1 |
gezelter |
1318 |
module shapes |
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use force_globals |
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use definitions |
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use atype_module |
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use vector_class |
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use simulation |
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use status |
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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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INTEGER, PARAMETER:: CHEBYSHEV_TN = 1 |
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INTEGER, PARAMETER:: CHEBYSHEV_UN = 2 |
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INTEGER, PARAMETER:: LAGUERRE = 3 |
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INTEGER, PARAMETER:: HERMITE = 4 |
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INTEGER, PARAMETER:: SH_COS = 0 |
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INTEGER, PARAMETER:: SH_SIN = 1 |
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logical, save :: haveShapeMap = .false. |
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public :: do_shape_pair |
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type :: ShapeList |
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integer :: nContactFuncs = 0 |
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integer :: nRangeFuncs = 0 |
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integer :: nStrengthFuncs = 0 |
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integer :: bigL = 0 |
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integer :: bigM = 0 |
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integer, allocatable, dimension(:) :: ContactFuncLValue |
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integer, allocatable, dimension(:) :: ContactFuncMValue |
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integer, allocatable, dimension(:) :: ContactFunctionType |
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real(kind=dp), allocatable, dimension(:) :: ContactFuncCoefficient |
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integer, allocatable, dimension(:) :: RangeFuncLValue |
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integer, allocatable, dimension(:) :: RangeFuncMValue |
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integer, allocatable, dimension(:) :: RangeFunctionType |
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real(kind=dp), allocatable, dimension(:) :: RangeFuncCoefficient |
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integer, allocatable, dimension(:) :: StrengthFuncLValue |
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integer, allocatable, dimension(:) :: StrengthFuncMValue |
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integer, allocatable, dimension(:) :: StrengthFunctionType |
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real(kind=dp), allocatable, dimension(:) :: StrengthFuncCoefficient |
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logical :: isLJ = .false. |
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real ( kind = dp ) :: epsilon = 0.0_dp |
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real ( kind = dp ) :: sigma = 0.0_dp |
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end type ShapeList |
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type(ShapeList), dimension(:),allocatable :: ShapeMap |
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integer :: lmax |
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real (kind=dp), allocatable, dimension(:,:) :: plm_i, dlm_i, plm_j, dlm_j |
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real (kind=dp), allocatable, dimension(:) :: tm_i, dtm_i, um_i, dum_i |
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real (kind=dp), allocatable, dimension(:) :: tm_j, dtm_j, um_j, dum_j |
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contains |
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subroutine createShapeMap(status) |
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integer :: nAtypes |
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integer :: status |
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integer :: i |
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real (kind=DP) :: thisDP |
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logical :: thisProperty |
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status = 0 |
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nAtypes = getSize(atypes) |
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if (nAtypes == 0) then |
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status = -1 |
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return |
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end if |
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if (.not. allocated(ShapeMap)) then |
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allocate(ShapeMap(nAtypes)) |
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endif |
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do i = 1, nAtypes |
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call getElementProperty(atypes, i, "is_SHAPE", thisProperty) |
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if (thisProperty) then |
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! do all of the shape stuff |
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endif |
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call getElementProperty(atypes, i, "is_LJ", thisProperty) |
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if (thisProperty) then |
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ShapeMap(i)%isLJ = .true. |
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call getElementProperty(atypes, i, "lj_epsilon", thisDP) |
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ShapeMap(i)%epsilon = thisDP |
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call getElementProperty(atypes, i, "lj_sigma", thisDP) |
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ShapeMap(i)%sigma = thisDP |
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else |
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ShapeMap(i)%isLJ = .false. |
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endif |
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end do |
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haveShapeMap = .true. |
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end subroutine createShapeMap |
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subroutine do_shape_pair(atom1, atom2, d, rij, r2, sw, vpair, fpair, & |
