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add DIIS algorithm for Roothaan-Hall SCF procedure

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This commit is contained in:
loos 2017-03-29 22:21:46 +02:00
parent 57c5892d47
commit f7da26ff09
4 changed files with 429 additions and 8 deletions
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166
plugins/Hartree_Fock/DIIS.irp.f Normal file
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@ -0,0 +1,166 @@
begin_provider [double precision, FPS_SPF_Matrix_AO, (AO_num_align, AO_num)]
implicit none
begin_doc
! Commutator FPS - SPF
end_doc
double precision, allocatable:: scratch(:,:)
allocate( &
scratch(AO_num_align, AO_num) &
)
! Compute FP
call dgemm('N','N',AO_num,AO_num,AO_num, &
1.d0, &
Fock_Matrix_AO,Size(Fock_Matrix_AO,1), &
HF_Density_Matrix_AO,Size(HF_Density_Matrix_AO,1), &
0.d0, &
scratch,Size(scratch,1))
! Compute FPS
call dgemm('N','N',AO_num,AO_num,AO_num, &
1.d0, &
scratch,Size(scratch,1), &
AO_Overlap,Size(AO_Overlap,1), &
0.d0, &
FPS_SPF_Matrix_AO,Size(FPS_SPF_Matrix_AO,1))
! Compute SP
call dgemm('N','N',AO_num,AO_num,AO_num, &
1.d0, &
AO_Overlap,Size(AO_Overlap,1), &
HF_Density_Matrix_AO,Size(HF_Density_Matrix_AO,1), &
0.d0, &
scratch,Size(scratch,1))
! Compute FPS - SPF
call dgemm('N','N',AO_num,AO_num,AO_num, &
-1.d0, &
scratch,Size(scratch,1), &
Fock_Matrix_AO,Size(Fock_Matrix_AO,1), &
1.d0, &
FPS_SPF_Matrix_AO,Size(FPS_SPF_Matrix_AO,1))
end_provider
BEGIN_PROVIDER [ double precision, eigenvalues_Fock_matrix_AO, (AO_num) ]
&BEGIN_PROVIDER [ double precision, eigenvectors_Fock_matrix_AO, (AO_num_align,AO_num) ]
BEGIN_DOC
! Eigenvalues and eigenvectors of the Fock matrix over the AO basis
END_DOC
implicit none
double precision, allocatable :: scratch(:,:),work(:),Xt(:,:)
integer :: lwork,info
integer :: i,j
lwork = 3*AO_num - 1
allocate( &
scratch(AO_num_align,AO_num), &
work(lwork), &
Xt(AO_num,AO_num) &
)
! Calculate Xt
do i=1,AO_num
do j=1,AO_num
Xt(i,j) = X_Matrix_AO(j,i)
enddo
enddo
! Calculate Fock matrix in orthogonal basis: F' = Xt.F.X
call dgemm('N','N',AO_num,AO_num,AO_num, &
1.d0, &
Fock_matrix_AO,size(Fock_matrix_AO,1), &
X_Matrix_AO,size(X_Matrix_AO,1), &
0.d0, &
eigenvectors_Fock_matrix_AO,size(eigenvectors_Fock_matrix_AO,1))
call dgemm('N','N',AO_num,AO_num,AO_num, &
1.d0, &
Xt,size(Xt,1), &
eigenvectors_Fock_matrix_AO,size(eigenvectors_Fock_matrix_AO,1), &
0.d0, &
scratch,size(scratch,1))
! Diagonalize F' to obtain eigenvectors in orthogonal basis C' and eigenvalues
call dsyev('V','U',AO_num, &
scratch,size(scratch,1), &
eigenvalues_Fock_matrix_AO, &
work,lwork,info)
if(info /= 0) then
print *, irp_here//' failed : ', info
stop 1
endif
! Back-transform eigenvectors: C =X.C'
call dgemm('N','N',AO_num,AO_num,AO_num, &
1.d0, &
X_matrix_AO,size(X_matrix_AO,1), &
scratch,size(scratch,1), &
0.d0, &
eigenvectors_Fock_matrix_AO,size(eigenvectors_Fock_matrix_AO,1))
END_PROVIDER
BEGIN_PROVIDER [ double precision, X_matrix_AO, (AO_num_align,AO_num) ]
BEGIN_DOC
! Matrix X = S^{-1/2} obtained by SVD
END_DOC
implicit none
integer :: LDA, LDC
double precision, allocatable :: U(:,:),Vt(:,:), D(:)
integer :: info, i, j, k
LDA = size(AO_overlap,1)
LDC = size(AO_overlap,1)
allocate( &
U(LDC,AO_num), &
Vt(LDA,AO_num), &
D(AO_num))
call svd( &
AO_overlap,LDA, &
U,LDC, &
D, &
Vt,LDA, &
AO_num,AO_num)
do i=1,AO_num
if(abs(D(i)) < threshold_overlap_AO_eigenvalues) then
D(i) = 0.d0
else
D(i) = 1.d0/sqrt(D(i))
endif
do j=1,AO_num
X_matrix_AO(j,i) = 0.d0
enddo
enddo
do k=1,AO_num
if(D(k) /= 0.d0) then
do j=1,AO_num
do i=1,MO_tot_num
X_matrix_AO(i,j) = X_matrix_AO(i,j) + U(i,k)*D(k)*Vt(k,j)
