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!! |
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!! Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
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!! |
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!! The University of Notre Dame grants you ("Licensee") a |
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!! non-exclusive, royalty free, license to use, modify and |
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!! redistribute this software in source and binary code form, provided |
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!! that the following conditions are met: |
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!! |
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!! 1. Acknowledgement of the program authors must be made in any |
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!! publication of scientific results based in part on use of the |
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!! program. An acceptable form of acknowledgement is citation of |
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!! the article in which the program was described (Matthew |
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!! A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
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!! J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
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!! Parallel Simulation Engine for Molecular Dynamics," |
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!! J. Comput. Chem. 26, pp. 252-271 (2005)) |
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!! |
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!! 2. Redistributions of source code must retain the above copyright |
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!! notice, this list of conditions and the following disclaimer. |
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!! |
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!! 3. Redistributions in binary form must reproduce the above copyright |
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!! notice, this list of conditions and the following disclaimer in the |
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!! documentation and/or other materials provided with the |
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!! distribution. |
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!! |
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!! This software is provided "AS IS," without a warranty of any |
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!! kind. All express or implied conditions, representations and |
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!! warranties, including any implied warranty of merchantability, |
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!! fitness for a particular purpose or non-infringement, are hereby |
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!! excluded. The University of Notre Dame and its licensors shall not |
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!! be liable for any damages suffered by licensee as a result of |
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!! using, modifying or distributing the software or its |
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!! derivatives. In no event will the University of Notre Dame or its |
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!! licensors be liable for any lost revenue, profit or data, or for |
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!! direct, indirect, special, consequential, incidental or punitive |
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!! damages, however caused and regardless of the theory of liability, |
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!! arising out of the use of or inability to use software, even if the |
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!! University of Notre Dame has been advised of the possibility of |
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!! such damages. |
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!! |
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|
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module eam |
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use simulation |
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use force_globals |
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use status |
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use atype_module |
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use vector_class |
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#ifdef IS_MPI |
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use mpiSimulation |
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#endif |
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implicit none |
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PRIVATE |
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#define __FORTRAN90 |
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#include "UseTheForce/DarkSide/fInteractionMap.h" |
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|
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INTEGER, PARAMETER :: DP = selected_real_kind(15) |
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|
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logical, save :: EAM_FF_initialized = .false. |
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integer, save :: EAM_Mixing_Policy |
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real(kind = dp), save :: EAM_rcut |
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logical, save :: haveRcut = .false. |
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|
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character(len = statusMsgSize) :: errMesg |
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integer :: eam_err |
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|
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character(len = 200) :: errMsg |
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character(len=*), parameter :: RoutineName = "EAM MODULE" |
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!! Logical that determines if eam arrays should be zeroed |
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logical :: cleanme = .true. |
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logical :: nmflag = .false. |
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|
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|
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type, private :: EAMtype |
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integer :: eam_atype |
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real( kind = DP ) :: eam_dr |
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integer :: eam_nr |
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integer :: eam_nrho |
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real( kind = DP ) :: eam_lattice |
