.015936e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 5.198964e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Powell/guarded restart at iteration_index 4 (reason: powell) Candidate Energy: -1.089929e+02 4 1.898684e-03 -108.992930338156 -6.304799e-04 -------------------------------------- norm(grad_E1) = 5.097738e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.460940e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.093198e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.091746e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.448299e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089931e+02 5 9.077491e-04 -108.993096310587 -1.659724e-04 -------------------------------------- norm(grad_E1) = 5.154629e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.203310e-02 -------------------------------------- norm(preconditioned_grad_E) = 7.146047e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 7.138526e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.641093e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089931e+02 6 5.867431e-04 -108.993154291951 -5.798136e-05 -------------------------------------- norm(grad_E1) = 2.589677e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 7.209788e-03 -------------------------------------- norm(preconditioned_grad_E) = 5.634977e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.630323e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.133353e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089932e+02 7 3.572462e-04 -108.993179258041 -2.496609e-05 -------------------------------------- norm(grad_E1) = 1.956215e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.831309e-03 -------------------------------------- norm(preconditioned_grad_E) = 5.044651e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.042196e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 9.285553e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089932e+02 8 2.327558e-04 -108.993191397949 -1.213991e-05 -------------------------------------- norm(grad_E1) = 1.282277e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.494770e-03 -------------------------------------- norm(preconditioned_grad_E) = 4.683340e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.681946e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 8.117428e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Powell/guarded restart at iteration_index 9 (reason: powell) Candidate Energy: -1.089932e+02 9 1.662764e-04 -108.993197685706 -6.287757e-06 -------------------------------------- norm(grad_E1) = 8.719163e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.488482e-03 -------------------------------------- norm(preconditioned_grad_E) = 4.488589e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.487812e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 7.502971e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089932e+02 10 1.093957e-04 -108.993201050154 -3.364447e-06 --------------------------------------------------------------------------- SCF converged in 10 iterations! =========================================================================== I would be nice to understand this mixture: can we trust it? Phi_np1 is computed via SCF procedure before I evaluate the gradient attached to the previous point Phi_n. Then I do steepest gradient descent, write it down to the reference Phi_n. The rest is continuation of SCF (since I did not modify the next part of the main loop): // Compute orbital updates OrbitalVector dPhi_n = orbital::add(1.0, Phi_np1, -1.0, Phi_n); so the update is Phi_np1 - Phi_n, where Phi_np1 = SCF(Phi_n) and Phi_n = RSGD(Phi_n) This mixture update is added to Phi_n, that is Phi_n = RSGD(Phi_n). So it actually looks, as if RSGD(Phi_n) just goes away when we sum the update and RSGD(Phi_n).

…hem (since the update was calculated with respect to grad_descent(Phi_n) which is closer to Phi_np1, obviously ). It is fixed, and now the algorithm runs the gradient descent with Polyak momentum. TODO: implement backtracking. =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 2.645751e+00 -108.269569447381 -1.082696e+02 -------------------------------------- norm(grad_E1) = 3.366493e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.554898e-01 -------------------------------------- norm(preconditioned_grad_E) = 8.074317e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.062482e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 1.864618e+00 -------------------------------------- Candidate Energy: -1.089553e+02 1 1.479554e-01 -108.955302310206 -6.857329e-01 -------------------------------------- norm(grad_E1) = 3.847288e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 5.943881e-01 -------------------------------------- norm(preconditioned_grad_E) = 1.607459e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.577367e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 6.495689e-01 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089825e+02 2 6.589890e-02 -108.982522280053 -2.721997e-02 -------------------------------------- norm(grad_E1) = 2.695767e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 9.156072e-01 -------------------------------------- norm(preconditioned_grad_E) = 9.880053e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 9.319314e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 5.229221e-01 -------------------------------------- Polak-Ribière coefficient = 6.358710e-01 Candidate Energy: -1.089877e+02 3 5.074700e-02 -108.987721846526 -5.199566e-03 -------------------------------------- norm(grad_E1) = 1.204399e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.095241e-01 -------------------------------------- norm(preconditioned_grad_E) = 6.469757e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 6.369373e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.406470e-01 -------------------------------------- Polak-Ribière coefficient = 3.545491e-01 Candidate Energy: -1.089894e+02 4 2.169312e-02 -108.989388796046 -1.666950e-03 -------------------------------------- norm(grad_E1) = 1.192711e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.684731e-01 -------------------------------------- norm(preconditioned_grad_E) = 5.092511e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.883805e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.490397e-01 -------------------------------------- Polak-Ribière coefficient = 5.487224e-01 Candidate Energy: -1.089922e+02 5 1.637716e-02 -108.992234964227 -2.846168e-03 -------------------------------------- norm(grad_E1) = 6.214460e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.469943e-01 -------------------------------------- norm(preconditioned_grad_E) = 2.490651e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.447566e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 1.223012e-01 -------------------------------------- Polak-Ribière coefficient = 6.693553e-02 Candidate Energy: -1.089930e+02 6 1.242580e-02 -108.992957303318 -7.223391e-04 -------------------------------------- norm(grad_E1) = 3.944082e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 7.323873e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.485547e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.443356e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 6.987706e-02 -------------------------------------- Polak-Ribière coefficient = 4.994435e-01 Candidate Energy: -1.089931e+02 7 7.883258e-03 -108.993105525576 -1.482223e-04 -------------------------------------- norm(grad_E1) = 2.070515e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.830372e-02 -------------------------------------- norm(preconditioned_grad_E) = 8.971594e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.915037e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 4.091528e-02 -------------------------------------- Polak-Ribière coefficient = 3.632810e-01 Candidate Energy: -1.089931e+02 8 4.084053e-03 -108.993140876078 -3.535050e-05 -------------------------------------- norm(grad_E1) = 2.117388e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.397777e-02 -------------------------------------- norm(preconditioned_grad_E) = 7.143143e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 6.970010e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 3.458931e-02 -------------------------------------- Polak-Ribière coefficient = 4.606847e-01 Candidate Energy: -1.089932e+02 9 3.020994e-03 -108.993178304520 -3.742844e-05 -------------------------------------- norm(grad_E1) = 1.257209e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.614856e-02 -------------------------------------- norm(preconditioned_grad_E) = 5.659481e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.642521e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.995531e-02 -------------------------------------- Polak-Ribière coefficient = 3.156476e-01 Candidate Energy: -1.089932e+02 10 2.626662e-03 -108.993189089864 -1.078534e-05 -------------------------------------- norm(grad_E1) = 1.567098e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.825169e-02 -------------------------------------- norm(preconditioned_grad_E) = 4.565195e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.526100e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 2.139635e-02 -------------------------------------- Polak-Ribière coefficient = 7.588397e-01 Candidate Energy: -1.089932e+02 11 1.674401e-03 -108.993189569908 -4.800442e-07 -------------------------------------- norm(grad_E1) = 1.224565e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 7.094875e-03 -------------------------------------- norm(preconditioned_grad_E) = 4.794847e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.783433e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.762663e-02 -------------------------------------- Polak-Ribière coefficient = 3.332226e-01 Powell/guarded restart at iteration_index 12 (reason: powell) Candidate Energy: -1.089932e+02 12 2.295812e-03 -108.993195933330 -6.363421e-06 -------------------------------------- norm(grad_E1) = 8.808236e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 5.730822e-03 -------------------------------------- norm(preconditioned_grad_E) = 4.548132e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.540505e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.461170e-02 -------------------------------------- Polak-Ribière coefficient = 9.301819e-01 Candidate Energy: -1.089932e+02 13 1.402526e-03 -108.993193713704 2.219626e-06 -------------------------------------- norm(grad_E1) = 6.469799e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.526138e-03 -------------------------------------- norm(preconditioned_grad_E) = 4.411906e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.396633e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.414325e-02 -------------------------------------- Polak-Ribière coefficient = 3.253397e-01 Candidate Energy: -1.089932e+02 14 1.456153e-03 -108.993198408556 -4.694852e-06 -------------------------------------- norm(grad_E1) = 4.375865e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.606203e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.898210e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.892488e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.010303e-02 -------------------------------------- Polak-Ribière coefficient = 4.238893e-01 Candidate Energy: -1.089932e+02 15 9.774299e-04 -108.993199800077 -1.391522e-06 -------------------------------------- norm(grad_E1) = 4.005792e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.898873e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.753063e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.746128e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 8.840622e-03 -------------------------------------- Polak-Ribière coefficient = 2.816766e-01 Candidate Energy: -1.089932e+02 16 8.113870e-04 -108.993200469839 -6.697614e-07 -------------------------------------- norm(grad_E1) = 3.634696e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.313325e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.663682e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.660230e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 7.662043e-03 -------------------------------------- Polak-Ribière coefficient = 3.601268e-01 Powell/guarded restart at iteration_index 17 (reason: powell) Candidate Energy: -1.089932e+02 17 8.622326e-04 -108.993200158540 3.112986e-07 -------------------------------------- norm(grad_E1) = 4.947285e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.531641e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.829889e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.825657e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 8.631665e-03 -------------------------------------- Polak-Ribière coefficient = 5.996202e-01 Candidate Energy: -1.089932e+02 18 8.061123e-04 -108.993200783598 -6.250578e-07 -------------------------------------- norm(grad_E1) = 3.271958e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.114456e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.657085e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.655698e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 7.283467e-03 -------------------------------------- Polak-Ribière coefficient = 3.221624e-01 Candidate Energy: -1.089932e+02 19 6.267200e-04 -108.993200854030 -7.043246e-08 -------------------------------------- norm(grad_E1) = 3.100696e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.145344e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.700800e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.698877e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 7.001818e-03 -------------------------------------- Polak-Ribière coefficient = 3.345680e-01 Candidate Energy: -1.089932e+02 20 5.436140e-04 -108.993200420083 4.339468e-07 -------------------------------------- norm(grad_E1) = 2.398148e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.996617e-03 -------------------------------------- norm(preconditioned_grad_E) = 4.001535e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.999307e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 6.868232e-03 -------------------------------------- Polak-Ribière coefficient = 4.245575e-01 Candidate Energy: -1.089932e+02 21 4.078736e-04 -108.993198643394 1.776690e-06 -------------------------------------- norm(grad_E1) = 1.593271e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.588745e-03 -------------------------------------- norm(preconditioned_grad_E) = 4.333969e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.332174e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 7.280274e-03 -------------------------------------- Polak-Ribière coefficient = 8.664518e-01 Powell/guarded restart at iteration_index 22 (reason: powell) Candidate Energy: -1.089932e+02 22 5.130719e-04 -108.993196432611 2.210782e-06