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pot, A, f, t, do_pot) |
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integer, intent(in) :: atom1, atom2 |
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real (kind=dp), intent(inout) :: rij, r2 |
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real (kind=dp), dimension(3), intent(in) :: d |
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real (kind=dp), dimension(3), intent(inout) :: fpair |
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real (kind=dp) :: pot, vpair, sw |
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real (kind=dp), dimension(9,nLocal) :: A |
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real (kind=dp), dimension(3,nLocal) :: f |
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real (kind=dp), dimension(3,nLocal) :: t |
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logical, intent(in) :: do_pot |
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real (kind=dp) :: r3, r5, rt2, rt3, rt5, rt6, rt11, rt12, rt126 |
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integer :: me1, me2, l, m, lm, id1, id2, localError, function_type |
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real (kind=dp) :: sigma_i, s_i, eps_i, sigma_j, s_j, eps_j |
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real (kind=dp) :: coeff |
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real (kind=dp) :: dsigmaidx, dsigmaidy, dsigmaidz |
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real (kind=dp) :: dsigmaidux, dsigmaiduy, dsigmaiduz |
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real (kind=dp) :: dsigmajdx, dsigmajdy, dsigmajdz |
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real (kind=dp) :: dsigmajdux, dsigmajduy, dsigmajduz |
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real (kind=dp) :: dsidx, dsidy, dsidz |
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real (kind=dp) :: dsidux, dsiduy, dsiduz |
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real (kind=dp) :: dsjdx, dsjdy, dsjdz |
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real (kind=dp) :: dsjdux, dsjduy, dsjduz |
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real (kind=dp) :: depsidx, depsidy, depsidz |
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real (kind=dp) :: depsidux, depsiduy, depsiduz |
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real (kind=dp) :: depsjdx, depsjdy, depsjdz |
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real (kind=dp) :: depsjdux, depsjduy, depsjduz |
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real (kind=dp) :: xi, yi, zi, xj, yj, zj, xi2, yi2, zi2, xj2, yj2, zj2 |
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145 |
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real (kind=dp) :: proji, proji3, projj, projj3 |
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real (kind=dp) :: cti, ctj, cpi, cpj, spi, spj |
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real (kind=dp) :: Phunc, sigma, s, eps, rtdenom, rt |
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149 |
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real (kind=dp) :: dctidx, dctidy, dctidz |
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real (kind=dp) :: dctidux, dctiduy, dctiduz |
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real (kind=dp) :: dctjdx, dctjdy, dctjdz |
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real (kind=dp) :: dctjdux, dctjduy, dctjduz |
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real (kind=dp) :: dcpidx, dcpidy, dcpidz |
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real (kind=dp) :: dcpidux, dcpiduy, dcpiduz |
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real (kind=dp) :: dcpjdx, dcpjdy, dcpjdz |
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real (kind=dp) :: dcpjdux, dcpjduy, dcpjduz |
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real (kind=dp) :: dspidx, dspidy, dspidz |
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real (kind=dp) :: dspidux, dspiduy, dspiduz |
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real (kind=dp) :: dspjdx, dspjdy, dspjdz |
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real (kind=dp) :: dspjdux, dspjduy, dspjduz |
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real (kind=dp) :: dPhuncdX, dPhuncdY, dPhuncdZ |
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real (kind=dp) :: dPhuncdUx, dPhuncdUy, dPhuncdUz |
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real (kind=dp) :: dsigmadxi, dsigmadyi, dsigmadzi |
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real (kind=dp) :: dsigmaduxi, dsigmaduyi, dsigmaduzi |
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real (kind=dp) :: dsigmadxj, dsigmadyj, dsigmadzj |
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real (kind=dp) :: dsigmaduxj, dsigmaduyj, dsigmaduzj |
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real (kind=dp) :: dsdxi, dsdyi, dsdzi |
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real (kind=dp) :: dsduxi, dsduyi, dsduzi |
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real (kind=dp) :: dsdxj, dsdyj, dsdzj |
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real (kind=dp) :: dsduxj, dsduyj, dsduzj |
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real (kind=dp) :: depsdxi, depsdyi, depsdzi |
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real (kind=dp) :: depsduxi, depsduyi, depsduzi |
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real (kind=dp) :: depsdxj, depsdyj, depsdzj |
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real (kind=dp) :: depsduxj, depsduyj, depsduzj |
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real (kind=dp) :: drtdxi, drtdyi, drtdzi |
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real (kind=dp) :: drtduxi, drtduyi, drtduzi |
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real (kind=dp) :: drtdxj, drtdyj, drtdzj |
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real (kind=dp) :: drtduxj, drtduyj, drtduzj |
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real (kind=dp) :: drdxi, drdyi, drdzi |
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real (kind=dp) :: drduxi, drduyi, drduzi |
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real (kind=dp) :: drdxj, drdyj, drdzj |
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real (kind=dp) :: drduxj, drduyj, drduzj |
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real (kind=dp) :: dvdxi, dvdyi, dvdzi |
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real (kind=dp) :: dvduxi, dvduyi, dvduzi |
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real (kind=dp) :: dvdxj, dvdyj, dvdzj |
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real (kind=dp) :: dvduxj, dvduyj, dvduzj |