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real( kind = DP ) :: eam_drho |
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real( kind = DP ) :: eam_rcut |
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integer :: eam_atype_map |
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|
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real( kind = DP ), pointer, dimension(:) :: eam_rvals => null() |
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real( kind = DP ), pointer, dimension(:) :: eam_rhovals => null() |
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real( kind = DP ), pointer, dimension(:) :: eam_F_rho => null() |
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real( kind = DP ), pointer, dimension(:) :: eam_Z_r => null() |
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real( kind = DP ), pointer, dimension(:) :: eam_rho_r => null() |
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real( kind = DP ), pointer, dimension(:) :: eam_phi_r => null() |
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real( kind = DP ), pointer, dimension(:) :: eam_F_rho_pp => null() |
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real( kind = DP ), pointer, dimension(:) :: eam_Z_r_pp => null() |
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real( kind = DP ), pointer, dimension(:) :: eam_rho_r_pp => null() |
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real( kind = DP ), pointer, dimension(:) :: eam_phi_r_pp => null() |
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end type EAMtype |
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|
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|
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!! Arrays for derivatives used in force calculation |
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real( kind = dp), dimension(:), allocatable :: frho |
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real( kind = dp), dimension(:), allocatable :: rho |
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|
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real( kind = dp), dimension(:), allocatable :: dfrhodrho |
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real( kind = dp), dimension(:), allocatable :: d2frhodrhodrho |
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|
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|
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!! Arrays for MPI storage |
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#ifdef IS_MPI |
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real( kind = dp),save, dimension(:), allocatable :: dfrhodrho_col |
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real( kind = dp),save, dimension(:), allocatable :: dfrhodrho_row |
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real( kind = dp),save, dimension(:), allocatable :: frho_row |
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real( kind = dp),save, dimension(:), allocatable :: frho_col |
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real( kind = dp),save, dimension(:), allocatable :: rho_row |
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real( kind = dp),save, dimension(:), allocatable :: rho_col |
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real( kind = dp),save, dimension(:), allocatable :: rho_tmp |
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real( kind = dp),save, dimension(:), allocatable :: d2frhodrhodrho_col |
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real( kind = dp),save, dimension(:), allocatable :: d2frhodrhodrho_row |
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#endif |
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|
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type, private :: EAMTypeList |
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integer :: n_eam_types = 0 |
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integer :: currentAddition = 0 |
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|
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type (EAMtype), pointer :: EAMParams(:) => null() |
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integer, pointer :: atidToEAMType(:) => null() |
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end type EAMTypeList |
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|
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|
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type (eamTypeList), save :: EAMList |
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|
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!! standard eam stuff |
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|
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|
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public :: init_EAM_FF |
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public :: setCutoffEAM |
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public :: do_eam_pair |
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public :: newEAMtype |
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public :: calc_eam_prepair_rho |
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public :: calc_eam_preforce_Frho |
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public :: clean_EAM |
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public :: destroyEAMTypes |
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public :: getEAMCut |
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|
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contains |
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|
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|
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subroutine newEAMtype(lattice_constant,eam_nrho,eam_drho,eam_nr,& |
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eam_dr,rcut,eam_Z_r,eam_rho_r,eam_F_rho,& |
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c_ident,status) |
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real (kind = dp ) :: lattice_constant |
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integer :: eam_nrho |
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real (kind = dp ) :: eam_drho |
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integer :: eam_nr |
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real (kind = dp ) :: eam_dr |
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real (kind = dp ) :: rcut |
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real (kind = dp ), dimension(eam_nr) :: eam_Z_r |
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real (kind = dp ), dimension(eam_nr) :: eam_rho_r |
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real (kind = dp ), dimension(eam_nrho) :: eam_F_rho |
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integer :: c_ident |
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integer :: status |
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|
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integer :: nAtypes,nEAMTypes,myATID |
