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Internal Redundant Coordinates

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DISCLAMIER: IRC is still in beta. It is integrated in the quantum chemistry code entos.

IRC is a modern C++ library for the determination of internal redundant coordinates (and transformation to and from Cartesian coordinates) for geometry optimization of molecules. The aim of this library is to provide an easy-to-use, flexible and portable implementation of internal redundant coordinates for modern electronic structure codes.

Compilation and Installation

Dependencies

IRC has the following dependencies:

BGL functionality is used determine the connectivity of the molecule and therefore the Boost is a requirement for the library to work.

IRC also needs a linear algebra library. Armadillo and Eigen are supported out-of-the-box, but other linear algebra libraries can be easily added.

For standalone installation and testing, IRC also requires CMake.

Build IRC

Armadillo

  mkdir build && cd build
  cmake -DWITH_ARMA=TRUE ..
  make -j

Eigen

  mkdir build && cd build
  cmake -DWITH_EIGEN=TRUE ..
  make -j

Test

  ctest

Include IRC in your project

IRC is an header-only library and its inclusion is quite straightforward.

With CMake

Libirc installs CMake configuration files that enable use of the library with find_package. The irc CMake target is named irc. Armadillo and Eigen dependencies are resolved at configuration time of this library and the relevant compile definitions and includes are set in the configuration files.

Without CMake

Armadillo

If you are using Armadillo as linear algebra library you just need to include the header files in include/ and define the variable HAVE_ARMA.

Eigen

If you are using Eigen3 as linear algebra library, you need to include the header files in include/ as well as the extension to Eigen3's matrix constructors to support std::initializer_lists located in external/eigen/plugins/. The content of the file Matrix_initializer_list.h must be included Eigen3's matrix class as described here, therefore you need to set the variable EIGEN_MATRIXBASE_PLUGIN to "path_to/Matrix_initializer_list.h". Finally, you have to define the variable HAVE_EIGEN3.

Custom Linear Algebra Library

If your are using a custom linear algebra library supporting the initialization of vectors and matrices from std::initializer_lists, you have to implement the linear algebra functions in include/libirc/linalg.h and you are good to go.

Usage

IRC is mainly based on free functions, therefore every function can be used out-of-the-box. However, a wrapper class IRC with the main functionalities needed in geomerty optimization is provided.

The first step to use IRC is to build a molecule. In IRC a molecule is represented as an std::vector of atoms (irc::atom::Atom<Vector3>):

template <typename Vector3>
using irc::molecule::Molecule<Vector3> = std::vector<irc::atoms::Atom<Vector3>>;

where an atom is simply defined by an atomic number and its position (stored in a three-dimensional vector of type Vector3). In order to use IRC, you will need to implement a function that converts your molecule to an irc::molecule::Molecule:

template<typename Vector3>
irc::molecule::Molecule<Vector3> convert_my_molecule_to_irc_molecule(const MyMolecule&);

Once you have an IRC molecule irc::molecule::Molecule<Vector3>, you can build an irc::IRC<Vector3,Vector,Matrix> object:

irc::IRC<Vector3, Vector, Matrix>(const irc::molecule::Molecule&);

The irc::IRC class provides an initial guess of the Hessian in redundant internal coordinates (Matrix projected_initial_hessian_inv()), a projector for the update Hessian (Matrix projected_hessian_inv(const Matrix &)), the transformation of the gradient from Cartesian to redundant internal coordinates (Vector grad_cartesian_to_projected_irc(const Vector &)) and the transformation from the updated redundant internal coordinates to Cartesian coordinates (Vector irc_to_cartesian(const Vector &, const Vector &, const Vector &x_c_old, size_t, double)). In addition, the transformation from Cartesian to redundant internal coordinates is also provided (Vector cartesian_to_irc(const Vector &)).

User-defined internal coordinates

Tests and Code Coverage

Catch2

Tests are written using the multi-paradigm test framework Catch2. Catch2 is included as a single header file in include/catch.

CTest

Tests are run using the CTest testing tool distributed as a part of CMake.

To run the test use:

  ctest

Code Formatting

The code is formatted using clang-format. The style configuration is based on LLVM style.

To format your code before opening a PR use:

bash tool/clang-format.sh

Contributions

Any contribution to this open-source project is very welcome. If you are considering contributing don't hesitate to contact the main contributors.

You may find beneficial to have a look at the Open Source Guides.

Sources

Papers

  • P. Puly and G. Fogarasi, Geometry optimization in redundant internal coordinates, J. Chem. Phys. 96 2856 (1992).

  • C. Peng, P. Y. Ayala and H. B. Schlegel, Using Redundant Internal Coordinates to Optimize Equilibrium Geometries and Transition States, J. Comp. Chem. 17, 49-56 (1996).

  • V. Bakken and T. Helgaker, The efficient optimization of molecular geometries using redundant internal coordinates, J. Chem. Phys. 117, 9160 (2002).

Books

  • E. Bright Wilson Jr., J. C. Decius and P. C. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra, Dover Publications Inc. (2003).