mc_npt_lj.f90

! mc_npt_lj.f90
! Monte Carlo, NPT ensemble
PROGRAM mc_npt_lj

  !------------------------------------------------------------------------------------------------!
  ! This software was written in 2016/17                                                           !
  ! by Michael P. Allen <m.p.allen@warwick.ac.uk>/<m.p.allen@bristol.ac.uk>                        !
  ! and Dominic J. Tildesley <d.tildesley7@gmail.com> ("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 isothermal-isobaric Monte Carlo at the given temperature and pressure
  ! Uses no special neighbour lists

  ! 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

  ! For the LJ potential we could use the known scaling of the separate parts
  ! with distances (i.e. with box scaling) to handle the volume move.
  ! However, this would require us to scale the cutoff distance with the box
  ! We do not do this here; instead we simply recalculate the potential energy,
  ! keeping r_cut fixed (in simulation units)

  ! Despite the program name, there is nothing here specific to Lennard-Jones
  ! The model is defined in mc_module

  ! The logarithm of the box length is sampled uniformly

  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, &
       &                       box_check, potential_1, potential, move, n, r, potential_type

  IMPLICIT NONE

  ! Most important variables
  REAL :: box         ! Box length
  REAL :: dr_max      ! Maximum MC particle displacement
  REAL :: db_max      ! Maximum MC box displacement
  REAL :: temperature ! Specified temperature
  REAL :: pressure    ! Specified pressure
  REAL :: r_cut       ! Potential cutoff distance

  ! Composite interaction = pot & vir & ovr variables
  TYPE(potential_type) :: total, total_new, partial_old, partial_new

  INTEGER            :: blk, stp, i, nstep, nblock, moves, ioerr
  REAL               :: box_scale, box_new, den_scale, delta, zeta, m_ratio, v_ratio
  REAL, DIMENSION(3) :: ri

  CHARACTER(len=4), PARAMETER :: cnf_prefix = 'cnf.'
  CHARACTER(len=3), PARAMETER :: inp_tag    = 'inp'
  CHARACTER(len=3), PARAMETER :: out_tag    = 'out'
  CHARACTER(len=3)            :: sav_tag    = 'sav' ! May be overwritten with block number

  NAMELIST /nml/ nblock, nstep, temperature, pressure, r_cut, dr_max, db_max

  WRITE ( unit=output_unit, fmt='(a)'   ) 'mc_npt_lj'
  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-NPT ensemble'
  WRITE ( unit=output_unit, fmt='(a)' ) 'Simulation uses cut (but not shifted) potential'
  CALL introduction

  CALL RANDOM_INIT ( .FALSE., .TRUE. ) ! Initialize random number generator

  ! Set sensible default run parameters for testing
  nblock      = 10
  nstep       = 10000
  temperature = 1.0
  pressure    = 0.69
  r_cut       = 2.5
  dr_max      = 0.15
  db_max      = 0.025

  ! Read run parameters from namelist
  ! Comment out, or replace, this section if you don't like namelists
  READ ( unit=input_unit, nml=nml, iostat=ioerr )
  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'
     STOP 'Error in mc_npt_lj'
  END IF

  ! 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)' ) 'Pressure',                  pressure
  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
  WRITE ( unit=output_unit, fmt='(a,t40,f15.6)' ) 'Maximum box displacement',  db_max

  ! Read in initial configuration and allocate necessary arrays
  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_npt_lj'
  END IF

  ! Initialize arrays for averaging and write column headings
  m_ratio = 0.0
  v_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

        CALL box_check ( box, r_cut ) ! Prepare for single-particle moves
        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_npt_lj'
           END IF

           ri(:) = random_translate_vector ( dr_max/box, r(:,i) ) ! Trial move to new position (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 non-overlapping configuration