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integer :: maxVals |
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integer :: alloc_stat |
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integer :: current |
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integer,pointer :: Matchlist(:) => null() |
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|
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status = 0 |
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|
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|
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!! Assume that atypes has already been set and get the total number of types in atypes |
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!! Also assume that every member of atypes is a EAM model. |
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|
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|
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! check to see if this is the first time into |
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if (.not.associated(EAMList%EAMParams)) then |
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call getMatchingElementList(atypes, "is_EAM", .true., nEAMtypes, MatchList) |
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EAMList%n_eam_types = nEAMtypes |
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allocate(EAMList%EAMParams(nEAMTypes)) |
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nAtypes = getSize(atypes) |
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allocate(EAMList%atidToEAMType(nAtypes)) |
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end if |
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|
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EAMList%currentAddition = EAMList%currentAddition + 1 |
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current = EAMList%currentAddition |
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|
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myATID = getFirstMatchingElement(atypes, "c_ident", c_ident) |
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EAMList%atidToEAMType(myATID) = current |
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|
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call allocate_EAMType(eam_nrho,eam_nr,EAMList%EAMParams(current),stat=alloc_stat) |
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if (alloc_stat /= 0) then |
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status = -1 |
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return |
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end if |
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|
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|
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EAMList%EAMParams(current)%eam_atype = c_ident |
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EAMList%EAMParams(current)%eam_lattice = lattice_constant |
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EAMList%EAMParams(current)%eam_nrho = eam_nrho |
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EAMList%EAMParams(current)%eam_drho = eam_drho |
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EAMList%EAMParams(current)%eam_nr = eam_nr |
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EAMList%EAMParams(current)%eam_dr = eam_dr |
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EAMList%EAMParams(current)%eam_rcut = rcut |
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EAMList%EAMParams(current)%eam_Z_r = eam_Z_r |
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EAMList%EAMParams(current)%eam_rho_r = eam_rho_r |
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EAMList%EAMParams(current)%eam_F_rho = eam_F_rho |
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|
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end subroutine newEAMtype |
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|
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|
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! kills all eam types entered and sets simulation to uninitalized |
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subroutine destroyEAMtypes() |
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integer :: i |
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type(EAMType), pointer :: tempEAMType=>null() |
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|
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do i = 1, EAMList%n_eam_types |
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tempEAMType => eamList%EAMParams(i) |
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call deallocate_EAMType(tempEAMType) |
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end do |
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if(associated( eamList%EAMParams)) deallocate( eamList%EAMParams) |
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eamList%EAMParams => null() |
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|
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eamList%n_eam_types = 0 |
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eamList%currentAddition = 0 |
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|
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end subroutine destroyEAMtypes |
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|
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function getEAMCut(atomID) result(cutValue) |
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integer, intent(in) :: atomID |
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integer :: eamID |
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real(kind=dp) :: cutValue |
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|
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eamID = EAMList%atidToEAMType(atomID) |
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cutValue = EAMList%EAMParams(eamID)%eam_rcut |
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end function getEAMCut |
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|
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subroutine init_EAM_FF(status) |
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integer :: status |
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integer :: i,j |
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real(kind=dp) :: current_rcut_max |
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integer :: alloc_stat |
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integer :: number_r, number_rho |
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|
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|
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status = 0 |
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if (EAMList%currentAddition == 0) then |
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call handleError("init_EAM_FF","No members in EAMList") |
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status = -1 |
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return |
