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smc_lj_module.f90
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smc_lj_module.f90
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! smc_lj_module.f90
! Energy, force, and move routines for SMC, LJ potential
MODULE smc_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 :: force, force_1
! Public data
INTEGER, PUBLIC :: n ! Number of atoms
REAL, DIMENSION(:,:), ALLOCATABLE, PUBLIC :: r ! Positions (3,n)
REAL, DIMENSION(:,:), ALLOCATABLE, PUBLIC :: r_old ! Old positions (3,n)
REAL, DIMENSION(:,:), ALLOCATABLE, PUBLIC :: v ! Velocities (3,n)
REAL, DIMENSION(:), ALLOCATABLE, PUBLIC :: zeta ! Random numbers (n)
LOGICAL, DIMENSION(:,:), ALLOCATABLE, PUBLIC :: move ! Mask for multi-atom moves (3,n)
! Private data
INTEGER, PARAMETER :: lt = -1, gt = 1 ! Options for j-range
! Public derived type
! At the time of writing gfortran, and some other compilers, do not implement
! parameterized derived types (part of the Fortran 2003 standard);
! hence the rather clumsy use of the n_max parameter here.
INTEGER, PARAMETER :: n_max = 256
TYPE, PUBLIC :: potential_type ! A composite variable for interactions comprising
REAL :: pot ! the cut-and-shifted potential energy and
REAL :: cut ! the cut (but not shifted) potential energy and
REAL :: vir ! the virial and
REAL :: lap ! the Laplacian
REAL, DIMENSION(3,n_max) :: f ! the forces 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 the two inputs
CLASS(potential_type), INTENT(in) :: a, b
c%pot = a%pot + b%pot
c%cut = a%cut + b%cut
c%vir = a%vir + b%vir
c%lap = a%lap + b%lap
c%f = a%f + b%f
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 the two inputs
CLASS(potential_type), INTENT(in) :: a, b
c%pot = a%pot - b%pot
c%cut = a%cut - b%cut
c%vir = a%vir - b%vir
c%lap = a%lap - b%lap
c%f = a%f - b%f
c%ovr = a%ovr .OR. b%ovr ! This is meaningless but inconsequential
END FUNCTION subtract_potential_type
SUBROUTINE introduction
IMPLICIT NONE
WRITE ( unit=output_unit, fmt='(a)' ) 'Lennard-Jones potential'
WRITE ( unit=output_unit, fmt='(a)' ) 'Cut-and-shifted version for SMC dynamics'
WRITE ( unit=output_unit, fmt='(a)' ) 'Cut (but not shifted) version also calculated'
WRITE ( unit=output_unit, fmt='(a)' ) 'Diameter, sigma = 1'
WRITE ( unit=output_unit, fmt='(a)' ) 'Well depth, epsilon = 1'
END SUBROUTINE introduction
SUBROUTINE conclusion
IMPLICIT NONE
WRITE ( unit=output_unit, fmt='(a)') 'Program ends'
END SUBROUTINE conclusion
SUBROUTINE allocate_arrays ( box, r_cut )
IMPLICIT NONE
REAL, INTENT(in) :: box ! Simulation box length
REAL, INTENT(in) :: r_cut ! Potential cutoff distance
REAL :: r_cut_box
IF ( n > n_max ) THEN
WRITE ( unit=error_unit, fmt='(a,2i5)' ) 'n too large ', n, n_max
STOP 'Error in allocate_arrays'
END IF
ALLOCATE ( r(3,n), r_old(3,n), v(3,n), zeta(n), move(3,n) )
r_cut_box = r_cut / box
IF ( r_cut_box > 0.5 ) THEN
WRITE ( unit=error_unit, fmt='(a,f15.6)' ) 'r_cut/box too large ', r_cut_box
STOP 'Error in allocate_arrays'
END IF
END SUBROUTINE allocate_arrays
SUBROUTINE deallocate_arrays
IMPLICIT NONE
DEALLOCATE ( r, r_old, v, zeta, move )
END SUBROUTINE deallocate_arrays
FUNCTION force ( box, r_cut ) RESULT ( total )
IMPLICIT NONE
TYPE(potential_type) :: total ! Returns composite of forces, pot, vir etc
REAL, INTENT(in) :: box ! Simulation box length
REAL, INTENT(in) :: r_cut ! Potential cutoff distance
! total%pot is the total cut-and-shifted potential energy for whole system
! total%cut is the total cut (but not shifted) version of the above
! total%vir is the total virial for whole system
! total%lap is the total Laplacian for whole system
