#include "macros.h" module LMat_freeze use IntegralsData, only: nFrozen, UMat, umat_win use UMatCache, only: numBasisIndices, UMatInd use constants use util_mod, only: operator(.div.), custom_findloc use OneEInts, only: TMat2D use SystemData, only: ECore use Parallel_neci use MPI_wrapper use mpi, only: MPI_DOUBLE_PRECISION implicit none private public :: freeze_lmat, t_freeze, map_indices, init_freeze_buffers, & flush_freeze_buffers, add_core_en !> Parameter for number of double excitations a single LMat entry can contribute to !! (counting permutations) integer, parameter :: num_ex = 4 integer, parameter :: num_inds = 6 ! Step corresponding to conjugation of an index integer, parameter :: step = (num_inds / 2) ! Local storage for ECore and TMat real(dp) :: ECore_local, ECore_tot HElement_t(dp), allocatable :: TMat_local(:, :), TMat_total(:, :) ! Direct orbital excitation = pair of indices in an index array which is apart by step contains !> Initialize the local storage for the diagonal and one-electron terms (two-electron !! terms are shared memory). This is called before reading in the 6-index integrals subroutine init_freeze_buffers() ! Setup the buffers for accumulating the correction per processor if(nFrozen > 0) then ECore_local = 0.0_dp if(allocated(TMat_local)) deallocate(TMat_local) allocate(TMat_local(size(TMat2D, dim=1), size(TMat2D, dim=2))) if(allocated(TMat_total)) deallocate(TMat_total) allocate(TMat_total(size(TMat2D, dim=1), size(TMat2D, dim=2))) TMat_local = 0.0_dp TMat_total = 0.0_dp end if end subroutine init_freeze_buffers !------------------------------------------------------------------------------------------! !> Sum the locally accumulated corrections to the diagonal and one-body terms up and !! add them to the global terms, then deallocate temporaries. This is called !! after reading in the 6-index integrals subroutine flush_freeze_buffers() integer(MPIArg) :: tmat_size integer(MPIArg) :: ierr if(nFrozen > 0) then if(.not. allocated(TMat_local) .or. .not. allocated(TMat_total)) & call stop_all("flush_freeze_buffers", & "Buffers for freezing three-body interaction not allocated") ! Sum the core energy from each proc on this node call MPI_Allreduce(ECore_local, ECore_tot, 1, MPI_DOUBLE_PRECISION, MPI_SUM, & mpi_comm_intra, ierr) ECore = ECore + ECore_tot tmat_size = size(TMat_local) ! Sum the 1-body terms from each proc on this node call MPI_Allreduce(TMat_local, TMat_total, tmat_size, MPI_DOUBLE_PRECISION, MPI_SUM, & mpi_comm_intra, ierr) TMat2D = TMat2D+TMat_total ! Deallocate the temporary for the 1-body integrals deallocate(TMat_local) deallocate(TMat_total) ! The 2-body terms are shared memory, no operation is required at this point end if end subroutine flush_freeze_buffers !------------------------------------------------------------------------------------------! !> Checks if an entry is zeroed due to frozen orbitals being included !> @param[in] indices array of size 6 containing the indices of the entry in question in the frozen orbital numbering !> @return t_freeze true if the entry is zeroed pure function t_freeze(indices) integer(int64), intent(in) :: indices(num_inds) logical :: t_freeze t_freeze = any(indices < 1) end function t_freeze !------------------------------------------------------------------------------------------! !> Maps a set of six indices from pre-freeze to post-freeze orbital indexing !> @param indices on entry: array of indices in pre-freeze indexing, on return: same array in post-freeze indexing subroutine map_indices(indices) integer(int64), intent(inout) :: indices(:) indices = indices - numBasisIndices(nFrozen) end subroutine map_indices !------------------------------------------------------------------------------------------! !> Checks if the entry is neglected due to frozen orbitals being included and absorbs entries !! into the lower order matrix elements if required subroutine freeze_lmat(matel, indices) HElement_t(dp), intent(inout) :: matel integer(int64), intent(inout) :: indices(num_inds) ! Offset the orbital indexing call map_indices(indices) call add_core_en(matel, indices) end subroutine freeze_lmat !------------------------------------------------------------------------------------------! !> Absorb entries with repeated frozen orbitals into the corresponding lower-order !! terms. subroutine add_core_en(matel, indices) HElement_t(dp), intent(inout) :: matel integer(int64), intent(in) :: indices(num_inds) integer :: counts integer(int64) :: idx(num_ex), ct real(dp) :: prefactor, delta integer(MPIArg) :: ierr if(t_freeze(indices)) then ! Count the number of different indices appearing counts = count_frozen_inds(indices) ! How many pairs of frozen orbitals do we have select case(counts) ! 