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QCModel_Huckel.f
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QCModel_Huckel.f
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#include "GPU.h"
module QCModel_Huckel
use MPI
use omp_lib
use f95_precision
use blas95
use lapack95
use type_m
use constants_m
use Matrix_Math
use MPI_definitions_m , only : ForceCrew , KernelCrew
use parameters_m , only : EnvField_ , Induced_ , driver , verbose , restart
use Overlap_Builder , only : Overlap_Matrix
use Hamiltonians , only : X_ij , even_more_extended_Huckel
use decoherence_m , only : Bcast_Matrices
public :: EigenSystem , S_root_inv
private
interface EigenSystem
module procedure EigenSystem
module procedure EigenSystem_just_erg
end interface
! module variables ...
real*8 , allocatable :: S_root_inv(:,:)
contains
!
!
!
!==================================================
subroutine EigenSystem( system , basis , QM , it )
!==================================================
implicit none
type(structure) , intent(in) :: system
type(STO_basis) , intent(in) :: basis(:)
type(R_eigen) , intent(inout) :: QM
integer , optional , intent(in) :: it
! local variables ...
real*8 , ALLOCATABLE :: Lv(:,:) , Rv(:,:)
real*8 , ALLOCATABLE :: h(:,:) , S_matrix(:,:) , S_root(:,:)
real*8 , ALLOCATABLE :: dumb_S(:,:) , tool(:,:) , S_eigen(:)
integer :: i , N , info
logical , save :: first_call_ = .true.
!xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CALL Overlap_Matrix( system , basis , S_matrix )
! After instantiating Overlap_matrix, processes wait outside ...
If( ForceCrew .OR. KernelCrew ) return
N = size(basis)
If( .NOT. allocated(QM%erg) ) ALLOCATE(QM%erg(N))
Allocate( h(N,N) )
Allocate( dumb_S(N,N) )
! clone S_matrix because SYGVD will destroy it ...
dumb_s = S_matrix
If( EnvField_ .OR. Induced_ ) then
h(:,:) = even_more_extended_Huckel( system , basis , S_matrix , it )
else
h(:,:) = Build_Huckel( basis , S_matrix )
end If
CALL SYGVD( h , dumb_S , QM%erg , 1 , 'V' , 'L' , info )
If ( info /= 0 ) write(*,*) 'info = ',info,' in SYGVD in EigenSystem '
select case ( driver )
case default
!---------------------------------------------------
! ROTATES THE HAMILTONIAN: H --> H*S_inv
!
! RIGHT EIGENVECTOR ALSO CHANGE: |C> --> S.|C>
!
! normalizes the L&R eigenvectors as < L(i) | R(i) > = 1
!---------------------------------------------------
Allocate( Lv(N,N) )
Allocate( Rv(N,N) )
Lv = h
Deallocate( h , dumb_S )
If( .NOT. allocated(QM%L) ) ALLOCATE(QM%L(N,N))
! eigenvectors in the rows of QM%L
QM%L = transpose(Lv)
! Rv = S * Lv ...
CALL symm( S_matrix , Lv , Rv )
if( driver == "slice_CSDM" ) CALL Bcast_Matrices( Rv , QM%L , S_matrix , N )
DEALLOCATE( S_matrix )
If( .NOT. ALLOCATED(QM%R) ) ALLOCATE(QM%R(N,N))
! eigenvectors in the columns of QM%R
QM%R = Rv
Deallocate( Lv , Rv )
case ("slice_FSSH")
!--------------------------------------------------------
! Overlap Matrix Factorization: S^(1/2) ...
dumb_s = S_matrix
Allocate( S_eigen(N) )
CALL SYEVD(dumb_S , S_eigen , 'V' , 'L' , info)
Allocate( tool(N,N) , source = transpose(dumb_S) )
forall( i=1:N ) tool(:,i) = sqrt(S_eigen) * tool(:,i)
allocate( S_root(N,N) )
CALL gemm(dumb_S , tool , S_root , 'N' , 'N')
!now S_root = S^(1/2) Lowdin Orthogonalization matrix ...
!now S_matrix = S ...
DEALLOCATE( S_eigen , dumb_S , tool )
!---------------------------------------------------
!RIGHT EIGENVECTOR ALSO CHANGE: |C> --> S^(1/2).|C>
!
!normalizes the L&R eigenvectors as < L(i) | R(i) > = 1
!---------------------------------------------------
Allocate( Lv(N,N) )
Allocate( Rv(N,N) )
Lv = h
Deallocate( h )
If( .NOT. allocated(QM%L) ) ALLOCATE(QM%L(N,N))
! eigenvectors in the rows of QM%L
! keeping the nonorthogonal representation of %L for future use ...
QM%L = transpose(Lv)
If( first_call_ .AND. (.NOT. restart) ) then
! Rv = S * Lv ...
call symm( S_matrix, Lv, Rv )
call invert( S_root )
first_call_ = .false.
else
! Rv = S^(1/2) * Lv ...
