C ******************************************************************* C ** FICHE F.30. CONSTANT-NPH MD - EXTENDED SYSTEM METHOD ** C ******************************************************************* PROGRAM ANDERS COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1, : RX2, RY2, RZ2, RX3, RY3, RZ3, : FX, FY, FZ COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES C ******************************************************************* C ** CONSTANT-NPH MOLECULAR DYNAMICS BY ANDERSEN'S METHOD. ** C ** ** C ** THE MODIFIED EQUATIONS OF MOTION ARE AS FOLLOWS: ** C ** R2 = F/M + (R/3)[V2/V - (2/3)*(V1/V)**2] ** C ** V2 = ( PRES - PRESUR ) / MP ** C ** WHERE R,R1,R2 ARE THE ATOM POSITIONS AND THEIR DERIVATIVES, ** C ** V,V1,V2 ARE THE VOLUME AND ITS DERIVATIVE, AND MP IS THE ** C ** MASS OF THE PISTON SURROUNDING THE BOX. PRES IS THE ** C ** CALCULATED PRESSURE, AND PRESUR THE REQUIRED PRESSURE. ** C ** WE SOLVE THESE EQUATIONS BY A GEAR 4-VALUE METHOD FOR SECOND ** C ** ORDER DIFFERENTIAL EQUATIONS. FOLLOWING BROWN AND CLARKE, WE ** C ** USE UNSCALED DISTANCE VARIABLES WHICH ARE REDUCED BY SIGMA. ** C ** ** C ** REFERENCES: ** C ** ** C ** ANDERSEN, J. CHEM. PHYS. 72, 283, 1980. ** C ** HAILE AND GRABEN, J. CHEM. PHYS., 73, 2412, 1980. ** C ** BROWN AND CLARKE, MOLEC. PHYS., 51, 1243, 1984. ** C ** ** C ** PRINCIPAL VARIABLES: ** C ** ** C ** INTEGER N NUMBER OF MOLECULES ** C ** REAL DT TIMESTEP ** C ** REAL MP PISTON MASS ** C ** REAL RX(N),RY(N),RZ(N) POSITIONS ** C ** REAL RX1(N),RY1(N),RZ1(N) FIRST DERIVATIVES ** C ** REAL RX2(N),RY2(N),RZ2(N) SECOND DERIVATIVES ** C ** REAL RX3(N),RY3(N),RZ3(N) THIRD DERIVATIVES ** C ** REAL VOL,VOL1,VOL2,VOL3 VOLUME AND DERIVATIVES ** C ** REAL FX(N),FY(N),FZ(N) TOTAL FORCES ** C ** ** C ** ROUTINES REFERENCED ** C ** ** C ** SUBROUTINE READCN ( CNFILE ) ** C ** READS IN CONFIGURATION AND BOX VARIABLES ** C ** SUBROUTINE FORCE ( RCUT, V, W ) ** C ** CALCULATES FORCES, POTENTIAL, AND VIRIAL ** C ** SUBROUTINE KINET ( K ) ** C ** CALCULATES KINETIC ENERGY ** C ** SUBROUTINE PREDIC ( DT ) ** C ** PREDICTOR ROUTINE FOR CONFIGURATION AND BOX VARIABLES ** C ** SUBROUTINE CORREC ( DT ) ** C ** CORRECTOR ROUTINE FOR CONFIGURATION AND BOX VARIABLES ** C ** SUBROUTINE WRITCN ( CNFILE ) ** C ** WRITES OUT CONFIGURATION AND BOX VARIABLES ** C ******************************************************************* INTEGER N PARAMETER ( N = 108 ) REAL RX(N), RY(N), RZ(N) REAL RX1(N), RY1(N), RZ1(N) REAL RX2(N), RY2(N), RZ2(N) REAL RX3(N), RY3(N), RZ3(N) REAL FX(N), FY(N), FZ(N) REAL VOL, VOL1, VOL2, VOL3, DPRES INTEGER STEP, NSTEP, IPRINT REAL