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mc-nvt.f
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********************************************************************************
** FICHE F.11. CONSTANT-NVT MONTE CARLO FOR LENNARD JONES ATOMS **
** This FORTRAN code is intended to illustrate points made in the text. **
** To our knowledge it works correctly. However it is the responsibility of **
** the user to test it, if it is to be used in a research application. **
********************************************************************************
PROGRAM MCNVT
COMMON / BLOCK1 / RX, RY, RZ
C *******************************************************************
C ** MONTE CARLO SIMULATION PROGRAM IN THE CONSTANT-NVT ENSEMBLE. **
C ** **
C ** THIS PROGRAM TAKES A CONFIGURATION OF LENNARD JONES ATOMS **
C ** AND PERFORMS A CONVENTIONAL NVT MC SIMULATION. THE BOX IS OF **
C ** UNIT LENGTH, -0.5 TO +0.5 AND THERE ARE NO LOOKUP TABLES. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF MOLECULES **
C ** INTEGER NSTEP MAXIMUM NUMBER OF CYCLES **
C ** REAL RX(N),RY(N),RZ(N) POSITIONS **
C ** REAL DENS REDUCED DENSITY **
C ** REAL TEMP REDUCED TEMPERATURE **
C ** REAL SIGMA REDUCED LJ DIAMETER **
C ** REAL RMIN MINIMUM REDUCED PAIR SEPARATION **
C ** REAL RCUT REDUCED CUTOFF DISTANCE **
C ** REAL DRMAX REDUCED MAXIMUM DISPLACEMENT **
C ** REAL V THE POTENTIAL ENERGY **
C ** REAL W THE VIRIAL **
C ** REAL PRES THE PRESSURE **
C ** **
C ** USAGE: **
C ** **
C ** THE PROGRAM TAKES IN A CONFIGURATION OF ATOMS **
C ** AND RUNS A MONTE CARLO SIMULATION AT THE GIVEN TEMPERATURE **
C ** FOR THE SPECIFIED NUMBER OF CYCLES. **
C ** **
C ** UNITS: **
C ** **
C ** THE PROGRAM USES LENNARD-JONES UNITS FOR USER INPUT AND **
C ** OUTPUT BUT CONDUCTS THE SIMULATION IN A BOX OF UNIT LENGTH. **
C ** FOR EXAMPLE, FOR A BOXLENGTH L, AND LENNARD-JONES PARAMETERS **
C ** EPSILON AND SIGMA, THE UNITS ARE: **
C ** **
C ** PROPERTY LJ UNITS PROGRAM UNITS **
C ** **
C ** TEMP EPSILON/K EPSILON/K **
C ** PRES EPSILON/SIGMA**3 EPSILON/L**3 **
C ** V EPSILON EPSILON **
C ** DENS 1/SIGMA**3 1/L**3 **
C ** **
C ** ROUTINES REFERENCED: **
C ** **
C ** SUBROUTINE SUMUP ( RCUT, RMIN, SIGMA, OVRLAP, V, W ) **
C ** CALCULATES THE TOTAL POTENTIAL ENERGY FOR A CONFIGURATION **
C ** SUBROUTINE ENERGY ( RXI, RYI, RZI, I, RCUT, SIGMA, V, W ) **
C ** CALCULATES THE POTENTIAL ENERGY OF ATOM I WITH ALL THE **