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real (kind=dp) :: fxi, fyi, fzi, fxj, fyj, fzj |
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real (kind=dp) :: txi, tyi, tzi, txj, tyj, tzj |
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real (kind=dp) :: fxii, fyii, fzii, fxij, fyij, fzij |
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real (kind=dp) :: fxji, fyji, fzji, fxjj, fyjj, fzjj |
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real (kind=dp) :: fxradial, fyradial, fzradial |
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if (.not.haveShapeMap) then |
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localError = 0 |
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call createShapeMap(localError) |
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if ( localError .ne. 0 ) then |
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call handleError("calc_shape", "ShapeMap creation failed!") |
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return |
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end if |
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endif |
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!! We assume that the rotation matrices have already been calculated |
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!! and placed in the A array. |
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r3 = r2*rij |
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r5 = r3*r2 |
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drdxi = -d(1) / rij |
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drdyi = -d(2) / rij |
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drdzi = -d(3) / rij |
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drdxj = d(1) / rij |
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drdyj = d(2) / rij |
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drdzj = d(3) / rij |
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#ifdef IS_MPI |
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me1 = atid_Row(atom1) |
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me2 = atid_Col(atom2) |
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#else |
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me1 = atid(atom1) |
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me2 = atid(atom2) |
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#endif |
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if (ShapeMap(me1)%isLJ) then |
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sigma_i = ShapeMap(me1)%sigma |
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s_i = ShapeMap(me1)%sigma |
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eps_i = ShapeMap(me1)%epsilon |
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dsigmaidx = 0.0d0 |
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dsigmaidy = 0.0d0 |
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dsigmaidz = 0.0d0 |
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dsigmaidux = 0.0d0 |
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dsigmaiduy = 0.0d0 |
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dsigmaiduz = 0.0d0 |
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dsidx = 0.0d0 |
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dsidy = 0.0d0 |
246 |
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dsidz = 0.0d0 |
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dsidux = 0.0d0 |
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dsiduy = 0.0d0 |
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dsiduz = 0.0d0 |
250 |
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depsidx = 0.0d0 |
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depsidy = 0.0d0 |
252 |
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depsidz = 0.0d0 |
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depsidux = 0.0d0 |
254 |
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depsiduy = 0.0d0 |
255 |
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depsiduz = 0.0d0 |
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else |
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258 |
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#ifdef IS_MPI |
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! rotate the inter-particle separation into the two different |
260 |
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! body-fixed coordinate systems: |
261 |
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xi = A_row(1,atom1)*d(1) + A_row(2,atom1)*d(2) + A_row(3,atom1)*d(3) |
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yi = A_row(4,atom1)*d(1) + A_row(5,atom1)*d(2) + A_row(6,atom1)*d(3) |
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zi = A_row(7,atom1)*d(1) + A_row(8,atom1)*d(2) + A_row(9,atom1)*d(3) |
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266 |
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#else |
267 |
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! rotate the inter-particle separation into the two different |
268 |
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! body-fixed coordinate systems: |
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270 |
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xi = a(1,atom1)*d(1) + a(2,atom1)*d(2) + a(3,atom1)*d(3) |
271 |
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yi = a(4,atom1)*d(1) + a(5,atom1)*d(2) + a(6,atom1)*d(3) |
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zi = a(7,atom1)*d(1) + a(8,atom1)*d(2) + a(9,atom1)*d(3) |
273 |
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274 |
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#endif |
275 |
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276 |
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xi2 = xi*xi |
277 |
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yi2 = yi*yi |
278 |
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zi2 = zi*zi |
279 |
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280 |
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proji = sqrt(xi2 + yi2) |
281 |
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proji3 = proji*proji*proji |
282 |
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283 |
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cti = zi / rij |
284 |
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dctidx = - zi * xi / r3 |
285 |
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dctidy = - zi * yi / r3 |
286 |
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dctidz = 1.0d0 / rij - zi2 / r3 |
287 |
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dctidux = yi / rij |
288 |
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dctiduy = -xi / rij |