TODO: move F.clear(); somewhere inside of the backtracking loop and fix the problem this move is causing: Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.133623e+00 Error: apply(), line 63: Uninitialized operator Error: apply(), line 63: Uninitialized operator Error: apply(), line 63: Uninitialized operator Error: apply(), line 63: Uninitialized operator Error: apply(), line 63: Uninitialized operator Error: apply(), line 63: Uninitialized operator update: 1.529064e-04 (step size = 1.000000e+00) Error: apply(), line 63: Uninitialized operator Error: apply(), line 63: Uninitialized operator Error: apply(), line 63: Uninitialized operator Error: apply(), line 63: Uninitialized operator Error: apply(), line 63: Uninitialized operator Error: apply(), line 63: Uninitialized operator 6 1.529064e-04 -1.133622724325 -1.249997e-07 WARNING: The latter could be done, likely, by computing all the nessesary H1-inner products before entering the backtracking loop. Otherwise, the algorithm produces reasonable results: WARNING: There is a difference between update and MO residual, provided the molecule has more than 2 electrons. Why does this happend? =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 1.000000e+00 -1.121259148073 -1.121259e+00 -------------------------------------- norm(grad_E1) = 7.719170e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.494689e-02 -------------------------------------- norm(preconditioned_grad_E) = 9.804705e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 9.804312e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.011383e-01 -------------------------------------- Candidate Energy: -1.133043e+00 update: 3.577833e-02 (step size = 1.000000e+00) 1 3.577833e-02 -1.133043149745 -1.178400e-02 -------------------------------------- norm(grad_E1) = 2.152317e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.065050e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.994583e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.994405e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 4.177150e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.133570e+00 update: 9.864078e-03 (step size = 1.000000e+00) 2 9.864078e-03 -1.133570490434 -5.273407e-04 -------------------------------------- norm(grad_E1) = 6.885801e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.296594e-03 -------------------------------------- norm(preconditioned_grad_E) = 5.838411e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.837626e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.232555e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.133616e+00 update: 3.145509e-03 (step size = 1.000000e+00) 3 3.145509e-03 -1.133616374354 -4.588392e-05 -------------------------------------- norm(grad_E1) = 2.364265e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.856565e-03 -------------------------------------- norm(preconditioned_grad_E) = 2.303092e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.302790e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 4.800344e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Powell/guarded restart at iteration_index 4 (reason: powell) Candidate Energy: -1.133622e+00 update: 1.079008e-03 (step size = 1.000000e+00) 4 1.079008e-03 -1.133621826990 -5.452636e-06 -------------------------------------- norm(grad_E1) = 8.641672e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.122543e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.433174e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.433094e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 2.908502e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.133623e+00 update: 3.947317e-04 (step size = 1.000000e+00) 5 3.947317e-04 -1.133622599326 -7.723354e-07 -------------------------------------- norm(grad_E1) = 3.340931e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.559445e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.268195e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.268179e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 2.543555e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.133623e+00 update: 1.529064e-04 (step size = 1.000000e+00) 6 1.529064e-04 -1.133622724325 -1.249997e-07 -------------------------------------- norm(grad_E1) = 1.350562e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.558561e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.239968e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.239965e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 2.481127e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.133623e+00 Precision is achieved inside line search at iteration_index = 7 7 6.191395e-05 -1.133622746180 -2.185525e-08 --------------------------------------------------------------------------- SCF converged in 7 iterations! =========================================================================== =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 1.414214e+00 -3.488804061639 -3.488804e+00 -------------------------------------- norm(grad_E1) = 1.754826e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.083659e-01 -------------------------------------- norm(preconditioned_grad_E) = 2.502909e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.499467e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 5.142178e-01 -------------------------------------- Candidate Energy: -3.569972e+00 update: 1.074611e-01 (step size = 1.000000e+00) 1 1.246000e-01 -3.569971941787 -8.116788e-02 -------------------------------------- norm(grad_E1) = 6.441079e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.271097e-01 -------------------------------------- norm(preconditioned_grad_E) = 7.895014e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 7.875516e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 1.660001e-01 -------------------------------------- Polak-Ribière coefficient = 3.754599e-01 Powell/guarded restart at iteration_index 2 (reason: non-descent) Candidate Energy: -3.578960e+00 update: 3.618460e-02 (step size = 1.000000e+00) 2 4.277635e-02 -3.578960281682 -8.988340e-03 -------------------------------------- norm(grad_E1) = 2.896750e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 6.781201e-02 -------------------------------------- norm(preconditioned_grad_E) = 3.438895e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.428819e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 7.429348e-02 -------------------------------------- Polak-Ribière coefficient = 6.151170e-01 Powell/guarded restart at iteration_index 3 (reason: non-descent) Candidate Energy: -3.581218e+00 update: 1.925415e-02 (step size = 1.400000e+00) 3 2.416199e-02 -3.581218429045 -2.258147e-03 -------------------------------------- norm(grad_E1) = 9.751692e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.548415e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.186562e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.183249e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.629240e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -3.581522e+00 update: 5.053329e-03 (step size = 1.400000e+00) 4 6.797610e-03 -3.581521882109 -3.034531e-04 -------------------------------------- norm(grad_E1) = 4.715239e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.113911e-02 -------------------------------------- norm(preconditioned_grad_E) = 5.319663e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.304058e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.195992e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -3.581594e+00 update: 3.332074e-03 (step size = 1.960000e+00) 5 4.347294e-03 -3.581593806624 -7.192451e-05 -------------------------------------- norm(grad_E1) = 1.283946e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.466355e-03 -------------------------------------- norm(preconditioned_grad_E) = 1.827515e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.825037e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 3.901037e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -3.581598e+00 update: 8.710196e-04 (step size = 1.960000e+00) 6 1.191361e-03 -3.581597847120 -4.040496e-06 -------------------------------------- norm(grad_E1) = 3.380339e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 6.579829e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.817511e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.817349e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 3.552292e-03 -------------------------------------- Polak-Ribière coefficient = 3.306023e-01 Candidate Energy: -3.581598e+00 update: 5.214281e-04 (step size = 1.960000e+00) 7 6.773147e-04 -3.581598028042 -1.809218e-07 -------------------------------------- norm(grad_E1) = 2.281824e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.401058e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.782207e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.782118e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 3.467297e-03 -------------------------------------- Polak-Ribière coefficient = 3.781103e-02 Powell/guarded restart at iteration_index 8 (reason: powell) Candidate Energy: -3.581598e+00 update: 1.667434e-04 (step size = 1.960000e+00) 8 2.268054e-04 -3.581598161368 -1.333256e-07 -------------------------------------- norm(grad_E1) = 6.129916e-05 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.203689e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.790778e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.790772e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 3.475273e-03 -------------------------------------- Polak-Ribière coefficient = 1.124366e-02 Candidate Energy: -3.581598e+00 Precision is achieved inside line search at iteration_index = 9 9 5.377371e-05 -3.581598186125 -2.475760e-08 --------------------------------------------------------------------------- SCF converged in 9 iterations! =========================================================================== =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 2.645751e+00 -108.269858135840 -1.082699e+02 -------------------------------------- norm(grad_E1) = 3.366493e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.556167e-01 -------------------------------------- norm(preconditioned_grad_E) = 8.066363e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.055610e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 1.864618e+00 -------------------------------------- Candidate Energy: -1.089514e+02 update: 6.610847e-02 (step size = 1.000000e+00) 1 1.504364e-01 -108.951433989118 -6.815759e-01 -------------------------------------- norm(grad_E1) = 4.362018e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 7.614407e-01 -------------------------------------- norm(preconditioned_grad_E) = 1.712984e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.672812e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 8.270964e-01 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089790e+02 update: 4.009396e-02 (step size = 1.000000e+00) 2 7.628516e-02 -108.978982990193 -2.754900e-02 -------------------------------------- norm(grad_E1) = 4.108391e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.144419e+00 -------------------------------------- norm(preconditioned_grad_E) = 1.119793e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.038896e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 6.657785e-01 -------------------------------------- Polak-Ribière coefficient = 8.482698e-01 Candidate Energy: -1.089769e+02 Error: setupInternal(), line 144: Exchange not properly cleared Candidate Energy: -1.090025e+02 update: 1.475477e-02 (step size = 5.000000e-01) 3 2.987554e-02 -108.983423286065 -4.440296e-03 -------------------------------------- norm(grad_E1) = 3.109682e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 9.489923e-01 -------------------------------------- norm(preconditioned_grad_E) = 9.202427e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.464515e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 5.843213e-01 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Powell/guarded restart at iteration_index 4 (reason: powell) Candidate Energy: -1.089912e+02 update: 1.751395e-02 (step size = 7.000000e-01) 4 3.624992e-02 -108.991239951660 -7.816666e-03 -------------------------------------- norm(grad_E1) = 1.433189e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.544179e-01 -------------------------------------- norm(preconditioned_grad_E) = 3.677516e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.467413e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.180608e-01 -------------------------------------- Polak-Ribière coefficient = 4.083161e-01 Candidate Energy: -1.089916e+02 update: 5.283514e-03 (step size = 7.000000e-01) 5 1.015818e-02 -108.991588232887 -3.482812e-04 -------------------------------------- norm(grad_E1) = 1.270847e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.218436e-01 -------------------------------------- norm(preconditioned_grad_E) = 3.694578e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.400963e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.387598e-01 -------------------------------------- Polak-Ribière coefficient = 1.788828e-01 Candidate Energy: -1.089928e+02 update: 7.423186e-03 (step size = 7.000000e-01) 6 1.500638e-02 -108.992828069293 -1.239836e-03 -------------------------------------- norm(grad_E1) = 5.471612e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.382420e-01 -------------------------------------- norm(preconditioned_grad_E) = 1.542698e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.451416e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 9.678810e-02 -------------------------------------- Polak-Ribière coefficient = 4.356812e-01 Candidate Energy: -1.089929e+02 update: 3.461197e-03 (step size = 7.000000e-01) 7 5.542874e-03 -108.992856413831 -2.834454e-05 -------------------------------------- norm(grad_E1) = 6.084478e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.779050e-01 -------------------------------------- norm(preconditioned_grad_E) = 1.807939e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.663359e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 1.160469e-01 -------------------------------------- Polak-Ribière coefficient = 5.028477e-01 Candidate Energy: -1.089931e+02 update: 5.579799e-03 (step size = 7.000000e-01) 8 7.796768e-03 -108.993118780881 -2.623671e-04 -------------------------------------- norm(grad_E1) = 3.076078e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 5.863346e-02 -------------------------------------- norm(preconditioned_grad_E) = 8.869554e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.488848e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 5.013986e-02 -------------------------------------- Polak-Ribière coefficient = 4.701155e-01 Candidate Energy: -1.089931e+02 update: 1.575834e-03 (step size = 7.000000e-01) 9 3.034280e-03 -108.993122729619 -3.948738e-06 -------------------------------------- norm(grad_E1) = 2.534145e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.243516e-02 -------------------------------------- norm(preconditioned_grad_E) = 9.906547e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 9.346897e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 5.195502e-02 -------------------------------------- Polak-Ribière coefficient = 4.489728e-01 Powell/guarded restart at iteration_index 10 (reason: powell) Candidate Energy: -1.089932e+02 update: 2.248146e-03 (step size = 7.000000e-01) 10 4.128492e-03 -108.993179090498 -5.636088e-05 -------------------------------------- norm(grad_E1) = 1.725758e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.340857e-02 -------------------------------------- norm(preconditioned_grad_E) = 5.320302e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.102866e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 2.927091e-02 -------------------------------------- Polak-Ribière coefficient = 6.136444e-01 Candidate Energy: -1.089932e+02 Error: setupInternal(), line 144: Exchange not properly cleared Candidate Energy: -1.089928e+02 Error: setupInternal(), line 144: Exchange not properly cleared Candidate Energy: -1.089927e+02 Error: setupInternal(), line 144: Exchange not properly cleared

