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allen-tildesley-book
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********************************************************************************
** FICHE F.9. RATTLE ALGORITHM FOR CONSTRAINT DYNAMICS OF A CHAIN MOLECULE **
** 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. **
********************************************************************************
C *******************************************************************
C ** CONSTRAINT DYNAMICS OF A CHAIN OF ATOMS USING RATTLE. **
C ** **
C ** WE APPLY BOND LENGTH CONSTRAINTS TO ADJACENT ATOMS ONLY IN A **
C ** CHAIN MOLECULE WHICH MAY BE CYCLIC. THE GENERALIZATION TO **
C ** MORE COMPLICATED SYSTEMS IS STRAIGHTFORWARD. THE CONSTRAINT **
C ** EQUATIONS ARE LINEARIZED, AND EACH CONSTRAINT IS TREATED IN **
C ** TURN, UNTIL BOND LENGTHS ARE SATISFIED TO WITHIN A SPECIFIED **
C ** TOLERANCE. **
C ** IN THIS EXAMPLE WE TAKE A 6-ATOM CHAIN. **
C ** **
C ** REFERENCE: **
C ** **
C ** HC ANDERSEN, J. COMPUT. PHYS. 52, 24, 1983. **
C ** **
C ** SUPPLIED ROUTINES: **
C ** **
C ** SUBROUTINE MOVEA ( DT, TOL, MAXIT, NB, BOX ) **
C ** ADVANCES POSITIONS AND HALF ADVANCES VELOCITIES WITH **
C ** APPLIED CONSTRAINTS **
C ** SUBROUTINE MOVEB ( DT, TOL, MAXIT, NB, BOX, K, WC ) **
C ** COMPLETES VELOCITY MOVE AND CALCULATES NEW KINETIC ENERGY **
C ** AND CONSTRAINT CONTRIBUTION TO VIRIAL. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF MOLECULES **
C ** INTEGER NA NUMBER OF ATOMS PER MOL. **
C ** REAL DT TIMESTEP **
C ** REAL TOL BOND LENGTH TOLERANCE **
C ** INTEGER MAXIT MAXIMUM ALLOWED ITERATIONS **
C ** INTEGER NB NUMBER OF BONDS **
C ** REAL BOX BOX LENGTH **
C ** REAL K KINETIC ENERGY **
C ** REAL WC CONSTRAINT VIRIAL **
C ** REAL RX(N,NA),RY(N,NA),RZ(N,NA) ATOM POSITIONS AT TIME T **
C ** REAL VX(N,NA),VY(N,NA),VZ(N,NA) ATOM VELOCITIES **
C ** REAL FX(N,NA),FY(N,NA),FZ(N,NA) ATOM FORCES **
C ** REAL DSQ(NA) SQUARED BOND LENGTHS **
C ** REAL M(NA) ATOMIC MASSES **
C ** **
C ** USAGE: **
C ** **
C ** THESE ROUTINES COMPUTE CONSTRAINT EFFECTS IN AN ITERATIVE WAY.**
C ** POSITIONS, VELOCITIES, AND FORCES AT TIME T ARE SUPPLIED TO **
C ** THE FIRST ROUTINE MOVEA. **
C ** THE VELOCITY VERLET ALGORITHM IS USED TO ADVANCE THE **
C ** POSITIONS THROUGH A TIMESTEP T -> T+DT FROM RX,RY,RZ TO **
C ** PX,PY,PZ, AND THE VELOCITIES VX,VY,VZ THROUGH HALF A TIMESTEP **
C ** T -> T+DT/2, WITHOUT ANY CONSTRAINTS APPLIED: **
C ** PX(T+DT) = RX(T) + VX(T)*DT + AX(T)*DT**2/2 ETC. **
C ** VX(T+DT/2) = VX(T) + AX(T)*DT/2 ETC. **
C ** THE DESIRED SQUARED BOND LENGTHS AND ATOMIC MASSES ARE THEN **
C ** USED TO APPLY CONSTRAINTS TO POSITIONS AND HALF-STEP **
C ** VELOCITIES. **