! Lowding representation ...
CALL symm( S_root , Lv , Rv )
end If
If( .NOT. ALLOCATED(QM%R) ) ALLOCATE(QM%R(N,N))
! eigenvectors in the columns of QM%R
QM%R = Rv
Deallocate( Lv , Rv , S_matrix , S_root )
case ("diagnostic")
deallocate(dumb_S)
call Lowdin( h , S_matrix , QM , N )
end select
!xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
! save energies of the TOTAL system ...
OPEN(unit=9,file='ancillary.trunk/system-ergs.dat',status='unknown')
do i = 1 , N
write(9,*) i , QM%erg(i)
end do
CLOSE(9)
If( verbose ) Print*, '>> EigenSystem done <<'
end subroutine EigenSystem
!
!
!
!===================================================
function Build_Huckel( basis , S_matrix ) result(h)
!===================================================
implicit none
type(STO_basis) , intent(in) :: basis(:)
real*8 , intent(in) :: S_matrix(:,:)
! local variables ...
integer :: i , j , N
real*8 , allocatable :: h(:,:)
!----------------------------------------------------------
! building the HUCKEL HAMILTONIAN
N = size(basis)
ALLOCATE( h(N,N) , source = D_zero )
do j = 1 , N
do i = j , N
h(i,j) = X_ij( i , j , basis ) * S_matrix(i,j)
end do
end do
end function Build_Huckel
!
!
!
!=======================================================
subroutine EigenSystem_just_erg( system , basis , erg )
!=======================================================
implicit none
type(structure) , intent(in) :: system
type(STO_basis) , intent(in) :: basis(:)
real*8 , intent(out) :: erg( size(basis) )
! local variables ...
real*8 , ALLOCATABLE :: h(:,:) , S_matrix(:,:)
integer :: i , j , N , info
N = size(basis)
CALL Overlap_Matrix(system,basis,S_matrix)
ALLOCATE( h(N,N) )
If( EnvField_ ) then
h(:,:) = even_more_extended_Huckel( system , basis , S_matrix )
else
do j = 1 , N
do i = 1 , j
h(i,j) = X_ij( i , j , basis ) * S_matrix(i,j)
end do
end do
end If
CALL SYGVD(h,S_matrix,erg,1,'N','U',info)
If ( info /= 0 ) write(*,*) 'info = ',info,' in SYGVD in EigenSystem '
DEALLOCATE( h , S_matrix )
end subroutine EigenSystem_just_erg
!
!
!
!===========================
subroutine invert( matrix )
!===========================
implicit none
real*8 , intent(inout) :: matrix(:,:)
!local variables ...
integer :: N
N = size(matrix(:,1))
CALL syInvert( matrix, return_full ) ! <== matrix content is destroyed and matrix_inv is returned
#define matrix_inv matrix
allocate( S_root_inv(N,N) , source = matrix_inv )
#undef matrix_inv
end subroutine invert
!
!
!
!
!==========================================
subroutine Lowdin( h , S_matrix , QM , N )
!==========================================
implicit none
real*8 , allocatable , intent(inout) :: h(:,:)
real*8 , allocatable , intent(inout) :: S_matrix(:,:)
type(R_eigen) , intent(inout) :: QM
integer , intent(in) :: N
! local variables ...
real*8 , ALLOCATABLE :: Lv(:,:) , Rv(:,:)
real*8 , ALLOCATABLE :: dumb_S(:,:), tool(:,:), S_eigen(:)
integer :: i , info
!--------------------------------------------------------
! Overlap Matrix Factorization: S^(1/2) ...
Allocate( dumb_S , source = S_matrix )
Allocate( S_eigen(N) )
CALL SYEVD(dumb_S , S_eigen , 'V' , 'L' , info)
Allocate( tool(N,N) , source = transpose(dumb_S) )
forall( i=1:N ) tool(:,i) = sqrt(S_eigen) * tool(:,i)
CALL gemm(dumb_S , tool , S_matrix , 'N' , 'N')
!now S_matrix = S^(1/2), Lowdin Orthogonalization matrix ...
DEALLOCATE( S_eigen , dumb_S , tool )
!---------------------------------------------------
!RIGHT EIGENVECTOR ALSO CHANGE: |C> --> S^(1/2).|C>
!
!normalizes the L&R eigenvectors as < L(i) | R(i) > = 1
!---------------------------------------------------
Allocate( Lv(N,N) )
Allocate( Rv(N,N) )
Lv = h
! Rv = S^(1/2) * Lv ...
CALL symm( S_matrix , Lv , Rv )
ALLOCATE(QM%R(N,N))
ALLOCATE(QM%L(N,N))
! eigenvectors in the columns of QM%R
QM%R = Rv
! eigenvectors in the rows of QM%L
QM%L = transpose(Rv)
Deallocate( h , Lv , Rv , S_matrix )
end subroutine Lowdin
!
!
!
!
end module QCModel_Huckel