It computes all the nessesary H1-inner products before entering the backtracking loop. TODO: Reduce the amount of H1-inner products, since we have repetitions. WARNING: There is a difference between update and MO residual, provided the molecule has more than 2 electrons. Why does this happend? The algorithm works. =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 2.645751e+00 -108.269580559548 -1.082696e+02 -------------------------------------- norm(grad_E1) = 3.366493e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.554835e-01 -------------------------------------- norm(preconditioned_grad_E) = 8.063311e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.052659e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 1.864618e+00 -------------------------------------- Descent directional H1-inner product: -1.307104e+00 Candidate Energy: -1.089514e+02 update: 6.903137e-02 (step size = 1.000000e+00) 1 1.495674e-01 -108.951387378237 -6.818068e-01 -------------------------------------- norm(grad_E1) = 4.275736e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 7.340633e-01 -------------------------------------- norm(preconditioned_grad_E) = 1.695690e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.655655e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 8.069306e-01 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -7.992043e-02 Candidate Energy: -1.089782e+02 update: 3.950068e-02 (step size = 1.000000e+00) 2 7.355680e-02 -108.978220786023 -2.683341e-02 -------------------------------------- norm(grad_E1) = 4.094094e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.137305e+00 -------------------------------------- norm(preconditioned_grad_E) = 1.141935e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.061179e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 6.767001e-01 -------------------------------------- Polak-Ribière coefficient = 9.029250e-01 Descent directional H1-inner product: -1.989164e-02 Candidate Energy: -1.089755e+02 Candidate Energy: -1.089825e+02 update: 1.506708e-02 (step size = 5.000000e-01) 3 2.999008e-02 -108.982494548364 -4.273762e-03 -------------------------------------- norm(grad_E1) = 3.283696e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 9.767331e-01 -------------------------------------- norm(preconditioned_grad_E) = 9.982993e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 9.223493e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 6.134913e-01 -------------------------------------- Polak-Ribière coefficient = 7.207114e-03 Powell/guarded restart at iteration_index 4 (reason: powell) Descent directional H1-inner product: -3.452045e-02 Candidate Energy: -1.089918e+02 update: 1.164892e-02 (step size = 5.000000e-01) 4 2.858415e-02 -108.991819827031 -9.325279e-03 -------------------------------------- norm(grad_E1) = 3.489606e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.024515e-01 -------------------------------------- norm(preconditioned_grad_E) = 2.674080e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.663133e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 8.954980e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -1.749085e-03 Candidate Energy: -1.089925e+02 update: 3.052657e-03 (step size = 5.000000e-01) 5 5.748032e-03 -108.992512602895 -6.927759e-04 -------------------------------------- norm(grad_E1) = 1.564060e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 6.198574e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.748761e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.746369e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 4.949483e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -7.015176e-04 Candidate Energy: -1.089929e+02 update: 2.630623e-03 (step size = 7.000000e-01) 6 4.783095e-03 -108.992889847714 -3.772448e-04 -------------------------------------- norm(grad_E1) = 7.992284e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.002379e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.101714e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.100572e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.779723e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -2.591948e-04 Candidate Energy: -1.089931e+02 update: 2.260068e-03 (step size = 9.800000e-01) 7 3.853757e-03 -108.993073491103 -1.836434e-04 -------------------------------------- norm(grad_E1) = 3.810932e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.486177e-02 -------------------------------------- norm(preconditioned_grad_E) = 7.106216e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 7.098264e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.558528e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -9.627896e-05 Candidate Energy: -1.089932e+02 update: 1.680785e-03 (step size = 1.372000e+00) 8 2.901951e-03 -108.993157031473 -8.354037e-05 -------------------------------------- norm(grad_E1) = 3.992984e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.082437e-02 -------------------------------------- norm(preconditioned_grad_E) = 4.968839e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.962999e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.080207e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Powell/guarded restart at iteration_index 9 (reason: powell) Descent directional H1-inner product: -4.074366e-05 Candidate Energy: -1.089932e+02 update: 7.169047e-04 (step size = 1.372000e+00) 9 1.431501e-03 -108.993183350892 -2.631942e-05 -------------------------------------- norm(grad_E1) = 3.503560e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 7.563484e-03 -------------------------------------- norm(preconditioned_grad_E) = 4.261954e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.253277e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 8.594771e-03 -------------------------------------- Polak-Ribière coefficient = 6.091757e-03 Descent directional H1-inner product: -2.634542e-05 Candidate Energy: -1.089932e+02 update: 6.287665e-04 (step size = 1.372000e+00) 10 1.101138e-03 -108.993192320190 -8.969298e-06 -------------------------------------- norm(grad_E1) = 5.428045e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 9.043855e-03 -------------------------------------- norm(preconditioned_grad_E) = 4.111609e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.089943e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.001237e-02 -------------------------------------- Polak-Ribière coefficient = 3.696432e-01 Descent directional H1-inner product: -3.031467e-05 Candidate Energy: -1.089932e+02 update: 6.145565e-04 (step size = 1.372000e+00) 11 1.215217e-03 -108.993197937855 -5.617665e-06 -------------------------------------- norm(grad_E1) = 4.551618e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 9.641346e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.938272e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.914520e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 9.599640e-03 -------------------------------------- Polak-Ribière coefficient = 4.992982e-01 Descent directional H1-inner product: -3.058956e-05 Candidate Energy: -1.089932e+02 update: 6.378605e-04 (step size = 1.372000e+00) 12 1.243030e-03 -108.993199485535 -1.547680e-06 -------------------------------------- norm(grad_E1) = 4.423287e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 6.245745e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.956215e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.944772e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 8.677535e-03 -------------------------------------- Polak-Ribière coefficient = 5.970886e-01 Descent directional H1-inner product: -3.330540e-05 Candidate Energy: -1.089932e+02 Candidate Energy: -1.089932e+02 update: 3.988129e-04 (step size = 6.860000e-01) 13 6.423889e-04 -108.993200932267 -1.446732e-06 -------------------------------------- norm(grad_E1) = 1.433797e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.975306e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.584088e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.581835e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 5.849550e-03 -------------------------------------- Polak-Ribière coefficient = 5.052187e-02 Powell/guarded restart at iteration_index 14 (reason: powell) Descent directional H1-inner product: -1.514005e-05 Candidate Energy: -1.089932e+02 update: 1.069337e-04 (step size = 6.860000e-01) 14 2.039519e-04 -108.993201173388 -2.411214e-07 -------------------------------------- norm(grad_E1) = 6.330527e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.496370e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.576803e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.576028e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 5.485308e-03 -------------------------------------- Polak-Ribière coefficient = 5.923642e-02 Descent directional H1-inner product: -1.556022e-05 Candidate Energy: -1.089932e+02 Precision is achieved inside line search at iteration_index = 15 15 1.412832e-04 -108.993201193095 -1.970696e-08 --------------------------------------------------------------------------- SCF converged in 15 iterations! =========================================================================== =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 1.414214e+00 -3.488804061639 -3.488804e+00 -------------------------------------- norm(grad_E1) = 1.754826e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.083659e-01 -------------------------------------- norm(preconditioned_grad_E) = 2.502909e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.499467e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 5.142178e-01 -------------------------------------- Descent directional H1-inner product: -1.253436e-01 Candidate Energy: -3.569972e+00 update: 1.074611e-01 (step size = 1.000000e+00) 1 1.246000e-01 -3.569971941787 -8.116788e-02 -------------------------------------- norm(grad_E1) = 6.441079e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.271097e-01 -------------------------------------- norm(preconditioned_grad_E) = 7.895014e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 7.875516e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 1.660001e-01 -------------------------------------- Polak-Ribière coefficient = 3.754599e-01 Powell/guarded restart at iteration_index 2 (reason: non-descent) Descent directional H1-inner product: -1.268430e-02 Candidate Energy: -3.578960e+00 update: 3.618460e-02 (step size = 1.000000e+00) 2 4.277635e-02 -3.578960281682 -8.988340e-03 -------------------------------------- norm(grad_E1) = 2.896750e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 6.781201e-02 -------------------------------------- norm(preconditioned_grad_E) = 3.438895e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.428819e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 7.429348e-02 -------------------------------------- Polak-Ribière coefficient = 6.151170e-01 Powell/guarded restart at iteration_index 3 (reason: non-descent) Descent directional H1-inner product: -2.481440e-03 Candidate Energy: -3.581218e+00 update: 1.925415e-02 (step size = 1.400000e+00) 3 2.416199e-02 -3.581218429045 -2.258147e-03 -------------------------------------- norm(grad_E1) = 9.751692e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.548415e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.186562e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.183249e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.629240e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -3.059431e-04 Candidate Energy: -3.581522e+00 update: 5.053329e-03 (step size = 1.400000e+00) 4 6.797610e-03 -3.581521882109 -3.034531e-04 -------------------------------------- norm(grad_E1) = 4.715239e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.113911e-02 -------------------------------------- norm(preconditioned_grad_E) = 5.319663e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.304058e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.195992e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -6.223704e-05 Candidate Energy: -3.581594e+00 update: 3.332074e-03 (step size = 1.960000e+00) 5 4.347294e-03 -3.581593806624 -7.192451e-05 -------------------------------------- norm(grad_E1) = 1.283946e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.466355e-03 -------------------------------------- norm(preconditioned_grad_E) = 1.827515e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.825037e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 3.901037e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -6.957867e-06 Candidate Energy: -3.581598e+00 update: 8.710196e-04 (step size = 1.960000e+00) 6 1.191361e-03 -3.581597847120 -4.040496e-06 -------------------------------------- norm(grad_E1) = 3.380339e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 6.579829e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.817511e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.817349e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 3.552292e-03 -------------------------------------- Polak-Ribière coefficient = 3.306023e-01 Descent directional H1-inner product: -7.568863e-06 Candidate Energy: -3.581598e+00 update: 5.214281e-04 (step size = 1.960000e+00) 7 6.773147e-04 -3.581598028042 -1.809218e-07 -------------------------------------- norm(grad_E1) = 2.281824e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.401058e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.782207e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.782118e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 3.467297e-03 -------------------------------------- Polak-Ribière coefficient = 3.781103e-02 Powell/guarded restart at iteration_index 8 (reason: powell) Descent directional H1-inner product: -5.992010e-06 Candidate Energy: -3.581598e+00 update: 1.667434e-04 (step size = 1.960000e+00) 8 2.268054e-04 -3.581598161368 -1.333256e-07 -------------------------------------- norm(grad_E1) = 6.129916e-05 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.203689e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.790778e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.790772e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 3.475273e-03 -------------------------------------- Polak-Ribière coefficient = 1.124366e-02 Descent directional H1-inner product: -6.104314e-06 Candidate Energy: -3.581598e+00 Precision is achieved inside line search at iteration_index = 9 9 5.377371e-05 -3.581598186125 -2.475760e-08 --------------------------------------------------------------------------- SCF converged in 9 iterations! =========================================================================== =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 1.000000e+00 -1.121259148073 -1.121259e+00 -------------------------------------- norm(grad_E1) = 7.719170e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.494689e-02 -------------------------------------- norm(preconditioned_grad_E) = 9.804705e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 9.804312e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.011383e-01 -------------------------------------- Descent directional H1-inner product: -1.970810e-02 Candidate Energy: -1.133043e+00 update: 3.577833e-02 (step size = 1.000000e+00) 1 3.577833e-02 -1.133043149745 -1.178400e-02 -------------------------------------- norm(grad_E1) = 2.152317e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.065050e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.994583e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.994405e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 4.177150e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -8.323323e-04 Candidate Energy: -1.133570e+00 update: 9.864078e-03 (step size = 1.000000e+00) 2 9.864078e-03 -1.133570490434 -5.273407e-04 -------------------------------------- norm(grad_E1) = 6.885801e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.296594e-03 -------------------------------------- norm(preconditioned_grad_E) = 5.838411e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.837626e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.232555e-02 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -7.188374e-05 Candidate Energy: -1.133616e+00 update: 3.145509e-03 (step size = 1.000000e+00) 3 3.145509e-03 -1.133616374354 -4.588392e-05 -------------------------------------- norm(grad_E1) = 2.364265e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.856565e-03 -------------------------------------- norm(preconditioned_grad_E) = 2.303092e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.302790e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 4.800344e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Powell/guarded restart at iteration_index 4 (reason: powell) Descent directional H1-inner product: -1.104301e-05 Candidate Energy: -1.133622e+00 update: 1.079008e-03 (step size = 1.000000e+00) 4 1.079008e-03 -1.133621826990 -5.452636e-06 -------------------------------------- norm(grad_E1) = 8.641672e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.122543e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.433174e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.433094e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 2.908502e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -4.165872e-06 Candidate Energy: -1.133623e+00 update: 3.947317e-04 (step size = 1.000000e+00) 5 3.947317e-04 -1.133622599326 -7.723354e-07 -------------------------------------- norm(grad_E1) = 3.340931e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.559445e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.268195e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.268179e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 2.543555e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -3.225298e-06 Candidate Energy: -1.133623e+00 update: 1.529064e-04 (step size = 1.000000e+00) 6 1.529064e-04 -1.133622724325 -1.249997e-07 -------------------------------------- norm(grad_E1) = 1.350562e-04 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.558561e-04 -------------------------------------- norm(preconditioned_grad_E) = 1.239968e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.239965e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 2.481127e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Descent directional H1-inner product: -3.076448e-06 Candidate Energy: -1.133623e+00 Precision is achieved inside line search at iteration_index = 7 7 6.191395e-05 -1.133622746180 -2.185525e-08 --------------------------------------------------------------------------- SCF converged in 7 iterations! ===========================================================================