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end if |
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|
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|
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do i = 1, EAMList%currentAddition |
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|
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! Build array of r values |
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|
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do j = 1,EAMList%EAMParams(i)%eam_nr |
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EAMList%EAMParams(i)%eam_rvals(j) = & |
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real(j-1,kind=dp)* & |
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EAMList%EAMParams(i)%eam_dr |
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end do |
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! Build array of rho values |
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do j = 1,EAMList%EAMParams(i)%eam_nrho |
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EAMList%EAMParams(i)%eam_rhovals(j) = & |
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real(j-1,kind=dp)* & |
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EAMList%EAMParams(i)%eam_drho |
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end do |
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! convert from eV to kcal / mol: |
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EAMList%EAMParams(i)%eam_F_rho = EAMList%EAMParams(i)%eam_F_rho * 23.06054E0_DP |
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|
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! precompute the pair potential and get it into kcal / mol: |
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EAMList%EAMParams(i)%eam_phi_r(1) = 0.0E0_DP |
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do j = 2, EAMList%EAMParams(i)%eam_nr |
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EAMList%EAMParams(i)%eam_phi_r(j) = (EAMList%EAMParams(i)%eam_Z_r(j)**2)/EAMList%EAMParams(i)%eam_rvals(j) |
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EAMList%EAMParams(i)%eam_phi_r(j) = EAMList%EAMParams(i)%eam_phi_r(j)*331.999296E0_DP |
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enddo |
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end do |
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|
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|
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do i = 1, EAMList%currentAddition |
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number_r = EAMList%EAMParams(i)%eam_nr |
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number_rho = EAMList%EAMParams(i)%eam_nrho |
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|
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call eam_spline(number_r, EAMList%EAMParams(i)%eam_rvals, & |
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EAMList%EAMParams(i)%eam_rho_r, & |
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EAMList%EAMParams(i)%eam_rho_r_pp, & |
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0.0E0_DP, 0.0E0_DP, 'N') |
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call eam_spline(number_r, EAMList%EAMParams(i)%eam_rvals, & |
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EAMList%EAMParams(i)%eam_Z_r, & |
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EAMList%EAMParams(i)%eam_Z_r_pp, & |
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0.0E0_DP, 0.0E0_DP, 'N') |
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call eam_spline(number_rho, EAMList%EAMParams(i)%eam_rhovals, & |
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EAMList%EAMParams(i)%eam_F_rho, & |
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EAMList%EAMParams(i)%eam_F_rho_pp, & |
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0.0E0_DP, 0.0E0_DP, 'N') |
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call eam_spline(number_r, EAMList%EAMParams(i)%eam_rvals, & |
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EAMList%EAMParams(i)%eam_phi_r, & |
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EAMList%EAMParams(i)%eam_phi_r_pp, & |
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0.0E0_DP, 0.0E0_DP, 'N') |
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enddo |
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|
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! current_rcut_max = EAMList%EAMParams(1)%eam_rcut |
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!! find the smallest rcut for any eam atype |
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! do i = 2, EAMList%currentAddition |
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! current_rcut_max =max(current_rcut_max,EAMList%EAMParams(i)%eam_rcut) |
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! end do |
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|
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! EAM_rcut = current_rcut_max |
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! EAM_rcut_orig = current_rcut_max |
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! do i = 1, EAMList%currentAddition |
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! EAMList%EAMParam(i)s%eam_atype_map(eam_atype(i)) = i |
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! end do |
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!! Allocate arrays for force calculation |
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|
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call allocateEAM(alloc_stat) |
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if (alloc_stat /= 0 ) then |
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write(*,*) "allocateEAM failed" |
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status = -1 |
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return |
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endif |
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|
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end subroutine init_EAM_FF |
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|
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!! routine checks to see if array is allocated, deallocates array if allocated |
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!! and then creates the array to the required size |
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subroutine allocateEAM(status) |
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integer, intent(out) :: status |
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|
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#ifdef IS_MPI |
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integer :: nAtomsInRow |
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integer :: nAtomsInCol |
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#endif |
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integer :: alloc_stat |
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|
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|