! total%f contains the forces on all the atoms
! 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 force_1
INTEGER :: i
TYPE(potential_type) :: partial ! atomic contributions to total
! Initialize
total = potential_type ( f=0.0, pot=0.0, cut=0.0, vir=0.0, lap=0.0, ovr=.FALSE. )
DO i = 1, n - 1 ! Begin loop over atoms
partial = force_1 ( i, box, r_cut, gt )
IF ( partial%ovr ) THEN
total%ovr = .TRUE. ! Overlap detected
RETURN ! Return immediately
END IF
total = total + partial
END DO ! End loop over atoms
total%ovr = .FALSE. ! No overlaps detected (redundant but for clarity)
END FUNCTION force
FUNCTION force_1 ( i, box, r_cut, j_range ) RESULT ( partial )
IMPLICIT NONE
TYPE(potential_type) :: partial ! Returns composite of forces, pot etc for one atom
INTEGER, INTENT(in) :: i ! Index of atom of interest
REAL, INTENT(in) :: box ! Simulation box length
REAL, INTENT(in) :: r_cut ! Potential cutoff distance
INTEGER, OPTIONAL, INTENT(in) :: j_range ! Optional partner index range
! partial%pot is the cut-and-shifted potential energy of atom i with a set of other atoms
! partial%cut is the cut (but not shifted) version of the above
! partial%vir is the corresponding virial of atom i
! partial%lap is the corresponding Laplacian of atom i
! partial%f contains the force on i and the reaction forces on all other atoms due to i
! 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 optional argument j_range restricts partner indices to j>i, or j<i
! It is assumed that positions are in units where box = 1
! Forces are calculated in units where sigma = 1 and epsilon = 1
! Note that we use a shifted LJ potential here
INTEGER :: j, j1, j2, ncut
REAL :: r_cut_box, r_cut_box_sq, box_sq
REAL :: rij_sq, sr2, sr6, sr12, cutij, virij, lapij
REAL, DIMENSION(3) :: rij, fij
REAL, PARAMETER :: sr2_ovr = 1.77 ! overlap threshold (pot > 100)
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 force1'
END SELECT
ELSE
j1 = 1
j2 = n
END IF
r_cut_box = r_cut / box
r_cut_box_sq = r_cut_box ** 2
box_sq = box ** 2
! Initialize
partial = potential_type ( f=0.0, pot=0.0, cut=0.0, vir=0.0, lap=0.0, ovr=.FALSE. )
ncut = 0
DO j = j1, j2 ! Begin loop over atoms
IF ( j == i ) CYCLE ! Skip self
rij(:) = r(:,i) - r(:,j) ! Separation vector
rij(:) = rij(:) - ANINT ( rij(:) ) ! Periodic boundary conditions in box=1 units
rij_sq = SUM ( rij**2 ) ! Squared separation
IF ( rij_sq < r_cut_box_sq ) THEN ! Check within cutoff
rij_sq = rij_sq * box_sq ! Now in sigma=1 units
rij(:) = rij(:) * box ! Now in sigma=1 units
sr2 = 1.0 / rij_sq
IF ( sr2 > sr2_ovr ) THEN
partial%ovr = .TRUE. ! Overlap detected
RETURN ! Return immediately
END IF
sr6 = sr2 ** 3
sr12 = sr6 ** 2
cutij = sr12 - sr6 ! LJ pair potential (cut but not shifted)
virij = cutij + sr12 ! LJ pair virial
lapij = ( 22.0*sr12 - 5.0*sr6 ) * sr2 ! LJ pair Laplacian
fij = rij * virij / rij_sq ! LJ pair force
partial%cut = partial%cut + cutij
partial%vir = partial%vir + virij
partial%lap = partial%lap + lapij
partial%f(:,i) = partial%f(:,i) + fij
partial%f(:,j) = partial%f(:,j) - fij
ncut = ncut + 1
END IF ! End check within cutoff
END DO ! End inner loop over atoms
! Calculate shifted potential
sr2 = 1.0 / r_cut**2 ! in sigma=1 units
sr6 = sr2 ** 3
sr12 = sr6 **2
cutij = sr12 - sr6
partial%pot = partial%cut - REAL ( ncut ) * cutij
! Multiply results by numerical factors
partial%f = partial%f * 24.0
partial%pot = partial%pot * 4.0
partial%cut = partial%cut * 4.0
partial%vir = partial%vir * 24.0 / 3.0
partial%lap = partial%lap * 24.0 * 2.0
partial%ovr = .FALSE. ! No overlaps detected (redundant but for clarity)
END FUNCTION force_1
END MODULE smc_module