=========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 2.645751e+00 -108.269928842464 -1.082699e+02 -------------------------------------- norm(grad_E1) = 3.366493e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.552659e-01 -------------------------------------- norm(preconditioned_grad_E) = 8.060775e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.050150e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 1.864618e+00 -------------------------------------- ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -1.306518e+00 Descent directional H1-inner product: -1.306518e+00 ============================================================= Candidate Energy: -1.089516e+02 update: 6.660031e-02 (step size = 1.000000e+00) 1 1.488470e-01 -108.951583774233 -6.816549e-01 -------------------------------------- norm(grad_E1) = 4.205152e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 7.118930e-01 -------------------------------------- norm(preconditioned_grad_E) = 1.649006e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.612702e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 7.880396e-01 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -7.571984e-02 Descent directional H1-inner product: -7.571984e-02 ============================================================= Candidate Energy: -1.089802e+02 update: 3.401848e-02 (step size = 1.000000e+00) 2 6.887889e-02 -108.980168585933 -2.858481e-02 -------------------------------------- norm(grad_E1) = 3.794982e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.033541e+00 -------------------------------------- norm(preconditioned_grad_E) = 1.044058e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 9.741397e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 5.986145e-01 -------------------------------------- Polak-Ribière coefficient = 7.184416e-01 ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -2.304804e-02 Descent directional H1-inner product: -2.304804e-02 ============================================================= Candidate Energy: -1.089841e+02 update: 2.857572e-02 (step size = 1.000000e+00) 3 5.800685e-02 -108.984083964658 -3.915379e-03 -------------------------------------- norm(grad_E1) = 2.340493e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 5.531497e-01 -------------------------------------- norm(preconditioned_grad_E) = 8.172395e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 7.878385e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 4.068627e-01 -------------------------------------- Polak-Ribière coefficient = 2.822775e-01 ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -1.524878e-02 Descent directional H1-inner product: -1.524878e-02 ============================================================= Candidate Energy: -1.089871e+02 update: 1.385453e-02 (step size = 1.000000e+00) 4 3.255557e-02 -108.987098334917 -3.014370e-03 -------------------------------------- norm(grad_E1) = 1.909765e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 5.679617e-01 -------------------------------------- norm(preconditioned_grad_E) = 7.231717e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 6.847560e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 3.782083e-01 -------------------------------------- Polak-Ribière coefficient = 1.051522e+00 ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -6.632889e-03 Descent directional H1-inner product: -6.632889e-03 ============================================================= Candidate Energy: -1.089877e+02 update: 1.367638e-02 (step size = 1.000000e+00) 5 2.712613e-02 -108.987729875113 -6.315402e-04 -------------------------------------- norm(grad_E1) = 2.543790e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 6.520956e-01 -------------------------------------- norm(preconditioned_grad_E) = 6.761418e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 6.283433e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 4.189827e-01 -------------------------------------- Polak-Ribière coefficient = 3.446593e-01 Powell/guarded restart at iteration_index 6 (reason: powell) ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -1.549116e-02 Descent directional H1-inner product: -1.549116e-02 ============================================================= Candidate Energy: -1.089905e+02 update: 1.583921e-02 (step size = 1.000000e+00) 6 3.234635e-02 -108.990548434265 -2.818559e-03 -------------------------------------- norm(grad_E1) = 2.071883e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.887184e-01 -------------------------------------- norm(preconditioned_grad_E) = 5.055794e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.547069e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 3.407497e-01 -------------------------------------- Polak-Ribière coefficient = 1.253690e+00 Powell/guarded restart at iteration_index 7 (reason: non-descent) ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -9.525183e-03 Descent directional H1-inner product: -9.525183e-03 ============================================================= Candidate Energy: -1.089909e+02 update: 1.474433e-02 (step size = 1.000000e+00) 7 2.774868e-02 -108.990926275203 -3.778409e-04 -------------------------------------- norm(grad_E1) = 1.793689e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.965874e-01 -------------------------------------- norm(preconditioned_grad_E) = 4.579879e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.105506e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 3.205437e-01 -------------------------------------- Polak-Ribière coefficient = 1.755097e+00 Powell/guarded restart at iteration_index 8 (reason: non-descent) ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -8.047012e-03 Descent directional H1-inner product: -8.047012e-03 ============================================================= Candidate Energy: -1.089916e+02 update: 1.217039e-02 (step size = 1.000000e+00) 8 2.515707e-02 -108.991589758450 -6.634832e-04 -------------------------------------- norm(grad_E1) = 1.499346e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.092637e-01 -------------------------------------- norm(preconditioned_grad_E) = 4.068301e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.655072e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.701478e-01 -------------------------------------- Polak-Ribière coefficient = 1.598762e+00 Powell/guarded restart at iteration_index 9 (reason: non-descent) ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -6.122159e-03 Descent directional H1-inner product: -6.122159e-03 ============================================================= Candidate Energy: -1.089917e+02 update: 1.102378e-02 (step size = 1.000000e+00) 9 2.265949e-02 -108.991702395894 -1.126374e-04 -------------------------------------- norm(grad_E1) = 1.474502e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.929835e-01 -------------------------------------- norm(preconditioned_grad_E) = 3.907259e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.535956e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.699924e-01 -------------------------------------- Polak-Ribière coefficient = 1.874752e+00 Powell/guarded restart at iteration_index 10 (reason: non-descent) ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -5.656236e-03 Descent directional H1-inner product: -5.656236e-03 ============================================================= Candidate Energy: -1.089918e+02 update: 1.029474e-02 (step size = 1.000000e+00) 10 2.292804e-02 -108.991788400248 -8.600435e-05 -------------------------------------- norm(grad_E1) = 1.355775e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.616531e-01 -------------------------------------- norm(preconditioned_grad_E) = 4.298525e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.030641e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 2.524292e-01 -------------------------------------- Polak-Ribière coefficient = 2.063845e+00 Powell/guarded restart at iteration_index 11 (reason: non-descent) ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -6.186133e-03 Descent directional H1-inner product: -6.186133e-03 ============================================================= Candidate Energy: -1.089910e+02 Candidate Energy: -1.089931e+02 update: 8.184726e-03 (step size = 5.000000e-01) 11 1.463521e-02 -108.993128946680 -1.340546e-03 -------------------------------------- norm(grad_E1) = 4.599120e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.074116e-02 -------------------------------------- norm(preconditioned_grad_E) = 7.632063e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 7.387220e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 5.816697e-02 -------------------------------------- Polak-Ribière coefficient = 1.593943e-01 ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -7.553466e-05 Descent directional H1-inner product: -7.553466e-05 ============================================================= Candidate Energy: -1.089931e+02 update: 1.033976e-03 (step size = 5.000000e-01) 12 1.840435e-03 -108.993137391423 -8.444743e-06 -------------------------------------- norm(grad_E1) = 3.683119e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 6.126577e-02 -------------------------------------- norm(preconditioned_grad_E) = 8.808536e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.449431e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 5.451856e-02 -------------------------------------- Polak-Ribière coefficient = 3.780509e-01 ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -2.429390e-04 Descent directional H1-inner product: -2.429390e-04 ============================================================= Candidate Energy: -1.089932e+02 update: 1.801440e-03 (step size = 5.000000e-01) 13 3.160356e-03 -108.993191635339 -5.424392e-05 -------------------------------------- norm(grad_E1) = 1.321387e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.269498e-02 -------------------------------------- norm(preconditioned_grad_E) = 4.380209e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.302014e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.908706e-02 -------------------------------------- Polak-Ribière coefficient = 8.928890e-02 ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -4.050204e-05 Descent directional H1-inner product: -4.050204e-05 ============================================================= Candidate Energy: -1.089932e+02 update: 5.363866e-04 (step size = 5.000000e-01) 14 8.732521e-04 -108.993198757840 -7.122500e-06 -------------------------------------- norm(grad_E1) = 5.764028e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 5.124149e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.679877e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.675264e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 9.027523e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -1.811043e-05 Descent directional H1-inner product: -1.811043e-05 ============================================================= Candidate Energy: -1.089932e+02 update: 2.002269e-04 (step size = 5.000000e-01) 15 3.833062e-04 -108.993200147970 -1.390130e-06 -------------------------------------- norm(grad_E1) = 1.866030e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.859815e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.583197e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.582407e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 6.181039e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Powell/guarded restart at iteration_index 16 (reason: powell) ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -1.555456e-05 Descent directional H1-inner product: -1.555456e-05 ============================================================= Candidate Energy: -1.089932e+02 update: 1.505127e-04 (step size = 5.000000e-01) 16 2.230325e-04 -108.993200732102 -5.841316e-07 -------------------------------------- norm(grad_E1) = 1.664202e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.405484e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.541186e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.540754e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 5.829836e-03 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 ============================================================= MUST BE THE SAME: Descent directional H1-inner product: -1.489461e-05 Descent directional H1-inner product: -1.489461e-05 ============================================================= Candidate Energy: -1.089932e+02 Precision is achieved inside line search at iteration_index = 17 17 1.473394e-04 -108.993201057903 -3.258013e-07 --------------------------------------------------------------------------- SCF converged in 17 iterations! ===========================================================================