ACV, ACK, ACE, ACP, ACT, ACH, ACD REAL ACVSQ, ACKSQ, ACESQ, ACPSQ, ACTSQ, ACHSQ, ACDSQ REAL AVV, AVK, AVE, AVP, AVT, AVH, AVD REAL FLV, FLK, FLE, FLP, FLT, FLH, FLD REAL DT, DENS, TEMP, RCUT, PRES, PRESUR, NORM REAL K, V, W, E, H, HAM REAL KN, VN, EN, HN, HAMN REAL SR3, SR9, VLRC, WLRC, VLRC0, WLRC0, PI, MP CHARACTER TITLE*80, CNFILE*30 REAL FREE PARAMETER ( FREE = 3.0 ) PARAMETER ( PI = 3.1415927 ) C ******************************************************************* WRITE(*,'(1H1, '' **** PROGRAM ANDERS **** '')') WRITE(*,'(//1X,'' MOLECULAR DYNAMICS OF LENNARD-JONES ATOMS'')') WRITE(*,'(1X, '' CONSTANT-NPH ALGORITHM OF ANDERSEN '')') C ** BASIC SIMULATION PARAMETERS ** WRITE(*,'('' ENTER RUN TITLE '')') READ (*,'(A)') TITLE WRITE(*,'('' ENTER CONFIGURATION FILENAME '')') READ (*,'(A)') CNFILE WRITE(*,'('' ENTER NUMBER OF STEPS '')') READ (*,*) NSTEP WRITE(*,'('' ENTER INTERVAL BETWEEN PRINTS '')') READ (*,*) IPRINT WRITE(*,'('' ENTER THE FOLLOWING IN L-J REDUCED UNITS '')') WRITE(*,'('' ENTER TIMESTEP '')') READ (*,*) DT WRITE(*,'('' ENTER POTENTIAL CUTOFF '')') READ (*,*) RCUT WRITE(*,'('' ENTER DESIRED PRESSURE '')') READ (*,*) PRESUR WRITE(*,'('' ENTER PISTON MASS PARAMETER, M '')') READ (*,*) MP WRITE(*,'(//1X,A)') TITLE WRITE(*,'('' CONFIGURATION FILENAME '',A)') CNFILE WRITE(*,'('' NUMBER OF STEPS = '',I6 )') NSTEP WRITE(*,'('' PRINT INTERVAL = '',I6 )') IPRINT WRITE(*,'('' TIMESTEP = '',F10.5)') DT WRITE(*,'('' POTENTIAL CUTOFF = '',F10.5)') RCUT WRITE(*,'('' DESIRED PRES. = '',F10.5)') PRESUR WRITE(*,'('' M PARAMETER = '',F10.5)') MP C ** READCN MUST READ IN INITIAL CONFIGURATION ** C ** AND ASSIGN VALUES TO BOX AND ITS DERIVATIVES ** CALL READCN ( CNFILE ) DENS = REAL ( N ) / VOL WRITE(*,'('' INITIAL DENS. = '',F10.5)') DENS IF ( IPRINT .LE. 0 ) IPRINT = NSTEP + 1 C ** PREPARE FACTORS FOR LONG-RANGE CORRECTIONS ** C ** NB: SPECIFIC TO LENNARD-JONES POTENTIAL ** SR3 = ( 1.0 / RCUT ) ** 3 SR9 = SR3 ** 3 VLRC0 = 8.0 * PI * REAL ( N ) * SR9 / 9.0 : - 8.0 * PI * REAL ( N ) * SR3 / 3.0 WLRC0 = 32.0 * PI * REAL ( N ) * SR9 / 9.0 : - 16.0 * PI * REAL ( N ) * SR3 / 3.0 C ** ZERO ACCUMULATORS ** ACV = 0.0 ACK = 0.0 ACE = 0.0 ACP = 0.0 ACT = 0.0 ACH = 0.0 ACD = 0.0 ACVSQ = 0.0 ACKSQ = 0.0 ACESQ = 0.0 ACPSQ = 0.0 ACTSQ = 0.0 ACHSQ = 0.0 ACDSQ = 0.0 FLV = 0.0 FLK = 0.0 FLE = 0.0 FLP = 0.0 FLT = 0.0 FLH = 0.0 FLD = 0.0 WRITE(*,'(//1X,''**** START OF DYNAMICS ****'')') WRITE(*,10001) C ******************************************************************* C ** MAIN LOOP STARTS ** C ******************************************************************* DO 1000 STEP = 1, NSTEP C ** IMPLEMENT ALGORITHM ** CALL