289 |
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dctiduz = 0.0d0 |
290 |
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291 |
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cpi = xi / proji |
292 |
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dcpidx = 1.0d0 / proji - xi2 / proji3 |
293 |
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dcpidy = - xi * yi / proji3 |
294 |
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dcpidz = 0.0d0 |
295 |
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dcpidux = xi * yi * zi / proji3 |
296 |
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dcpiduy = -zi * (1.0d0 / proji - xi2 / proji3) |
297 |
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dcpiduz = -yi * (1.0d0 / proji - xi2 / proji3) - (xi2 * yi / proji3) |
298 |
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299 |
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spi = yi / proji |
300 |
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dspidx = - xi * yi / proji3 |
301 |
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dspidy = 1.0d0 / proji - yi2 / proji3 |
302 |
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dspidz = 0.0d0 |
303 |
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dspidux = -zi * (1.0d0 / proji - yi2 / proji3) |
304 |
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dspiduy = xi * yi * zi / proji3 |
305 |
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dspiduz = xi * (1.0d0 / proji - yi2 / proji3) + (xi * yi2 / proji3) |
306 |
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307 |
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call Associated_Legendre(cti, ShapeMap(me1)%bigL, & |
308 |
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ShapeMap(me1)%bigM, lmax, plm_i, dlm_i) |
309 |
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310 |
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call Orthogonal_Polynomial(cpi, ShapeMap(me1)%bigM, CHEBYSHEV_TN, & |
311 |
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tm_i, dtm_i) |
312 |
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call Orthogonal_Polynomial(cpi, ShapeMap(me1)%bigM, CHEBYSHEV_UN, & |
313 |
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um_i, dum_i) |
314 |
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315 |
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sigma_i = 0.0d0 |
316 |
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s_i = 0.0d0 |
317 |
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eps_i = 0.0d0 |
318 |
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dsigmaidx = 0.0d0 |
319 |
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dsigmaidy = 0.0d0 |
320 |
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dsigmaidz = 0.0d0 |
321 |
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dsigmaidux = 0.0d0 |
322 |
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dsigmaiduy = 0.0d0 |
323 |
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dsigmaiduz = 0.0d0 |
324 |
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dsidx = 0.0d0 |
325 |
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dsidy = 0.0d0 |
326 |
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dsidz = 0.0d0 |
327 |
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dsidux = 0.0d0 |
328 |
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dsiduy = 0.0d0 |
329 |
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dsiduz = 0.0d0 |
330 |
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depsidx = 0.0d0 |
331 |
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depsidy = 0.0d0 |
332 |
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depsidz = 0.0d0 |
333 |
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depsidux = 0.0d0 |
334 |
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depsiduy = 0.0d0 |
335 |
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depsiduz = 0.0d0 |
336 |
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337 |
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do lm = 1, ShapeMap(me1)%nContactFuncs |
338 |
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l = ShapeMap(me1)%ContactFuncLValue(lm) |
339 |
|
|
m = ShapeMap(me1)%ContactFuncMValue(lm) |
340 |
|
|
coeff = ShapeMap(me1)%ContactFuncCoefficient(lm) |
341 |
|
|
function_type = ShapeMap(me1)%ContactFunctionType(lm) |
342 |
|
|
|
343 |
|
|
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
344 |
|
|
Phunc = coeff * tm_i(m) |
345 |
|
|
dPhuncdX = coeff * dtm_i(m) * dcpidx |
346 |
|
|
dPhuncdY = coeff * dtm_i(m) * dcpidy |
347 |
|
|
dPhuncdZ = coeff * dtm_i(m) * dcpidz |
348 |
|
|
dPhuncdUz = coeff * dtm_i(m) * dcpidux |
349 |
|
|
dPhuncdUy = coeff * dtm_i(m) * dcpiduy |
350 |
|
|
dPhuncdUz = coeff * dtm_i(m) * dcpiduz |
351 |
|
|
else |
352 |
|
|
Phunc = coeff * spi * um_i(m-1) |
353 |
|
|
dPhuncdX = coeff * (spi * dum_i(m-1) * dcpidx + dspidx *um_i(m-1)) |
354 |
|
|
dPhuncdY = coeff * (spi * dum_i(m-1) * dcpidy + dspidy *um_i(m-1)) |
355 |
|
|
dPhuncdZ = coeff * (spi * dum_i(m-1) * dcpidz + dspidz *um_i(m-1)) |
356 |
|
|
dPhuncdUx = coeff*(spi * dum_i(m-1)*dcpidux + dspidux *um_i(m-1)) |
357 |
|
|
dPhuncdUy = coeff*(spi * dum_i(m-1)*dcpiduy + dspiduy *um_i(m-1)) |
358 |
|
|
dPhuncdUz = coeff*(spi * dum_i(m-1)*dcpiduz + dspiduz *um_i(m-1)) |
359 |
|
|
endif |
360 |
|
|
|
361 |
|
|
sigma_i = sigma_i + plm_i(l,m)*Phunc |
362 |
|
|
|
363 |
|
|
dsigmaidx = dsigmaidx + plm_i(l,m)*dPhuncdX + & |
364 |
|
|
Phunc * dlm_i(l,m) * dctidx |
365 |
|
|
dsigmaidy = dsigmaidy + plm_i(l,m)*dPhuncdY + & |
366 |
|
|
Phunc * dlm_i(l,m) * dctidy |
367 |
|
|
dsigmaidz = dsigmaidz + plm_i(l,m)*dPhuncdZ + & |
368 |
|
|
Phunc * dlm_i(l,m) * dctidz |
369 |
|
|
|
370 |
|
|
dsigmaidux = dsigmaidux + plm_i(l,m)* dPhuncdUx + & |
371 |
|
|
Phunc * dlm_i(l,m) * dctidux |
372 |
|
|
dsigmaiduy = dsigmaiduy + plm_i(l,m)* dPhuncdUy + & |
373 |
|
|
Phunc * dlm_i(l,m) * dctiduy |
374 |
|
|
dsigmaiduz = dsigmaiduz + plm_i(l,m)* dPhuncdUz + & |
375 |
|
|
Phunc * dlm_i(l,m) * dctiduz |
376 |
|
|
|
377 |
|
|
end do |
378 |
|
|
|
379 |
|
|
do lm = 1, ShapeMap(me1)%nRangeFuncs |
380 |
|
|
l = ShapeMap(me1)%RangeFuncLValue(lm) |
381 |
|
|
m = ShapeMap(me1)%RangeFuncMValue(lm) |
382 |
|
|
coeff = ShapeMap(me1)%RangeFuncCoefficient(lm) |
383 |
|
|
function_type = ShapeMap(me1)%RangeFunctionType(lm) |
384 |
|
|
|
385 |
|
|
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
386 |
|
|
Phunc = coeff * tm_i(m) |
387 |
|
|
dPhuncdX = coeff * dtm_i(m) * dcpidx |
388 |
|
|
dPhuncdY = coeff * dtm_i(m) * dcpidy |
389 |
|
|
dPhuncdZ = coeff * dtm_i(m) * dcpidz |
390 |
|
|
dPhuncdUz = coeff * dtm_i(m) * dcpidux |
391 |
|
|
dPhuncdUy = coeff * dtm_i(m) * dcpiduy |
392 |
|
|
dPhuncdUz = coeff * dtm_i(m) * dcpiduz |
393 |
|
|
else |
394 |
|
|