C ** DSQ(A) CONTAINS SQUARED BOND LENGTH BETWEEN ATOMS A AND A+1. **
C ** IF NB=NA THE MOLECULE IS CYCLIC, IF NB=NA-1 IT IS NOT. **
C ** THE ROUTINE ALSO REQUIRES THE DESIRED TOLERANCE AND AN UPPER **
C ** LIMIT TO THE NUMBER OF ITERATIONS IN CASE OF NON-CONVERGENCE. **
C ** THE ROUTINE USES TWO LOGICAL ARRAYS TO KEEP TRACK OF WHETHER **
C ** OR NOT WE HAVE MOVED (I.E. CORRECTED) THE ATOM POSITIONS: **
C ** MOVING(A) A=1,NA SAYS WHETHER WE ARE MOVING ATOM A THIS TIME **
C ** MOVED(A) A=1,NA SAYS WHETHER WE MOVED ATOM A LAST TIME. **
C ** THIS IS SO THAT WE CAN STOP CORRECTING THE POSITIONS OF ATOMS **
C ** WHENEVER POSSIBLE, SO AS TO CUT DOWN ON UNNECESSARY WORK. **
C ** THE ROUTINE RETURNS FINAL VALUES IN RX,RY,RZ,VX,VY,VZ. **
C ** NEW FORCES ARE COMPUTED FROM THE POSITIONS IN A FORCE ROUTINE **
C ** (NOT SUPPLIED HERE) AND THE SECOND ROUTINE MOVEB CALLED. **
C ** THIS ADVANCES THE VELOCITIES FROM T+DT/2 TO T+DT: **
C ** VX(T+DT) = VX(T+DT/2) + AX(T+DT)*DT/2 ETC. **
C ** AND COMPLETES THE CONSTRAINT PROCEDURE ON VX,VY,VZ. **
C ** IT ALSO COMPUTES KINETIC ENERGY AND CONSTRAINT VIRIAL. **
C *******************************************************************
SUBROUTINE MOVEA ( DT, TOL, MAXIT, NB, BOX )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ, FX, FY, FZ
COMMON / BLOCK2 / DSQ, M
C *******************************************************************
C ** FIRST PART OF VELOCITY VERLET ALGORITHM WITH CONSTRAINTS **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
INTEGER NA
PARAMETER ( NA = 6 )
REAL DT, TOL, BOX
INTEGER MAXIT, NB
REAL RX(N,NA), RY(N,NA), RZ(N,NA)
REAL VX(N,NA), VY(N,NA), VZ(N,NA)
REAL FX(N,NA), FY(N,NA), FZ(N,NA)
REAL DSQ(NA), M(NA)
LOGICAL DONE
LOGICAL MOVING(NA), MOVED(NA)
REAL RXI(NA), RYI(NA), RZI(NA)
REAL PXI(NA), PYI(NA), PZI(NA)
REAL VXI(NA), VYI(NA), VZI(NA)
REAL TOL2, PXAB, PYAB, PZAB, PABSQ, DT2, DTSQ2
REAL RABSQ, DIFFSQ, RXAB, RYAB, RZAB, RPAB, GAB
REAL DX, DY, DZ, RMA, RMB, BOXINV, RPTOL
REAL AXIA, AYIA, AZIA
INTEGER I, A, B, IT
PARAMETER ( RPTOL = 1.0E-6 )
C *******************************************************************
IF ( ( NB .NE. NA ) .AND. ( NB .NE. NA-1 ) ) STOP 'NB IN ERROR'
BOXINV = 1.0 / BOX
TOL2 = 2.0 * TOL
DT2 = DT / 2.0
DTSQ2 = DT * DT2
C ** LOOP OVER MOLECULES **
DO 2000 I = 1, N
C ** VELOCITY VERLET ALGORITHM PART A **
DO 100 A = 1, NA
AXIA = FX(I,A) / M(A)
AYIA = FY(I,A) / M(A)
AZIA = FZ(I,A) / M(A)
RXI(A) = RX(I,A)
RYI(A) = RY(I,A)
RZI(A) = RZ(I,A)
PXI(A) = RX(I,A) + DT * VX(I,A) + DTSQ2 * AXIA
PYI(A) = RY(I,A) + DT * VY(I,A) + DTSQ2 * AYIA
PZI(A) = RZ(I,A) + DT * VZ(I,A) + DTSQ2 * AZIA
VXI(A) = VX(I,A) + DT2 * AXIA
VYI(A) = VY(I,A) + DT2 * AYIA
VZI(A) = VZ(I,A) + DT2 * AZIA
MOVING(A) = .FALSE.
