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C *******************************************************************
C ** THIS FORTRAN CODE IS INTENDED TO ILLUSTRATE POINTS MADE IN **
C ** THE TEXT. TO OUR KNOWLEDGE IT WORKS CORRECTLY. HOWEVER IT IS **
C ** THE RESPONSIBILITY OF THE USER TO TEST IT, IF IT IS USED IN A **
C ** RESEARCH APPLICATION. **
C *******************************************************************
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
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