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mc_poly_lj_module.f90
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mc_poly_lj_module.f90
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! mc_poly_lj_module.f90
! Routines for MC simulation, polyatomic molecule, LJ atoms
MODULE mc_module
!------------------------------------------------------------------------------------------------!
! This software was written in 2016/17 !
! by Michael P. Allen <[email protected]>/<[email protected]> !
! and Dominic J. Tildesley <[email protected]> ("the authors"), !
! to accompany the book "Computer Simulation of Liquids", second edition, 2017 ("the text"), !
! published by Oxford University Press ("the publishers"). !
! !
! LICENCE !
! Creative Commons CC0 Public Domain Dedication. !
! To the extent possible under law, the authors have dedicated all copyright and related !
! and neighboring rights to this software to the PUBLIC domain worldwide. !
! This software is distributed without any warranty. !
! You should have received a copy of the CC0 Public Domain Dedication along with this software. !
! If not, see <http://creativecommons.org/publicdomain/zero/1.0/>. !
! !
! DISCLAIMER !
! The authors and publishers make no warranties about the software, and disclaim liability !
! for all uses of the software, to the fullest extent permitted by applicable law. !
! The authors and publishers do not recommend use of this software for any purpose. !
! It is made freely available, solely to clarify points made in the text. When using or citing !
! the software, you should not imply endorsement by the authors or publishers. !
!------------------------------------------------------------------------------------------------!
USE, INTRINSIC :: iso_fortran_env, ONLY : output_unit, error_unit
IMPLICIT NONE
PRIVATE
! Public routines
PUBLIC :: introduction, conclusion, allocate_arrays, deallocate_arrays
PUBLIC :: potential_1, potential
! Public data
INTEGER, PUBLIC :: n ! number of molecules
REAL, DIMENSION(:,:), ALLOCATABLE, PUBLIC :: r ! centre of mass positions (3,n)
REAL, DIMENSION(:,:), ALLOCATABLE, PUBLIC :: e ! quaternions (0:3,n)
REAL, DIMENSION(:,:,:), ALLOCATABLE, PUBLIC :: d ! bond vectors (0:3,na,n)
! Bond vectors in body-fixed frame (na and db are public)
! Isosceles triangle, 3 sites, with unit bond length and bond angle alpha, which we set to 75 degrees here
REAL, PARAMETER :: pi = 4.0*ATAN(1.0)
REAL, PARAMETER :: alpha = 75.0 * pi / 180.0, alpha2 = alpha / 2.0
INTEGER, PARAMETER, PUBLIC :: na = 3
REAL, DIMENSION(3,na), PARAMETER, PUBLIC :: db = RESHAPE ( [ &
& -SIN(alpha2), 0.0, -COS(alpha2)/3.0, &
& 0.0, 0.0, 2.0*COS(alpha2)/3.0, &
& SIN(alpha2), 0.0, -COS(alpha2)/3.0 ], [3,na] )
! Cutoff distance and force-shift parameters (all private) chosen as per the reference:
! S Mossa, E La Nave, HE Stanley, C Donati, F Sciortino, P Tartaglia, Phys Rev E, 65, 041205 (2002)
REAL, PARAMETER :: r_cut = 2.612 ! in sigma=1 units, where r_cut = 1.2616 nm, sigma = 0.483 nm
REAL, PARAMETER :: sr_cut = 1.0/r_cut, sr_cut6 = sr_cut**6, sr_cut12 = sr_cut6**2
REAL, PARAMETER :: lambda1 = 4.0*(7.0*sr_cut6-13.0*sr_cut12)
REAL, PARAMETER :: lambda2 = -24.0*(sr_cut6-2.0*sr_cut12)*sr_cut
INTEGER, PARAMETER :: lt = -1, gt = 1 ! Options for j-range
! Public derived type
TYPE, PUBLIC :: potential_type ! A composite variable for interactions comprising
REAL :: pot ! the potential energy
REAL :: vir ! the virial and
LOGICAL :: ovr ! a flag indicating overlap (i.e. pot too high to use)
CONTAINS
PROCEDURE :: add_potential_type
PROCEDURE :: subtract_potential_type
GENERIC :: OPERATOR(+) => add_potential_type