C ** OTHER ATOMS IN THE LIQUID **
C ** SUBROUTINE READCN (CNFILE ) **
C ** READS IN A CONFIGURATION **
C ** SUBROUTINE WRITCN ( CNFILE ) **
C ** WRITES OUT A CONFIGURATION **
C ** REAL FUNCTION RANF ( DUMMY ) **
C ** RETURNS A UNIFORM RANDOM NUMBER BETWEEN ZERO AND ONE **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N)
REAL DRMAX, DENS, TEMP, DENSLJ, SIGMA, RMIN, RCUT, BETA
REAL RANF, DUMMY, ACM, ACATMA, PI, RATIO, SR9, SR3
REAL V, VNEW, VOLD, VEND, VN, DELTV, DELTVB, VS
REAL W, WEND, WNEW, WOLD, PRES, DELTW, WS, PS
REAL VLRC, VLRC6, VLRC12, WLRC, WLRC6, WLRC12
REAL RXIOLD, RYIOLD, RZIOLD, RXINEW, RYINEW, RZINEW
REAL AVV, AVP, AVW, ACV, ACP, ACVSQ, ACPSQ, FLV, FLP
INTEGER STEP, I, NSTEP, IPRINT, ISAVE, IRATIO
LOGICAL OVRLAP
CHARACTER TITLE*80, CNFILE*30
PARAMETER ( PI = 3.1415927 )
C ****************************************************************
C ** READ INPUT DATA **
WRITE(*,'(1H1,'' **** PROGRAM MCLJ **** ''/)')
WRITE(*,'('' CONSTANT-NVT MONTE CARLO PROGRAM '' )')
WRITE(*,'('' FOR LENNARD JONES ATOMS '')')
WRITE(*,'('' ENTER THE RUN TITLE '')')
READ (*,'(A)') TITLE
WRITE(*,'('' ENTER NUMBER OF CYCLES '')')
READ (*,*) NSTEP
WRITE(*,'('' ENTER NUMBER OF STEPS BETWEEN OUTPUT LINES '')')
READ (*,*) IPRINT
WRITE(*,'('' ENTER NUMBER OF STEPS BETWEEN DATA SAVES '')')
READ (*,*) ISAVE
WRITE(*,'('' ENTER INTERVAL FOR UPDATE OF MAX. DISPL. '')')
READ (*,*) IRATIO
WRITE(*,'('' ENTER THE CONFIGURATION FILE NAME '')')
READ (*,'(A)') CNFILE
WRITE(*,'('' ENTER THE FOLLOWING IN LENNARD-JONES UNITS '',/)')
WRITE(*,'('' ENTER THE DENSITY '')')
READ (*,*) DENS
WRITE(*,'('' ENTER THE TEMPERATURE '')')
READ (*,*) TEMP
WRITE(*,'('' ENTER THE POTENTIAL CUTOFF DISTANCE '')')
READ (*,*) RCUT
C ** WRITE INPUT DATA **
WRITE(*,'( //1X ,A )') TITLE
WRITE(*,'('' NUMBER OF ATOMS '',I10 )') N
WRITE(*,'('' NUMBER OF CYCLES '',I10 )') NSTEP
WRITE(*,'('' OUTPUT FREQUENCY '',I10 )') IPRINT
WRITE(*,'('' SAVE FREQUENCY '',I10 )') ISAVE
WRITE(*,'('' RATIO UPDATE FREQUENCY '',I10 )') IRATIO
WRITE(*,'('' CONFIGURATION FILE NAME '',A )') CNFILE
WRITE(*,'('' TEMPERATURE '',F10.4 )') TEMP
WRITE(*,'('' DENSITY '',F10.4 )') DENS
WRITE(*,'('' POTENTIAL CUTOFF '',F10.4 )') RCUT
C ** READ INITIAL CONFIGURATION **
CALL READCN ( CNFILE )
C ** CONVERT INPUT DATA TO PROGRAM UNITS **
BETA = 1.0 / TEMP
SIGMA = ( DENS / REAL ( N ) ) ** ( 1.0 / 3.0 )
RMIN = 0.70 * SIGMA
RCUT = RCUT * SIGMA