1 => double excitation case(1) idx = frozen_double_entry(indices, prefactor) ! There are up to eight potential double excitations with four given indices ! to which the LMat entry contributes - this is because LMat is hermitian ! but UMat is not do ct = 1, num_ex ! If the index is assigned, there is a duplicate frozen orb if(idx(ct) > 0) then ! Absorb the matrix element into UMat (with the corresponding prefactor ! according to permutation and number of possible spin terms ! UMat(idx(ct)) = UMat(idx(ct)) + prefactor*matel delta = prefactor * matel ! Use a remote update of UMat call MPI_Accumulate(delta, 1, MPI_DOUBLE_PRECISION, 0, & idx(ct) - 1, 1, MPI_DOUBLE_PRECISION, MPI_SUM, umat_win, ierr) endif end do ! 2 => single excitation case(2) idx(1:2) = frozen_single_entry(indices, prefactor) if(idx(1) > 0) then ! Absorb the matrix element into TMat ! TMat2D is indexed with spin orbs call add_to_tmat(spatToSpinAlpha(idx(1)), spatToSpinAlpha(idx(2))) call add_to_tmat(spatToSpinBeta(idx(1)), spatToSpinBeta(idx(2))) endif ! 3 => diagonal element case(3) call frozen_diagonal_entry(indices, prefactor) ECore_local = ECore_local + prefactor * matel end select ! Zero the matrix element for further usage (i.e. will not turn up anymore) matel = 0.0_dp endif contains subroutine add_to_tmat(ind1, ind2) integer(int64), intent(in) :: ind1, ind2 TMat_local(ind1, ind2) = TMat_local(ind1, ind2) + prefactor * matel ! TMat is hermitian, as is the 3-body term if(ind1 /= ind2) & TMat_local(ind2, ind1) = TMat_local(ind2, ind1) + prefactor * matel end subroutine add_to_tmat end subroutine add_core_en !------------------------------------------------------------------------------------------! !> Count how many frozen indices there are, determine if the entry has to be added !! to a lower-order term and if yes, which one. !> @param[in] indices array of size 6 with the orbital indices of the entry !> @return level indicates to which lower order term this entry has to be added !! and therefore, which subroutine has to be called in the following !! 0 - none !! 1 - one frozen index pair -> two-body term !! 2 - two frozen index pairs -> one-body term !! 3 - three frozen index pairs -> diagonal term pure function count_frozen_inds(indices) result(level) integer(int64), intent(in) :: indices(num_inds) integer :: level integer :: counts integer :: ct level = 0 ! If there is an unpaired frozen orbital, the entry is discarded, it does not ! contribute to any contraction do ct = 1, num_inds if(count(indices(ct) == indices) == 1 .and. indices(ct) < 1) return end do ! Else, it contributes to a contraction according to the number of frozen indices counts = count(indices < 1) ! An even number of frozen orbital indices is required if(modulo(counts, 2) /= 0) return level = counts.div.2 end function count_frozen_inds !------------------------------------------------------------------------------------------! !> Get the index of the UMat entry to which the LMat entry with given indices shall be !! added if it is frozen. !> @param[in] indices array of lenght 6 with the orbital indices of the LMat entry !> @param[ou] t_par flag indicating if the matrix element enters UMat with a -1 !> @return index index of the UMat entry to add the LMat entry to, 0 if entry is not frozen function frozen_double_entry(indices, prefactor) result(idx) integer(int64), intent(in) :: indices(num_inds) real(dp), intent(out) :: prefactor integer(int64) :: idx(num_ex) integer :: f_one, f_two, ct, counts, i, rs, marks(3) logical :: unfrozen(num_inds) integer(int64) :: uf_idx(4) idx = 0 unfrozen = indices > 0 ! Mark where the unfrozen indices are marks = 0 ! Identify the direct unfrozen pair ! Look for the direct pair of unfrozen indices (these shall stay direct) do ct = 1, step if(unfrozen(ct) .and. unfrozen(ct + step)) then uf_idx(1) = indices(ct) uf_idx(3) = indices(ct + step) ! Mark the extracted indices so they are not taken again marks(1) = ct marks(2) = ct + step exit end if end do ! Now, find the other two (direct or exchange) unfrozen indices rs = 2 do ct = 1, num_inds if(unfrozen(ct) .and. .not. any(ct == marks)) then uf_idx(rs) = indices(ct) marks(3) = ct rs = rs + 2 endif end do ! Now, get the required UMat indices, including all transposed index pairs idx = permute_umat_inds(int(uf_idx(1)), int(uf_idx(2)), int(uf_idx(3)), int(uf_idx(4))) ! Check the permutation and possible factor of two due to spin ! First, get the two frozen orbitals f_one = custom_findloc(unfrozen, .false., back=.false.) f_two = custom_findloc(unfrozen, .false., back=.true.) ! There are two spin configurations in a close-shell frozen scenario for terms ! with a direct frozen orbital (i.e. no permutation required) ! All others enter with a prefactor of -1 if(is_direct(f_one, f_two)) then prefactor = 2.0_dp else prefactor = -1.0_dp ! If this is a diagonal term (only three different indices), permutational symmetry ! gives an extra factor of 2 for the exchange term. If only two different ! indices appear, also the direct term gets this prefactor counts = 1 ! Count the number of different indices do ct = 2, num_inds if(.not. any(indices(ct) == indices(1:ct - 1))) counts = counts + 1 end do if(counts == 2) then prefactor = 2.0_dp * prefactor elseif(counts == 3) then ! If there are three different indices, only add the extra factor if there is no direct unfrozen pair do ct = 1, step if(is_repeated_pair(indices, ct) .and. unfrozen(ct)) return end do prefactor = 2.0_dp * prefactor end if end if end function frozen_double_entry !------------------------------------------------------------------------------------------! !> Returns the UMatInd values of all possible permutations of the input indices !> @param[in] a,b,c,d orbital indices of a two-body element !> @return inds array of size 4 containing the indices of UMat corresponding to these !! four orbitals (in this order) and their hermitian conjugates !! entries of 0 indicate that no position in UMat has to be addressed function permute_umat_inds(a, b, c, d) result(inds) integer, intent(in) :: a, b, c, d integer(int64) :: inds(num_ex) integer :: ct inds = 0 ! These are adjoint to each other, they are the same in LMat, but not UMat inds(1) = UMatInd(a, b, c, d) inds(2) = UMatInd(c, b, a, d) inds(3) = UMatInd(a, d, c, b) inds(4) = UMatInd(c, d, a, b) ! All terms are only counted if they are different from a previously occuring index ! This approach might be less performant than competing ways of doing this check, ! but it is very clear and less prone to bugs. If this proves to be a performance ! bottleneck, it can be changed to a faster implementation later on do ct = 2, num_ex ! If the index already appeared, delete it if(any(inds(ct) == inds(1:ct - 1))) inds(ct) = 0 end do end function permute_umat_inds !------------------------------------------------------------------------------------------! !> For a given set of 6 orbital indices with two pairs of frozen orbitals, !! returns the orbital indices of the corresponding single excitation and the prefactor !! for the matrix element due to spin !> @param[in] indices array of size 6 with orbital indices, four of which have to be !! repeated frozen indices !> @param[out] prefactor on return, the prefactor of the matrix element when added to !! the one-body terms !> @return orbs the two non-frozen orbitals function frozen_single_entry(indices, prefactor) result(orbs) integer(int64), intent(in) :: indices(num_inds) real(dp), intent(out) :: prefactor integer :: orbs(2) integer :: f_orbs(num_inds - 2), ct integer :: uf_one, uf_two, directs logical :: unfrozen(num_inds) orbs = 0 unfrozen = indices > 0 f_orbs = int(pack(indices,.not. unfrozen)) ! For the single entry, there are only two unfrozen orbs, find these and return them orbs = int(pack(indices, unfrozen)) ! Again, two things to check: The number of direct orbitals and the permutation ! At this point, there is no unpaired frozen orbital, so there are two options: ! a) there are two different orbs prefactor = 1.0_dp if(count(f_orbs(1) == f_orbs) < size(f_orbs)) then ! We have to count how many potential spin configurations contribute ! The parity is counting the number of permutations required to end up ! with a completely direct expression ! -> The parity is odd if and only if the number of direct excitations is exactly one ! (then, one permutation is required to fix the two non-direct excits, else, ! (either zero or two are needed) ! -> count every direct excitation with a factor -1 directs = 0 ! Count the number of direct excitations do ct = 1, step ! Each direct repeated orbital doubles the number of spin configs ! (the case of four identical orbs is excluded) if(is_repeated_pair(indices, ct) .or. (unfrozen(ct) .and. unfrozen(ct + step))) then directs = directs + 1 endif end do