GENERIC :: OPERATOR(-) => subtract_potential_type
END TYPE potential_type
CONTAINS
FUNCTION add_potential_type ( a, b ) RESULT (c)
IMPLICIT NONE
TYPE(potential_type) :: c ! Result is the sum of
CLASS(potential_type), INTENT(in) :: a, b ! the two inputs
c%pot = a%pot + b%pot
c%vir = a%vir + b%vir
c%ovr = a%ovr .OR. b%ovr
END FUNCTION add_potential_type
FUNCTION subtract_potential_type ( a, b ) RESULT (c)
IMPLICIT NONE
TYPE(potential_type) :: c ! Result is the difference of
CLASS(potential_type), INTENT(in) :: a, b ! the two inputs
c%pot = a%pot - b%pot
c%vir = a%vir - b%vir
c%ovr = a%ovr .OR. b%ovr ! This is meaningless, but inconsequential
END FUNCTION subtract_potential_type
SUBROUTINE introduction
IMPLICIT NONE
INTEGER :: i
REAL :: diameter
WRITE ( unit=output_unit, fmt='(a)' ) 'Lennard-Jones potential'
WRITE ( unit=output_unit, fmt='(a)' ) 'Cut-and-force-shifted'
WRITE ( unit=output_unit, fmt='(a)' ) 'Diameter, sigma = 1'
WRITE ( unit=output_unit, fmt='(a)' ) 'Well depth, epsilon = 1'
WRITE ( unit=output_unit, fmt='(a,t40,i15)' ) 'Number of atoms per molecule', na
DO i = 1, na ! Loop over atoms
WRITE ( unit=output_unit, fmt='(a,i1,t40,3f15.6)' ) 'Body-fixed atom vector ', i, db(:,i)
END DO ! End loop over atoms
diameter = 2.0 * SQRT ( MAXVAL ( SUM(db**2,dim=1) ) )
WRITE ( unit=output_unit, fmt='(a,t40,f15.6)' ) 'Molecular diameter', diameter
WRITE ( unit=output_unit, fmt='(a,t40,f15.6)' ) 'r_cut', r_cut
WRITE ( unit=output_unit, fmt='(a,t40,f15.6)' ) 'Force-shift lambda1', lambda1
WRITE ( unit=output_unit, fmt='(a,t40,f15.6)' ) 'Force-shift lambda2', lambda2
END SUBROUTINE introduction
SUBROUTINE conclusion
IMPLICIT NONE
WRITE ( unit=output_unit, fmt='(a)') 'Program ends'
END SUBROUTINE conclusion
SUBROUTINE allocate_arrays ( box )
IMPLICIT NONE
REAL, INTENT(in) :: box ! simulation box length
REAL :: rm_cut_box, diameter
ALLOCATE ( r(3,n), e(0:3,n), d(3,na,n) )
diameter = 2.0 * SQRT ( MAXVAL ( SUM(db**2,dim=1) ) )
rm_cut_box = ( r_cut+diameter ) / box
IF ( rm_cut_box > 0.5 ) THEN
WRITE ( unit=error_unit, fmt='(a,f15.6)') 'rm_cut/box too large ', rm_cut_box
STOP 'Error in allocate_arrays'
END IF
END SUBROUTINE allocate_arrays
SUBROUTINE deallocate_arrays
IMPLICIT NONE
DEALLOCATE ( r, e, d )
END SUBROUTINE deallocate_arrays
FUNCTION potential ( box ) RESULT ( total )
IMPLICIT NONE
TYPE(potential_type) :: total ! Returns a composite of pot, vir etc
REAL, INTENT(in) :: box ! Simulation box length
! total%pot is the nonbonded cut-and-shifted potential energy for whole system
! total%vir is the corresponding virial for whole system
! total%ovr is a flag indicating overlap (potential too high) to avoid overflow
! If this flag is .true., the values of total%pot etc should not be used
! Actual calculation is performed by function potential_1
TYPE(potential_type) :: partial ! Molecular contribution to total
INTEGER :: i
IF ( ANY ( SHAPE(r) /= [3,n] ) ) THEN ! should never happen
WRITE ( unit=error_unit, fmt='(a,3i15)' ) 'Array bounds error for r', n, SHAPE(r)
STOP 'Error in potential'
END IF
IF ( ANY ( SHAPE(d) /= [3,na,n] ) ) THEN ! should never happen
WRITE ( unit=error_unit, fmt='(a,5i15)' ) 'Array bounds error for d', na, n, SHAPE(d)
STOP 'Error in potential'
END IF
total = potential_type ( pot=0.0, vir=0.0, ovr=.FALSE. ) ! Initialize
DO i = 1, n - 1
partial = potential_1 ( r(:,i), d(:,:,i), i, box, gt )
IF ( partial%ovr ) THEN
total%ovr = .TRUE. ! Overlap detected
RETURN ! Return immediately
END IF
total = total + partial
END DO
total%ovr = .FALSE. ! No overlaps detected (redundant, but for clarity)
END FUNCTION potential
FUNCTION potential_1 ( ri, di, i, box, j_range ) RESULT ( partial )
IMPLICIT NONE