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status = 0 |
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#ifdef IS_MPI |
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nAtomsInRow = getNatomsInRow(plan_atom_row) |
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nAtomsInCol = getNatomsInCol(plan_atom_col) |
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#endif |
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|
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if (allocated(frho)) deallocate(frho) |
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allocate(frho(nlocal),stat=alloc_stat) |
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if (alloc_stat /= 0) then |
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status = -1 |
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return |
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end if |
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if (allocated(rho)) deallocate(rho) |
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allocate(rho(nlocal),stat=alloc_stat) |
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if (alloc_stat /= 0) then |
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status = -1 |
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return |
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end if |
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|
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if (allocated(dfrhodrho)) deallocate(dfrhodrho) |
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allocate(dfrhodrho(nlocal),stat=alloc_stat) |
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if (alloc_stat /= 0) then |
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status = -1 |
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return |
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end if |
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|
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if (allocated(d2frhodrhodrho)) deallocate(d2frhodrhodrho) |
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allocate(d2frhodrhodrho(nlocal),stat=alloc_stat) |
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if (alloc_stat /= 0) then |
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status = -1 |
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return |
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end if |
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|
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#ifdef IS_MPI |
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|
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if (allocated(rho_tmp)) deallocate(rho_tmp) |
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allocate(rho_tmp(nlocal),stat=alloc_stat) |
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if (alloc_stat /= 0) then |
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status = -1 |
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return |
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end if |
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|
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|
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if (allocated(frho_row)) deallocate(frho_row) |
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allocate(frho_row(nAtomsInRow),stat=alloc_stat) |
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if (alloc_stat /= 0) then |
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status = -1 |
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return |
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end if |
| 382 |
if (allocated(rho_row)) deallocate(rho_row) |
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allocate(rho_row(nAtomsInRow),stat=alloc_stat) |
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if (alloc_stat /= 0) then |
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status = -1 |
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return |
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end if |
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if (allocated(dfrhodrho_row)) deallocate(dfrhodrho_row) |
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allocate(dfrhodrho_row(nAtomsInRow),stat=alloc_stat) |
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if (alloc_stat /= 0) then |
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status = -1 |
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return |
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end if |
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if (allocated(d2frhodrhodrho_row)) deallocate(d2frhodrhodrho_row) |
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allocate(d2frhodrhodrho_row(nAtomsInRow),stat=alloc_stat) |
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if (alloc_stat /= 0) then |
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status = -1 |
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return |
| 399 |
end if |
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|
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|
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! Now do column arrays |
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|
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if (allocated(frho_col)) deallocate(frho_col) |
| 405 |
allocate(frho_col(nAtomsInCol),stat=alloc_stat) |
| 406 |
if (alloc_stat /= 0) then |
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status = -1 |
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return |
| 409 |
end if |
| 410 |
if (allocated(rho_col)) deallocate(rho_col) |
| 411 |
allocate(rho_col(nAtomsInCol),stat=alloc_stat) |
| 412 |
if (alloc_stat /= 0) then |
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status = -1 |
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return |
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end if |
| 416 |
if (allocated(dfrhodrho_col)) deallocate(dfrhodrho_col) |
| 417 |
allocate(dfrhodrho_col(nAtomsInCol),stat=alloc_stat) |
| 418 |
if (alloc_stat /= 0) then |
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status = -1 |
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return |
| 421 |
end if |
| 422 |
if (allocated(d2frhodrhodrho_col)) deallocate(d2frhodrhodrho_col) |
| 423 |
allocate(d2frhodrhodrho_col(nAtomsInCol),stat=alloc_stat) |
| 424 |
if (alloc_stat /= 0) then |
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status = -1 |
| 426 |
return |
| 427 |
end if |
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|
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#endif |
| 430 |
|
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end subroutine allocateEAM |
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|
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!! C sets rcut to be the largest cutoff of any atype |
| 434 |
!! present in this simulation. Doesn't include all atypes |
| 435 |
!! sim knows about, just those in the simulation. |
| 436 |
subroutine setCutoffEAM(rcut, status) |
| 437 |
real(kind=dp) :: rcut |