PREDIC ( DT ) CALL FORCE ( RCUT, V, W ) CALL KINET ( K ) C ** INCLUDE LONG-RANGE CORRECTIONS IN ALGORITHM ** KN = K / REAL ( N ) DENS = REAL ( N ) / VOL WLRC = WLRC0 * DENS TEMP = 2.0 * KN / FREE PRES = DENS * TEMP + ( W + WLRC ) / VOL DPRES = ( PRES - PRESUR ) / MP CALL CORREC ( DT ) C ** CALCULATE INSTANTANEOUS VALUES ** C ** INCLUDING LONG-RANGE CORRECTIONS ** DENS = REAL ( N ) / VOL VLRC = VLRC0 * DENS WLRC = WLRC0 * DENS V = V + VLRC W = W + WLRC E = K + V VN = V / REAL ( N ) EN = E / REAL ( N ) TEMP = 2.0 * KN / FREE PRES = DENS * TEMP + W / VOL H = E + PRES * VOL + 0.5 * MP * VOL1 ** 2 HAM = E + PRESUR * VOL + 0.5 * MP * VOL1 ** 2 HN = H / REAL ( N ) HAMN = HAM / REAL ( N ) C ** INCREMENT ACCUMULATORS ** ACE = ACE + EN ACK = ACK + KN ACV = ACV + VN ACP = ACP + PRES ACH = ACH + HN ACD = ACD + DENS ACESQ = ACESQ + EN ** 2 ACKSQ = ACKSQ + KN ** 2 ACVSQ = ACVSQ + VN ** 2 ACPSQ = ACPSQ + PRES ** 2 ACHSQ = ACHSQ + HN ** 2 ACDSQ = ACDSQ + DENS ** 2 C ** OPTIONALLY PRINT INFORMATION ** IF ( MOD ( STEP, IPRINT ) .EQ. 0 ) THEN WRITE(*,'(1X,I8,9(2X,F10.5))') : STEP, EN, HN, KN, VN, PRES, TEMP, DENS, HAMN, VOL ENDIF 1000 CONTINUE C ******************************************************************* C ** MAIN LOOP ENDS ** C ******************************************************************* WRITE(*,'(/1X,''**** END OF DYNAMICS **** ''//)') C ** WRITE OUT FINAL CONFIGURATION ** C ** INCLUDING VOL,VOL1,VOL2,VOL3 ** CALL WRITCN ( CNFILE ) C ** WRITE OUT FINAL AVERAGES ** NORM = REAL ( NSTEP ) AVE = ACE / NORM AVK = ACK / NORM AVV = ACV / NORM AVP = ACP / NORM AVH = ACH / NORM AVD = ACD / NORM ACESQ = ( ACESQ / NORM ) - AVE ** 2 ACKSQ = ( ACKSQ / NORM ) - AVK ** 2 ACVSQ = ( ACVSQ / NORM ) - AVV ** 2 ACPSQ = ( ACPSQ / NORM ) - AVP ** 2 ACHSQ = ( ACHSQ / NORM ) - AVH ** 2 ACDSQ = ( ACDSQ / NORM ) - AVD ** 2 IF ( ACESQ .GT. 0.0 ) FLE = SQRT ( ACESQ ) IF ( ACKSQ .GT. 0.0 ) FLK = SQRT ( ACKSQ ) IF ( ACVSQ .GT. 0.0 ) FLV = SQRT ( ACVSQ ) IF ( ACPSQ .GT. 0.0 ) FLP = SQRT ( ACPSQ ) IF ( ACHSQ .GT. 0.0 ) FLH = SQRT ( ACHSQ ) IF ( ACDSQ .GT. 0.0 ) FLD = SQRT ( ACDSQ ) AVT = AVK / 1.5 FLT = FLK / 1.5 WRITE(*,'('' AVERAGES'',7(2X,F10.5))') : AVE, AVH, AVK, AVV, AVP, AVT, AVD WRITE(*,'('' FLUCTS '',7(2X,F10.5))') : FLE, FLH, FLK, FLV, FLP, FLT, FLD STOP 10001 FORMAT(//1X,'TIMESTEP ..ENERGY.. .ENTHALPY. ..KINETIC.', : ' ..POTENT.. .PRESSURE. ..TEMPER.. ..DENSITY.', : ' ...HAMIL.. ..VOLUME..') END SUBROUTINE FORCE ( RCUT, V, W ) COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1, : RX2, RY2, RZ2, RX3, RY3, RZ3, : FX, FY, FZ COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES C ******************************************************************* C ** LENNARD-JONES FORCE ROUTINE IN REDUCED UNITS ** C ** ** C ** THE POTENTIAL IS V(R) = 4*((1/R)**12-(1/R)**6) ** C ** WE INCLUDE SPHERICAL CUTOFF AND MINIMUM IMAGING IN CUBIC BOX. ** C ** ** C ** PRINCIPAL VARIABLES: ** C ** ** C ** INTEGER N NUMBER OF MOLECULES ** C ** REAL RX(N),RY(N),RZ(N) MOLECULAR POSITIONS ** C ** REAL FX(N),FY(N),FZ(N) MOLECULAR FORCES ** C ** REAL VOL SIMULATION VOLUME ** C ** REAL BOX SIMULATION BOX LENGTH ** C ** REAL RCUT PAIR POTENTIAL CUTOFF ** C ** REAL V POTENTIAL ENERGY ** C ** REAL W VIRIAL FUNCTION ** C ******************************************************************* INTEGER N PARAMETER ( N = 108 ) REAL RX(N), RY(N), RZ(N) REAL RX1(N), RY1(N), RZ1(N) REAL RX2(N), RY2(N), RZ2(N) REAL RX3(N), RY3(N), RZ3(N) REAL FX(N), FY(N), FZ(N) REAL VOL, VOL1, VOL2, VOL3, DPRES INTEGER I, J REAL RCUT, V, W, BOX REAL BOXINV, RCUTSQ REAL RXI, RYI, RZI, RXIJ, RYIJ, RZIJ, RIJSQ REAL FXI, FYI, FZI, FXIJ, FYIJ, FZIJ REAL SR2, SR6, SR12, VIJ, WIJ, FIJ C ******************************************************************* C ** USEFUL QUANTITIES ** BOX = VOL ** ( 1.0 / 3.0 ) BOXINV = 1.0 / BOX RCUTSQ = RCUT ** 2 C ** ZERO FORCES, POTENTIAL, VIRIAL ** DO 100 I = 1, N FX(I) = 0.0 FY(I) = 0.0 FZ(I) = 0.0 100 CONTINUE 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 = 1.0 / RIJSQ SR6 = SR2 * SR2 * SR2 VIJ = SR6 * ( SR6 - 1.0 ) V = V + VIJ WIJ = SR6 * ( SR6 - 0.5 ) W = W + WIJ FIJ = WIJ * SR2 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 ENDIF 199 CONTINUE C ** INNER LOOP ENDS ** FX(I) = FXI FY(I) = FYI FZ(I) = FZI 200 CONTINUE C ** OUTER LOOP ENDS ** C ** MULTIPLY RESULTS BY NUMERICAL FACTORS ** DO 300 I = 1, N FX(I) = FX(I) * 48.0 FY(I) = FY(I) * 48.0 FZ(I) = FZ(I) * 48.0 300 CONTINUE V = V * 4.0 W = W * 48.0 / 3.0 RETURN END SUBROUTINE KINET ( K ) COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1, : RX2, RY2, RZ2, RX3, RY3, RZ3, : FX, FY, FZ COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES C ******************************************************************* C ** ROUTINE TO COMPUTE KINETIC ENERGY. ** C ** ** C ** MOMENTUM AND VELOCITY ARE RELATED THROUGH THE FOLLOWING ** C ** DIFFERENTIAL EQUATION: P = R1 - V1*R/3.0/V ** C ******************************************************************* INTEGER N PARAMETER ( N = 108 ) REAL RX(N), RY(N), RZ(N) REAL RX1(N), RY1(N), RZ1(N) REAL RX2(N), RY2(N), RZ2(N) REAL RX3(N), RY3(N), RZ3(N) REAL FX(N), FY(N), FZ(N) REAL VOL, VOL1, VOL2, VOL3, DPRES REAL K, V1V3, PX, PY, PZ INTEGER I C ******************************************************************* K = 