DRMAX = 0.15 * SIGMA
DENSLJ = DENS
DENS = DENS / ( SIGMA ** 3 )
IF ( RCUT .GT. 0.5 ) STOP ' CUT-OFF TOO LARGE '
C ** ZERO ACCUMULATORS **
ACV = 0.0
ACVSQ = 0.0
ACP = 0.0
ACPSQ = 0.0
FLV = 0.0
FLP = 0.0
ACM = 0.0
ACATMA = 0.0
C ** CALCULATE LONG RANGE CORRECTIONS **
C ** SPECIFIC TO THE LENNARD JONES FLUID **
SR3 = ( SIGMA / RCUT ) ** 3
SR9 = SR3 ** 3
VLRC12 = 8.0 * PI * DENSLJ * REAL ( N ) * SR9 / 9.0
VLRC6 = - 8.0 * PI * DENSLJ * REAL ( N ) * SR3 / 3.0
VLRC = VLRC12 + VLRC6
WLRC12 = 4.0 * VLRC12
WLRC6 = 2.0 * VLRC6
WLRC = WLRC12 + WLRC6
C ** WRITE OUT SOME USEFUL INFORMATION **
WRITE(*,'('' SIGMA/BOX = '',F10.4)') SIGMA
WRITE(*,'('' RMIN/BOX = '',F10.4)') RMIN
WRITE(*,'('' RCUT/BOX = '',F10.4)') RCUT
WRITE(*,'('' LRC FOR <V> = '',F10.4)') VLRC
WRITE(*,'('' LRC FOR <W> = '',F10.4)') WLRC
C ** CALCULATE INITIAL ENERGY AND CHECK FOR OVERLAPS **
CALL SUMUP ( RCUT, RMIN, SIGMA, OVRLAP, V, W )
IF ( OVRLAP ) STOP ' OVERLAP IN INITIAL CONFIGURATION '
VS = ( V + VLRC ) / REAL ( N )
WS = ( W + WLRC ) / REAL ( N )
PS = DENS * TEMP + W + WLRC
PS = PS * SIGMA ** 3
WRITE(*,'('' INITIAL V = '', F10.4 )' ) VS
WRITE(*,'('' INITIAL W = '', F10.4 )' ) WS
WRITE(*,'('' INITIAL P = '', F10.4 )' ) PS
WRITE(*,'(//'' START OF MARKOV CHAIN ''//)')
WRITE(*,'('' NMOVE RATIO V/N P''/)')
C *******************************************************************
C ** LOOPS OVER ALL CYCLES AND ALL MOLECULES **
C *******************************************************************
DO 100 STEP = 1, NSTEP
DO 99 I = 1, N
RXIOLD = RX(I)
RYIOLD = RY(I)
RZIOLD = RZ(I)
C ** CALCULATE THE ENERGY OF I IN THE OLD CONFIGURATION **
CALL ENERGY ( RXIOLD, RYIOLD, RZIOLD, I, RCUT, SIGMA,
: VOLD, WOLD )
C ** MOVE I AND PICKUP THE CENTRAL IMAGE **
RXINEW = RXIOLD + ( 2.0 * RANF ( DUMMY ) - 1.0 ) * DRMAX
RYINEW = RYIOLD + ( 2.0 * RANF ( DUMMY ) - 1.0 ) * DRMAX
RZINEW = RZIOLD + ( 2.0 * RANF ( DUMMY ) - 1.0 ) * DRMAX
RXINEW = RXINEW - ANINT ( RXINEW )
RYINEW = RYINEW - ANINT ( RYINEW )
RZINEW = RZINEW - ANINT ( RZINEW )
C ** CALCULATE THE ENERGY OF I IN THE NEW CONFIGURATION **
CALL ENERGY ( RXINEW, RYINEW, RZINEW, I, RCUT, SIGMA,
: VNEW, WNEW )
C ** CHECK FOR ACCEPTANCE **
DELTV = VNEW - VOLD
DELTW = WNEW - WOLD
DELTVB = BETA * DELTV
IF ( DELTVB .LT. 75.0 ) THEN
IF ( DELTV .LE. 0.0 ) THEN
V = V + DELTV
W = W + DELTW
RX(I) = RXINEW
RY(I) = RYINEW
RZ(I) = RZINEW
ACATMA = ACATMA + 1.0
ELSEIF ( EXP ( - DELTVB ) .GT. RANF ( DUMMY ) ) THEN