enddo
enddo
endif
enddo
END_PROVIDER

26
plugins/Hartree_Fock/EZFIO.cfg
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@ -1,3 +1,21 @@
[threshold_overlap_ao_eigenvalues]
type: Threshold
doc: Threshold on the magnitude of the smallest eigenvalues of the overlap matrix in the AO basis
interface: ezfio,provider,ocaml
default: 1.e-6
[max_dim_diis]
type: integer
doc: Maximum size of the DIIS extrapolation procedure
interface: ezfio,provider,ocaml
default: 15
[threshold_diis]
type: Threshold
doc: Threshold on the convergence of the DIIS error vector during a Hartree-Fock calculation
interface: ezfio,provider,ocaml
default: 1.e-5
[thresh_scf]
type: Threshold
doc: Threshold on the convergence of the Hartree Fock energy
@ -8,7 +26,7 @@ default: 1.e-10
type: Strictly_positive_int
doc: Maximum number of SCF iterations
interface: ezfio,provider,ocaml
default: 200
default: 128
[level_shift]
type: Positive_float
@ -16,6 +34,12 @@ doc: Energy shift on the virtual MOs to improve SCF convergence
interface: ezfio,provider,ocaml
default: 0.5
[scf_algorithm]
type: character*(32)
doc: Type of SCF algorithm used. Possible choices are [ damp | DIIS]
interface: ezfio,provider,ocaml
default: damp
[mo_guess_type]
type: MO_guess
doc: Initial MO guess. Can be [ Huckel | HCore ]

218
plugins/Hartree_Fock/Roothaan_Hall_SCF.irp.f Normal file
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@ -0,0 +1,218 @@
subroutine Roothaan_Hall_SCF
BEGIN_DOC
! Roothaan-Hall algorithm for SCF Hartree-Fock calculation
END_DOC
implicit none
double precision :: energy_SCF,energy_SCF_previous,Delta_energy_SCF,max_error_DIIS
double precision, allocatable :: Fock_matrix_DIIS(:,:,:),error_matrix_DIIS(:,:,:)
integer :: iteration_SCF,dim_DIIS,index_dim_DIIS
integer :: i,j
allocate( &
Fock_matrix_DIIS(AO_num,AO_num,max_dim_DIIS), &
error_matrix_DIIS(AO_num,AO_num,max_dim_DIIS) &
)
call write_time(output_hartree_fock)
write(output_hartree_fock,'(A4, 1X, A16, 1X, A16, 1X, A16)') &
'====','================','================','================'
write(output_hartree_fock,'(A4, 1X, A16, 1X, A16, 1X, A16)') &
' N ', 'Energy ', 'Energy diff ', 'DIIS error '
write(output_hartree_fock,'(A4, 1X, A16, 1X, A16, 1X, A16)') &
'====','================','================','================'
! Initialize energies and density matrices
energy_SCF_previous = HF_energy
Delta_energy_SCF = 0.d0
iteration_SCF = 0
dim_DIIS = 0
max_error_DIIS = 1.d0
!
! Start of main SCF loop
!
do while((max_error_DIIS > threshold_DIIS) .and. (iteration_SCF < n_it_SCF_max))
! Increment cycle number
iteration_SCF += 1
! Current size of the DIIS space
dim_DIIS = min(dim_DIIS+1,max_dim_DIIS)
! Store Fock and error matrices at each iteration
do j=1,AO_num
do i=1,AO_num
index_dim_DIIS = mod(dim_DIIS-1,max_dim_DIIS)+1
Fock_matrix_DIIS(i,j,index_dim_DIIS) = Fock_matrix_AO(i,j)
error_matrix_DIIS(i,j,index_dim_DIIS) = FPS_SPF_Matrix_AO(i,j)
enddo
enddo
! Compute the extrapolated Fock matrix
call extrapolate_Fock_matrix( &
error_matrix_DIIS,Fock_matrix_DIIS, &
iteration_SCF,dim_DIIS &
)
touch Fock_matrix_AO
MO_coef = eigenvectors_Fock_matrix_AO
! This algorithm still have an issue with linear dependencies
! do i=1,AO_num
! write(*,*) i,eigenvalues_Fock_matrix_AO(i)
! enddo
touch MO_coef
! Calculate error vectors
max_error_DIIS = maxval(Abs(FPS_SPF_Matrix_AO))
! SCF energy
energy_SCF = HF_energy
Delta_Energy_SCF = energy_SCF - energy_SCF_previous
energy_SCF_previous = energy_SCF
! Print results at the end of each iteration
write(output_hartree_fock,'(I4, 1X, F16.10, 1X, F16.10, 1X, F16.10)') &
iteration_SCF, energy_SCF, Delta_energy_SCF, max_error_DIIS
enddo
!