Phunc = coeff * spi * um_i(m-1) |
395 |
|
|
dPhuncdX = coeff * (spi * dum_i(m-1) * dcpidx + dspidx *um_i(m-1)) |
396 |
|
|
dPhuncdY = coeff * (spi * dum_i(m-1) * dcpidy + dspidy *um_i(m-1)) |
397 |
|
|
dPhuncdZ = coeff * (spi * dum_i(m-1) * dcpidz + dspidz *um_i(m-1)) |
398 |
|
|
dPhuncdUx = coeff*(spi * dum_i(m-1)*dcpidux + dspidux *um_i(m-1)) |
399 |
|
|
dPhuncdUy = coeff*(spi * dum_i(m-1)*dcpiduy + dspiduy *um_i(m-1)) |
400 |
|
|
dPhuncdUz = coeff*(spi * dum_i(m-1)*dcpiduz + dspiduz *um_i(m-1)) |
401 |
|
|
endif |
402 |
|
|
|
403 |
|
|
s_i = s_i + plm_i(l,m)*Phunc |
404 |
|
|
|
405 |
|
|
dsidx = dsidx + plm_i(l,m)*dPhuncdX + & |
406 |
|
|
Phunc * dlm_i(l,m) * dctidx |
407 |
|
|
dsidy = dsidy + plm_i(l,m)*dPhuncdY + & |
408 |
|
|
Phunc * dlm_i(l,m) * dctidy |
409 |
|
|
dsidz = dsidz + plm_i(l,m)*dPhuncdZ + & |
410 |
|
|
Phunc * dlm_i(l,m) * dctidz |
411 |
|
|
|
412 |
|
|
dsidux = dsidux + plm_i(l,m)* dPhuncdUx + & |
413 |
|
|
Phunc * dlm_i(l,m) * dctidux |
414 |
|
|
dsiduy = dsiduy + plm_i(l,m)* dPhuncdUy + & |
415 |
|
|
Phunc * dlm_i(l,m) * dctiduy |
416 |
|
|
dsiduz = dsiduz + plm_i(l,m)* dPhuncdUz + & |
417 |
|
|
Phunc * dlm_i(l,m) * dctiduz |
418 |
|
|
|
419 |
|
|
end do |
420 |
|
|
|
421 |
|
|
do lm = 1, ShapeMap(me1)%nStrengthFuncs |
422 |
|
|
l = ShapeMap(me1)%StrengthFuncLValue(lm) |
423 |
|
|
m = ShapeMap(me1)%StrengthFuncMValue(lm) |
424 |
|
|
coeff = ShapeMap(me1)%StrengthFuncCoefficient(lm) |
425 |
|
|
function_type = ShapeMap(me1)%StrengthFunctionType(lm) |
426 |
|
|
|
427 |
|
|
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
428 |
|
|
Phunc = coeff * tm_i(m) |
429 |
|
|
dPhuncdX = coeff * dtm_i(m) * dcpidx |
430 |
|
|
dPhuncdY = coeff * dtm_i(m) * dcpidy |
431 |
|
|
dPhuncdZ = coeff * dtm_i(m) * dcpidz |
432 |
|
|
dPhuncdUz = coeff * dtm_i(m) * dcpidux |
433 |
|
|
dPhuncdUy = coeff * dtm_i(m) * dcpiduy |
434 |
|
|
dPhuncdUz = coeff * dtm_i(m) * dcpiduz |
435 |
|
|
else |
436 |
|
|
Phunc = coeff * spi * um_i(m-1) |
437 |
|
|
dPhuncdX = coeff * (spi * dum_i(m-1) * dcpidx + dspidx *um_i(m-1)) |
438 |
|
|
dPhuncdY = coeff * (spi * dum_i(m-1) * dcpidy + dspidy *um_i(m-1)) |
439 |
|
|
dPhuncdZ = coeff * (spi * dum_i(m-1) * dcpidz + dspidz *um_i(m-1)) |
440 |
|
|
dPhuncdUx = coeff*(spi * dum_i(m-1)*dcpidux + dspidux *um_i(m-1)) |
441 |
|
|
dPhuncdUy = coeff*(spi * dum_i(m-1)*dcpiduy + dspiduy *um_i(m-1)) |
442 |
|
|
dPhuncdUz = coeff*(spi * dum_i(m-1)*dcpiduz + dspiduz *um_i(m-1)) |
443 |
|
|
endif |
444 |
|
|
|
445 |
|
|
eps_i = eps_i + plm_i(l,m)*Phunc |
446 |
|
|
|
447 |
|
|
depsidx = depsidx + plm_i(l,m)*dPhuncdX + & |
448 |
|
|
Phunc * dlm_i(l,m) * dctidx |
449 |
|
|
depsidy = depsidy + plm_i(l,m)*dPhuncdY + & |
450 |
|
|
Phunc * dlm_i(l,m) * dctidy |
451 |
|
|
depsidz = depsidz + plm_i(l,m)*dPhuncdZ + & |
452 |
|
|
Phunc * dlm_i(l,m) * dctidz |
453 |
|
|
|
454 |
|
|
depsidux = depsidux + plm_i(l,m)* dPhuncdUx + & |
455 |
|
|
Phunc * dlm_i(l,m) * dctidux |
456 |
|
|
depsiduy = depsiduy + plm_i(l,m)* dPhuncdUy + & |
457 |
|
|
Phunc * dlm_i(l,m) * dctiduy |
458 |
|
|
depsiduz = depsiduz + plm_i(l,m)* dPhuncdUz + & |
459 |
|
|
Phunc * dlm_i(l,m) * dctiduz |
460 |
|
|
|
461 |
|
|
end do |
462 |
|
|
|
463 |
|
|
endif |
464 |
|
|
|
465 |
|
|
! now do j: |
466 |
|
|
|
467 |
|
|
if (ShapeMap(me2)%isLJ) then |
468 |
|
|
sigma_j = ShapeMap(me2)%sigma |
469 |
|
|
s_j = ShapeMap(me2)%sigma |
470 |
|
|
eps_j = ShapeMap(me2)%epsilon |
471 |
|
|
dsigmajdx = 0.0d0 |
472 |
|
|
dsigmajdy = 0.0d0 |
473 |
|
|
dsigmajdz = 0.0d0 |
474 |
|
|
dsigmajdux = 0.0d0 |
475 |
|
|
dsigmajduy = 0.0d0 |
476 |
|
|
dsigmajduz = 0.0d0 |
477 |
|
|
dsjdx = 0.0d0 |
478 |
|
|
dsjdy = 0.0d0 |
479 |
|
|
dsjdz = 0.0d0 |
480 |
|
|
dsjdux = 0.0d0 |
481 |
|
|
dsjduy = 0.0d0 |
482 |
|
|
dsjduz = 0.0d0 |
483 |
|
|
depsjdx = 0.0d0 |
484 |
|
|
depsjdy = 0.0d0 |
485 |
|
|
depsjdz = 0.0d0 |
486 |
|
|
depsjdux = 0.0d0 |
487 |
|
|
depsjduy = 0.0d0 |
488 |
|
|
depsjduz = 0.0d0 |
489 |
|
|
else |
490 |
|
|
|
491 |
|
|
#ifdef IS_MPI |
492 |
|
|
! rotate the inter-particle separation into the two different |
493 |
|
|
! body-fixed coordinate systems: |
494 |
|
|
! negative sign because this is the vector from j to i: |
495 |
|
|
|
496 |
|
|
xj = -(A_Col(1,atom2)*d(1) + A_Col(2,atom2)*d(2) + A_Col(3,atom2)*d(3)) |
497 |
|
|
yj = -(A_Col(4,atom2)*d(1) + A_Col(5,atom2)*d(2) + A_Col(6,atom2)*d(3)) |
498 |
|
|
zj = -(A_Col(7,atom2)*d(1) + A_Col(8,atom2)*d(2) + A_Col(9,atom2)*d(3)) |
499 |
|
|
#else |
500 |
|
|
! rotate the inter-particle separation into the two different |
501 |
|
|
! body-fixed coordinate systems: |
502 |
|
|
! negative sign because this is the vector from j to i: |
503 |
|
|
|
504 |
|
|
xj = -(a(1,atom2)*d(1) + a(2,atom2)*d(2) + a(3,atom2)*d(3)) |
505 |
|
|
yj = -(a(4,atom2)*d(1) + a(5,atom2)*d(2) + a(6,atom2)*d(3)) |
506 |
|
|
zj = -(a(7,atom2)*d(1) + a(8,atom2)*d(2) + a(9,atom2)*d(3)) |
507 |
|
|
#endif |
508 |
|
|
|
509 |
|
|
xj2 = xj*xj |
510 |
|
|
yj2 = yj*yj |
511 |
|
|
zj2 = zj*zj |
512 |
|
|
|
513 |
|
|
projj = sqrt(xj2 + yj2) |
514 |
|
|
projj3 = projj*projj*projj |
515 |
|
|
|
516 |
|
|
ctj = zj / rij |
517 |
|
|
dctjdx = - zj * xj / r3 |
518 |
|
|
dctjdy = - zj * yj / r3 |
519 |
|
|
dctjdz = 1.0d0 / rij - zj2 / r3 |
520 |
|
|
dctjdux = yj / rij |
521 |
|
|
dctjduy = -xj / rij |
522 |
|
|
dctjduz = 0.0d0 |
523 |
|
|
|
524 |
|
|
cpj = xj / projj |
525 |
|
|
dcpjdx = 1.0d0 / projj - xj2 / projj3 |
526 |
|
|
dcpjdy = - xj * yj / projj3 |
527 |
|
|
dcpjdz = 0.0d0 |
528 |
|
|
dcpjdux = xj * yj * zj / projj3 |
529 |
|
|
dcpjduy = -zj * (1.0d0 / projj - xj2 / projj3) |
530 |
|
|
dcpjduz = -yj * (1.0d0 / projj - xj2 / projj3) - (xj2 * yj / projj3) |
531 |
|
|
|
532 |
|
|
spj = yj / projj |
533 |
|
|
dspjdx = - xj * yj / projj3 |
534 |
|
|
dspjdy = 1.0d0 / projj - yj2 / projj3 |
535 |
|
|
dspjdz = 0.0d0 |
536 |
|
|
dspjdux = -zj * (1.0d0 / projj - yj2 / projj3) |
537 |
|
|
dspjduy = xj * yj * zj / projj3 |
538 |
|
|
dspjduz = xj * (1.0d0 / projj - yi2 / projj3) + (xj * yj2 / projj3) |
539 |
|
|
|
540 |
|
|
call Associated_Legendre(ctj, ShapeMap(me2)%bigL, & |
541 |
|
|
ShapeMap(me2)%bigM, lmax, plm_j, dlm_j) |
542 |
|
|
|
543 |
|
|
call Orthogonal_Polynomial(cpj, ShapeMap(me2)%bigM, CHEBYSHEV_TN, & |
544 |
|
|
tm_j, dtm_j) |
545 |
|
|
call Orthogonal_Polynomial(cpj, ShapeMap(me2)%bigM, CHEBYSHEV_UN, & |
546 |
|
|
um_j, dum_j) |
547 |
|
|
|
548 |
|
|
sigma_j = 0.0d0 |
549 |
|
|
s_j = 0.0d0 |
550 |
|
|
eps_j = 0.0d0 |
551 |
|
|
dsigmajdx = 0.0d0 |
552 |
|
|
dsigmajdy = 0.0d0 |
553 |
|
|
dsigmajdz = 0.0d0 |
554 |
|
|
dsigmajdux = 0.0d0 |
555 |
|
|
dsigmajduy = 0.0d0 |
556 |
|
|
dsigmajduz = 0.0d0 |
557 |
|
|
dsjdx = 0.0d0 |
558 |
|
|
dsjdy = 0.0d0 |
559 |
|
|
dsjdz = 0.0d0 |
560 |
|
|
dsjdux = 0.0d0 |
561 |
|
|
dsjduy = 0.0d0 |
562 |
|
|
dsjduz = 0.0d0 |
563 |
|
|
depsjdx = 0.0d0 |
564 |
|
|
depsjdy = 0.0d0 |
565 |
|
|
depsjdz = 0.0d0 |