V = V + DELTV
W = W + DELTW
RX(I) = RXINEW
RY(I) = RYINEW
RZ(I) = RZINEW
ACATMA = ACATMA + 1.0
ENDIF
ENDIF
ACM = ACM + 1.0
C ** CALCULATE INSTANTANEOUS VALUES **
VN = ( V + VLRC ) / REAL ( N )
PRES = DENS * TEMP + W + WLRC
C ** CONVERT PRESSURE TO LJ UNITS **
PRES = PRES * SIGMA ** 3
C ** ACCUMULATE AVERAGES **
ACV = ACV + VN
ACP = ACP + PRES
ACVSQ = ACVSQ + VN * VN
ACPSQ = ACPSQ + PRES * PRES
C *************************************************************
C ** ENDS LOOP OVER ATOMS **
C *************************************************************
99 CONTINUE
C ** PERFORM PERIODIC OPERATIONS **
IF ( MOD ( STEP, IRATIO ) .EQ. 0 ) THEN
C ** ADJUST MAXIMUM DISPLACEMENT **
RATIO = ACATMA / REAL ( N * IRATIO )
IF ( RATIO .GT. 0.5 ) THEN
DRMAX = DRMAX * 1.05
ELSE
DRMAX = DRMAX * 0.95
ENDIF
ACATMA = 0.0
ENDIF
IF ( MOD ( STEP, IPRINT ) .EQ. 0 ) THEN
C ** WRITE OUT RUNTIME INFORMATION **
WRITE(*,'(I8,3F12.6)') INT(ACM), RATIO, VN, PRES
ENDIF
IF ( MOD ( STEP, ISAVE ) .EQ. 0 ) THEN
C ** WRITE OUT THE CONFIGURATION AT INTERVALS **
CALL WRITCN ( CNFILE )
ENDIF
100 CONTINUE
C *******************************************************************
C ** ENDS THE LOOP OVER CYCLES **
C *******************************************************************
WRITE(*,'(//'' END OF MARKOV CHAIN ''//)')
C ** CHECKS FINAL VALUE OF THE POTENTIAL ENERGY IS CONSISTENT **
CALL SUMUP ( RCUT, RMIN, SIGMA, OVRLAP, VEND, WEND )
IF ( ABS ( VEND - V ) .GT. 1.0E-03 ) THEN
WRITE(*,'('' PROBLEM WITH ENERGY,'')')
WRITE(*,'('' VEND = '', E20.6)') VEND
WRITE(*,'('' V = '', E20.6)') V
ENDIF
C ** WRITE OUT THE FINAL CONFIGURATION FROM THE RUN **
CALL WRITCN ( CNFILE )
C ** CALCULATE AND WRITE OUT RUNNING AVERAGES **
AVV = ACV / ACM
ACVSQ = ( ACVSQ / ACM ) - AVV ** 2
AVP = ACP / ACM
ACPSQ = ( ACPSQ / ACM ) - AVP ** 2
C ** CALCULATE FLUCTUATIONS **
IF ( ACVSQ .GT. 0.0 ) FLV = SQRT ( ACVSQ )
IF ( ACPSQ .GT. 0.0 ) FLP = SQRT ( ACPSQ )
WRITE(*,'(/'' AVERAGES ''/ )')
WRITE(*,'('' <V/N> = '',F10.6)') AVV
WRITE(*,'('' <P> = '',F10.6)') AVP
WRITE(*,'(/'' FLUCTUATIONS ''/)')
WRITE(*,'('' FLUCTUATION IN <V/N> = '',F10.6)') FLV
WRITE(*,'('' FLUCTUATION IN <P> = '',F10.6)') FLP
WRITE(*,'(/'' END OF SIMULATION '')')
STOP
END
SUBROUTINE SUMUP ( RCUT, RMIN, SIGMA, OVRLAP, V, W )
COMMON / BLOCK1 / RX, RY, RZ
C *******************************************************************
