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allen-tildesley-book
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********************************************************************************
** FICHE F.1. PERIODIC BOUNDARY CONDITIONS IN VARIOUS GEOMETRIES **
** 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 ** THREE ROUTINES ILLUSTRATING THE IMPLEMENTATION OF PERIODIC **
C ** BOUNDARY CONDITIONS FOR SIMULATIONS IN DIFFERENT GEOMETRIES. **
C ** **
C ** REFERENCES: **
C ** **
C ** ADAMS DJ, CCP5 QUARTERLY, 10, 30, 1983. **
C ** SMITH W, CCP5 QUARTERLY, 10, 37, 1983. **
C ** TALBOT J, PRIVATE COMMUNICATION, 1987. **
C ** **
C ** SUPPLIED ROUTINES: **
C ** **
C ** SUBROUTINE TOBOUN ( I ) **
C ** IMPLEMENTS THE PERIODIC BOUNDARY CONDITIONS FOR MOLECULE **
C ** I IN A TRUNCATED OCTAHEDRAL BOX **
C ** SUBROUTINE RDBOUN ( I ) **
C ** IMPLEMENTS THE PERIODIC BOUNDARY CONDITIONS FOR MOLECULE **
C ** I IN A RHOMBIC DODECAHEDRAL BOX **
C ** SUBROUTINE RHBOUN ( I ) **
C ** IMPLEMENTS THE PERIODIC BOUNDARY CONDITIONS FOR MOLECULE **
C ** I IN A TWO DIMENSIONAL RHOMBOIDAL BOX. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N THE NUMBER OF ATOMS **
C ** INTEGER I A PARTICULAR ATOM **
C ** REAL RX(N),RY(N),RZ(N) POSITIONS **
C ** **
C ** USAGE: **
C ** **
C ** THESE SUBROUTINES ARE CALLED AFTER THE ATOMS HAVE BEEN MOVED **
C ** IN AN MC OR MD CODE. IF AN ATOM HAS MOVED OUT OF THE BOX, IT **
C ** WILL BE REPLACED IN THE CENTRAL BOX ACCORDING TO THE PERIODIC **
C ** BOUNDARY CONDITIONS. THIS CODE HAS BEEN WRITTEN AS SEPARATE **
C ** SUBROUTINES FOR CONVENIENCE. IN YOUR PARTICULAR APPLICATION **
C ** IT MAY NOT BE APPROPRIATE TO CALL IT AS A SUBROUTINE. **
C ** SIMILAR CODE MAY BE USED TO CALCULATE THE MINIMUM IMAGE **
C ** DISTANCE BETWEEN A PAIR I, J. IN THIS CASE RX(I) SHOULD **
C ** BE REPLACED BY RXIJ, RY(I) BY RYIJ, AND RZ(I) BY RZIJ. **
C *******************************************************************
SUBROUTINE TOBOUN ( I )
COMMON / BLOCK1 / RX, RY, RZ
C *******************************************************************
C ** PERIODIC BOUNDARY CONDITIONS FOR A TRUNCATED OCTAHEDRON **
C ** **
C ** THE BOX IS CENTRED AT THE ORIGIN. THE AXES PASS THROUGH THE **
C ** CENTRES OF THE SIX SQUARE FACES OF THE TRUNCATED OCTAHEDRON **
C ** (SEE F1G. 1.10(A)). THE CONTAINING CUBE IS OF UNIT LENGTH **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
INTEGER I
REAL RX(N), RY(N), RZ(N)
REAL CORR, R75
PARAMETER ( R75 = 4.0 / 3.0 )
C *******************************************************************
RX(I) = RX(I) - ANINT ( RX(I) )
RY(I) = RY(I) - ANINT ( RY(I) )
RZ(I) = RZ(I) - ANINT ( RZ(I) )
CORR = 0.5 * AINT ( R75 * ( ABS ( RX(I) ) +