566 |
|
|
depsjdux = 0.0d0 |
567 |
|
|
depsjduy = 0.0d0 |
568 |
|
|
depsjduz = 0.0d0 |
569 |
|
|
|
570 |
|
|
do lm = 1, ShapeMap(me2)%nContactFuncs |
571 |
|
|
l = ShapeMap(me2)%ContactFuncLValue(lm) |
572 |
|
|
m = ShapeMap(me2)%ContactFuncMValue(lm) |
573 |
|
|
coeff = ShapeMap(me2)%ContactFuncCoefficient(lm) |
574 |
|
|
function_type = ShapeMap(me2)%ContactFunctionType(lm) |
575 |
|
|
|
576 |
|
|
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
577 |
|
|
Phunc = coeff * tm_j(m) |
578 |
|
|
dPhuncdX = coeff * dtm_j(m) * dcpjdx |
579 |
|
|
dPhuncdY = coeff * dtm_j(m) * dcpjdy |
580 |
|
|
dPhuncdZ = coeff * dtm_j(m) * dcpjdz |
581 |
|
|
dPhuncdUz = coeff * dtm_j(m) * dcpjdux |
582 |
|
|
dPhuncdUy = coeff * dtm_j(m) * dcpjduy |
583 |
|
|
dPhuncdUz = coeff * dtm_j(m) * dcpjduz |
584 |
|
|
else |
585 |
|
|
Phunc = coeff * spj * um_j(m-1) |
586 |
|
|
dPhuncdX = coeff * (spj * dum_j(m-1) * dcpjdx + dspjdx *um_j(m-1)) |
587 |
|
|
dPhuncdY = coeff * (spj * dum_j(m-1) * dcpjdy + dspjdy *um_j(m-1)) |
588 |
|
|
dPhuncdZ = coeff * (spj * dum_j(m-1) * dcpjdz + dspjdz *um_j(m-1)) |
589 |
|
|
dPhuncdUx = coeff*(spj * dum_j(m-1)*dcpjdux + dspjdux *um_j(m-1)) |
590 |
|
|
dPhuncdUy = coeff*(spj * dum_j(m-1)*dcpjduy + dspjduy *um_j(m-1)) |
591 |
|
|
dPhuncdUz = coeff*(spj * dum_j(m-1)*dcpjduz + dspjduz *um_j(m-1)) |
592 |
|
|
endif |
593 |
|
|
|
594 |
|
|
sigma_j = sigma_j + plm_j(l,m)*Phunc |
595 |
|
|
|
596 |
|
|
dsigmajdx = dsigmajdx + plm_j(l,m)*dPhuncdX + & |
597 |
|
|
Phunc * dlm_j(l,m) * dctjdx |
598 |
|
|
dsigmajdy = dsigmajdy + plm_j(l,m)*dPhuncdY + & |
599 |
|
|
Phunc * dlm_j(l,m) * dctjdy |
600 |
|
|
dsigmajdz = dsigmajdz + plm_j(l,m)*dPhuncdZ + & |
601 |
|
|
Phunc * dlm_j(l,m) * dctjdz |
602 |
|
|
|
603 |
|
|
dsigmajdux = dsigmajdux + plm_j(l,m)* dPhuncdUx + & |
604 |
|
|
Phunc * dlm_j(l,m) * dctjdux |
605 |
|
|
dsigmajduy = dsigmajduy + plm_j(l,m)* dPhuncdUy + & |
606 |
|
|
Phunc * dlm_j(l,m) * dctjduy |
607 |
|
|
dsigmajduz = dsigmajduz + plm_j(l,m)* dPhuncdUz + & |
608 |
|
|
Phunc * dlm_j(l,m) * dctjduz |
609 |
|
|
|
610 |
|
|
end do |
611 |
|
|
|
612 |
|
|
do lm = 1, ShapeMap(me2)%nRangeFuncs |
613 |
|
|
l = ShapeMap(me2)%RangeFuncLValue(lm) |
614 |
|
|
m = ShapeMap(me2)%RangeFuncMValue(lm) |
615 |
|
|
coeff = ShapeMap(me2)%RangeFuncCoefficient(lm) |
616 |
|
|
function_type = ShapeMap(me2)%RangeFunctionType(lm) |
617 |
|
|
|
618 |
|
|
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
619 |
|
|
Phunc = coeff * tm_j(m) |
620 |
|
|
dPhuncdX = coeff * dtm_j(m) * dcpjdx |
621 |
|
|
dPhuncdY = coeff * dtm_j(m) * dcpjdy |
622 |
|
|
dPhuncdZ = coeff * dtm_j(m) * dcpjdz |
623 |
|
|
dPhuncdUz = coeff * dtm_j(m) * dcpjdux |
624 |
|
|
dPhuncdUy = coeff * dtm_j(m) * dcpjduy |
625 |
|
|
dPhuncdUz = coeff * dtm_j(m) * dcpjduz |
626 |
|
|
else |
627 |
|
|
Phunc = coeff * spj * um_j(m-1) |
628 |
|
|
dPhuncdX = coeff * (spj * dum_j(m-1) * dcpjdx + dspjdx *um_j(m-1)) |
629 |
|
|
dPhuncdY = coeff * (spj * dum_j(m-1) * dcpjdy + dspjdy *um_j(m-1)) |
630 |
|
|
dPhuncdZ = coeff * (spj * dum_j(m-1) * dcpjdz + dspjdz *um_j(m-1)) |
631 |
|
|
dPhuncdUx = coeff*(spj * dum_j(m-1)*dcpjdux + dspjdux *um_j(m-1)) |
632 |
|
|
dPhuncdUy = coeff*(spj * dum_j(m-1)*dcpjduy + dspjduy *um_j(m-1)) |
633 |
|
|
dPhuncdUz = coeff*(spj * dum_j(m-1)*dcpjduz + dspjduz *um_j(m-1)) |
634 |
|
|
endif |
635 |
|
|
|
636 |
|
|
s_j = s_j + plm_j(l,m)*Phunc |
637 |
|
|
|
638 |
|
|
dsjdx = dsjdx + plm_j(l,m)*dPhuncdX + & |
639 |
|
|
Phunc * dlm_j(l,m) * dctjdx |
640 |
|
|
dsjdy = dsjdy + plm_j(l,m)*dPhuncdY + & |
641 |
|
|
Phunc * dlm_j(l,m) * dctjdy |
642 |
|
|
dsjdz = dsjdz + plm_j(l,m)*dPhuncdZ + & |
643 |
|
|
Phunc * dlm_j(l,m) * dctjdz |
644 |
|
|
|
645 |
|
|
dsjdux = dsjdux + plm_j(l,m)* dPhuncdUx + & |
646 |
|
|
Phunc * dlm_j(l,m) * dctjdux |
647 |
|
|
dsjduy = dsjduy + plm_j(l,m)* dPhuncdUy + & |
648 |
|
|
Phunc * dlm_j(l,m) * dctjduy |
649 |
|
|
dsjduz = dsjduz + plm_j(l,m)* dPhuncdUz + & |
650 |
|
|
Phunc * dlm_j(l,m) * dctjduz |
651 |
|
|
|
652 |
|
|
end do |
653 |
|
|
|
654 |
|
|
do lm = 1, ShapeMap(me2)%nStrengthFuncs |
655 |
|
|
l = ShapeMap(me2)%StrengthFuncLValue(lm) |
656 |
|
|
m = ShapeMap(me2)%StrengthFuncMValue(lm) |
657 |
|
|
coeff = ShapeMap(me2)%StrengthFuncCoefficient(lm) |
658 |
|
|
function_type = ShapeMap(me2)%StrengthFunctionType(lm) |
659 |
|
|
|
660 |
|
|
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
661 |
|
|
Phunc = coeff * tm_j(m) |
662 |
|
|
dPhuncdX = coeff * dtm_j(m) * dcpjdx |
663 |
|
|
dPhuncdY = coeff * dtm_j(m) * dcpjdy |
664 |
|
|
dPhuncdZ = coeff * dtm_j(m) * dcpjdz |
665 |
|
|
dPhuncdUz = coeff * dtm_j(m) * dcpjdux |
666 |
|
|
dPhuncdUy = coeff * dtm_j(m) * dcpjduy |
667 |
|
|
dPhuncdUz = coeff * dtm_j(m) * dcpjduz |
668 |
|
|
else |
669 |
|
|
Phunc = coeff * spj * um_j(m-1) |
670 |
|
|
dPhuncdX = coeff * (spj * dum_j(m-1) * dcpjdx + dspjdx *um_j(m-1)) |
671 |
|
|
dPhuncdY = coeff * (spj * dum_j(m-1) * dcpjdy + dspjdy *um_j(m-1)) |
672 |
|
|
dPhuncdZ = coeff * (spj * dum_j(m-1) * dcpjdz + dspjdz *um_j(m-1)) |
673 |
|
|
dPhuncdUx = coeff*(spj * dum_j(m-1)*dcpjdux + dspjdux *um_j(m-1)) |
674 |
|
|
dPhuncdUy = coeff*(spj * dum_j(m-1)*dcpjduy + dspjduy *um_j(m-1)) |
675 |
|
|
dPhuncdUz = coeff*(spj * dum_j(m-1)*dcpjduz + dspjduz *um_j(m-1)) |
676 |
|
|
endif |
677 |
|
|
|
678 |
|
|
eps_j = eps_j + plm_j(l,m)*Phunc |
679 |
|
|
|
680 |
|
|
depsjdx = depsjdx + plm_j(l,m)*dPhuncdX + & |
681 |
|
|
Phunc * dlm_j(l,m) * dctjdx |
682 |
|
|
depsjdy = depsjdy + plm_j(l,m)*dPhuncdY + & |
683 |
|
|
Phunc * dlm_j(l,m) * dctjdy |
684 |
|
|
depsjdz = depsjdz + plm_j(l,m)*dPhuncdZ + & |
685 |
|
|
Phunc * dlm_j(l,m) * dctjdz |
686 |
|
|
|
687 |
|
|
depsjdux = depsjdux + plm_j(l,m)* dPhuncdUx + & |
688 |
|
|
Phunc * dlm_j(l,m) * dctjdux |
689 |
|
|
depsjduy = depsjduy + plm_j(l,m)* dPhuncdUy + & |
690 |
|
|
Phunc * dlm_j(l,m) * dctjduy |
691 |
|
|
depsjduz = depsjduz + plm_j(l,m)* dPhuncdUz + & |
692 |
|
|
Phunc * dlm_j(l,m) * dctjduz |
693 |
|
|
|
694 |
|
|
end do |
695 |
|
|
|
696 |
|
|
endif |
697 |
|
|
|
698 |
|
|
! phew, now let's assemble the potential energy: |
699 |
|
|
|
700 |
|
|
sigma = 0.5*(sigma_i + sigma_j) |
701 |
|
|
|
702 |
|
|
dsigmadxi = 0.5*dsigmaidx |
703 |
|
|
dsigmadyi = 0.5*dsigmaidy |
704 |
|
|
dsigmadzi = 0.5*dsigmaidz |
705 |
|
|
dsigmaduxi = 0.5*dsigmaidux |
706 |
|
|
dsigmaduyi = 0.5*dsigmaiduy |
707 |
|
|
dsigmaduzi = 0.5*dsigmaiduz |
708 |
|
|
|
709 |
|
|
dsigmadxj = 0.5*dsigmajdx |
710 |
|
|
dsigmadyj = 0.5*dsigmajdy |
711 |
|
|
dsigmadzj = 0.5*dsigmajdz |
712 |
|
|
dsigmaduxj = 0.5*dsigmajdux |
713 |
|
|
dsigmaduyj = 0.5*dsigmajduy |
714 |
|
|
dsigmaduzj = 0.5*dsigmajduz |
715 |
|
|
|
716 |
|
|
s = 0.5*(s_i + s_j) |
717 |
|
|
|
718 |
|
|
dsdxi = 0.5*dsidx |
719 |
|
|
dsdyi = 0.5*dsidy |
720 |
|
|
dsdzi = 0.5*dsidz |
721 |
|
|
dsduxi = 0.5*dsidux |
722 |
|
|
dsduyi = 0.5*dsiduy |