        END DO ! End loop over atoms

        m_ratio = REAL(moves) / REAL(n)

        v_ratio = 0.0                   ! Zero volume move counter
        CALL RANDOM_NUMBER ( zeta )     ! Uniform random number in range (0,1)
        zeta      = 2.0*zeta - 1.0      ! Now in range (-1,+1)
        box_scale = EXP ( zeta*db_max ) ! Sampling log(box) and log(vol) uniformly
        box_new   = box * box_scale     ! New box (in sigma units)
        den_scale = 1.0 / box_scale**3  ! Density scaling factor

        total_new = potential ( box_new, r_cut ) ! New total energy, virial etc

        IF ( .NOT. total_new%ovr ) THEN ! Test for non-overlapping configuration

           delta = total_new%pot - total%pot                  ! Use cut (but not shifted) potential
           delta = delta + pressure * ( box_new**3 - box**3 ) ! Add PV term
           delta = delta / temperature                        ! Divide by temperature
           delta = delta + REAL(n+1) * LOG(den_scale)         ! Factor (n+1) consistent with log(box) sampling

           IF ( metropolis ( delta ) ) THEN ! Accept Metropolis test
              total  = total_new ! Update total values
              box     = box_new  ! Update box
              v_ratio = 1.0      ! Set move counter
           END IF ! reject Metropolis test

        END IF ! End test for overlapping configuration

        ! 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
  CALL conclusion

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(11) :: variables ! The 11 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
    ! Accordingly, < p_c > should match the input pressure and 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, v_r, density, p_c, p_f, e_c, e_f, t_c
    TYPE(variable_type) :: c_c, c_f, vol_msd

    REAL :: fsq, vol, rho, enp

    ! Preliminary calculations (m_ratio, total etc are known already)
    fsq = force_sq ( box, r_cut )
    vol = box**3
    rho = REAL(n) / vol

    ! 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 volume acceptance ratios
    m_r = variable_type ( nam = 'Move ratio',   val = m_ratio, instant = .FALSE. )
    v_r = variable_type ( nam = 'Volume ratio', val = v_ratio, instant = .FALSE. )

    ! Density
    density = variable_type ( nam = 'Density', val = rho )

    ! Internal energy per atom for simulated, cut, potential
    ! Ideal gas contribution plus total cut (but not shifted) PE divided by N
    e_c = variable_type ( nam = 'E/N cut', val = 1.5*temperature + total%pot/REAL(n) )

    ! Internal energy per atom for full potential with LRC
    ! LRC plus ideal gas contribution plus total cut (but not shifted) PE divided by N
    e_f = variable_type ( nam = 'E/N 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 (cut but not shifted)
    ! MSD of excess "enthalpy" divided by temperature and sqrt(N) to make result intensive
    ! NB this is not really the excess Cp/NkB, it simply omits the kinetic energy fluctuations
    ! i.e. we add the ideal gas part of Cv/NkB, 1.5, to get total Cp/NkB
    enp = total%pot+pressure*vol
    c_c = variable_type ( nam = 'Cp/N cut', val = enp/(temperature*SQRT(REAL(n))), &
         &                method = msd, add = 1.5, instant = .FALSE. )

    ! Heat capacity (full)
    ! MSD of excess "enthalpy" divided by temperature and sqrt(N) to make result intensive
    ! NB this is not really the excess Cp/NkB, it simply omits the kinetic energy fluctuations
    ! i.e. we add the ideal gas part of Cv/NkB, 1.5, to get total Cp/NkB
    enp = REAL(n)*potential_lrc(rho,r_cut)+total%pot+pressure*vol
    c_f = variable_type ( nam = 'Cp/N full', val = enp/(temperature*SQRT(REAL(n))), &
         &                method = msd, add = 1.5, instant = .FALSE. )

    ! Volume MSD
    vol_msd = variable_type ( nam = 'Volume MSD', val = vol, method = msd, instant = .FALSE. )

    ! Collect together for averaging
    variables = [ m_r, v_r, density, e_c, p_c, e_f, p_f, t_c, c_c, c_f, vol_msd ]

  END FUNCTION calc_variables

END PROGRAM mc_npt_lj