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mc_lj_module.f90
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mc_lj_module.f90
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! mc_lj_module.f90
! Energy and move routines for MC simulation, LJ potential
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, force_sq
PUBLIC :: move, create, destroy
! Public data
INTEGER, PUBLIC :: n ! Number of atoms
REAL, DIMENSION(:,:), ALLOCATABLE, PUBLIC :: r ! Positions (3,n)
! Private data
REAL, DIMENSION(:,:), ALLOCATABLE :: f ! Forces for force_sq calculation (3,n)
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 cut at r_cut and
REAL :: vir ! the virial and
REAL :: lap ! the Laplacian 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%lap = a%lap + b%lap
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%lap = a%lap - b%lap
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 (but not shifted)'
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
ALLOCATE ( r(3,n), f(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, f )
END SUBROUTINE deallocate_arrays
FUNCTION potential ( box, r_cut ) RESULT ( total )
IMPLICIT NONE
TYPE(potential_type) :: total ! Returns a composite of pot, vir etc
REAL, INTENT(in) :: box ! Simulation box length
REAL, INTENT(in) :: r_cut ! Potential cutoff distance
! total%pot is the nonbonded cut (not shifted) potential energy for whole system
! total%vir is the corresponding virial for whole system
! total%lap is the corresponding Laplacian 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 ! Atomic contribution to total
INTEGER :: i
IF ( n > SIZE(r,dim=2) ) THEN ! should never happen
WRITE ( unit=error_unit, fmt='(a,2i15)' ) 'Array bounds error for r', n, SIZE(r,dim=2)
STOP 'Error in potential'
END IF
total = potential_type ( pot=0.0, vir=0.0, lap=0.0, ovr=.FALSE. ) ! Initialize
DO i = 1, n - 1
partial = potential_1 ( r(:,i), i, box, r_cut, 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, i, box, r_cut, j_range ) RESULT ( partial )
IMPLICIT NONE
TYPE(potential_type) :: partial ! Returns a composite of pot, vir etc for given atom
REAL, DIMENSION(3), INTENT(in) :: ri ! Coordinates of atom of interest
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 nonbonded cut (not shifted) potential energy of atom ri with a set of other atoms
! partial%vir is the corresponding virial of atom ri
! partial%lap is the corresponding Laplacian of atom ri
! 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 are not necessarily identical with those in r(:,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
INTEGER :: j, j1, j2
REAL :: r_cut_box, r_cut_box_sq, box_sq
REAL :: sr2, sr6, sr12, rij_sq
REAL, DIMENSION(3) :: rij
REAL, PARAMETER :: sr2_ovr = 1.77 ! overlap threshold (pot > 100)
TYPE(potential_type) :: pair
IF ( n > SIZE(r,dim=2) ) THEN ! should never happen
WRITE ( unit=error_unit, fmt='(a,2i15)' ) 'Array bounds error for r', n, SIZE(r,dim=2)
STOP 'Error in potential_1'
END IF
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
r_cut_box = r_cut / box
r_cut_box_sq = r_cut_box**2
box_sq = box**2
partial = potential_type ( pot=0.0, vir=0.0, lap=0.0, ovr=.FALSE. ) ! Initialize
DO j = j1, j2 ! Loop over selected range of partners
IF ( i == j ) CYCLE ! Skip self
rij(:) = ri(:) - r(:,j) ! Separation vector
rij(:) = rij(:) - ANINT ( rij(:) ) ! Periodic boundaries in box=1 units
rij_sq = SUM ( rij**2 ) ! Squared separation in box=1 units
IF ( rij_sq < r_cut_box_sq ) THEN ! Check within range
rij_sq = rij_sq * box_sq ! Now in sigma=1 units
sr2 = 1.0 / rij_sq ! (sigma/rij)**2
pair%ovr = sr2 > sr2_ovr ! Overlap if too close
IF ( pair%ovr ) THEN
partial%ovr = .TRUE. ! Overlap detected
RETURN ! Return immediately
END IF
sr6 = sr2**3
sr12 = sr6**2
pair%pot = sr12 - sr6 ! LJ pair potential (cut but not shifted)
pair%vir = pair%pot + sr12 ! LJ pair virial
pair%lap = ( 22.0*sr12 - 5.0*sr6 ) * sr2 ! LJ pair Laplacian
partial = partial + pair
END IF ! End check within range
END DO ! End loop over selected range of partners
! Include numerical factors
partial%pot = partial%pot * 4.0 ! 4*epsilon
partial%vir = partial%vir * 24.0 / 3.0 ! 24*epsilon and divide virial by 3
partial%lap = partial%lap * 24.0 * 2.0 ! 24*epsilon and factor 2 for ij and ji
partial%ovr = .FALSE. ! No overlaps detected (redundant, but for clarity)
END FUNCTION potential_1
FUNCTION force_sq ( box, r_cut ) RESULT ( fsq )
IMPLICIT NONE
REAL :: fsq ! Returns total squared force
REAL, INTENT(in) :: box ! Simulation box length
REAL, INTENT(in) :: r_cut ! Potential cutoff distance
! Calculates total squared force (using array f)
INTEGER :: i, j
REAL :: r_cut_box, r_cut_box_sq, box_sq, rij_sq
REAL :: sr2, sr6, sr12
REAL, DIMENSION(3) :: rij, fij
r_cut_box = r_cut / box
r_cut_box_sq = r_cut_box ** 2
box_sq = box ** 2
f = 0.0 ! Initialize
DO i = 1, n - 1 ! Begin outer loop over atoms
DO j = i + 1, n ! Begin inner loop over atoms
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
sr6 = sr2 ** 3
sr12 = sr6 ** 2
fij = rij * (2.0*sr12 - sr6) *sr2 ! LJ pair forces
f(:,i) = f(:,i) + fij
f(:,j) = f(:,j) - fij
END IF ! End check within cutoff
END DO ! End inner loop over atoms
END DO ! End outer loop over atoms
f = f * 24.0 ! Numerical factor 24*epsilon
fsq = SUM ( f**2 ) ! Result
END FUNCTION force_sq
SUBROUTINE move ( i, ri )
IMPLICIT NONE
INTEGER, INTENT(in) :: i
REAL, DIMENSION(3), INTENT(in) :: ri
r(:,i) = ri ! New position
END SUBROUTINE move
SUBROUTINE create ( ri )
IMPLICIT NONE
REAL, DIMENSION(3), INTENT(in) :: ri
n = n+1 ! Increase number of atoms
r(:,n) = ri ! Add new atom at the end
END SUBROUTINE create
SUBROUTINE destroy ( i )
IMPLICIT NONE
INTEGER, INTENT(in) :: i
r(:,i) = r(:,n) ! Replace atom i coordinates with atom n
n = n - 1 ! Reduce number of atoms
END SUBROUTINE destroy
END MODULE mc_module