723 |
|
|
dsduzi = 0.5*dsiduz |
724 |
|
|
|
725 |
|
|
dsdxj = 0.5*dsjdx |
726 |
|
|
dsdyj = 0.5*dsjdy |
727 |
|
|
dsdzj = 0.5*dsjdz |
728 |
|
|
dsduxj = 0.5*dsjdux |
729 |
|
|
dsduyj = 0.5*dsjduy |
730 |
|
|
dsduzj = 0.5*dsjduz |
731 |
|
|
|
732 |
|
|
eps = sqrt(eps_i * eps_j) |
733 |
|
|
|
734 |
|
|
depsdxi = eps_j * depsidx / (2.0d0 * eps) |
735 |
|
|
depsdyi = eps_j * depsidy / (2.0d0 * eps) |
736 |
|
|
depsdzi = eps_j * depsidz / (2.0d0 * eps) |
737 |
|
|
depsduxi = eps_j * depsidux / (2.0d0 * eps) |
738 |
|
|
depsduyi = eps_j * depsiduy / (2.0d0 * eps) |
739 |
|
|
depsduzi = eps_j * depsiduz / (2.0d0 * eps) |
740 |
|
|
|
741 |
|
|
depsdxj = eps_i * depsjdx / (2.0d0 * eps) |
742 |
|
|
depsdyj = eps_i * depsjdy / (2.0d0 * eps) |
743 |
|
|
depsdzj = eps_i * depsjdz / (2.0d0 * eps) |
744 |
|
|
depsduxj = eps_i * depsjdux / (2.0d0 * eps) |
745 |
|
|
depsduyj = eps_i * depsjduy / (2.0d0 * eps) |
746 |
|
|
depsduzj = eps_i * depsjduz / (2.0d0 * eps) |
747 |
|
|
|
748 |
|
|
rtdenom = rij-sigma+s |
749 |
|
|
rt = s / rtdenom |
750 |
|
|
|
751 |
|
|
drtdxi = (dsdxi + rt * (drdxi - dsigmadxi + dsdxi)) / rtdenom |
752 |
|
|
drtdyi = (dsdyi + rt * (drdyi - dsigmadyi + dsdyi)) / rtdenom |
753 |
|
|
drtdzi = (dsdzi + rt * (drdzi - dsigmadzi + dsdzi)) / rtdenom |
754 |
|
|
drtduxi = (dsduxi + rt * (drduxi - dsigmaduxi + dsduxi)) / rtdenom |
755 |
|
|
drtduyi = (dsduyi + rt * (drduyi - dsigmaduyi + dsduyi)) / rtdenom |
756 |
|
|
drtduzi = (dsduzi + rt * (drduzi - dsigmaduzi + dsduzi)) / rtdenom |
757 |
|
|
drtdxj = (dsdxj + rt * (drdxj - dsigmadxj + dsdxj)) / rtdenom |
758 |
|
|
drtdyj = (dsdyj + rt * (drdyj - dsigmadyj + dsdyj)) / rtdenom |
759 |
|
|
drtdzj = (dsdzj + rt * (drdzj - dsigmadzj + dsdzj)) / rtdenom |
760 |
|
|
drtduxj = (dsduxj + rt * (drduxj - dsigmaduxj + dsduxj)) / rtdenom |
761 |
|
|
drtduyj = (dsduyj + rt * (drduyj - dsigmaduyj + dsduyj)) / rtdenom |
762 |
|
|
drtduzj = (dsduzj + rt * (drduzj - dsigmaduzj + dsduzj)) / rtdenom |
763 |
|
|
|
764 |
|
|
rt2 = rt*rt |
765 |
|
|
rt3 = rt2*rt |
766 |
|
|
rt5 = rt2*rt3 |
767 |
|
|
rt6 = rt3*rt3 |
768 |
|
|
rt11 = rt5*rt6 |
769 |
|
|
rt12 = rt6*rt6 |
770 |
|
|
rt126 = rt12 - rt6 |
771 |
|
|
|
772 |
|
|
if (do_pot) then |
773 |
|
|
#ifdef IS_MPI |
774 |
|
|
pot_row(atom1) = pot_row(atom1) + 2.0d0*eps*rt126*sw |
775 |
|
|
pot_col(atom2) = pot_col(atom2) + 2.0d0*eps*rt126*sw |
776 |
|
|
#else |
777 |
|
|
pot = pot + 4.0d0*eps*rt126*sw |
778 |
|
|
#endif |
779 |
|
|
endif |
780 |
|
|
|
781 |
|
|
dvdxi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdxi + 4.0d0*depsdxi*rt126 |
782 |
|
|
dvdyi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdyi + 4.0d0*depsdyi*rt126 |
783 |
|
|
dvdzi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdzi + 4.0d0*depsdzi*rt126 |
784 |
|
|
dvduxi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduxi + 4.0d0*depsduxi*rt126 |
785 |
|
|
dvduyi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduyi + 4.0d0*depsduyi*rt126 |
786 |
|
|
dvduzi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduzi + 4.0d0*depsduzi*rt126 |
787 |
|
|
|
788 |
|
|
dvdxj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdxj + 4.0d0*depsdxj*rt126 |
789 |
|
|
dvdyj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdyj + 4.0d0*depsdyj*rt126 |
790 |
|
|
dvdzj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdzj + 4.0d0*depsdzj*rt126 |
791 |
|
|
dvduxj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduxj + 4.0d0*depsduxj*rt126 |
792 |
|
|
dvduyj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduyj + 4.0d0*depsduyj*rt126 |
793 |
|
|
dvduzj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduzj + 4.0d0*depsduzj*rt126 |
794 |
|
|
|
795 |
|
|
! do the torques first since they are easy: |
796 |
|
|
! remember that these are still in the body fixed axes |
797 |
|
|
|
798 |
|
|
txi = dvduxi * sw |
799 |
|
|
tyi = dvduyi * sw |
800 |
|
|
tzi = dvduzi * sw |
801 |
|
|
|
802 |
|
|
txj = dvduxj * sw |
803 |
|
|
tyj = dvduyj * sw |
804 |
|
|
tzj = dvduzj * sw |
805 |
|
|
|
806 |
|
|
! go back to lab frame using transpose of rotation matrix: |
807 |
|
|
|
808 |
|
|
#ifdef IS_MPI |
809 |
|
|
t_Row(1,atom1) = t_Row(1,atom1) + a_Row(1,atom1)*txi + & |
810 |
|
|
a_Row(4,atom1)*tyi + a_Row(7,atom1)*tzi |
811 |
|
|
t_Row(2,atom1) = t_Row(2,atom1) + a_Row(2,atom1)*txi + & |
812 |
|
|
a_Row(5,atom1)*tyi + a_Row(8,atom1)*tzi |
813 |
|
|
t_Row(3,atom1) = t_Row(3,atom1) + a_Row(3,atom1)*txi + & |
814 |
|
|
a_Row(6,atom1)*tyi + a_Row(9,atom1)*tzi |
815 |
|
|
|
816 |
|
|
t_Col(1,atom2) = t_Col(1,atom2) + a_Col(1,atom2)*txj + & |
817 |
|
|
a_Col(4,atom2)*tyj + a_Col(7,atom2)*tzj |
818 |
|
|
t_Col(2,atom2) = t_Col(2,atom2) + a_Col(2,atom2)*txj + & |
819 |
|
|
a_Col(5,atom2)*tyj + a_Col(8,atom2)*tzj |
820 |
|
|
t_Col(3,atom2) = t_Col(3,atom2) + a_Col(3,atom2)*txj + & |
821 |
|
|
a_Col(6,atom2)*tyj + a_Col(9,atom2)*tzj |
822 |
|
|
#else |
823 |
|
|
t(1,atom1) = t(1,atom1) + a(1,atom1)*txi + a(4,atom1)*tyi + a(7,atom1)*tzi |
824 |
|
|
t(2,atom1) = t(2,atom1) + a(2,atom1)*txi + a(5,atom1)*tyi + a(8,atom1)*tzi |
825 |
|
|
t(3,atom1) = t(3,atom1) + a(3,atom1)*txi + a(6,atom1)*tyi + a(9,atom1)*tzi |
826 |
|
|
|
827 |
|
|
t(1,atom2) = t(1,atom2) + a(1,atom2)*txj + a(4,atom2)*tyj + a(7,atom2)*tzj |
828 |
|
|
t(2,atom2) = t(2,atom2) + a(2,atom2)*txj + a(5,atom2)*tyj + a(8,atom2)*tzj |
829 |
|
|
t(3,atom2) = t(3,atom2) + a(3,atom2)*txj + a(6,atom2)*tyj + a(9,atom2)*tzj |
830 |
|
|
#endif |
831 |
|
|
! Now, on to the forces: |
832 |
|
|
|
833 |
|
|
! first rotate the i terms back into the lab frame: |
834 |
|
|
|
835 |
|
|
fxi = dvdxi * sw |
836 |
|
|
fyi = dvdyi * sw |
837 |
|
|
fzi = dvdzi * sw |
838 |
|
|
|
839 |
|
|
fxj = dvdxj * sw |
840 |
|
|
fyj = dvdyj * sw |
841 |
|
|
fzj = dvdzj * sw |
842 |
|
|
|
843 |
|
|
#ifdef IS_MPI |
844 |
|
|
fxii = a_Row(1,atom1)*fxi + a_Row(4,atom1)*fyi + a_Row(7,atom1)*fzi |
845 |
|
|
fyii = a_Row(2,atom1)*fxi + a_Row(5,atom1)*fyi + a_Row(8,atom1)*fzi |
846 |
|
|
fzii = a_Row(3,atom1)*fxi + a_Row(6,atom1)*fyi + a_Row(9,atom1)*fzi |
847 |
|
|
|
848 |
|
|
fxjj = a_Col(1,atom2)*fxj + a_Col(4,atom2)*fyj + a_Col(7,atom2)*fzj |
849 |
|
|
fyjj = a_Col(2,atom2)*fxj + a_Col(5,atom2)*fyj + a_Col(8,atom2)*fzj |
850 |
|
|
fzjj = a_Col(3,atom2)*fxj + a_Col(6,atom2)*fyj + a_Col(9,atom2)*fzj |
851 |
|
|
#else |
852 |
|
|
fxii = a(1,atom1)*fxi + a(4,atom1)*fyi + a(7,atom1)*fzi |
853 |
|
|
fyii = a(2,atom1)*fxi + a(5,atom1)*fyi + a(8,atom1)*fzi |
854 |
|
|
fzii = a(3,atom1)*fxi + a(6,atom1)*fyi + a(9,atom1)*fzi |
855 |
|
|
|
856 |
|
|
fxjj = a(1,atom2)*fxj + a(4,atom2)*fyj + a(7,atom2)*fzj |
857 |
|
|
fyjj = a(2,atom2)*fxj + a(5,atom2)*fyj + a(8,atom2)*fzj |
858 |
|
|
fzjj = a(3,atom2)*fxj + a(6,atom2)*fyj + a(9,atom2)*fzj |
859 |
|
|
#endif |
860 |
|
|
|
861 |
|
|
fxij = -fxii |
862 |
|
|
fyij = -fyii |
863 |
|
|
fzij = -fzii |
864 |
|
|
|
865 |