C ** CALCULATES THE TOTAL POTENTIAL ENERGY FOR A CONFIGURATION. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N THE NUMBER OF ATOMS **
C ** REAL RX(N(,RY(N),RZ(N) THE POSITIONS OF THE ATOMS **
C ** REAL V THE POTENTIAL ENERGY **
C ** REAL W THE VIRIAL **
C ** LOGICAL OVRLAP TRUE FOR SUBSTANTIAL ATOM OVERLAP **
C ** **
C ** USAGE: **
C ** **
C ** THE SUBROUTINE RETURNS THE TOTAL POTENTIAL ENERGY AT THE **
C ** BEGINNING AND END OF THE RUN. **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N)
REAL SIGMA, RMIN, RCUT, V, W
LOGICAL OVRLAP
REAL RCUTSQ, RMINSQ, SIGSQ, RXIJ, RYIJ, RZIJ
REAL RXI, RYI, RZI, VIJ, WIJ, SR2, SR6, RIJSQ
INTEGER I, J
C *******************************************************************
OVRLAP = .FALSE.
RCUTSQ = RCUT * RCUT
RMINSQ = RMIN * RMIN
SIGSQ = SIGMA * SIGMA
V = 0.0
W = 0.0
C ** LOOP OVER ALL THE PAIRS IN THE LIQUID **
DO 100 I = 1, N - 1
RXI = RX(I)
RYI = RY(I)
RZI = RZ(I)
DO 99 J = I + 1, N
RXIJ = RXI - RX(J)
RYIJ = RYI - RY(J)
RZIJ = RZI - RZ(J)
C ** MINIMUM IMAGE THE PAIR SEPARATIONS **
RXIJ = RXIJ - ANINT ( RXIJ )
RYIJ = RYIJ - ANINT ( RYIJ )
RZIJ = RZIJ - ANINT ( RZIJ )
RIJSQ = RXIJ * RXIJ + RYIJ * RYIJ + RZIJ * RZIJ
IF ( RIJSQ .LT. RMINSQ ) THEN
OVRLAP = .TRUE.
RETURN
ELSEIF ( RIJSQ .LT. RCUTSQ ) THEN
SR2 = SIGSQ / RIJSQ
SR6 = SR2 * SR2 * SR2
VIJ = SR6 * ( SR6 - 1.0 )
WIJ = SR6 * ( SR6 - 0.5 )
V = V + VIJ
W = W + WIJ
ENDIF
99 CONTINUE
100 CONTINUE
V = 4.0 * V
W = 48.0 * W / 3.0
RETURN
END
SUBROUTINE ENERGY ( RXI, RYI, RZI, I, RCUT, SIGMA, V, W )
COMMON / BLOCK1 / RX, RY, RZ
C *******************************************************************
C ** RETURNS THE POTENTIAL ENERGY OF ATOM I WITH ALL OTHER ATOMS. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER I THE ATOM OF INTEREST **
C ** INTEGER N THE NUMBER OF ATOMS **
C ** REAL RX(N),RY(N),RZ(N) THE ATOM POSITIONS **
C ** REAL RXI,RYI,RZI THE COORDINATES OF ATOM I **
C ** REAL V THE POTENTIAL ENERGY OF ATOM I **
C ** REAL W THE VIRIAL OF ATOM I **
C ** **
C ** USAGE: **
C ** **
C ** THIS SUBROUTINE IS USED TO CALCULATE THE CHANGE OF ENERGY **
C ** DURING A TRIAL MOVE OF ATOM I. IT IS CALLED BEFORE AND **
C ** AFTER THE RANDOM DISPLACEMENT OF I. **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N)
REAL RCUT, SIGMA, RXI, RYI, RZI, V, W
INTEGER I
REAL RCUTSQ, SIGSQ, SR2, SR6
REAL RXIJ, RYIJ, RZIJ, RIJSQ, VIJ, WIJ
INTEGER J
C ******************************************************************