TYPE(potential_type) :: partial ! Returns a composite of pot, vir etc for given molecule
REAL, DIMENSION(3), INTENT(in) :: ri ! Coordinates of molecule of interest
REAL, DIMENSION(3,na), INTENT(in) :: di ! Bond vectors of molecule of interest
INTEGER, INTENT(in) :: i ! Index of molecule of interest
REAL, INTENT(in) :: box ! Simulation box length
INTEGER, OPTIONAL, INTENT(in) :: j_range ! Optional partner index range
! partial%pot is the nonbonded cut-and-shifted potential energy of molecule ri,ei with a set of other molecules
! partial%vir is the corresponding virial of molecule ri,ei
! partial%ovr is a flag indicating overlap (potential too high) to avoid overflow
! If this is .true., the values of partial%pot etc should not be used
! The coordinates in ri and ei are not necessarily identical with those in r(:,i) and e(:,i)
! The optional argument j_range restricts partner indices to j>i, or j<i
! It is assumed that r has been divided by box
! Results are in LJ units where sigma = 1, epsilon = 1
! Note that this is the force-shifted LJ potential with a linear smoothing term
! S Mossa, E La Nave, HE Stanley, C Donati, F Sciortino, P Tartaglia, Phys Rev E, 65, 041205 (2002)
INTEGER :: j, j1, j2, a, b
REAL :: diameter, rm_cut_box, rm_cut_box_sq, r_cut_sq
REAL :: sr2, sr6, sr12, rij_sq, rab_sq, virab, rmag
REAL, DIMENSION(3) :: rij, rab, fab
REAL, PARAMETER :: sr2_ovr = 1.77 ! overlap threshold (pot > 100)
TYPE(potential_type) :: pair
IF ( PRESENT ( j_range ) ) THEN
SELECT CASE ( j_range )
CASE ( lt ) ! j < i
j1 = 1
j2 = i-1
CASE ( gt ) ! j > i
j1 = i+1
j2 = n
CASE default ! should never happen
WRITE ( unit = error_unit, fmt='(a,i10)') 'j_range error ', j_range
STOP 'Impossible error in potential_1'
END SELECT
ELSE
j1 = 1
j2 = n
END IF
diameter = 2.0 * SQRT ( MAXVAL ( SUM(db**2,dim=1) ) )
rm_cut_box = ( r_cut + diameter ) / box ! Molecular cutoff in box=1 units
rm_cut_box_sq = rm_cut_box**2 ! squared
r_cut_sq = r_cut**2 ! Potential cutoff squared in sigma=1 units
partial = potential_type ( pot=0.0, vir=0.0, ovr=.FALSE. ) ! Initialize
DO j = j1, j2 ! Loop over selected range of partner molecules
IF ( i == j ) CYCLE ! Skip self
rij(:) = ri(:) - r(:,j) ! Centre-centre separation vector
rij(:) = rij(:) - ANINT ( rij(:) ) ! Periodic boundaries in box=1 units
rij_sq = SUM ( rij**2 ) ! Squared centre-centre separation in box=1 units
IF ( rij_sq < rm_cut_box_sq ) THEN ! Test within molecular cutoff
rij = rij * box ! Now in sigma = 1 units
! Double loop over atoms on both molecules
DO a = 1, na
DO b = 1, na
rab = rij + di(:,a) - d(:,b,j) ! Atom-atom vector, sigma=1 units
rab_sq = SUM ( rab**2 ) ! Squared atom-atom separation, sigma=1 units
IF ( rab_sq < r_cut_sq ) THEN ! Test within potential cutoff
sr2 = 1.0 / rab_sq ! (sigma/rab)**2
pair%ovr = sr2 > sr2_ovr ! Overlap if too close
IF ( pair%ovr ) THEN
partial%ovr = .TRUE. ! Overlap detected
RETURN ! Return immediately
END IF
rmag = SQRT(rab_sq)
sr6 = sr2**3
sr12 = sr6**2
pair%pot = 4.0*(sr12-sr6) + lambda1 + lambda2*rmag ! LJ atom-atom pair potential (force-shifted)
virab = 24.0*(2.0*sr12-sr6 ) - lambda2*rmag ! LJ atom-atom pair virial
fab = rab * virab * sr2 ! LJ atom-atom pair force
pair%vir = DOT_PRODUCT ( rij, fab ) ! Contribution to molecular virial
partial = partial + pair
END IF ! End test within potential cutoff
END DO
END DO
! End double loop over atoms on both molecules
END IF ! End test within molecular cutoff
END DO ! End loop over selected range of partner molecules
! Include numerical factors
partial%vir = partial%vir / 3.0 ! Divide virial by 3
partial%ovr = .FALSE. ! No overlaps detected (redundant, but for clarity)
END FUNCTION potential_1
END MODULE mc_module