|
|
fxji = -fxjj |
866 |
|
|
fyji = -fyjj |
867 |
|
|
fzji = -fzjj |
868 |
|
|
|
869 |
|
|
fxradial = fxii + fxji |
870 |
|
|
fyradial = fyii + fyji |
871 |
|
|
fzradial = fzii + fzji |
872 |
|
|
|
873 |
|
|
#ifdef IS_MPI |
874 |
|
|
f_Row(1,atom1) = f_Row(1,atom1) + fxradial |
875 |
|
|
f_Row(2,atom1) = f_Row(2,atom1) + fyradial |
876 |
|
|
f_Row(3,atom1) = f_Row(3,atom1) + fzradial |
877 |
|
|
|
878 |
|
|
f_Col(1,atom2) = f_Col(1,atom2) - fxradial |
879 |
|
|
f_Col(2,atom2) = f_Col(2,atom2) - fyradial |
880 |
|
|
f_Col(3,atom2) = f_Col(3,atom2) - fzradial |
881 |
|
|
#else |
882 |
|
|
f(1,atom1) = f(1,atom1) + fxradial |
883 |
|
|
f(2,atom1) = f(2,atom1) + fyradial |
884 |
|
|
f(3,atom1) = f(3,atom1) + fzradial |
885 |
|
|
|
886 |
|
|
f(1,atom2) = f(1,atom2) - fxradial |
887 |
|
|
f(2,atom2) = f(2,atom2) - fyradial |
888 |
|
|
f(3,atom2) = f(3,atom2) - fzradial |
889 |
|
|
#endif |
890 |
|
|
|
891 |
|
|
#ifdef IS_MPI |
892 |
|
|
id1 = AtomRowToGlobal(atom1) |
893 |
|
|
id2 = AtomColToGlobal(atom2) |
894 |
|
|
#else |
895 |
|
|
id1 = atom1 |
896 |
|
|
id2 = atom2 |
897 |
|
|
#endif |
898 |
|
|
|
899 |
|
|
if (molMembershipList(id1) .ne. molMembershipList(id2)) then |
900 |
|
|
|
901 |
|
|
fpair(1) = fpair(1) + fxradial |
902 |
|
|
fpair(2) = fpair(2) + fyradial |
903 |
|
|
fpair(3) = fpair(3) + fzradial |
904 |
|
|
|
905 |
|
|
endif |
906 |
|
|
|
907 |
|
|
end subroutine do_shape_pair |
908 |
|
|
|
909 |
|
|
SUBROUTINE Associated_Legendre(x, l, m, lmax, plm, dlm) |
910 |
|
|
|
911 |
|
|
! Purpose: Compute the associated Legendre functions |
912 |
|
|
! Plm(x) and their derivatives Plm'(x) |
913 |
|
|
! Input : x --- Argument of Plm(x) |
914 |
|
|
! l --- Order of Plm(x), l = 0,1,2,...,n |
915 |
|
|
! m --- Degree of Plm(x), m = 0,1,2,...,N |
916 |
|
|
! lmax --- Physical dimension of PLM and DLM |
917 |
|
|
! Output: PLM(l,m) --- Plm(x) |
918 |
|
|
! DLM(l,m) --- Plm'(x) |
919 |
|
|
! |
920 |
|
|
! adapted from the routines in |
921 |
|
|
! COMPUTATION OF SPECIAL FUNCTIONS by Shanjie Zhang and Jianming Jin |
922 |
|
|
! ISBN 0-471-11963-6 |
923 |
|
|
! |
924 |
|
|
! The original Fortran77 codes can be found here: |
925 |
|
|
! http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html |
926 |
|
|
|
927 |
|
|
real (kind=8), intent(in) :: x |
928 |
|
|
integer, intent(in) :: l, m, lmax |
929 |
|
|
real (kind=8), dimension(0:lmax,0:m), intent(out) :: PLM, DLM |
930 |
|
|
integer :: i, j, ls |
931 |
|
|
real (kind=8) :: xq, xs |
932 |
|
|
|
933 |
|
|
! zero out both arrays: |
934 |
|
|
DO I = 0, m |
935 |
|
|
DO J = 0, l |
936 |
|
|
PLM(J,I) = 0.0D0 |
937 |
|
|
DLM(J,I) = 0.0D0 |
938 |
|
|
end DO |
939 |
|
|
end DO |
940 |
|
|
|
941 |
|
|
! start with 0,0: |
942 |
|
|
PLM(0,0) = 1.0D0 |
943 |
|
|
|
944 |
|
|
! x = +/- 1 functions are easy: |
945 |
|
|
IF (abs(X).EQ.1.0D0) THEN |
946 |
|
|
DO I = 1, m |
947 |
|
|
PLM(0, I) = X**I |
948 |
|
|
DLM(0, I) = 0.5D0*I*(I+1.0D0)*X**(I+1) |
949 |
|
|
end DO |
950 |
|
|
DO J = 1, m |
951 |
|
|
DO I = 1, l |
952 |
|
|
IF (I.EQ.1) THEN |
953 |
|
|
DLM(I, J) = 1.0D+300 |
954 |
|
|
ELSE IF (I.EQ.2) THEN |
955 |
|
|
DLM(I, J) = -0.25D0*(J+2)*(J+1)*J*(J-1)*X**(J+1) |
956 |
|
|
ENDIF |
957 |
|
|
end DO |
958 |
|
|
end DO |
959 |
|
|
RETURN |
960 |
|
|
ENDIF |
961 |
|
|
|
962 |
|
|
LS = 1 |
963 |
|
|
IF (abs(X).GT.1.0D0) LS = -1 |
964 |
|
|
XQ = sqrt(LS*(1.0D0-X*X)) |
965 |
|
|
XS = LS*(1.0D0-X*X) |
966 |
|
|
|
967 |
|
|
DO I = 1, l |
968 |
|
|
PLM(I, I) = -LS*(2.0D0*I-1.0D0)*XQ*PLM(I-1, I-1) |
969 |
|
|
enddo |
970 |
|
|
|
971 |
|
|
DO I = 0, l |
972 |
|
|
PLM(I, I+1)=(2.0D0*I+1.0D0)*X*PLM(I, I) |
973 |
|
|
enddo |
974 |
|
|
|
975 |
|
|
DO I = 0, l |
976 |
|
|
DO J = I+2, m |
977 |
|
|
PLM(I, J)=((2.0D0*J-1.0D0)*X*PLM(I,J-1) - & |
978 |
|
|
(I+J-1.0D0)*PLM(I,J-2))/(J-I) |
979 |
|
|
end DO |
980 |
|
|
end DO |
981 |
|
|
|
982 |
|
|
DLM(0, 0)=0.0D0 |
983 |
|
|
|
984 |
|
|
DO J = 1, m |
985 |
|
|
DLM(0, J)=LS*J*(PLM(0,J-1)-X*PLM(0,J))/XS |
986 |
|
|
end DO |
987 |
|
|
|
988 |
|
|
DO I = 1, l |
989 |
|
|
DO J = I, m |
990 |
|
|
DLM(I,J) = LS*I*X*PLM(I, J)/XS + (J+I)*(J-I+1.0D0)/XQ*PLM(I-1, J) |
991 |
|
|
end DO |
992 |
|
|
end DO |
993 |
|
|
|
994 |
|
|
RETURN |
995 |
|
|
END SUBROUTINE Associated_Legendre |
996 |
|
|
|
997 |
|
|
|
998 |
|
|
subroutine Orthogonal_Polynomial(x, m, function_type, pl, dpl) |
999 |
|
|
|
1000 |
|
|
! Purpose: Compute orthogonal polynomials: Tn(x) or Un(x), |
1001 |
|
|
! or Ln(x) or Hn(x), and their derivatives |
1002 |
|
|
! Input : function_type --- Function code |
1003 |
|
|
! =1 for Chebyshev polynomial Tn(x) |
1004 |
|
|
! =2 for Chebyshev polynomial Un(x) |
1005 |
|
|
! =3 for Laguerre polynomial Ln(x) |
1006 |
|
|
! =4 for Hermite polynomial Hn(x) |
1007 |
|
|
! n --- Order of orthogonal polynomials |
1008 |
|
|
! x --- Argument of orthogonal polynomials |
1009 |
|
|
! Output: PL(n) --- Tn(x) or Un(x) or Ln(x) or Hn(x) |
1010 |
|
|
! DPL(n)--- Tn'(x) or Un'(x) or Ln'(x) or Hn'(x) |
1011 |
|
|
! |
1012 |
|
|
! adapted from the routines in |
1013 |
|
|
! COMPUTATION OF SPECIAL FUNCTIONS by Shanjie Zhang and Jianming Jin |
1014 |
|
|
! ISBN 0-471-11963-6 |
1015 |
|
|
! |
1016 |
|
|
! The original Fortran77 codes can be found here: |
1017 |
|
|
! http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html |
1018 |
|
|
|
1019 |
|
|
real(kind=8), intent(in) :: x |
1020 |
|
|
integer, intent(in):: m |
1021 |
|
|
integer, intent(in):: function_type |
1022 |
|
|
real(kind=8), dimension(0:m), intent(inout) :: pl, dpl |
1023 |
|
|
|
1024 |
|
|
real(kind=8) :: a, b, c, y0, y1, dy0, dy1, yn, dyn |
1025 |
|
|
integer :: k |
1026 |
|
|
|
1027 |
|
|
A = 2.0D0 |
1028 |
|
|
B = 0.0D0 |
1029 |
|
|
C = 1.0D0 |
1030 |
|
|
Y0 = 1.0D0 |
1031 |
|
|
Y1 = 2.0D0*X |
1032 |
|
|
DY0 = 0.0D0 |
1033 |
|
|
DY1 = 2.0D0 |
1034 |
|
|
PL(0) = 1.0D0 |
1035 |
|
|
PL(1) = 2.0D0*X |
1036 |
|
|
DPL(0) = 0.0D0 |
1037 |
|
|
DPL(1) = 2.0D0 |
1038 |
|
|
IF (function_type.EQ.CHEBYSHEV_TN) THEN |
1039 |
|
|
Y1 = X |
1040 |
|
|
DY1 = 1.0D0 |
1041 |
|
|
PL(1) = X |
1042 |
|
|
DPL(1) = 1.0D0 |
1043 |
|
|
ELSE IF (function_type.EQ.LAGUERRE) THEN |
1044 |
|
|
Y1 = 1.0D0-X |
1045 |
|
|
DY1 = -1.0D0 |
1046 |
|
|
PL(1) = 1.0D0-X |
1047 |
|
|
DPL(1) = -1.0D0 |
1048 |
|
|
ENDIF |
1049 |
|
|
DO K = 2, m |
1050 |
|
|
IF (function_type.EQ.LAGUERRE) THEN |
1051 |
|
|
A = -1.0D0/K |
1052 |
|
|
B = 2.0D0+A |
1053 |
|
|
C = 1.0D0+A |
1054 |
|
|
ELSE IF (function_type.EQ.HERMITE) THEN |
1055 |
|
|
C = 2.0D0*(K-1.0D0) |
1056 |
|
|
ENDIF |
1057 |
|
|
YN = (A*X+B)*Y1-C*Y0 |
1058 |
|
|
DYN = A*Y1+(A*X+B)*DY1-C*DY0 |
1059 |
|
|
PL(K) = YN |
1060 |
|
|
DPL(K) = DYN |
1061 |
|
|
Y0 = Y1 |
1062 |
|
|
Y1 = YN |
1063 |
|
|
DY0 = DY1 |
1064 |
|
|
DY1 = DYN |
1065 |
|
|
end DO |
1066 |
|
|
RETURN |
1067 |
|
|
|
1068 |
|
|
end subroutine Orthogonal_Polynomial |
1069 |
|
|
|
1070 |
|
|
end module shapes |