0.0 V1V3 = VOL1 / VOL / 3.0 DO 1000 I = 1, N PX = RX1(I) - RX(I) * V1V3 PY = RY1(I) - RY(I) * V1V3 PZ = RZ1(I) - RZ(I) * V1V3 K = K + PX ** 2 + PY ** 2 + PZ ** 2 1000 CONTINUE K = 0.5 * K RETURN END SUBROUTINE READCN ( CNFILE ) COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1, : RX2, RY2, RZ2, RX3, RY3, RZ3, : FX, FY, FZ COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES C ******************************************************************* C ** SUBROUTINE TO READ IN INITIAL CONFIGURATION FROM UNIT 10 ** C ******************************************************************* INTEGER N PARAMETER ( N = 108 ) REAL RX(N), RY(N), RZ(N) REAL RX1(N), RY1(N), RZ1(N) REAL RX2(N), RY2(N), RZ2(N) REAL RX3(N), RY3(N), RZ3(N) REAL FX(N), FY(N), FZ(N) REAL VOL, VOL1, VOL2, VOL3, DPRES CHARACTER CNFILE*(*) INTEGER CNUNIT, NN PARAMETER ( CNUNIT = 10 ) C ****************************************************************** OPEN ( UNIT = CNUNIT, FILE = CNFILE, : STATUS = 'OLD', FORM = 'UNFORMATTED' ) READ ( CNUNIT ) NN, VOL, VOL1, VOL2, VOL3 IF ( NN .NE. N ) STOP 'INCORRECT VALUE OF N' READ ( CNUNIT ) RX, RY, RZ READ ( CNUNIT ) RX1, RY1, RZ1 READ ( CNUNIT ) RX2, RY2, RZ2 READ ( CNUNIT ) RX3, RY3, RZ3 CLOSE ( UNIT = CNUNIT ) RETURN END SUBROUTINE WRITCN ( CNFILE ) COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1, : RX2, RY2, RZ2, RX3, RY3, RZ3, : FX, FY, FZ COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES C ******************************************************************* C ** ROUTINE TO WRITE OUT FINAL CONFIGURATION TO UNIT 10 ** C ******************************************************************* INTEGER N PARAMETER ( N = 108 ) REAL RX(N), RY(N), RZ(N) REAL RX1(N), RY1(N), RZ1(N) REAL RX2(N), RY2(N), RZ2(N) REAL RX3(N), RY3(N), RZ3(N) REAL FX(N), FY(N), FZ(N) REAL VOL, VOL1, VOL2, VOL3, DPRES CHARACTER CNFILE*(*) INTEGER CNUNIT PARAMETER ( CNUNIT = 10 ) C ******************************************************************* OPEN ( UNIT = CNUNIT, FILE = CNFILE, : STATUS = 'OLD', FORM = 'UNFORMATTED' ) WRITE ( CNUNIT ) N, VOL, VOL1, VOL2, VOL3 WRITE ( CNUNIT ) RX, RY, RZ WRITE ( CNUNIT ) RX1, RY1, RZ1 WRITE ( CNUNIT ) RX2, RY2, RZ2 WRITE ( CNUNIT ) RX3, RY3, RZ3 CLOSE ( UNIT = CNUNIT ) RETURN END SUBROUTINE PREDIC ( DT ) COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1, : RX2, RY2, RZ2, RX3, RY3, RZ3, : FX, FY, FZ COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES C ******************************************************************* C ** STANDARD TAYLOR SERIES PREDICTORS ** C ******************************************************************* INTEGER N PARAMETER ( N = 108 ) REAL RX(N), RY(N), RZ(N) REAL RX1(N), RY1(N), RZ1(N) REAL RX2(N), RY2(N), RZ2(N) REAL RX3(N), RY3(N), RZ3(N) REAL FX(N), FY(N), FZ(N) REAL VOL, VOL1, VOL2, VOL3, DPRES REAL DT INTEGER I REAL C1, C2, C3 C ******************************************************************* C1 = DT C2 = C1 * DT / 2.0 C3 = C2 * DT / 3.0 DO 100 I = 1, N RX(I) = RX(I) + C1*RX1(I) + C2*RX2(I) + C3*RX3(I) RY(I) = RY(I) + C1*RY1(I) + C2*RY2(I) + C3*RY3(I) RZ(I) = RZ(I) + C1*RZ1(I) + C2*RZ2(I) + C3*RZ3(I) RX1(I) = RX1(I) + C1*RX2(I) + C2*RX3(I) RY1(I) = RY1(I) + C1*RY2(I) + C2*RY3(I) RZ1(I) = RZ1(I) + C1*RZ2(I) + C2*RZ3(I) RX2(I) = RX2(I) + C1*RX3(I) RY2(I) = RY2(I) + C1*RY3(I) RZ2(I) = RZ2(I) + C1*RZ3(I) 100 CONTINUE VOL = VOL + C1*VOL1 + C2*VOL2 + C3*VOL3 VOL1 = VOL1 + C1*VOL2 + C2*VOL3 VOL2 = VOL2 + C1*VOL3 RETURN END SUBROUTINE CORREC ( DT ) COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1, : RX2, RY2, RZ2, RX3, RY3, RZ3, : FX, FY, FZ COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES C ******************************************************************* C ** GEAR CORRECTOR ALGORITHM. ** C ** ** C ** FOR TIMESTEP-SCALED VARIABLES, GEAR COEFFICIENTS WOULD BE AS ** C ** FOLLOWS (4-VALUE METHOD, 2ND-ORDER D.E.): 1/6, 5/6, 1, 1/3. ** C ******************************************************************* INTEGER N PARAMETER ( N = 108 ) REAL RX(N), RY(N), RZ(N) REAL RX1(N), RY1(N), RZ1(N) REAL RX2(N), RY2(N), RZ2(N) REAL RX3(N), RY3(N), RZ3(N) REAL FX(N), FY(N), FZ(N) REAL VOL, VOL1, VOL2, VOL3, DPRES REAL DT INTEGER I REAL C1, C2, C3, COEFF0, COEFF1, COEFF3 REAL CORV, CORRX, CORRY, CORRZ, VFAC REAL RX2I, RY2I, RZ2I REAL GEAR0, GEAR1, GEAR3 PARAMETER ( GEAR0 = 1.0 / 6.0, : GEAR1 = 5.0 / 6.0, : GEAR3 = 1.0 / 3.0 ) C ******************************************************************* C1 = DT C2 = C1 * DT / 2.0 C3 = C2 * DT / 3.0 COEFF0 = GEAR0 * C2 COEFF1 = GEAR1 * C2 / C1 COEFF3 = GEAR3 * C2 / C3 VFAC = ( ( VOL2 / VOL ) - 2.0 * ( VOL1 / VOL ) ** 2 / 3.0 ) : / 3.0 DO 400 I = 1, N RX2I = FX(I) + VFAC * RX(I) RY2I = FY(I) + VFAC * RY(I) RZ2I = FZ(I) + VFAC * RZ(I) CORRX = RX2I - RX2(I) CORRY = RY2I - RY2(I) CORRZ = RZ2I - RZ2(I) RX(I) = RX(I) + COEFF0 * CORRX RY(I) = RY(I) + COEFF0 * CORRY RZ(I) = RZ(I) + COEFF0 * CORRZ RX1(I) = RX1(I) + COEFF1 * CORRX RY1(I) = RY1(I) + COEFF1 * CORRY RZ1(I) = RZ1(I) + COEFF1 * CORRZ RX2(I) = RX2I RY2(I) = RY2I RZ2(I) = RZ2I RX3(I) = RX3(I) + COEFF3 * CORRX RY3(I) = RY3(I) + COEFF3 * CORRY RZ3(I) = RZ3(I) + COEFF3 * CORRZ 400 CONTINUE CORV = DPRES - VOL2 VOL = VOL + COEFF0 * CORV VOL1 = VOL1 + COEFF1 * CORV VOL2 = DPRES VOL3 = VOL3 + COEFF3 * CORV RETURN END