…identified. It is left to clean a bit the code. WARNING: There is still a difference between update and MO residual, provided the molecule has more than 2 electrons. Why does this happend? WARNING: Different runs for N2 molecule are not identical. Could be parallelization related? =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 2.645751e+00 -108.270487404025 -1.082705e+02 -------------------------------------- norm(grad_E1) = 3.366493e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.553361e-01 -------------------------------------- norm(preconditioned_grad_E) = 8.100363e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 8.088078e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 1.864618e+00 -------------------------------------- Descent directional H1-inner product: -1.314760e+00 Candidate Energy: -1.089581e+02 update: 6.938764e-02 (step size = 1.000000e+00) 1 1.472060e-01 -108.958091792121 -6.876044e-01 -------------------------------------- norm(grad_E1) = 2.764326e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 5.317091e-01 -------------------------------------- norm(preconditioned_grad_E) = 1.502855e-01 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.477018e-01 -------------------------------------- -------------------------------------- norm(grad_E) = 5.530943e-01 -------------------------------------- Polak-Ribière coefficient = 1.450836e-02 Descent directional H1-inner product: -5.747786e-02 Candidate Energy: -1.089855e+02 update: 3.138246e-02 (step size = 1.000000e+00) 2 5.489076e-02 -108.985514311892 -2.742252e-02 -------------------------------------- norm(grad_E1) = 1.769811e-01 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 7.087432e-01 -------------------------------------- norm(preconditioned_grad_E) = 7.299533e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 6.905592e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 3.553270e-01 -------------------------------------- Polak-Ribière coefficient = 3.249523e-01 Descent directional H1-inner product: -1.499712e-02 Candidate Energy: -1.089914e+02 update: 2.032043e-02 (step size = 1.000000e+00) 3 3.839633e-02 -108.991437881785 -5.923570e-03 -------------------------------------- norm(grad_E1) = 8.273076e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.034647e-01 -------------------------------------- norm(preconditioned_grad_E) = 3.272623e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.247190e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 1.476569e-01 -------------------------------------- Polak-Ribière coefficient = 2.880157e-01 ============================================================= MUST BE THE SAME: 1.585534e-02 1.585534e-02 ============================================================= Descent directional H1-inner product: -1.995168e-03 Candidate Energy: -1.089923e+02 update: 6.355835e-03 (step size = 1.000000e+00) 4 1.313206e-02 -108.992336132823 -8.982510e-04 -------------------------------------- norm(grad_E1) = 4.415386e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.143986e-01 -------------------------------------- norm(preconditioned_grad_E) = 2.356529e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 2.301567e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 9.450855e-02 -------------------------------------- Polak-Ribière coefficient = 1.614717e-01 ============================================================= MUST BE THE SAME: 2.880090e-03 2.880090e-03 ============================================================= Powell/guarded restart at iteration_index 5 (reason: powell) Descent directional H1-inner product: -1.438624e-03 Candidate Energy: -1.089930e+02 update: 5.592169e-03 (step size = 1.000000e+00) 5 1.020354e-02 -108.992985513539 -6.493807e-04 -------------------------------------- norm(grad_E1) = 3.878081e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 9.837625e-02 -------------------------------------- norm(preconditioned_grad_E) = 1.275734e-02 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 1.207934e-02 -------------------------------------- -------------------------------------- norm(grad_E) = 6.610984e-02 -------------------------------------- Polak-Ribière coefficient = 4.135496e-01 Descent directional H1-inner product: -4.412770e-04 Candidate Energy: -1.089931e+02 update: 4.709531e-03 (step size = 1.000000e+00) 6 6.776245e-03 -108.993145815139 -1.603016e-04 -------------------------------------- norm(grad_E1) = 1.034542e-02 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.201023e-02 -------------------------------------- norm(preconditioned_grad_E) = 6.512635e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 6.484377e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 2.018125e-02 -------------------------------------- Polak-Ribière coefficient = 2.373889e-01 Descent directional H1-inner product: -6.870893e-05 Candidate Energy: -1.089932e+02 update: 1.207235e-03 (step size = 1.000000e+00) 7 2.248658e-03 -108.993171908432 -2.609329e-05 -------------------------------------- norm(grad_E1) = 9.603170e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.312428e-02 -------------------------------------- norm(preconditioned_grad_E) = 5.417717e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 5.343427e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.863479e-02 -------------------------------------- Polak-Ribière coefficient = 2.085172e-01 Descent directional H1-inner product: -6.409837e-05 Candidate Energy: -1.089932e+02 update: 1.096350e-03 (step size = 1.000000e+00) 8 1.910293e-03 -108.993193376949 -2.146852e-05 -------------------------------------- norm(grad_E1) = 7.053862e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.501822e-02 -------------------------------------- norm(preconditioned_grad_E) = 4.164423e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 4.111559e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 1.316179e-02 -------------------------------------- Polak-Ribière coefficient = 3.089713e-01 Descent directional H1-inner product: -3.282019e-05 Candidate Energy: -1.089932e+02 update: 6.149843e-04 (step size = 1.000000e+00) 9 1.168307e-03 -108.993199366711 -5.989761e-06 -------------------------------------- norm(grad_E1) = 2.229068e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.387060e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.734212e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.728725e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 6.560535e-03 -------------------------------------- Polak-Ribière coefficient = 1.328943e-01 ============================================================= MUST BE THE SAME: 2.833552e-05 2.833552e-05 ============================================================= Powell/guarded restart at iteration_index 10 (reason: powell) Descent directional H1-inner product: -1.678701e-05 Candidate Energy: -1.089932e+02 update: 2.564358e-04 (step size = 1.000000e+00) 10 4.517438e-04 -108.993200282558 -9.158476e-07 -------------------------------------- norm(grad_E1) = 2.196016e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.076009e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.725741e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.719156e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 6.312548e-03 -------------------------------------- Polak-Ribière coefficient = 1.952046e-01 Descent directional H1-inner product: -1.873781e-05 Candidate Energy: -1.089932e+02 update: 2.079925e-04 (step size = 1.000000e+00) 11 3.776010e-04 -108.993200524881 -2.423227e-07 -------------------------------------- norm(grad_E1) = 1.618501e-03 -------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.613433e-03 -------------------------------------- norm(preconditioned_grad_E) = 3.708661e-03 -------------------------------------- -------------------------------------- norm(preconditioned_grad_E and projected) = 3.704449e-03 -------------------------------------- -------------------------------------- norm(grad_E) = 6.103645e-03 -------------------------------------- Polak-Ribière coefficient = 2.395824e-01 Descent directional H1-inner product: -1.940657e-05 Candidate Energy: -1.089932e+02 Candidate Energy: -1.089932e+02 Precision is achieved inside line search at iteration_index = 12 12 1.461984e-04 -108.993200862967 -3.380860e-07 --------------------------------------------------------------------------- SCF converged in 12 iterations! ===========================================================================

