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mc_nvt_lj_re.f90
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! mc_nvt_lj_re.f90
! Monte Carlo, NVT ensemble, replica exchange
PROGRAM mc_nvt_lj_re
!------------------------------------------------------------------------------------------------!
! 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. !
!------------------------------------------------------------------------------------------------!
! Takes in a configuration of atoms (positions)
! Cubic periodic boundary conditions
! Conducts Monte Carlo at the given temperature
! Uses no special neighbour lists
! Uses MPI to run replica exchange of configurations with neighbouring temperatures
! Assume at most 100 processes numbered 0 to 99
! There are a couple of MPI-related points that need particular attention
! Firstly, it is assumed that this program is compiled with a compiler option such as "-fdefault-real-8"
! defining the precision of REAL variables. We set the parameter MY_MPI_REAL = MPI_DOUBLE_PRECISION
! to be compatible with this. Your implementation may require MY_MPI_REAL = MPI_REAL.
! Secondly, all processes write to their standard output, output_unit, but the default in MPI is for all this output
! to be collated (in an undefined order) and written to a single channel. We assume that the program
! will be run with a command-line which includes an option for each process to write to separate files, such as
! mpirun -np 8 -output-filename out ./mc_nvt_lj_re < mc.inp
! where the standard output files are named out##, the ## part being determined by the process rank.
! If your implementation does not have this option, you should edit the code to explicitly open a file for
! standard output, with a process-rank-dependent name, and associate the output_unit with it.
! Note that configurations are read, saved, and written to files named cnf##.inp etc
! NB a program intended for real-world application would be much more careful about
! closing down all the MPI processes cleanly in the event of an error on any one process.
! Reads several variables and options from standard input using a namelist nml
! Leave namelist empty to accept supplied defaults
! Positions r are divided by box length after reading in
! However, input configuration, output configuration, most calculations, and all results
! are given in simulation units defined by the model
! For example, for Lennard-Jones, sigma = 1, epsilon = 1
! Despite the program name, there is nothing here specific to Lennard-Jones
! The model is defined in mc_module
USE, INTRINSIC :: iso_fortran_env, ONLY : input_unit, output_unit, error_unit, iostat_end, iostat_eor, &
& COMPILER_VERSION, COMPILER_OPTIONS
USE config_io_module, ONLY : read_cnf_atoms, write_cnf_atoms
USE averages_module, ONLY : run_begin, run_end, blk_begin, blk_end, blk_add
USE maths_module, ONLY : metropolis, random_translate_vector
USE mc_module, ONLY : introduction, conclusion, allocate_arrays, deallocate_arrays, &
& potential_1, potential, move, n, r, potential_type
USE mpi
IMPLICIT NONE
! Most important variables
REAL :: box ! Box length
REAL :: dr_max ! Maximum MC displacement
REAL :: temperature ! Specified temperature
REAL :: r_cut ! Potential cutoff distance
! Composite interaction = pot & vir & ovr variables
TYPE(potential_type) :: total, partial_old, partial_new
! Arrays holding values for all processes
REAL, DIMENSION(:), ALLOCATABLE :: every_temperature, every_beta, every_dr_max
LOGICAL :: swap, exists, all_exist
INTEGER :: blk, stp, i, nstep, nblock, moves, updown, ioerr
REAL :: beta, other_beta, other_pot, delta, zeta, m_ratio, x_ratio
REAL, DIMENSION(3) :: ri
CHARACTER(len=3), PARAMETER :: inp_tag = 'inp'
CHARACTER(len=3), PARAMETER :: out_tag = 'out'
CHARACTER(len=6) :: cnf_prefix = 'cnf##.' ! Will have rank inserted
CHARACTER(len=3) :: sav_tag = 'sav' ! May be overwritten with block number
CHARACTER(len=2) :: m_tag ! Will contain rank number
INTEGER :: m ! MPI process rank (id of this process)
