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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.17 **
C ** FORCE CALCULATION FOR LENNARD-JONES ATOMS. **
C *******************************************************************
SUBROUTINE FORCE ( EPSLON, SIGMA, RCUT, BOX, V, VC, W )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ, FX, FY, FZ
C *******************************************************************
C ** FORCE CALCULATION FOR LENNARD-JONES ATOMS. **
C ** **
C ** IN THIS WE AIM TO SHOW HOW THE FORCES, POTENTIAL ENERGY AND **
C ** VIRIAL FUNCTION ARE CALCULATED IN A FAIRLY EFFICIENT WAY. **
C ** UNDOUBTEDLY FURTHER IMPROVEMENT WOULD BE POSSIBLE ON SPECIFIC **
C ** MACHINES. **
C ** THE POTENTIAL IS V(R) = 4*EPSLON*((SIGMA/R)**12-(SIGMA/R)**6) **
C ** WE INCLUDE SPHERICAL CUTOFF AND MINIMUM IMAGING IN CUBIC BOX. **
C ** THE BOX LENGTH IS BOX. THE CUTOFF IS RCUT. **
C ** THE ROUTINE ACTUALLY RETURNS TWO DIFFERENT POTENTIAL ENERGIES.**
C ** V IS CALCULATED USING THE LENNARD-JONES POTENTIAL TO BE USED **
C ** FOR CALCULATING THE THERMODYNAMIC INTERNAL ENERGY. **
C ** LONG-RANGE CORRECTIONS SHOULD BE APPLIED TO THIS OUTSIDE THE **
C ** ROUTINE, IN THE FORM **
C ** SR3 = ( SIGMA / RCUT ) ** 3 **
C ** SR9 = SR3 ** 3 **
C ** DENS = REAL(N) * ( SIGMA / BOX ) ** 3 **
C ** VLRC = ( 8.0 /9.0 ) * PI * EPSLON * DENS * REAL ( N ) **
C ** : * ( SR9 - 3.0 * SR3 ) **
C ** WLRC = ( 16.0 / 9.0 ) * PI * EPSLON * DENS * REAL( N )**
C ** : * ( 2.0 * SR9 - 3.0 * SR3 ) **
C ** V = V + VLRC **
C ** W = W + WLRC **
C ** VC IS CALCULATED USING THE SHIFTED LENNARD-JONES POTENTIAL, **
C ** WITH NO DISCONTINUITY AT THE CUTOFF, TO BE USED IN ASSESSING **
C ** ENERGY CONSERVATION. **
C ** NO REDUCED UNITS ARE USED: FOR THIS POTENTIAL WE COULD SET **
C ** EPSLON = 1 AND EITHER SIGMA = 1 OR BOX = 1 TO IMPROVE SPEED. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF MOLECULES **
C ** REAL RX(N),RY(N),RZ(N) MOLECULAR POSITIONS **
C ** REAL VX(N),VY(N),VZ(N) MOLECULAR VELOCITIES (NOT USED) **
C ** REAL FX(N),FY(N),FZ(N) MOLECULAR FORCES **
C ** REAL SIGMA PAIR POTENTIAL LENGTH PARAMETER **
C ** REAL EPSLON PAIR POTENTIAL ENERGY PARAMETER **
C ** REAL RCUT PAIR POTENTIAL CUTOFF **
C ** REAL BOX SIMULATION BOX LENGTH **
C ** REAL V POTENTIAL ENERGY **
C ** REAL VC SHIFTED POTENTIAL **
C ** REAL W VIRIAL FUNCTION **
C ** REAL VIJ PAIR POTENTIAL BETWEEN I AND J **
C ** REAL WIJ NEGATIVE OF PAIR VIRIAL FUNCTION W **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL SIGMA, EPSLON, RCUT, BOX, V, VC, W
REAL RX(N), RY(N), RZ(N)
REAL VX(N), VY(N), VZ(N)
REAL FX(N), FY(N), FZ(N)
INTEGER I, J, NCUT
REAL BOXINV, RCUTSQ, SIGSQ, EPS4, EPS24
REAL RXI, RYI, RZI, FXI, FYI, FZI
REAL RXIJ, RYIJ, RZIJ, RIJSQ, FXIJ, FYIJ, FZIJ
REAL SR2, SR6, SR12, VIJ, WIJ, FIJ
C *******************************************************************
C ** CALCULATE USEFUL QUANTITIES **
BOXINV = 1.0 / BOX
RCUTSQ = RCUT ** 2
SIGSQ = SIGMA ** 2
EPS4 = EPSLON * 4.0
EPS24 = EPSLON * 24.0
C ** ZERO FORCES, POTENTIAL, VIRIAL **
DO 100 I = 1, N
FX(I) = 0.0
FY(I) = 0.0
FZ(I) = 0.0
100 CONTINUE
NCUT = 0
V = 0.0
W = 0.0
C ** OUTER LOOP BEGINS **
DO 200 I = 1, N - 1
RXI = RX(I)
RYI = RY(I)
RZI = RZ(I)
FXI = FX(I)
FYI = FY(I)
FZI = FZ(I)
C ** INNER LOOP BEGINS **
DO 199 J = I + 1, N
RXIJ = RXI - RX(J)
RYIJ = RYI - RY(J)
RZIJ = RZI - RZ(J)
RXIJ = RXIJ - ANINT ( RXIJ * BOXINV ) * BOX
RYIJ = RYIJ - ANINT ( RYIJ * BOXINV ) * BOX
RZIJ = RZIJ - ANINT ( RZIJ * BOXINV ) * BOX
RIJSQ = RXIJ ** 2 + RYIJ ** 2 + RZIJ ** 2
IF ( RIJSQ .LT. RCUTSQ ) THEN
SR2 = SIGSQ / RIJSQ
SR6 = SR2 * SR2 * SR2
SR12 = SR6 ** 2
VIJ = SR12 - SR6
V = V + VIJ
WIJ = VIJ + SR12
W = W + WIJ
FIJ = WIJ / RIJSQ
FXIJ = FIJ * RXIJ
FYIJ = FIJ * RYIJ
FZIJ = FIJ * RZIJ
FXI = FXI + FXIJ
FYI = FYI + FYIJ
FZI = FZI + FZIJ
FX(J) = FX(J) - FXIJ
FY(J) = FY(J) - FYIJ
FZ(J) = FZ(J) - FZIJ
NCUT = NCUT + 1
ENDIF
199 CONTINUE
C ** INNER LOOP ENDS **
FX(I) = FXI
FY(I) = FYI
FZ(I) = FZI
200 CONTINUE
C ** OUTER LOOP ENDS **
C ** CALCULATE SHIFTED POTENTIAL **
SR2 = SIGSQ / RCUTSQ
SR6 = SR2 * SR2 * SR2
SR12 = SR6 * SR6
VIJ = SR12 - SR6
VC = V - REAL ( NCUT ) * VIJ
C ** MULTIPLY RESULTS BY ENERGY FACTORS **
DO 300 I = 1, N
FX(I) = FX(I) * EPS24
FY(I) = FY(I) * EPS24
FZ(I) = FZ(I) * EPS24
300 CONTINUE
V = V * EPS4
VC = VC * EPS4
W = W * EPS24 / 3.0
RETURN
END
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