MOVED(A) = .TRUE.
100 CONTINUE
IT = 0
DONE = .FALSE.
C ** START OF ITERATIVE LOOP **
1000 IF ( ( .NOT. DONE ) .AND. ( IT .LE. MAXIT ) ) THEN
DONE = .TRUE.
DO 300 A = 1, NB
B = A + 1
IF ( B .GT. NA ) B = 1
IF ( MOVED(A) .OR. MOVED(B) ) THEN
PXAB = PXI(A) - PXI(B)
PYAB = PYI(A) - PYI(B)
PZAB = PZI(A) - PZI(B)
PXAB = PXAB - ANINT ( PXAB * BOXINV ) * BOX
PYAB = PYAB - ANINT ( PYAB * BOXINV ) * BOX
PZAB = PZAB - ANINT ( PZAB * BOXINV ) * BOX
PABSQ = PXAB ** 2 + PYAB ** 2 + PZAB ** 2
RABSQ = DSQ(A)
DIFFSQ = RABSQ - PABSQ
IF ( ABS ( DIFFSQ ) .GT. ( RABSQ * TOL2 ) ) THEN
RXAB = RXI(A) - RXI(B)
RYAB = RYI(A) - RYI(B)
RZAB = RZI(A) - RZI(B)
RXAB = RXAB - ANINT ( RXAB * BOXINV ) * BOX
RYAB = RYAB - ANINT ( RYAB * BOXINV ) * BOX
RZAB = RZAB - ANINT ( RZAB * BOXINV ) * BOX
RPAB = RXAB * PXAB + RYAB * PYAB + RZAB * PZAB
IF ( RPAB .LT. ( RABSQ * RPTOL ) ) THEN
WRITE(*,'('' CONSTRAINT FAILURE '')')
STOP
ENDIF
RMA = 1.0 / M(A)
RMB = 1.0 / M(B)
GAB = DIFFSQ / ( 2.0 * ( RMA + RMB ) * RPAB )
DX = RXAB * GAB
DY = RYAB * GAB
DZ = RZAB * GAB
PXI(A) = PXI(A) + RMA * DX
PYI(A) = PYI(A) + RMA * DY
PZI(A) = PZI(A) + RMA * DZ
PXI(B) = PXI(B) - RMB * DX
PYI(B) = PYI(B) - RMB * DY
PZI(B) = PZI(B) - RMB * DZ
DX = DX / DT
DY = DY / DT
DZ = DZ / DT
VXI(A) = VXI(A) + RMA * DX
VYI(A) = VYI(A) + RMA * DY
VZI(A) = VZI(A) + RMA * DZ
VXI(B) = VXI(B) - RMB * DX
VYI(B) = VYI(B) - RMB * DY
VZI(B) = VZI(B) - RMB * DZ
MOVING(A) = .TRUE.
MOVING(B) = .TRUE.
DONE = .FALSE.
ENDIF
ENDIF
300 CONTINUE
DO 500 A = 1, NA
MOVED(A) = MOVING(A)
MOVING(A) = .FALSE.