INTEGER :: nproc ! MPI world size (number of processes)
INTEGER :: error ! MPI error return
INTEGER :: msg_error ! MPI error return
INTEGER, DIMENSION(MPI_STATUS_SIZE) :: msg_status ! MPI status return
INTEGER, PARAMETER :: msg1_id = 999 ! MPI message identifier
INTEGER, PARAMETER :: msg2_id = 888 ! MPI message identifier
INTEGER, PARAMETER :: msg3_id = 777 ! MPI message identifier
INTEGER, PARAMETER :: msg4_id = 666 ! MPI message identifier
INTEGER, PARAMETER :: MY_MPI_REAL = MPI_DOUBLE_PRECISION ! Specifies precision of MPI reals
NAMELIST /nml/ nblock, nstep, every_temperature, r_cut, every_dr_max
CALL MPI_Init ( error )
CALL MPI_Comm_rank ( MPI_COMM_WORLD, m, error )
CALL MPI_Comm_size ( MPI_COMM_WORLD, nproc, error )
IF ( nproc > 100 ) THEN
WRITE ( unit=error_unit, fmt='(a,i15)') 'Number of processes is too large', nproc
STOP 'Error in mc_nvt_lj_re'
END IF
WRITE(m_tag,fmt='(i2.2)') m ! Convert rank into character form
cnf_prefix(4:5) = m_tag ! Insert process rank into configuration filename
WRITE ( unit=output_unit, fmt='(a)' ) 'mc_nvt_lj_re'
WRITE ( unit=output_unit, fmt='(2a)' ) 'Compiler: ', COMPILER_VERSION()
WRITE ( unit=output_unit, fmt='(2a/)' ) 'Options: ', COMPILER_OPTIONS()
WRITE ( unit=output_unit, fmt='(a)' ) 'Monte Carlo, constant-NVT, replica exchange'
WRITE ( unit=output_unit, fmt='(a)' ) 'Simulation uses cut (but not shifted) potential'
CALL introduction
WRITE( unit=output_unit, fmt='(a,t40,i15)') 'This is process rank', m
WRITE( unit=output_unit, fmt='(a,t40,i15)') 'Number of processes is', nproc
CALL RANDOM_INIT ( .FALSE., .TRUE. ) ! Initialize random number generator (hopefully differently on each process)
CALL RANDOM_NUMBER ( zeta )
WRITE( unit=output_unit, fmt='(a,t40,f15.6)') 'Random # (different for each process?)', zeta
! Allocate processor-dependent arrays
ALLOCATE ( every_temperature(0:nproc-1), every_beta(0:nproc-1), every_dr_max(0:nproc-1) )
! Set sensible default run parameters for testing
! Empirical choices for temperature and dr_max give approx 20% swap rate and 35-40% move rate for 256 LJ atoms
nblock = 10
nstep = 10000
r_cut = 2.5
every_temperature = [ ( 1.00*(1.14)**(i-1), i = 0, nproc-1 ) ]
every_dr_max = [ ( 0.15*(1.11)**(i-1), i = 0, nproc-1 ) ]
! Read run parameters from namelist
! Comment out, or replace, this section if you don't like namelists
IF ( m == 0 ) THEN ! Process 0 reads data from standard input
READ ( unit=input_unit, nml=nml, iostat=ioerr )
END IF
! Process 0 sends error outcome to all other processes (to allow check and clean failure)
CALL MPI_Bcast ( ioerr, 1, MPI_INTEGER, 0, MPI_COMM_WORLD, msg_error )
IF ( ioerr /= 0 ) THEN
WRITE ( unit=error_unit, fmt='(a,i15)') 'Error reading namelist nml from standard input', ioerr
IF ( ioerr == iostat_eor ) WRITE ( unit=error_unit, fmt='(a)') 'End of record'
IF ( ioerr == iostat_end ) WRITE ( unit=error_unit, fmt='(a)') 'End of file'
CALL MPI_Finalize ( msg_error )
STOP 'Error in mc_nvt_lj_re'
END IF
! Process 0 sends run parameters to all other processes
CALL MPI_Bcast ( nblock, 1, MPI_INTEGER, 0, MPI_COMM_WORLD, msg_error )
CALL MPI_Bcast ( nstep, 1, MPI_INTEGER, 0, MPI_COMM_WORLD, msg_error )
CALL MPI_Bcast ( r_cut, 1, MY_MPI_REAL, 0, MPI_COMM_WORLD, msg_error )
CALL MPI_Bcast ( every_temperature(0), nproc, MY_MPI_REAL, 0, MPI_COMM_WORLD, msg_error )
CALL MPI_Bcast ( every_dr_max(0), nproc, MY_MPI_REAL, 0, MPI_COMM_WORLD, msg_error )
every_beta = 1.0 / every_temperature ! All the inverse temperatures
temperature = every_temperature(m) ! Temperature for this process
dr_max = every_dr_max(m) ! Max displacement for this process
beta = every_beta(m) ! Inverse temperature for this process
! Write out run parameters
WRITE ( unit=output_unit, fmt='(a,t40,i15)' ) 'Number of blocks', nblock
WRITE ( unit=output_unit, fmt='(a,t40,i15)' ) 'Number of steps per block', nstep
WRITE ( unit=output_unit, fmt='(a,t40,f15.6)' ) 'Temperature', temperature
WRITE ( unit=output_unit, fmt='(a,t40,f15.6)' ) 'Potential cutoff distance', r_cut
WRITE ( unit=output_unit, fmt='(a,t40,f15.6)' ) 'Maximum displacement', dr_max
