C ******************************************************************* C ** FICHE F.9 ** 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