! End of Main SCF loop
!
write(output_hartree_fock,'(A4, 1X, A16, 1X, A16, 1X, A16)') &
'====','================','================','================'
write(output_hartree_fock,*)
if(.not.no_oa_or_av_opt)then
call mo_as_eigvectors_of_mo_matrix(Fock_matrix_mo,size(Fock_matrix_mo,1),size(Fock_matrix_mo,2),mo_label,1)
endif
call write_double(output_hartree_fock, Energy_SCF, 'Hartree-Fock energy')
call ezfio_set_hartree_fock_energy(Energy_SCF)
call write_time(output_hartree_fock)
end
subroutine extrapolate_Fock_matrix( &
error_matrix_DIIS,Fock_matrix_DIIS, &
iteration_SCF,dim_DIIS &
)
BEGIN_DOC
! Compute the extrapolated Fock matrix using the DIIS procedure
END_DOC
implicit none
double precision,intent(in) :: Fock_matrix_DIIS(AO_num,AO_num,*),error_matrix_DIIS(AO_num,AO_num,*)
integer,intent(in) :: iteration_SCF
integer,intent(inout) :: dim_DIIS
double precision,allocatable :: B_matrix_DIIS(:,:),X_vector_DIIS(:)
double precision,allocatable :: scratch(:,:)
integer :: i,j,k,i_DIIS,j_DIIS
allocate( &
B_matrix_DIIS(dim_DIIS+1,dim_DIIS+1), &
X_vector_DIIS(dim_DIIS+1), &
scratch(AO_num,AO_num) &
)
! Compute the matrices B and X
do j=1,dim_DIIS
do i=1,dim_DIIS
j_DIIS = mod(iteration_SCF-j,max_dim_DIIS)+1
i_DIIS = mod(iteration_SCF-i,max_dim_DIIS)+1
! Compute product of two errors vectors
call dgemm('N','N',AO_num,AO_num,AO_num, &
1.d0, &
error_matrix_DIIS(1,1,i_DIIS),size(error_matrix_DIIS,1), &
error_matrix_DIIS(1,1,j_DIIS),size(error_matrix_DIIS,1), &
0.d0, &
scratch,size(scratch,1))
! Compute Trace
B_matrix_DIIS(i,j) = 0.d0
do k=1,AO_num
B_matrix_DIIS(i,j) += scratch(k,k)
enddo
enddo
enddo
! Pad B matrix and build the X matrix
do i=1,dim_DIIS
B_matrix_DIIS(i,dim_DIIS+1) = -1.d0
B_matrix_DIIS(dim_DIIS+1,i) = -1.d0
X_vector_DIIS(i) = 0.d0
enddo
B_matrix_DIIS(dim_DIIS+1,dim_DIIS+1) = 0.d0
X_vector_DIIS(dim_DIIS+1) = -1.d0
! Solve the linear system C = B.X
integer :: info
integer,allocatable :: ipiv(:)
allocate( &
ipiv(dim_DIIS+1) &
)
call dsysv('U',dim_DIIS+1,1, &
B_matrix_DIIS,size(B_matrix_DIIS,1), &
ipiv, &
X_vector_DIIS,size(X_vector_DIIS,1), &
scratch,size(scratch), &
info &
)
if(info == 0) then
! Compute extrapolated Fock matrix
Fock_matrix_AO(:,:) = 0.d0
do k=1,dim_DIIS
do j=1,AO_num
do i=1,AO_num
Fock_matrix_AO(i,j) += X_vector_DIIS(k)*Fock_matrix_DIIS(i,j,dim_DIIS-k+1)
enddo
enddo
enddo
else
write(*,*) 'Re-initialize DIIS!!'
dim_DIIS = 0
endif
! do i=1,AO_num
! do j=1,AO_num
! write(*,*) Fock_matrix_AO(i,j)
! enddo
! enddo
end

27
plugins/Hartree_Fock/SCF.irp.f
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@ -13,7 +13,7 @@ end
subroutine create_guess
implicit none
BEGIN_DOC
! Create an MO guess if no MOs are present in the EZFIO directory
! Create a MO guess if no MOs are present in the EZFIO directory
END_DOC
logical :: exists
PROVIDE ezfio_filename
@ -34,21 +34,34 @@ subroutine create_guess
endif
end
ao_to_mo
subroutine run
BEGIN_DOC
! Run SCF calculation
END_DOC
use bitmasks
implicit none
BEGIN_DOC
! Run SCF calculation
END_DOC
double precision :: SCF_energy_before,SCF_energy_after,diag_H_mat_elem
double precision :: E0
double precision :: EHF
integer :: i_it, i, j, k
E0 = HF_energy
EHF = HF_energy
mo_label = "Canonical"
call damping_SCF
! Choose SCF algorithm
if(scf_algorithm == 'damp') then
call damping_SCF
else if(scf_algorithm == 'DIIS') then
call Roothaan_Hall_SCF
else
write(*,*) 'Unrecognized SCF algorithm: '//scf_algorithm
stop 1
endif
end