| 438 |
integer :: status |
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status = 0 |
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|
| 441 |
EAM_rcut = rcut |
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|
| 443 |
end subroutine setCutoffEAM |
| 444 |
|
| 445 |
|
| 446 |
|
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subroutine clean_EAM() |
| 448 |
|
| 449 |
! clean non-IS_MPI first |
| 450 |
frho = 0.0_dp |
| 451 |
rho = 0.0_dp |
| 452 |
dfrhodrho = 0.0_dp |
| 453 |
! clean MPI if needed |
| 454 |
#ifdef IS_MPI |
| 455 |
frho_row = 0.0_dp |
| 456 |
frho_col = 0.0_dp |
| 457 |
rho_row = 0.0_dp |
| 458 |
rho_col = 0.0_dp |
| 459 |
rho_tmp = 0.0_dp |
| 460 |
dfrhodrho_row = 0.0_dp |
| 461 |
dfrhodrho_col = 0.0_dp |
| 462 |
#endif |
| 463 |
end subroutine clean_EAM |
| 464 |
|
| 465 |
|
| 466 |
|
| 467 |
subroutine allocate_EAMType(eam_n_rho,eam_n_r,thisEAMType,stat) |
| 468 |
integer, intent(in) :: eam_n_rho |
| 469 |
integer, intent(in) :: eam_n_r |
| 470 |
type (EAMType) :: thisEAMType |
| 471 |
integer, optional :: stat |
| 472 |
integer :: alloc_stat |
| 473 |
|
| 474 |
|
| 475 |
|
| 476 |
if (present(stat)) stat = 0 |
| 477 |
|
| 478 |
allocate(thisEAMType%eam_rvals(eam_n_r),stat=alloc_stat) |
| 479 |
if (alloc_stat /= 0 ) then |
| 480 |
if (present(stat)) stat = -1 |
| 481 |
return |
| 482 |
end if |
| 483 |
allocate(thisEAMType%eam_rhovals(eam_n_rho),stat=alloc_stat) |
| 484 |
if (alloc_stat /= 0 ) then |
| 485 |
if (present(stat)) stat = -1 |
| 486 |
return |
| 487 |
end if |
| 488 |
allocate(thisEAMType%eam_F_rho(eam_n_rho),stat=alloc_stat) |
| 489 |
if (alloc_stat /= 0 ) then |
| 490 |
if (present(stat)) stat = -1 |
| 491 |
return |
| 492 |
end if |
| 493 |
allocate(thisEAMType%eam_Z_r(eam_n_r),stat=alloc_stat) |
| 494 |
if (alloc_stat /= 0 ) then |
| 495 |
if (present(stat)) stat = -1 |
| 496 |
return |
| 497 |
end if |
| 498 |
allocate(thisEAMType%eam_rho_r(eam_n_r),stat=alloc_stat) |
| 499 |
if (alloc_stat /= 0 ) then |
| 500 |
if (present(stat)) stat = -1 |
| 501 |
return |
| 502 |
end if |
| 503 |
allocate(thisEAMType%eam_phi_r(eam_n_r),stat=alloc_stat) |
| 504 |
if (alloc_stat /= 0 ) then |
| 505 |
if (present(stat)) stat = -1 |
| 506 |
return |
| 507 |
end if |
| 508 |
allocate(thisEAMType%eam_F_rho_pp(eam_n_rho),stat=alloc_stat) |
| 509 |
if (alloc_stat /= 0 ) then |
| 510 |
if (present(stat)) stat = -1 |
| 511 |
return |
| 512 |
end if |
| 513 |
allocate(thisEAMType%eam_Z_r_pp(eam_n_r),stat=alloc_stat) |
| 514 |
if (alloc_stat /= 0 ) then |
| 515 |
if (present(stat)) stat = -1 |
| 516 |
return |
| 517 |
end if |
| 518 |
allocate(thisEAMType%eam_rho_r_pp(eam_n_r),stat=alloc_stat) |
| 519 |
if (alloc_stat /= 0 ) then |
| 520 |
if (present(stat)) stat = -1 |
| 521 |
return |
| 522 |
end if |
| 523 |
allocate(thisEAMType%eam_phi_r_pp(eam_n_r),stat=alloc_stat) |
| 524 |
if (alloc_stat /= 0 ) then |
| 525 |
if (present(stat)) stat = -1 |
| 526 |
return |
| 527 |
end if |
| 528 |
|
| 529 |
|
| 530 |
end subroutine allocate_EAMType |
| 531 |
|
| 532 |
|
| 533 |
subroutine deallocate_EAMType(thisEAMType) |
| 534 |
type (EAMtype), pointer :: thisEAMType |
| 535 |
|
| 536 |
! free Arrays in reverse order of allocation... |
| 537 |
if(associated(thisEAMType%eam_phi_r_pp)) deallocate(thisEAMType%eam_phi_r_pp) |
| 538 |
if(associated(thisEAMType%eam_rho_r_pp)) deallocate(thisEAMType%eam_rho_r_pp) |
| 539 |
if(associated(thisEAMType%eam_Z_r_pp)) deallocate(thisEAMType%eam_Z_r_pp) |
| 540 |
if(associated(thisEAMType%eam_F_rho_pp)) deallocate(thisEAMType%eam_F_rho_pp) |
| 541 |
if(associated(thisEAMType%eam_phi_r)) deallocate(thisEAMType%eam_phi_r) |
| 542 |
if(associated(thisEAMType%eam_rho_r)) deallocate(thisEAMType%eam_rho_r) |
| 543 |
if(associated(thisEAMType%eam_Z_r)) deallocate(thisEAMType%eam_Z_r) |
| 544 |
if(associated(thisEAMType%eam_F_rho)) deallocate(thisEAMType%eam_F_rho) |
| 545 |
if(associated(thisEAMType%eam_rhovals)) deallocate(thisEAMType%eam_rhovals) |
| 546 |
if(associated(thisEAMType%eam_rvals)) deallocate(thisEAMType%eam_rvals) |
| 547 |
|
| 548 |
end subroutine deallocate_EAMType |
| 549 |
|
| 550 |
!! Calculates rho_r |
| 551 |
subroutine calc_eam_prepair_rho(atom1,atom2,d,r,rijsq) |
| 552 |
integer :: atom1,atom2 |
| 553 |
real(kind = dp), dimension(3) :: d |
| 554 |
real(kind = dp), intent(inout) :: r |
| 555 |
real(kind = dp), intent(inout) :: rijsq |
| 556 |
! value of electron density rho do to atom i at atom j |
| 557 |
real(kind = dp) :: rho_i_at_j |
| 558 |
! value of electron density rho do to atom j at atom i |
| 559 |
real(kind = dp) :: rho_j_at_i |
| 560 |
|
| 561 |
! we don't use the derivatives, dummy variables |
| 562 |
real( kind = dp) :: drho,d2rho |
| 563 |
integer :: eam_err |
| 564 |
|
| 565 |
integer :: atid1,atid2 ! Global atid |
| 566 |
integer :: myid_atom1 ! EAM atid |
| 567 |
integer :: myid_atom2 |
| 568 |
|
| 569 |
|
| 570 |
! check to see if we need to be cleaned at the start of a force loop |
| 571 |
|
| 572 |
|
| 573 |
|
| 574 |
|
| 575 |
#ifdef IS_MPI |
| 576 |
Atid1 = Atid_row(Atom1) |
| 577 |
Atid2 = Atid_col(Atom2) |
| 578 |
#else |
| 579 |
Atid1 = Atid(Atom1) |
| 580 |
Atid2 = Atid(Atom2) |
| 581 |
#endif |
| 582 |
|
| 583 |
Myid_atom1 = Eamlist%atidtoeamtype(Atid1) |
| 584 |
Myid_atom2 = Eamlist%atidtoeamtype(Atid2) |
| 585 |
|
| 586 |
if (r.lt.EAMList%EAMParams(myid_atom1)%eam_rcut) then |
| 587 |
|
| 588 |
|
| 589 |
|
| 590 |
call eam_splint(EAMList%EAMParams(myid_atom1)%eam_nr, & |
| 591 |
EAMList%EAMParams(myid_atom1)%eam_rvals, & |
| 592 |
EAMList%EAMParams(myid_atom1)%eam_rho_r, & |
| 593 |
EAMList%EAMParams(myid_atom1)%eam_rho_r_pp, & |
| 594 |
r, rho_i_at_j,drho,d2rho) |
| 595 |
|
| 596 |
|
| 597 |
|
| 598 |
#ifdef IS_MPI |
| 599 |
rho_col(atom2) = rho_col(atom2) + rho_i_at_j |
| 600 |
#else |
| 601 |
rho(atom2) = rho(atom2) + rho_i_at_j |
| 602 |
#endif |
| 603 |
! write(*,*) atom1,atom2,r,rho_i_at_j |
| 604 |
endif |
| 605 |
|
| 606 |
if (r.lt.EAMList%EAMParams(myid_atom2)%eam_rcut) then |
| 607 |
call eam_splint(EAMList%EAMParams(myid_atom2)%eam_nr, & |
| 608 |
EAMList%EAMParams(myid_atom2)%eam_rvals, & |
| 609 |
EAMList%EAMParams(myid_atom2)%eam_rho_r, & |
| 610 |
EAMList%EAMParams(myid_atom2)%eam_rho_r_pp, & |
| 611 |
r, rho_j_at_i,drho,d2rho) |
| 612 |
|
| 613 |
|
| 614 |
|
| 615 |
|
| 616 |
#ifdef IS_MPI |
| 617 |
rho_row(atom1) = rho_row(atom1) + rho_j_at_i |
| 618 |
#else |
| 619 |
rho(atom1) = rho(atom1) + rho_j_at_i |
| 620 |
#endif |
| 621 |
endif |
| 622 |
|
| 623 |
|
| 624 |
|
| 625 |
|
| 626 |
|
| 627 |
|
| 628 |
end subroutine calc_eam_prepair_rho |
| 629 |
|
| 630 |
|
| 631 |
|
| 632 |
|
| 633 |
!! Calculate the functional F(rho) for all local atoms |
| 634 |
subroutine calc_eam_preforce_Frho(nlocal,pot) |
| 635 |
integer :: nlocal |
| 636 |
real(kind=dp) :: pot |
| 637 |
integer :: i,j |
| 638 |
integer :: atom |
| 639 |
real(kind=dp) :: U,U1,U2 |
| 640 |
integer :: atype1 |
| 641 |
integer :: me,atid1 |
| 642 |
integer :: n_rho_points |
| 643 |
|
| 644 |
|
| 645 |
cleanme = .true. |
| 646 |
!! Scatter the electron density from pre-pair calculation back to local atoms |