: ABS ( RY(I) ) +
: ABS ( RZ(I) ) ) )
RX(I) = RX(I) - SIGN ( CORR, RX(I) )
RY(I) = RY(I) - SIGN ( CORR, RY(I) )
RZ(I) = RZ(I) - SIGN ( CORR, RZ(I) )
RETURN
END
SUBROUTINE RDBOUN ( I )
COMMON / BLOCK1 / RX, RY, RZ
C *******************************************************************
C ** PERIODIC BOUNDARY CONDITIONS FOR A RHOMBIC DODECAHEDRON **
C ** **
C ** THE BOX IS CENTRED AT THE ORIGIN. THE X AND Y AXES JOIN THE **
C ** CENTRES OF OPPOSITE FACES OF THE DODECAHEDRON. THE Z AXIS **
C ** JOINS OPPOSITE VERTICES OF THE RHOMBIC DODECAHEDRON (SEE FIG. **
C ** 1.10(B)). THE DIAGONAL OF THE RHOMBIC FACE IS OF UNIT LENGTH **
C ** AND THE SIDE OF THE CONTAINING CUBE IS SQRT(2.0). **
C ** NOTE THAT THE X AND Y AXES PASS THROUGH THE CUBE EDGES, WHILE **
C ** THE Z AXIS PASSES THROUGH THE CUBE FACES. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** REAL RT2 SQRT(2.0) TO MACHINE ACCURACY **
C ** REAL RRT2 1.0/SQRT(2.0) **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
INTEGER I
REAL RX(N), RY(N), RZ(N)
REAL RT2, RRT2, CORR
PARAMETER ( RT2 = 1.4142136, RRT2 = 1.0 / RT2 )
C *******************************************************************
RX(I) = RX(I) - ANINT ( RX(I) )
RY(I) = RY(I) - ANINT ( RY(I) )
RZ(I) = RZ(I) - RT2 * ANINT ( RRT2 * RZ(I) )
CORR = 0.5 * AINT ( ( ABS ( RX(I) ) +
: ABS ( RY(I) ) +
: RT2 * ABS ( RZ(I) ) )
RX(I) = RX(I) - SIGN ( CORR, RX(I) )
RY(I) = RY(I) - SIGN ( CORR, RY(I) )
RZ(I) = RZ(I) - SIGN ( CORR, RZ(I) ) * RT2
RETURN
END
SUBROUTINE RHBOUN ( I )
COMMON / BLOCK1 / RX, RY, RZ
C *******************************************************************
C ** PERIODIC BOUNDARY CONDITIONS FOR A RHOMBIC BOX. **
C ** **
C ** PERIODIC CORRECTIONS ARE APPLIED IN TWO DIMENSIONS X, Y. **
C ** IN MOST APPLICATIONS THE MOLECULES WILL BE CONFINED IN THE **
C ** Z DIRECTION BY REAL WALLS RATHER THAN BY PERIODIC BOUNDARIES. **
C ** THE BOX IS CENTRED AT THE ORIGIN. THE X AXIS LIES ALONG THE **
C ** SIDE OF THE RHOMBUS, WHICH IS OF UNIT LENGTH. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** REAL RT3 SQRT(3.0) TO MACHINE ACCURACY **
C ** REAL RT32 SQRT(3.0)/2.0 **
C ** REAL RRT3 1.0/SQRT(3.0) **
C ** REAL RRT32 2.0/SQRT(3.0) **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
INTEGER I
REAL RX(N), RY(N), RZ(N)
REAL RT3, RRT3, RT32, RRT32
PARAMETER ( RT3 = 1.7320508, RRT3 = 1.0 / RT3 )
PARAMETER ( RT32 = RT3 / 2.0, RRT32 = 1.0 / RT32 )
C *******************************************************************
RX(I) = RX(I) - ANINT ( RX(I) - RRT3 * RY(I) )
: - ANINT ( RRT32 * RY(I) ) * 0.5
RY(I) = RY(I) - ANINT ( RRT32 * RY(I) ) * RT32
RETURN
END
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