! Read in initial configuration and allocate necessary arrays
INQUIRE ( file = cnf_prefix//inp_tag, exist = exists ) ! Check that our configuration file exists
CALL MPI_Allreduce ( exists, all_exist, 1, MPI_LOGICAL, MPI_LAND, MPI_COMM_WORLD, msg_error ) ! Combine results
IF ( .NOT. all_exist ) THEN ! This is a fairly likely error, so we check and allow clean failure
WRITE ( unit=error_unit, fmt='(a,2l15)') 'One or more configuration files do not exist', exists, all_exist
CALL MPI_Finalize ( msg_error )
STOP 'Error in mc_nvt_lj_re'
END IF
CALL read_cnf_atoms ( cnf_prefix//inp_tag, n, box ) ! First call is just to get n and box
WRITE ( unit=output_unit, fmt='(a,t40,i15)' ) 'Number of particles', n
WRITE ( unit=output_unit, fmt='(a,t40,f15.6)' ) 'Simulation box length', box
WRITE ( unit=output_unit, fmt='(a,t40,f15.6)' ) 'Density', REAL(n) / box**3
CALL allocate_arrays ( box, r_cut ) ! Allocate r
CALL read_cnf_atoms ( cnf_prefix//inp_tag, n, box, r ) ! Second call is to get r
r(:,:) = r(:,:) / box ! Convert positions to box units
r(:,:) = r(:,:) - ANINT ( r(:,:) ) ! Periodic boundaries
! Initial energy and overlap check
total = potential ( box, r_cut )
IF ( total%ovr ) THEN
WRITE ( unit=error_unit, fmt='(a)') 'Overlap in initial configuration'
STOP 'Error in mc_nvt_lj_re'
END IF
! Initialize arrays for averaging and write column headings
m_ratio = 0.0
x_ratio = 0.0
CALL run_begin ( calc_variables() )
DO blk = 1, nblock ! Begin loop over blocks
CALL blk_begin
DO stp = 1, nstep ! Begin loop over steps
moves = 0
DO i = 1, n ! Begin loop over atoms
partial_old = potential_1 ( r(:,i), i, box, r_cut ) ! Old atom potential, virial etc
IF ( partial_old%ovr ) THEN ! should never happen
WRITE ( unit=error_unit, fmt='(a)') 'Overlap in current configuration'
STOP 'Error in mc_nvt_lj_re'
END IF
ri(:) = random_translate_vector ( dr_max/box, r(:,i) ) ! Trial move to new position (in box=1 units)
ri(:) = ri(:) - ANINT ( ri(:) ) ! Periodic boundary correction
partial_new = potential_1 ( ri, i, box, r_cut ) ! New atom potential, virial etc
IF ( .NOT. partial_new%ovr ) THEN ! Test for non-overlapping configuration
delta = partial_new%pot - partial_old%pot ! Use cut (but not shifted) potential
delta = delta / temperature
IF ( metropolis ( delta ) ) THEN ! Accept Metropolis test
total = total + partial_new - partial_old ! Update total values
CALL move ( i, ri ) ! Update position
moves = moves + 1 ! Increment move counter
END IF ! End accept Metropolis test
END IF ! End test for overlapping configuration
END DO ! End loop over atoms
m_ratio = REAL(moves) / REAL(n)
x_ratio = 0.0
DO updown = 0, 1 ! Loop to look one way then the other
IF ( MOD(m,2) == updown ) THEN ! Look up, partner is m+1
IF ( m+1 < nproc ) THEN ! Ensure partner exists
other_beta = every_beta(m+1) ! We already know the other beta
CALL MPI_Recv ( other_pot, 1, MY_MPI_REAL, m+1, msg1_id, &
& MPI_COMM_WORLD, msg_status, msg_error ) ! Receive pot from other process
delta = -(beta - other_beta) * ( total%pot - other_pot ) ! Delta for Metropolis decision
swap = metropolis ( delta ) ! Decision taken on this process
CALL MPI_Send ( swap, 1, MPI_LOGICAL, m+1, msg2_id, &
& MPI_COMM_WORLD, msg_error ) ! Send decision to other process
IF ( swap ) THEN ! Exchange configurations
CALL MPI_Sendrecv_replace ( r, 3*n, MY_MPI_REAL, m+1, msg3_id, m+1, msg4_id, &
& MPI_COMM_WORLD, msg_status, msg_error )
total = potential ( box, r_cut ) ! Alternatively, we could get this from m+1
x_ratio = 1.0
END IF ! End exchange configurations
END IF ! End ensure partner exists
ELSE ! Look down, partner is m-1
IF ( m-1 >= 0 ) THEN ! Ensure partner exists
CALL MPI_Send ( total%pot, 1, MY_MPI_REAL, m-1, msg1_id, &
& MPI_COMM_WORLD, msg_error ) ! Send pot to other process
CALL MPI_Recv ( swap, 1, MPI_LOGICAL, m-1, msg2_id, &
& MPI_COMM_WORLD, msg_status, msg_error ) ! Receive decision from other process
IF ( swap ) THEN ! Exchange configurations
CALL MPI_Sendrecv_replace ( r, 3*n, MY_MPI_REAL, m-1, msg4_id, m-1, msg3_id, &