The following tests FAILED: 25 - H_SCF_finite_electric_field (Failed) electric_field h_el_field hf integration mrchem scf 26 - H2_SCF_HartreeFock (Failed) H2_SCF_HartreeFock energy h2_scf_hf hartree_fock integration mrchem scf 32 - Li_SCF_PBE0 (Failed) Li_SCF_PBE0 dft energy integration li_scf_pbe0 mrchem scf 34 - HF_molecular_gradient_LDA (Failed) HF_molecular_gradient_LDA gradient hf_grad_lda integration mrchem 37 - H2_SCF_CUBE (Failed) cube_guess energy h2_scf_cube integration mrchem scf 41 - He_ZORA_SCF_LDA (Failed) He_ZORA_SCF_LDA energy he he_zora_scf_lda helium integration lda mrchem scf zora 42 - He_AZORA_SCF_LDA (Failed) He_AZORA_SCF_LDA azora energy he he_azora_scf_lda helium integration lda mrchem scf zora 43 - Ne_ZORA_SCF_PBE (Failed) Ne_ZORA_SCF_PBE energy integration mrchem ne ne_zora_scf_pbe neon pbe scf zora Errors while running CTest Output from these tests are in: /Users/edi011/Documents/Projects/git-repositories/mrchem/build/Testing/Temporary/LastTest.log Use "--rerun-failed --output-on-failure" to re-run the failed cases verbosely. make: *** [test] Error 8 This 26 - H2_SCF_HartreeFock (Failed) is strange. I do not see much of a difference with the reference. Of course, I do not use KAIN. Reference: 3 8.741007e-03 -1.133775887261 -4.103856e-04 --------------------------------------------------------------------------- SCF converged in 3 iterations! =========================================================================== Gradient Descent: 4 5.060629e-03 -1.133781391155 -1.652565e-04 --------------------------------------------------------------------------- SCF converged in 4 iterations! ===========================================================================