500 CONTINUE
IT = IT + 1
GOTO 1000
ENDIF
C ** END OF ITERATIVE LOOP **
IF (.NOT. DONE) THEN
WRITE(*,'('' TOO MANY CONSTRAINT ITERATIONS IN MOVEA '')')
WRITE(*,'('' MOLECULE '',I5)') I
STOP
ENDIF
C ** STORE AWAY NEW VALUES **
DO 600 A = 1, NA
RX(I,A) = PXI(A)
RY(I,A) = PYI(A)
RZ(I,A) = PZI(A)
VX(I,A) = VXI(A)
VY(I,A) = VYI(A)
VZ(I,A) = VZI(A)
600 CONTINUE
2000 CONTINUE
C ** END OF LOOP OVER MOLECULES **
RETURN
END
SUBROUTINE MOVEB ( DT, TOL, MAXIT, NB, BOX, K, WC )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ, FX, FY, FZ
COMMON / BLOCK2 / DSQ, M
C *******************************************************************
C ** SECOND PART OF VELOCITY VERLET WITH CONSTRAINTS **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
INTEGER NA
PARAMETER ( NA = 6 )
REAL DT, TOL, BOX, K, WC
INTEGER MAXIT, NB
REAL RX(N,NA), RY(N,NA), RZ(N,NA)
REAL VX(N,NA), VY(N,NA), VZ(N,NA)
REAL FX(N,NA), FY(N,NA), FZ(N,NA)
REAL DSQ(NA), M(NA)
LOGICAL DONE
LOGICAL MOVING(NA), MOVED(NA)
REAL RXI(NA), RYI(NA), RZI(NA)
REAL VXI(NA), VYI(NA), VZI(NA)
REAL RXAB, RYAB, RZAB, RVAB, GAB
REAL VXAB, VYAB, VZAB
REAL DX, DY, DZ, DT2, RMA, RMB, BOXINV
INTEGER I, A, B, IT
C *******************************************************************
BOXINV = 1.0 / BOX
DT2 = DT / 2.0
K = 0.0
WC = 0.0
C ** LOOP OVER ALL MOLECULES **
DO 2000 I = 1, N
C ** VELOCITY VERLET ALGORITHM PART B **
DO 100 A = 1, NA
RXI(A) = RX(I,A)
RYI(A) = RY(I,A)
RZI(A) = RZ(I,A)
VXI(A) = VX(I,A) + DT2 * FX(I,A) / M(A)
VYI(A) = VY(I,A) + DT2 * FY(I,A) / M(A)
VZI(A) = VZ(I,A) + DT2 * FZ(I,A) / M(A)
MOVING(A) = .FALSE.
MOVED(A) = .TRUE.
100 CONTINUE
C ** START OF ITERATIVE LOOP **
IT = 0
DONE = .FALSE.
1000 IF ( ( .NOT. DONE ) .AND. ( IT .LE. MAXIT ) ) THEN
DONE = .TRUE.
DO 300 A = 1, NB
B = A + 1
IF ( B .GT. NA ) B = 1
IF ( MOVED(A) .OR. MOVED(B) ) THEN
VXAB = VXI(A) - VXI(B)
VYAB = VYI(A) - VYI(B)
VZAB = VZI(A) - VZI(B)
RXAB = RXI(A) - RXI(B)
RYAB = RYI(A) - RYI(B)
RZAB = RZI(A) - RZI(B)
RXAB = RXAB - ANINT ( RXAB * BOXINV ) * BOX
RYAB = RYAB - ANINT ( RYAB * BOXINV ) * BOX
RZAB = RZAB - ANINT ( RZAB * BOXINV ) * BOX
RVAB = RXAB * VXAB + RYAB * VYAB + RZAB * VZAB
RMA = 1.0 / M(A)
RMB = 1.0 / M(B)
GAB = -RVAB / ( ( RMA + RMB ) * DSQ(A) )
IF ( ABS ( GAB ) .GT. TOL ) THEN
WC = WC + GAB * DSQ(A)
DX = RXAB * GAB
DY = RYAB * GAB
DZ = RZAB * GAB
VXI(A) = VXI(A) + RMA * DX
VYI(A) = VYI(A) + RMA * DY
VZI(A) = VZI(A) + RMA * DZ
VXI(B) = VXI(B) - RMB * DX
VYI(B) = VYI(B) - RMB * DY
VZI(B) = VZI(B) - RMB * DZ
MOVING(A) = .TRUE.
MOVING(B) = .TRUE.
DONE = .FALSE.
ENDIF
ENDIF
300 CONTINUE
DO 500 A = 1, NA
MOVED(A) = MOVING(A)
MOVING(A) = .FALSE.
500 CONTINUE
IT = IT + 1
GOTO 1000
ENDIF
C ** END OF ITERATIVE LOOP **
IF (.NOT. DONE) THEN
WRITE(*,'('' TOO MANY CONSTRAINT ITERATIONS IN MOVEB '')')
WRITE(*,'('' MOLECULE '',I5)') I
STOP
ENDIF
DO 600 A = 1, NA
VX(I,A) = VXI(A)
VY(I,A) = VYI(A)
VZ(I,A) = VZI(A)
K = K + M(A) * ( VXI(A) ** 2 + VYI(A) ** 2 + VZI(A) ** 2 )
600 CONTINUE
2000 CONTINUE
C ** END OF LOOP OVER MOLECULES **
K = K * 0.5
WC = WC / DT2 / 3.0
RETURN
END
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