RCUTSQ = RCUT * RCUT
SIGSQ = SIGMA * SIGMA
V = 0.0
W = 0.0
C ** LOOP OVER ALL MOLECULES EXCEPT I **
DO 100 J = 1, N
IF ( I .NE. J ) THEN
RXIJ = RXI - RX(J)
RYIJ = RYI - RY(J)
RZIJ = RZI - RZ(J)
RXIJ = RXIJ - ANINT ( RXIJ )
RYIJ = RYIJ - ANINT ( RYIJ )
RZIJ = RZIJ - ANINT ( RZIJ )
RIJSQ = RXIJ * RXIJ + RYIJ * RYIJ + RZIJ * RZIJ
IF ( RIJSQ .LT. RCUTSQ ) THEN
SR2 = SIGSQ / RIJSQ
SR6 = SR2 * SR2 * SR2
VIJ = SR6 * ( SR6 - 1.0 )
WIJ = SR6 * ( SR6 - 0.5 )
V = V + VIJ
W = W + WIJ
ENDIF
ENDIF
100 CONTINUE
V = 4.0 * V
W = 48.0 * W / 3.0
RETURN
END
REAL FUNCTION RANF ( DUMMY )
C *******************************************************************
C ** RETURNS A UNIFORM RANDOM VARIATE IN THE RANGE 0 TO 1. **
C ** **
C ** *************** **
C ** ** WARNING ** **
C ** *************** **
C ** **
C ** GOOD RANDOM NUMBER GENERATORS ARE MACHINE SPECIFIC. **
C ** PLEASE USE THE ONE RECOMMENDED FOR YOUR MACHINE. **
C *******************************************************************
INTEGER L, C, M
PARAMETER ( L = 1029, C = 221591, M = 1048576 )
INTEGER SEED
REAL DUMMY
SAVE SEED
DATA SEED / 0 /
C *******************************************************************
SEED = MOD ( SEED * L + C, M )
RANF = REAL ( SEED ) / M
RETURN
END
SUBROUTINE READCN ( CNFILE )
COMMON / BLOCK1 / RX, RY, RZ
C *******************************************************************
C ** SUBROUTINE TO READ IN THE CONFIGURATION FROM UNIT 10 **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
CHARACTER CNFILE*(*)
REAL RX(N), RY(N), RZ(N)
INTEGER CNUNIT
PARAMETER ( CNUNIT = 10 )
INTEGER NN
C ********************************************************************
OPEN ( UNIT = CNUNIT, FILE = CNFILE, STATUS = 'OLD',
: FORM = 'UNFORMATTED' )
READ ( CNUNIT ) NN
IF ( NN .NE. N ) STOP 'N ERROR IN READCN'
READ ( CNUNIT ) RX, RY, RZ
CLOSE ( UNIT = CNUNIT )
RETURN
END
SUBROUTINE WRITCN ( CNFILE )
COMMON / BLOCK1 / RX, RY, RZ
C *******************************************************************
C ** SUBROUTINE TO WRITE OUT THE CONFIGURATION TO UNIT 10 **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
CHARACTER CNFILE*(*)
REAL RX(N), RY(N), RZ(N)
INTEGER CNUNIT
PARAMETER ( CNUNIT = 10 )
C ********************************************************************
OPEN ( UNIT = CNUNIT, FILE = CNFILE, STATUS = 'UNKNOWN',
: FORM = 'UNFORMATTED' )
WRITE ( CNUNIT ) N
WRITE ( CNUNIT ) RX, RY, RZ
CLOSE ( UNIT = CNUNIT )
RETURN
END