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Calculation : Optimize ground state orbitals Method : Hartree-Fock Relativity : None Environment : None External fields : None Checkpointing : Off Max iterations : 100 KAIN solver : Off Localization : First two iterations Diagonalization : Off Start precision : 1.00000e-05 Final precision : 1.00000e-05 Helmholtz precision : Dynamic Energy threshold : Off Orbital threshold : 1.00000e-04 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ =========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 2.645751e+00 -108.269858110393 -1.082699e+02 norm(A_proj - 4 * F_mat.real()) = 8.556165e-01 -------------------------------------- norm(grad_E) = 1.856270e+00 -------------------------------------- Candidate Energy: -1.089578e+02 update: 6.818573e-02 (step size = 1.000000e+00) 1 1.472751e-01 -108.957822592488 -6.879645e-01 norm(A_proj - 4 * F_mat.real()) = 5.181604e-01 -------------------------------------- norm(grad_E) = 5.424490e-01 -------------------------------------- Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089855e+02 update: 2.885844e-02 (step size = 1.000000e+00) 2 5.341173e-02 -108.985507988916 -2.768540e-02 norm(A_proj - 4 * F_mat.real()) = 7.227088e-01 -------------------------------------- norm(grad_E) = 3.553530e-01 -------------------------------------- Polak-Ribière coefficient = 2.930624e-01 Candidate Energy: -1.089918e+02 update: 1.929937e-02 (step size = 1.000000e+00) 3 3.852659e-02 -108.991772400336 -6.264411e-03 norm(A_proj - 4 * F_mat.real()) = 1.038191e-01 -------------------------------------- norm(grad_E) = 1.481974e-01 -------------------------------------- Polak-Ribière coefficient = 3.319607e-01 Candidate Energy: -1.089923e+02 update: 8.034765e-03 (step size = 1.000000e+00) 4 1.318605e-02 -108.992342448503 -5.700482e-04 norm(A_proj - 4 * F_mat.real()) = 9.904635e-02 -------------------------------------- norm(grad_E) = 8.723344e-02 -------------------------------------- Polak-Ribière coefficient = 2.107476e-01 Powell/guarded restart at iteration_index 5 (reason: powell) Candidate Energy: -1.089930e+02 update: 5.463023e-03 (step size = 1.000000e+00) 5 1.053572e-02 -108.993017176844 -6.747283e-04 norm(A_proj - 4 * F_mat.real()) = 7.544441e-02 -------------------------------------- norm(grad_E) = 5.837603e-02 -------------------------------------- Polak-Ribière coefficient = 2.987561e-01 Candidate Energy: -1.089932e+02 update: 3.457509e-03 (step size = 1.000000e+00) 6 5.972786e-03 -108.993156726616 -1.395498e-04 norm(A_proj - 4 * F_mat.real()) = 1.989172e-02 -------------------------------------- norm(grad_E) = 1.940181e-02 -------------------------------------- Polak-Ribière coefficient = 3.275686e-01 Candidate Energy: -1.089932e+02 update: 1.223429e-03 (step size = 1.000000e+00) 7 2.326441e-03 -108.993172530183 -1.580357e-05 norm(A_proj - 4 * F_mat.real()) = 2.617930e-02 -------------------------------------- norm(grad_E) = 1.781211e-02 -------------------------------------- Polak-Ribière coefficient = 3.537565e-01 Candidate Energy: -1.089932e+02 update: 9.739402e-04 (step size = 1.000000e+00) 8 1.815748e-03 -108.993192540193 -2.001001e-05 norm(A_proj - 4 * F_mat.real()) = 1.267430e-02 -------------------------------------- norm(grad_E) = 1.172321e-02 -------------------------------------- Polak-Ribière coefficient = 2.532918e-01 Candidate Energy: -1.089932e+02 update: 7.216277e-04 (step size = 1.000000e+00) 9 1.338923e-03 -108.993198428200 -5.888007e-06 norm(A_proj - 4 * F_mat.real()) = 5.396968e-03 -------------------------------------- norm(grad_E) = 7.896475e-03 -------------------------------------- Polak-Ribière coefficient = 2.628296e-01 Powell/guarded restart at iteration_index 10 (reason: powell) Candidate Energy: -1.089932e+02 update: 5.258331e-04 (step size = 1.000000e+00) 10 7.812204e-04 -108.993199594959 -1.166759e-06 norm(A_proj - 4 * F_mat.real()) = 4.725900e-03 -------------------------------------- norm(grad_E) = 6.581432e-03 -------------------------------------- Polak-Ribière coefficient = 2.804497e-01 Candidate Energy: -1.089932e+02 update: 2.418666e-04 (step size = 1.000000e+00) 11 4.298756e-04 -108.993200257937 -6.629771e-07 norm(A_proj - 4 * F_mat.real()) = 2.650957e-03 -------------------------------------- norm(grad_E) = 5.525865e-03 -------------------------------------- Polak-Ribière coefficient = 1.342689e-01 Candidate Energy: -1.089932e+02 update: 1.520457e-04 (step size = 1.000000e+00) 12 2.660700e-04 -108.993200286851 -2.891431e-08 norm(A_proj - 4 * F_mat.real()) = 1.878348e-03 -------------------------------------- norm(grad_E) = 5.429640e-03 -------------------------------------- Polak-Ribière coefficient = 2.295852e-01 Candidate Energy: -1.089932e+02 Candidate Energy: -1.089932e+02 Precision is achieved inside line search at iteration_index = 13 13 1.416109e-04 -108.993200516887 -2.300357e-07 --------------------------------------------------------------------------- SCF converged in 13 iterations! ===========================================================================

WARNING: Different runs for N2 molecule are not identical. Could be parallelization related?

