C ******************************************************************* C ** FICHE F.24. INITIAL VELOCITY DISTRIBUTION ** C ******************************************************************* C ******************************************************************* C ** CENTRE OF MASS AND ANGULAR VELOCITIES FOR LINEAR MOLECULES ** C ** ** C ** PRINCIPAL VARIABLES: ** C ** ** C ** INTEGER N THE NUMBER OF MOLECULES ** C ** REAL RX(N),RY(N),RZ(N) POSITIONS ** C ** REAL VX(N),VY(N),VZ(N) VELOCITIES ** C ** REAL EX(N),EY(N),EZ(N) ORIENTATIONS ** C ** REAL OX(N),OY(N),OZ(N) SPACE-FIXED ANGULAR VELOCITIES ** C ** REAL TEMP REDUCED TEMPERATURE ** C ** REAL INERT REDUCED MOMENT OF INERTIA ** C ** ** C ** SUPPLIED ROUTINES: ** C ** ** C ** SUBROUTINE COMVEL ( TEMP ) ** C ** SETS THE CENTRE OF MASS VELOCITIES FOR A CONFIGURATION OF ** C ** LINEAR MOLECULES AT A GIVEN TEMPERATURE. ** C ** SUBROUTINE ANGVEL ( TEMP, INERT ) ** C ** SETS THE ANGULAR VELOCITIES FOR A CONFIGURATION OF LINEAR ** C ** MOLECULES AT A GIVEN TEMPERATURE. ** C ** REAL FUNCTION RANF ( DUMMY ) ** C ** RETURNS A UNIFORM RANDOM VARIATE ON THE RANGE ZERO TO ONE ** C ** REAL FUNCTION GAUSS ( DUMMY ) ** C ** RETURNS A UNIFORM RANDOM NORMAL VARIATE FROM A ** C ** DISTRIBUTION WITH ZERO MEAN AND UNIT VARIANCE. ** C ** ** C ** UNITS: ** C ** ** C ** WE ASSUME UNIT MOLECULAR MASS AND EMPLOY LENNARD-JONES UNITS ** C ** PROPERTY UNITS ** C ** RX, RY, RZ (EPSILON/M)**(1.0/2.0) ** C ** OX, OY, OZ (EPSILON/M*SIGMA**2)**(1.0/2.0) ** C ** INERT M*SIGMA**2 ** C ******************************************************************* SUBROUTINE COMVEL ( TEMP ) COMMON / BLOCK1 / RX, RY, RZ, EX, EY, EZ, : VX, VY, VZ, OX, OY, OZ C ******************************************************************* C ** TRANSLATIONAL VELOCITIES FROM MAXWELL-BOLTZMANN DISTRIBUTION ** C ** ** C ** THE DISTRIBUTION IS DETERMINED BY TEMPERATURE AND (UNIT) MASS.** C ** THIS ROUTINE IS GENERAL, AND CAN BE USED FOR ATOMS, LINEAR ** C ** MOLECULES, AND NON-LINEAR MOLECULES. ** C ** ** C ** ROUTINE REFERENCED: ** C ** ** C ** REAL FUNCTION GAUSS ( DUMMY ) ** C ** RETURNS A UNIFORM RANDOM NORMAL VARIATE FROM A ** C ** DISTRIBUTION WITH ZERO MEAN AND UNIT VARIANCE. ** C ******************************************************************* INTEGER N PARAMETER ( N = 108 ) REAL RX(N), RY(N), RZ(N), EX(N), EY(N), EZ(N) REAL VX(N), VY(N), VZ(N), OX(N), OY(N), OZ(N) REAL TEMP REAL RTEMP, SUMX, SUMY, SUMZ REAL GAUSS, DUMMY INTEGER I C ******************************************************************* RTEMP = SQRT ( TEMP ) DO 100 I = 1, N VX(I) = RTEMP * GAUSS ( DUMMY ) VY(I) = RTEMP * GAUSS ( DUMMY ) VZ(I) = RTEMP * GAUSS ( DUMMY ) 100 CONTINUE C ** REMOVE NET MOMENTUM ** SUMX = 0.0 SUMY = 0.0 SUMZ = 0.0 DO 200 I = 1, N SUMX = SUMX + VX(I) SUMY = SUMY + VY(I) SUMZ = SUMZ + VZ(I) 200 CONTINUE SUMX = SUMX / REAL ( N ) SUMY = SUMY / REAL ( N ) SUMZ = SUMZ / REAL ( N ) DO 300 I = 1, N VX(I) = VX(I) - SUMX VY(I) = VY(I) - SUMY VZ(I) = VZ(I) - SUMZ 300 CONTINUE RETURN END SUBROUTINE ANGVEL ( TEMP, INERT ) COMMON / BLOCK1 / RX, RY, RZ, EX, EY, EZ, : VX, VY, VZ, OX, OY, OZ C ******************************************************************* C ** ANGULAR VELOCITIES FROM THE MAXWELL-BOLTZMANN DISTRIBUTION. ** C ** ** C ** THE DISTRIBUTION IS DETERMINED BY TEMPERATURE AND INERTIA. ** C ** THIS ROUTINE IS SPECIFIC TO LINEAR MOLECULES. ** C ** IT CHOOSES THE DIRECTION OF THE ANGULAR VELOCITY RANDOMLY BUT ** C ** PERPENDICULAR TO THE MOLECULAR AXIS. THE SQUARE OF THE ** C ** MAGNITUDE OF THE ANGULAR VELOCITY IS CHOSEN FROM AN ** C ** EXPONENTIAL DISTRIBUTION. THERE IS NO ATTEMPT TO SET THE ** C ** TOTAL ANGULAR MOMENTUM TO ZERO. ** C ** ** C ** ROUTINE REFERENCED: ** C ** ** C ** REAL FUNCTION RANF ( DUMMY ) ** C ** RETURNS A UNIFORM RANDOM VARIATE ON THE RANGE ZERO TO ONE ** C ******************************************************************* INTEGER N PARAMETER ( N = 108 ) REAL RX(N), RY(N), RZ(N), EX(N), EY(N), EZ(N) REAL VX(N), VY(N), VZ(N), OX(N), OY(N), OZ(N) REAL TEMP, INERT REAL NORM, DOT, OSQ, O, MEAN REAL XISQ, XI1, XI2, XI REAL RANF, DUMMY INTEGER I C **************************************************************** MEAN = 2.0 * TEMP / INERT C ** SET DIRECTION OF THE ANGULAR VELOCITY ** DO 100 I = 1, N C ** CHOOSE A RANDOM VECTOR IN SPACE ** XISQ = 1.0 1000 IF ( XISQ .GE. 1.0 ) THEN XI1 = RANF ( DUMMY ) * 2.0 - 1.0 XI2 = RANF ( DUMMY ) * 2.0 - 1.0 XISQ = XI1 * XI1 + XI2 * XI2 GO TO 1000 ENDIF XI = SQRT ( 1.0 - XISQ ) OX(I) = 2.0 * XI1 * XI OY(I) = 2.0 * XI2 * XI OZ(I) = 1.0 - 2.0 * XISQ C ** CONSTRAIN THE VECTOR TO BE PERPENDICULAR TO THE MOLECULE ** DOT = OX(I) * EX(I) + OY(I) * EY(I) + OZ(I) * EZ(I) OX(I) = OX(I) - DOT * EX(I) OY(I) = OY(I) - DOT * EY(I) OZ(I) = OZ(I) - DOT * EZ(I) C ** RENORMALIZE ** OSQ = OX(I) * OX(I) + OY(I) * OY(I) + OZ(I) * OZ(I) NORM = SQRT ( OSQ ) OX(I) = OX(I) / NORM OY(I) = OY(I) / NORM OZ(I) = OZ(I) / NORM C ** CHOOSE THE MAGNITUDE OF THE ANGULAR VELOCITY ** OSQ = - MEAN * LOG ( RANF ( DUMMY ) ) O = SQRT ( OSQ ) OX(I) = O * OX(I) OY(I) = O * OY(I) OZ(I) = O * OZ(I) 100 CONTINUE RETURN END REAL FUNCTION GAUSS ( DUMMY ) C ******************************************************************* C ** RANDOM VARIATE FROM THE STANDARD NORMAL DISTRIBUTION. ** C ** ** C ** THE DISTRIBUTION IS GAUSSIAN WITH ZERO MEAN AND UNIT VARIANCE.** C ** ** C ** REFERENCE: ** C ** ** C ** KNUTH D, THE ART OF COMPUTER PROGRAMMING, (2ND EDITION ** C ** ADDISON-WESLEY), 1978 ** C ** ** C ** ROUTINE REFERENCED: ** C ** ** C ** REAL FUNCTION RANF ( DUMMY ) ** C ** RETURNS A UNIFORM RANDOM VARIATE ON THE RANGE ZERO TO ONE ** C ******************************************************************* REAL A1, A3, A5, A7, A9 PARAMETER ( A1 = 3.949846138, A3 = 0.252408784 ) PARAMETER ( A5 = 0.076542912, A7 = 0.008355968 ) PARAMETER ( A9 = 0.029899776 ) REAL SUM, R, R2 REAL RANF, DUMMY INTEGER I C ******************************************************************* SUM = 0.0 DO 10 I = 1, 12 SUM = SUM + RANF ( DUMMY ) 10 CONTINUE R = ( SUM - 6.0 ) / 4.0 R2 = R * R GAUSS = (((( A9 * R2 + A7 ) * R2 + A5 ) * R2 + A3 ) * R2 +A1 ) : * R 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