& MPI_COMM_WORLD, msg_status, msg_error )
total = potential ( box, r_cut ) ! Alternatively, we could get this from m-1
END IF ! End exchange configurations
END IF ! End ensure partner exists
END IF ! End choice of which way to look
END DO ! End loop to look one way then the other
! Calculate and accumulate variables for this step
CALL blk_add ( calc_variables() )
END DO ! End loop over steps
CALL blk_end ( blk ) ! Output block averages
IF ( nblock < 1000 ) WRITE(sav_tag,fmt='(i3.3)') blk ! Number configuration by block
CALL write_cnf_atoms ( cnf_prefix//sav_tag, n, box, r*box ) ! Save configuration
END DO ! End loop over blocks
CALL run_end ( calc_variables() ) ! Output run averages
CALL write_cnf_atoms ( cnf_prefix//out_tag, n, box, r*box ) ! Write out final configuration
CALL deallocate_arrays
DEALLOCATE ( every_temperature, every_beta, every_dr_max )
CALL conclusion
CALL MPI_Finalize(error)
CONTAINS
FUNCTION calc_variables () RESULT ( variables )
USE lrc_module, ONLY : potential_lrc, pressure_lrc, pressure_delta
USE mc_module, ONLY : force_sq
USE averages_module, ONLY : variable_type, msd
IMPLICIT NONE
TYPE(variable_type), DIMENSION(8) :: variables ! The 8 variables listed below
! This routine calculates all variables of interest and (optionally) writes them out
! They are collected together in the variables array, for use in the main program
! In this example we simulate using the cut (but not shifted) potential
! The values of < p_c >, < e_c > and density should be consistent (for this potential)
! For comparison, long-range corrections are also applied to give
! estimates of < e_f > and < p_f > for the full (uncut) potential
! The value of the cut-and-shifted potential is not used, in this example
TYPE(variable_type) :: m_r, x_r, e_c, p_c, e_f, p_f, t_c, c_f
REAL :: vol, rho, fsq
! Preliminary calculations (m_ratio, total etc are known already)
vol = box**3 ! Volume
rho = REAL(n) / vol ! Density
fsq = force_sq ( box, r_cut ) ! Total squared force
! Variables of interest, of type variable_type, containing three components:
! %val: the instantaneous value
! %nam: used for headings
! %method: indicating averaging method
! If not set below, %method adopts its default value of avg
! The %nam and some other components need only be defined once, at the start of the program,
! but for clarity and readability we assign all the values together below
! Move and exchange acceptance ratios
m_r = variable_type ( nam = 'Move ratio', val = m_ratio, instant = .FALSE. )
x_r = variable_type ( nam = 'Swap ratio', val = x_ratio, instant = .FALSE. )
! Internal energy per atom for simulated, cut, potential
! Ideal gas contribution plus cut (but not shifted) PE divided by N
e_c = variable_type ( nam = 'E cut', val = 1.5*temperature + total%pot/REAL(n) )
! Internal energy per atom for full potential with LRC
! LRC plus ideal gas contribution plus cut (but not shifted) PE divided by N
e_f = variable_type ( nam = 'E full', val = potential_lrc(rho,r_cut) + 1.5*temperature + total%pot/REAL(n) )
! Pressure for simulated, cut, potential
! Delta correction plus ideal gas contribution plus total virial divided by V
p_c = variable_type ( nam = 'P cut', val = pressure_delta(rho,r_cut) + rho*temperature + total%vir/vol )
! Pressure for full potential with LRC
! LRC plus ideal gas contribution plus total virial divided by V
p_f = variable_type ( nam = 'P full', val = pressure_lrc(rho,r_cut) + rho*temperature + total%vir/vol )
! Configurational temperature
! Total squared force divided by total Laplacian
t_c = variable_type ( nam = 'T config', val = fsq/total%lap )
! Heat capacity (full)
! MSD potential energy divided by temperature and sqrt(N) to make result intensive; LRC does not contribute
! We add ideal gas contribution, 1.5, afterwards
c_f = variable_type ( nam = 'Cv/N full', val = total%pot/(temperature*SQRT(REAL(n))), &
& method = msd, add = 1.5, instant = .FALSE. )
! Collect together for averaging
variables = [ m_r, x_r, e_c, p_c, e_f, p_f, t_c, c_f ]
END FUNCTION calc_variables
END PROGRAM mc_nvt_lj_re