select case(directs) ! If there are none, there is no freedom for spin choice, but the LMat entry ! appears twice in the matrix element evaluation due to symmetry if the ! unfrozen entry is repeated case(0) if(orbs(1) == orbs(2)) prefactor = 2.0_dp ! If there is one, two possible spin configs contribute, and we have odd parity case(1) prefactor = -2.0_dp case(3) ! If there are three (just two is not possible), there are two spin degrees of ! freedom -> factor of 4 prefactor = 4.0_dp end select else ! b) All frozen orbs are the same -> only one spin config is allowed, only parity of ! the permutation counts ! Here, only a direct exctiation has even parity (same rule as above) ! Get the posisitons of the unfrozen orbs uf_one = custom_findloc(unfrozen, .true., back=.false.) uf_two = custom_findloc(unfrozen, .true., back=.true.) if(.not. is_direct(uf_one, uf_two)) prefactor = -1.0_dp * prefactor end if end function frozen_single_entry !------------------------------------------------------------------------------------------! !> Determine the prefactor for a diagonal contribution (i.e. three pairs of frozen orbitals) !> @param[in] indices orbital indices of the frozen entry - need to belong to a contribution ! to a diagonal matrix element of only frozen orbitals !> @param[out] prefactor prefactor with which this LMat entry enters the matrix element pure subroutine frozen_diagonal_entry(indices, prefactor) integer(int64), intent(in) :: indices(num_inds) real(dp), intent(out) :: prefactor integer :: ct, directs logical :: t_quad ! Only one info is needed here, that is the parity and number of contributing spin ! configs. ! If there are five or more repeated indices, the LMat entry does not contribute ! (it would require three same-spin electrons t_quad = .false. do ct = 1, 3 if(count(indices(ct) == indices) > 4) then prefactor = 0.0_dp return end if if(count(indices(ct) == indices) > 3) t_quad = .true. end do ! Both relate to the number of different direct excits, so count these directs = 0 do ct = 1, step if(is_repeated_pair(indices, ct)) directs = directs + 1 end do ! If there is a quadruple index, the spin of it is fixed (both have to be occupied), then, ! the prefactor is always +/- 2, depending on if there is more than one direct pair if(t_quad) then ! The only options with a quadruple index are ! a) one direct excitation => -2 ! b) three direct exctiations => +2 prefactor = merge(-2.0_dp, 2.0_dp, directs == 1) else ! In the other case, there are three relevant cases: ! a) All excitations are direct => prefactor 8 = 2**3 (all spins are free) ! b) One excitation is direct => prefactor -4 (from the spin freedom of the direct orb + overall spin) ! c) No excitation is direct => prefactor 4 ! the factor of 4 comes from two sources: a factor of 2 from the overall spin ! and another factor of two from permutational symmetry: both indirect terms ! are identical in this case, so this entry has to be counted as both if(directs == 0) then prefactor = 4.0_dp elseif(directs == 1) then prefactor = -4.0_dp else ! directs == 3 prefactor = 8.0_dp endif endif end subroutine frozen_diagonal_entry !------------------------------------------------------------------------------------------! !> For two positions of indices in a 6-index set, return if these are a direct pair !> @param[in] one, two integers between 1 and 6 !> @return t_dir true if the two integers correspond to positions that are direct, i.e. !! for which the LMat entry is symmetric under exchange of the values pure function is_direct(one, two) result(t_dir) integer, intent(in) :: one, two logical :: t_dir t_dir = (one + step == two) end function is_direct !------------------------------------------------------------------------------------------! !> For a set of 6 orbital indices, return whether the pair at a given position is repeated !> @param[in] indices array of size 6 containing a set of indices indexing an LMat entry !> @param[in] ct integer between 1 and 3 labeling a position in the index set !> @return t_dir true if the two indices at the position ct (i.e. ct and ct+step in indices) !! are the same pure function is_repeated_pair(indices, ct) result(t_dir) integer(int64), intent(in) :: indices(num_inds) integer, intent(in) :: ct logical :: t_dir t_dir = (indices(ct) == indices(ct + step)) end function is_repeated_pair !------------------------------------------------------------------------------------------! end module LMat_freeze

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