=========================================================================== Iter MO residual Total energy Update --------------------------------------------------------------------------- 0 2.645751e+00 -108.269858178882 -1.082699e+02 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.556167e-01 norm(grad_E) = 1.856270e+00 Candidate Energy: -1.089514e+02 update: 6.948613e-02 (step size = 1.000000e+00) ---------------------------------------------------------------------------- 1 1.502225e-01 -108.951400239938 -6.815421e-01 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 7.544503e-01 norm(grad_E) = 8.222362e-01 Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089773e+02 update: 4.063573e-02 (step size = 1.000000e+00) ---------------------------------------------------------------------------- 2 7.597157e-02 -108.977349370825 -2.594913e-02 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.191599e+00 norm(grad_E) = 7.031510e-01 Polak-Ribière coefficient = 1.004465e+00 Candidate Energy: -1.089714e+02 Candidate Energy: -1.089813e+02 update: 1.772670e-02 (step size = 5.000000e-01) ---------------------------------------------------------------------------- 3 3.362842e-02 -108.981334103267 -3.984732e-03 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.052635e+00 norm(grad_E) = 6.411952e-01 Polak-Ribière coefficient = 1.011467e-02 Candidate Energy: -1.089918e+02 update: 1.399893e-02 (step size = 5.000000e-01) ---------------------------------------------------------------------------- 4 3.195203e-02 -108.991762240603 -1.042814e-02 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.037579e-01 norm(grad_E) = 1.027622e-01 Polak-Ribière coefficient = 1.071906e-02 Candidate Energy: -1.089926e+02 update: 4.161355e-03 (step size = 5.000000e-01) ---------------------------------------------------------------------------- 5 7.002679e-03 -108.992554660217 -7.924196e-04 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 5.163698e-02 norm(grad_E) = 5.277459e-02 Polak-Ribière coefficient = 0.000000e+00 Powell/guarded restart at iteration_index 6 (reason: powell) Candidate Energy: -1.089929e+02 update: 2.863964e-03 (step size = 7.000000e-01) ---------------------------------------------------------------------------- 6 5.687472e-03 -108.992931405160 -3.767449e-04 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 3.803882e-02 norm(grad_E) = 2.745151e-02 Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089931e+02 update: 2.240730e-03 (step size = 9.800000e-01) ---------------------------------------------------------------------------- 7 4.469521e-03 -108.993094351301 -1.629461e-04 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 2.548708e-02 norm(grad_E) = 1.621089e-02 Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089932e+02 update: 1.540513e-03 (step size = 1.372000e+00) ---------------------------------------------------------------------------- 8 2.830091e-03 -108.993163792084 -6.944078e-05 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.008244e-02 norm(grad_E) = 1.073616e-02 Polak-Ribière coefficient = 0.000000e+00 Candidate Energy: -1.089932e+02 update: 9.055415e-04 (step size = 1.372000e+00) ---------------------------------------------------------------------------- 9 1.546700e-03 -108.993184453341 -2.066126e-05 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.575015e-02 norm(grad_E) = 1.212366e-02 Polak-Ribière coefficient = 2.293722e-01 Candidate Energy: -1.089932e+02 update: 6.512670e-04 (step size = 1.372000e+00) ---------------------------------------------------------------------------- 10 1.314841e-03 -108.993194554071 -1.010073e-05 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 1.733224e-02 norm(grad_E) = 1.203153e-02 Polak-Ribière coefficient = 5.478255e-01 Candidate Energy: -1.089932e+02 update: 6.541450e-04 (step size = 1.372000e+00) ---------------------------------------------------------------------------- 11 1.157032e-03 -108.993198938993 -4.384922e-06 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 8.464090e-03 norm(grad_E) = 7.778366e-03 Polak-Ribière coefficient = 3.947157e-01 Powell/guarded restart at iteration_index 12 (reason: powell) Candidate Energy: -1.089932e+02 Candidate Energy: -1.089932e+02 update: 2.258976e-04 (step size = 6.860000e-01) ---------------------------------------------------------------------------- 12 3.853901e-04 -108.993200114094 -1.175101e-06 ---------------------------------------------------------------------------- norm(A_proj - 4 * F_mat.real()) = 4.066541e-03 norm(grad_E) = 5.683517e-03 Polak-Ribière coefficient = 1.142381e-01 Candidate Energy: -1.089932e+02 Line search step is negligible; accepting. ---------------------------------------------------------------------------- 13 1.707861e-04 -108.993200446752 -3.326584e-07 --------------------------------------------------------------------------- SCF converged in 13 iterations! ===========================================================================

This change fixes the following problem: Line search step is negligible; accepting. Energy cannot be decreased more in the backtracking search. ---------------------------------------------------------------------------- Error: getUpdate(), line 131: Invalid argument 13 1.880506e-04 0.000000000000 1.089932e+02

… type: "Stiefel" for 0 and "Grassmann" for 1. It is parsed through the SCF variable kain.

…mentation fault, but it probably also blocks the computations further.

… add more distribute()

…tal projection.

Grassmann case as well. Now we have communication-dominated regime while projecting to the horizontal space: Every h1_inner product reduces while waiting for derivatives nabla to finish. TODO: compute full matrix locally then reduce once.

…>= grad_max

gitpeterwind added the WIP Work in progress label Jan 10, 2026

started learning mrchem and do not understand printing

da28be4

edinvay force-pushed the grad branch from a6c3bc5 to 62c2bdc Compare January 19, 2026 11:17

edinvay added 5 commits January 20, 2026 18:48

projected preconditioned gradient to Stiefel

9601ebd

added the real L2 inner product of two OrbitalVectors. I recommend to…

4c58011

… check the correctness of MPI use

added the real h1 inner product of two OrbitalVectors. I recommend to…

799d171

… check the correctness of MPI use

H1 norm works perfectly, so I removed the print test added in the pre…

31794a4

…vious commit 48d73b2

edinvay force-pushed the grad branch from 728707f to 31794a4 Compare January 20, 2026 18:00

edinvay added 20 commits January 20, 2026 19:44

added h1_norm() and checked its correctness. TODO: # Safeguard: if no…

604c012

…t descent direction, skip preconditioning and then polak_ribiere momentum

updated test printing to check that the projection deminishes the norm

0ff6c16

started momentum implementation: defined the steepest descent direction

ab7980f

added direction with restart

412d7a5

Prepared for removing outdated Helmholtz and the corresponding objects.

b203fa1

Removed unnecessary heavy calculations after the backtracking search.

b4f9ebc

The code works.

cf2e020

WARNING: Different runs for N2 molecule are not identical. Could be parallelization related?

Added Grassman treatment of the unitary gauge invariance.

59f3ccb

Exploit unused variable this->history as a flag denoting the manifold…

d34421d

… type: "Stiefel" for 0 and "Grassmann" for 1. It is parsed through the SCF variable kain.

edinvay and others added 24 commits January 28, 2026 15:20

Merge branch 'MRChemSoft:master' into grad

1afc6b1

Added some printing for analysis of convergence.

432c7da

Fixing respect of MPI by h1 inner product.

915dca4

Use of mrcpp::mpi::my_func in H1 inner product helps to avoid the seg…

716ed46

…mentation fault, but it probably also blocks the computations further.

distribute() of OrbitalVectors used throughout of grad iterations

9f236dc

Initialize previous_h1_inner_product_preconditioned_grad_E_grad_E and…

0b19a81

… add more distribute()

added mpi::barrier

25691be

added more of distribute()

be791fc

added more of distribute()

9dcd9f7

Fixed MPI bug by adding MPI_Allreduce() to h1_inner_product()

4406f5c

No segmentation fault, but there is a miscommunication in the horizon…

852895e

…tal projection.

No error messages, but MPI in a deadlock

5688479

optimised MPI use in project_to_horizontal()

95c8fee

started cleaning away the debugging code

c8d8d8e

removed some distribute()

14ab321

removed all distribute from GroundStateSolver.cpp

4f36514

Fixed printing: now it is MPI rank independent

da7ad13

Merge branch 'master' into grad

cc26392

added treatment of pathologically big norm(grad E) and momentum

e01efbb

ensure steepest descent in the pathological situation of grad_E_norm …

d075272

…>= grad_max

added print for debugging of pathologically big gradient norms

837c6d8

comment out the lines where MPI gets stuck

5bd85a1

Rollback grad branch to pre-gradient-debug state (cc26392)

4498474

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

Grad(E) #537

Grad(E) #537

Uh oh!

edinvay commented Jan 9, 2026 •

edited

Loading

Uh oh!

ilfreddy commented Jan 19, 2026

Uh oh!

Reviewers

Assignees

Labels

Projects

Milestone

Development

Uh oh!

3 participants

Grad(E) #537

Are you sure you want to change the base?

Grad(E) #537

Uh oh!

Conversation

edinvay commented Jan 9, 2026 • edited Loading Uh oh! There was an error while loading. Please reload this page.

Uh oh!

Uh oh!

ilfreddy commented Jan 19, 2026

Uh oh!

Reviewers

Assignees

Labels

Projects

Milestone

Development

Uh oh!

3 participants

edinvay commented Jan 9, 2026 •

edited

Loading