| 647 |
#ifdef IS_MPI |
| 648 |
call scatter(rho_row,rho,plan_atom_row,eam_err) |
| 649 |
if (eam_err /= 0 ) then |
| 650 |
write(errMsg,*) " Error scattering rho_row into rho" |
| 651 |
call handleError(RoutineName,errMesg) |
| 652 |
endif |
| 653 |
call scatter(rho_col,rho_tmp,plan_atom_col,eam_err) |
| 654 |
if (eam_err /= 0 ) then |
| 655 |
write(errMsg,*) " Error scattering rho_col into rho" |
| 656 |
call handleError(RoutineName,errMesg) |
| 657 |
endif |
| 658 |
|
| 659 |
rho(1:nlocal) = rho(1:nlocal) + rho_tmp(1:nlocal) |
| 660 |
#endif |
| 661 |
|
| 662 |
|
| 663 |
|
| 664 |
!! Calculate F(rho) and derivative |
| 665 |
do atom = 1, nlocal |
| 666 |
atid1 = atid(atom) |
| 667 |
me = eamList%atidToEAMtype(atid1) |
| 668 |
n_rho_points = EAMList%EAMParams(me)%eam_nrho |
| 669 |
! Check to see that the density is not greater than the larges rho we have calculated |
| 670 |
if (rho(atom) < EAMList%EAMParams(me)%eam_rhovals(n_rho_points)) then |
| 671 |
call eam_splint(n_rho_points, & |
| 672 |
EAMList%EAMParams(me)%eam_rhovals, & |
| 673 |
EAMList%EAMParams(me)%eam_f_rho, & |
| 674 |
EAMList%EAMParams(me)%eam_f_rho_pp, & |
| 675 |
rho(atom), & ! Actual Rho |
| 676 |
u, u1, u2) |
| 677 |
else |
| 678 |
! Calculate F(rho with the largest available rho value |
| 679 |
call eam_splint(n_rho_points, & |
| 680 |
EAMList%EAMParams(me)%eam_rhovals, & |
| 681 |
EAMList%EAMParams(me)%eam_f_rho, & |
| 682 |
EAMList%EAMParams(me)%eam_f_rho_pp, & |
| 683 |
EAMList%EAMParams(me)%eam_rhovals(n_rho_points), & ! Largest rho |
| 684 |
u,u1,u2) |
| 685 |
end if |
| 686 |
|
| 687 |
|
| 688 |
frho(atom) = u |
| 689 |
dfrhodrho(atom) = u1 |
| 690 |
d2frhodrhodrho(atom) = u2 |
| 691 |
pot = pot + u |
| 692 |
|
| 693 |
enddo |
| 694 |
|
| 695 |
|
| 696 |
|
| 697 |
#ifdef IS_MPI |
| 698 |
!! communicate f(rho) and derivatives back into row and column arrays |
| 699 |
call gather(frho,frho_row,plan_atom_row, eam_err) |
| 700 |
if (eam_err /= 0) then |
| 701 |
call handleError("cal_eam_forces()","MPI gather frho_row failure") |
| 702 |
endif |
| 703 |
call gather(dfrhodrho,dfrhodrho_row,plan_atom_row, eam_err) |
| 704 |
if (eam_err /= 0) then |
| 705 |
call handleError("cal_eam_forces()","MPI gather dfrhodrho_row failure") |
| 706 |
endif |
| 707 |
call gather(frho,frho_col,plan_atom_col, eam_err) |
| 708 |
if (eam_err /= 0) then |
| 709 |
call handleError("cal_eam_forces()","MPI gather frho_col failure") |
| 710 |
endif |
| 711 |
call gather(dfrhodrho,dfrhodrho_col,plan_atom_col, eam_err) |
| 712 |
if (eam_err /= 0) then |
| 713 |
call handleError("cal_eam_forces()","MPI gather dfrhodrho_col failure") |
| 714 |
endif |
| 715 |
|
| 716 |
|
| 717 |
|
| 718 |
|
| 719 |
|
| 720 |
if (nmflag) then |
| 721 |
call gather(d2frhodrhodrho,d2frhodrhodrho_row,plan_atom_row) |
| 722 |
call gather(d2frhodrhodrho,d2frhodrhodrho_col,plan_atom_col) |
| 723 |
endif |
| 724 |
#endif |
| 725 |
|
| 726 |
|
| 727 |
end subroutine calc_eam_preforce_Frho |
| 728 |
|
| 729 |
|
| 730 |
|
| 731 |
|
| 732 |
!! Does EAM pairwise Force calculation. |
| 733 |
subroutine do_eam_pair(atom1, atom2, d, rij, r2, sw, vpair, fpair, & |
| 734 |
pot, f, do_pot) |
| 735 |
!Arguments |
| 736 |
integer, intent(in) :: atom1, atom2 |
| 737 |
real( kind = dp ), intent(in) :: rij, r2 |
| 738 |
real( kind = dp ) :: pot, sw, vpair |
| 739 |
real( kind = dp ), dimension(3,nLocal) :: f |
| 740 |
real( kind = dp ), intent(in), dimension(3) :: d |
| 741 |
real( kind = dp ), intent(inout), dimension(3) :: fpair |
| 742 |
|
| 743 |
logical, intent(in) :: do_pot |
| 744 |
|
| 745 |
real( kind = dp ) :: drdx,drdy,drdz |
| 746 |
real( kind = dp ) :: d2 |
| 747 |
real( kind = dp ) :: phab,pha,dvpdr,d2vpdrdr |
| 748 |
real( kind = dp ) :: rha,drha,d2rha, dpha |
| 749 |
real( kind = dp ) :: rhb,drhb,d2rhb, dphb |
| 750 |
real( kind = dp ) :: dudr |
| 751 |
real( kind = dp ) :: rci,rcj |
| 752 |
real( kind = dp ) :: drhoidr,drhojdr |
| 753 |
real( kind = dp ) :: d2rhoidrdr |
| 754 |
real( kind = dp ) :: d2rhojdrdr |
| 755 |
real( kind = dp ) :: Fx,Fy,Fz |
| 756 |
real( kind = dp ) :: r,d2pha,phb,d2phb |
| 757 |
|
| 758 |
integer :: id1,id2 |
| 759 |
integer :: mytype_atom1 |
| 760 |
integer :: mytype_atom2 |
| 761 |
integer :: atid1,atid2 |
| 762 |
!Local Variables |
| 763 |
|
| 764 |
! write(*,*) "Frho: ", Frho(atom1) |
| 765 |
|
| 766 |
phab = 0.0E0_DP |
| 767 |
dvpdr = 0.0E0_DP |
| 768 |
d2vpdrdr = 0.0E0_DP |
| 769 |
|
| 770 |
if (rij .lt. EAM_rcut) then |
| 771 |
|
| 772 |
#ifdef IS_MPI |
| 773 |
atid1 = atid_row(atom1) |
| 774 |
atid2 = atid_col(atom2) |
| 775 |
#else |
| 776 |
atid1 = atid(atom1) |
| 777 |
atid2 = atid(atom2) |
| 778 |
#endif |
| 779 |
|
| 780 |
mytype_atom1 = EAMList%atidToEAMType(atid1) |
| 781 |
mytype_atom2 = EAMList%atidTOEAMType(atid2) |
| 782 |
|
| 783 |
|
| 784 |
! get cutoff for atom 1 |
| 785 |
rci = EAMList%EAMParams(mytype_atom1)%eam_rcut |
| 786 |
! get type specific cutoff for atom 2 |
| 787 |
rcj = EAMList%EAMParams(mytype_atom2)%eam_rcut |
| 788 |
|
| 789 |
drdx = d(1)/rij |
| 790 |
drdy = d(2)/rij |
| 791 |
drdz = d(3)/rij |
| 792 |
|
| 793 |
if (rij.lt.rci) then |
| 794 |
call eam_splint(EAMList%EAMParams(mytype_atom1)%eam_nr, & |
| 795 |
EAMList%EAMParams(mytype_atom1)%eam_rvals, & |
| 796 |
EAMList%EAMParams(mytype_atom1)%eam_rho_r, & |
| 797 |
EAMList%EAMParams(mytype_atom1)%eam_rho_r_pp, & |
| 798 |
rij, rha,drha,d2rha) |
| 799 |
!! Calculate Phi(r) for atom1. |
| 800 |
call eam_splint(EAMList%EAMParams(mytype_atom1)%eam_nr, & |
| 801 |
EAMList%EAMParams(mytype_atom1)%eam_rvals, & |
| 802 |
EAMList%EAMParams(mytype_atom1)%eam_phi_r, & |
| 803 |
EAMList%EAMParams(mytype_atom1)%eam_phi_r_pp, & |
| 804 |
rij, pha,dpha,d2pha) |
| 805 |
endif |
| 806 |
|
| 807 |
if (rij.lt.rcj) then |
| 808 |
! Calculate rho,drho and d2rho for atom1 |
| 809 |
call eam_splint(EAMList%EAMParams(mytype_atom2)%eam_nr, & |
| 810 |
EAMList%EAMParams(mytype_atom2)%eam_rvals, & |
| 811 |
EAMList%EAMParams(mytype_atom2)%eam_rho_r, & |
| 812 |
EAMList%EAMParams(mytype_atom2)%eam_rho_r_pp, & |
| 813 |
rij, rhb,drhb,d2rhb) |
| 814 |
|
| 815 |
!! Calculate Phi(r) for atom2. |
| 816 |
call eam_splint(EAMList%EAMParams(mytype_atom2)%eam_nr, & |
| 817 |
EAMList%EAMParams(mytype_atom2)%eam_rvals, & |
| 818 |
EAMList%EAMParams(mytype_atom2)%eam_phi_r, & |
| 819 |
EAMList%EAMParams(mytype_atom2)%eam_phi_r_pp, & |
| 820 |
rij, phb,dphb,d2phb) |
| 821 |
endif |
| 822 |
|
| 823 |
if (rij.lt.rci) then |
| 824 |
phab = phab + 0.5E0_DP*(rhb/rha)*pha |
| 825 |
dvpdr = dvpdr + 0.5E0_DP*((rhb/rha)*dpha + & |
| 826 |
pha*((drhb/rha) - (rhb*drha/rha/rha))) |
| 827 |
d2vpdrdr = d2vpdrdr + 0.5E0_DP*((rhb/rha)*d2pha + & |
| 828 |
2.0E0_DP*dpha*((drhb/rha) - (rhb*drha/rha/rha)) + & |
| 829 |
pha*((d2rhb/rha) - 2.0E0_DP*(drhb*drha/rha/rha) + & |
| 830 |
(2.0E0_DP*rhb*drha*drha/rha/rha/rha) - (rhb*d2rha/rha/rha))) |
| 831 |
endif |
| 832 |
|
| 833 |
if (rij.lt.rcj) then |
| 834 |
phab = phab + 0.5E0_DP*(rha/rhb)*phb |
| 835 |
dvpdr = dvpdr + 0.5E0_DP*((rha/rhb)*dphb + & |
| 836 |
phb*((drha/rhb) - (rha*drhb/rhb/rhb))) |
| 837 |
d2vpdrdr = d2vpdrdr + 0.5E0_DP*((rha/rhb)*d2phb + & |
| 838 |
2.0E0_DP*dphb*((drha/rhb) - (rha*drhb/rhb/rhb)) + & |
| 839 |
phb*((d2rha/rhb) - 2.0E0_DP*(drha*drhb/rhb/rhb) + & |
| 840 |
(2.0E0_DP*rha*drhb*drhb/rhb/rhb/rhb) - (rha*d2rhb/rhb/rhb))) |
| 841 |
endif |
| 842 |
|
| 843 |
drhoidr = drha |
| 844 |
drhojdr = drhb |
| 845 |
|
| 846 |
d2rhoidrdr = d2rha |
| 847 |
d2rhojdrdr = d2rhb |
| 848 |
|
| 849 |
|
| 850 |
#ifdef IS_MPI |
| 851 |
dudr = drhojdr*dfrhodrho_row(atom1)+drhoidr*dfrhodrho_col(atom2) & |
| 852 |
+ dvpdr |
| 853 |
|
| 854 |
#else |
| 855 |
dudr = drhojdr*dfrhodrho(atom1)+drhoidr*dfrhodrho(atom2) & |
| 856 |
+ dvpdr |
| 857 |
! write(*,*) "Atom1,Atom2, dfrhodrho(atom1) dfrhodrho(atom2): ", atom1,atom2,dfrhodrho(atom1),dfrhodrho(atom2) |
| 858 |
#endif |
| 859 |
|
| 860 |
fx = dudr * drdx |
| 861 |
fy = dudr * drdy |
| 862 |
fz = dudr * drdz |
| 863 |
|
| 864 |
|
| 865 |
#ifdef IS_MPI |
| 866 |
if (do_pot) then |
| 867 |
pot_Row(METALLIC_POT,atom1) = pot_Row(METALLIC_POT,atom1) + phab*0.5 |
| 868 |
pot_Col(METALLIC_POT,atom2) = pot_Col(METALLIC_POT,atom2) + phab*0.5 |
| 869 |
end if |
| 870 |
|
| 871 |
f_Row(1,atom1) = f_Row(1,atom1) + fx |
| 872 |
f_Row(2,atom1) = f_Row(2,atom1) + fy |
| 873 |
f_Row(3,atom1) = f_Row(3,atom1) + fz |
| 874 |
|
| 875 |
f_Col(1,atom2) = f_Col(1,atom2) - fx |
| 876 |
f_Col(2,atom2) = f_Col(2,atom2) - fy |
| 877 |
f_Col(3,atom2) = f_Col(3,atom2) - fz |
| 878 |
#else |
| 879 |
|
| 880 |
if(do_pot) then |
| 881 |
pot = pot + phab |
| 882 |
end if |
| 883 |
|
| 884 |
f(1,atom1) = f(1,atom1) + fx |
| 885 |
f(2,atom1) = f(2,atom1) + fy |
| 886 |
f(3,atom1) = f(3,atom1) + fz |
| 887 |
|
| 888 |
f(1,atom2) = f(1,atom2) - fx |
| 889 |
f(2,atom2) = f(2,atom2) - fy |
| 890 |
f(3,atom2) = f(3,atom2) - fz |
| 891 |
#endif |
| 892 |
|
| 893 |
vpair = vpair + phab |
| 894 |
#ifdef IS_MPI |
| 895 |
id1 = AtomRowToGlobal(atom1) |
| 896 |
id2 = AtomColToGlobal(atom2) |
| 897 |
#else |
| 898 |
id1 = atom1 |
| 899 |
id2 = atom2 |
| 900 |
#endif |
| 901 |
|
| 902 |
if (molMembershipList(id1) .ne. molMembershipList(id2)) then |
| 903 |
|
| 904 |
fpair(1) = fpair(1) + fx |
| 905 |
fpair(2) = fpair(2) + fy |
| 906 |
fpair(3) = fpair(3) + fz |
| 907 |
|
| 908 |
endif |
| 909 |
|
| 910 |
if (nmflag) then |
| 911 |
|
| 912 |
drhoidr = drha |
| 913 |
drhojdr = drhb |
| 914 |
d2rhoidrdr = d2rha |
| 915 |
d2rhojdrdr = d2rhb |
| 916 |
|
| 917 |
#ifdef IS_MPI |
| 918 |
d2 = d2vpdrdr + & |
| 919 |
d2rhoidrdr*dfrhodrho_col(atom2) + & |
| 920 |
d2rhojdrdr*dfrhodrho_row(atom1) + & |
| 921 |
drhoidr*drhoidr*d2frhodrhodrho_col(atom2) + & |
| 922 |
drhojdr*drhojdr*d2frhodrhodrho_row(atom1) |
| 923 |
|
| 924 |
#else |
| 925 |
|
| 926 |
d2 = d2vpdrdr + & |
| 927 |
d2rhoidrdr*dfrhodrho(atom2) + & |
| 928 |
d2rhojdrdr*dfrhodrho(atom1) + & |
| 929 |
drhoidr*drhoidr*d2frhodrhodrho(atom2) + & |
| 930 |
drhojdr*drhojdr*d2frhodrhodrho(atom1) |
| 931 |
#endif |
| 932 |
end if |
| 933 |
|
| 934 |
endif |
| 935 |
end subroutine do_eam_pair |
| 936 |
|
| 937 |
|
| 938 |
subroutine eam_splint(nx, xa, ya, yppa, x, y, dy, d2y) |
| 939 |
|
| 940 |
integer :: atype, nx, j |
| 941 |
real( kind = DP ), dimension(:) :: xa |
| 942 |
real( kind = DP ), dimension(:) :: ya |
| 943 |
real( kind = DP ), dimension(:) :: yppa |
| 944 |
real( kind = DP ) :: x, y |
| 945 |
real( kind = DP ) :: dy, d2y |
| 946 |
real( kind = DP ) :: del, h, a, b, c, d |
| 947 |
integer :: pp_arraySize |
| 948 |
|
| 949 |
|
| 950 |
! this spline code assumes that the x points are equally spaced |
| 951 |
! do not attempt to use this code if they are not. |
| 952 |
|
| 953 |
|
| 954 |
! find the closest point with a value below our own: |
| 955 |
j = FLOOR(real((nx-1),kind=dp) * (x - xa(1)) / (xa(nx) - xa(1))) + 1 |
| 956 |
|
| 957 |
! check to make sure we're inside the spline range: |
| 958 |
if ((j.gt.nx).or.(j.lt.1)) then |
| 959 |
write(errMSG,*) "EAM_splint: x is outside bounds of spline: ",x,j |
| 960 |
call handleError(routineName,errMSG) |
| 961 |
endif |
| 962 |
! check to make sure we haven't screwed up the calculation of j: |
| 963 |
if ((x.lt.xa(j)).or.(x.gt.xa(j+1))) then |
| 964 |
if (j.ne.nx) then |
| 965 |
write(errMSG,*) "EAM_splint:",x," x is outside bounding range" |
| 966 |
call handleError(routineName,errMSG) |
| 967 |
endif |
| 968 |
endif |
| 969 |
|
| 970 |
del = xa(j+1) - x |
| 971 |
h = xa(j+1) - xa(j) |
| 972 |
|
| 973 |
a = del / h |
| 974 |
b = 1.0E0_DP - a |
| 975 |
c = a*(a*a - 1.0E0_DP)*h*h/6.0E0_DP |
| 976 |
d = b*(b*b - 1.0E0_DP)*h*h/6.0E0_DP |
| 977 |
|
| 978 |
y = a*ya(j) + b*ya(j+1) + c*yppa(j) + d*yppa(j+1) |
| 979 |
|
| 980 |
dy = (ya(j+1)-ya(j))/h & |
| 981 |
- (3.0E0_DP*a*a - 1.0E0_DP)*h*yppa(j)/6.0E0_DP & |
| 982 |
+ (3.0E0_DP*b*b - 1.0E0_DP)*h*yppa(j+1)/6.0E0_DP |
| 983 |
|
| 984 |
|
| 985 |
d2y = a*yppa(j) + b*yppa(j+1) |
| 986 |
|
| 987 |
|
| 988 |
end subroutine eam_splint |
| 989 |
|
| 990 |
|
| 991 |
subroutine eam_spline(nx, xa, ya, yppa, yp1, ypn, boundary) |
| 992 |
|
| 993 |
|
| 994 |
! yp1 and ypn are the first derivatives of y at the two endpoints |
| 995 |
! if boundary is 'L' the lower derivative is used |
| 996 |
! if boundary is 'U' the upper derivative is used |
| 997 |
! if boundary is 'B' then both derivatives are used |
| 998 |
! if boundary is anything else, then both derivatives are assumed to be 0 |
| 999 |
|
| 1000 |
integer :: nx, i, k, max_array_size |
| 1001 |
|
| 1002 |
real( kind = DP ), dimension(:) :: xa |
| 1003 |
real( kind = DP ), dimension(:) :: ya |
| 1004 |
real( kind = DP ), dimension(:) :: yppa |
| 1005 |
real( kind = DP ), dimension(size(xa)) :: u |
| 1006 |
real( kind = DP ) :: yp1,ypn,un,qn,sig,p |
| 1007 |
character(len=*) :: boundary |
| 1008 |
|
| 1009 |
! make sure the sizes match |
| 1010 |
if ((nx /= size(xa)) .or. (nx /= size(ya))) then |
| 1011 |
call handleWarning("EAM_SPLINE","Array size mismatch") |
| 1012 |
end if |
| 1013 |
|
| 1014 |
if ((boundary.eq.'l').or.(boundary.eq.'L').or. & |
| 1015 |
(boundary.eq.'b').or.(boundary.eq.'B')) then |
| 1016 |
yppa(1) = -0.5E0_DP |
| 1017 |
u(1) = (3.0E0_DP/(xa(2)-xa(1)))*((ya(2)-& |
| 1018 |
ya(1))/(xa(2)-xa(1))-yp1) |
| 1019 |
else |
| 1020 |
yppa(1) = 0.0E0_DP |
| 1021 |
u(1) = 0.0E0_DP |
| 1022 |
endif |
| 1023 |
|
| 1024 |
do i = 2, nx - 1 |
| 1025 |
sig = (xa(i) - xa(i-1)) / (xa(i+1) - xa(i-1)) |
| 1026 |
p = sig * yppa(i-1) + 2.0E0_DP |
| 1027 |
yppa(i) = (sig - 1.0E0_DP) / p |
| 1028 |
u(i) = (6.0E0_DP*((ya(i+1)-ya(i))/(xa(i+1)-xa(i)) - & |
| 1029 |
(ya(i)-ya(i-1))/(xa(i)-xa(i-1)))/ & |
| 1030 |
(xa(i+1)-xa(i-1)) - sig * u(i-1))/p |
| 1031 |
enddo |
| 1032 |
|
| 1033 |
if ((boundary.eq.'u').or.(boundary.eq.'U').or. & |
| 1034 |
(boundary.eq.'b').or.(boundary.eq.'B')) then |
| 1035 |
qn = 0.5E0_DP |
| 1036 |
un = (3.0E0_DP/(xa(nx)-xa(nx-1)))* & |
| 1037 |
(ypn-(ya(nx)-ya(nx-1))/(xa(nx)-xa(nx-1))) |
| 1038 |
else |
| 1039 |
qn = 0.0E0_DP |
| 1040 |
un = 0.0E0_DP |
| 1041 |
endif |
| 1042 |
|
| 1043 |
yppa(nx)=(un-qn*u(nx-1))/(qn*yppa(nx-1)+1.0E0_DP) |
| 1044 |
|
| 1045 |
do k = nx-1, 1, -1 |
| 1046 |
yppa(k)=yppa(k)*yppa(k+1)+u(k) |
| 1047 |
enddo |
| 1048 |
|
| 1049 |
end subroutine eam_spline |
| 1050 |
|
| 1051 |
end module eam |
