CFG-CI

Configuration based CI
- TODO[0/3] Convert basis from DET to CSF

Configuration based CI

Here we write the main functions that perform the functions necessary for the Configuration based CI.

There are three main functions required for doing the CI

Convert wavefunction from determinant basis to configuration state function (CSF) basis
Apply the Hamiltonian to the wavefunction in CSF basis
Convert the converged wavefunction back to determinant basis

TODO`[0/3]` Convert basis from DET to CSF

The conversion of basis is done by going via bonded functions (BFs). Importantly, all the CSFs of a chosen configuration (CFG) are kept.

The advantage is that the sigma-vector can be performed efficiently via BLAS level 3 operations.

Write a function to calculate the maximum dimensions required

Prototype array contains the \( <I|\hat{E}_{pq}|J> \) for all possible CFGs \( I, J\) and all \(4\) types of excitations for all possible model orbitals \(p,q\). Note that the orbital ids \(p,q\) here do not refer to the actual MO ids, they simply refer to the orbitals involved in that spefcific SOMO, for e.g. an excitation of the type [2 2 2 1 1 1 1 0] -> [ 2 2 1 1 1 1 1] implies an excitation from orbital \(3\) to orbital \(8\) which are the real MO ids. However, the prototype only concerns the SOMOs like so [2 1 1 1 1 0] -> [ 1 1 1 1 1 1] therefore \(p,q\) are model space ids \(1,6\).
```
BEGIN_PROVIDER [ integer*8, NSOMOMax]
&BEGIN_PROVIDER [ integer*8, NCSFMax]
&BEGIN_PROVIDER [ integer*8, NMO]
implicit none
BEGIN_DOC
! Documentation for NSOMOMax
! The maximum number of SOMOs for the current calculation.
! required for the calculation of prototype arrays.
END_DOC
NSOMOMax = 8
NCSFMax = 14 ! TODO: NCSFs for MS=0
NMO = NSOMOMax ! TODO: remove this
END_PROVIDER
```
The prototype matrix AIJpqMatrixList has the following dimensions \(\left(NSOMOMax, NSOMOMax, 4, NSOMOMax, NSOMOMax,NCSFMAx,NCSFMax\right)\) where the first two indices represent the somos in \(I,J\) followed by the type of excitation and finally the two model space orbitals \(p,q\).

The dimensions for each Isomo, Jsomo pair are precalculated and stored in the AIJpqMatrixDimsList variable which is provided here.

BEGIN_PROVIDER [ double precision, AIJpqMatrixDimsList, (NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,2)]
use cfunctions
implicit none
BEGIN_DOC
! Documentation for AIJpqMatrixList
! The prototype matrix containing the <I|E_{pq}|J>
! matrices for each I,J somo pair and orb ids.
END_DOC
integer i,j,k,l
integer*8 Isomo, Jsomo
Isomo = 0
Jsomo = 0
integer*8 rows, cols
rows = -1
cols = -1
integer*8 MS
MS = 0
print *,"NSOMOMax = ",NSOMOMax
!allocate(AIJpqMatrixDimsList(NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,2))
do i = 2, NSOMOMax, 2
   Isomo = ISHFT(1,i)-1
   do j = i-2,i+2, 2
      Jsomo = ISHFT(1,j)-1
      if(j .GT. NSOMOMax .OR. j .LE. 0) then
         cycle
      end if
      do k = 1,NSOMOMax
         do l = k,NSOMOMax
            call getApqIJMatrixDims(Isomo,           &
                 Jsomo, &
                 MS,                       &
                 rows,                     &
                 cols)
            print *, i,j,k,l,">",Isomo,Jsomo,">",rows, cols
            ! i -> j
            AIJpqMatrixDimsList(i,j,1,k,l,1) = rows
            AIJpqMatrixDimsList(i,j,1,k,l,2) = cols
            AIJpqMatrixDimsList(i,j,1,l,k,1) = rows
            AIJpqMatrixDimsList(i,j,1,l,k,2) = cols
            ! j -> i
            AIJpqMatrixDimsList(j,i,1,k,l,1) = rows
            AIJpqMatrixDimsList(j,i,1,k,l,2) = cols
            AIJpqMatrixDimsList(j,i,1,l,k,1) = rows
            AIJpqMatrixDimsList(j,i,1,l,k,2) = cols
         end do
      end do
   end do
end do
END_PROVIDER

Read the transformation matrix based on the number of SOMOs

We go through all the possible SOMOs and build the matrix-elements \(<I|E_{pq}|I>\) and store it in the AIJpq container.

BEGIN_PROVIDER [ real*8, AIJpqContainer, (NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,NSOMOMax,NSOMOMax)]
use cfunctions
implicit none
BEGIN_DOC
! Documentation for AIJpqMatrixList
! The prototype matrix containing the <I|E_{pq}|J>
! matrices for each I,J somo pair and orb ids.
END_DOC
integer i,j,k,l, orbp, orbq, ri, ci
orbp = 0
orbq = 0
integer*8 Isomo, Jsomo
Isomo = 0
Jsomo = 0
integer*8 rows, cols
rows = -1
cols = -1
integer*8 MS
MS = 0
real*8,dimension(:),allocatable :: meMatrix
print *,"NSOMOMax = ",NSOMOMax
!allocate(AIJpqMatrixDimsList(NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,2))
do i = 2, NSOMOMax, 2
   Isomo = ISHFT(1,i)-1
   do j = i-2,i+2, 2
      Jsomo = ISHFT(1,j)-1
      if(j .GT. NSOMOMax .OR. j .LE. 0) then
         cycle
      end if
      do k = 1,NSOMOMax
         do l = k,NSOMOMax
            call getApqIJMatrixDims(Isomo,           &
                 Jsomo, &
                 MS,                       &
                 rows,                     &
                 cols)

            ! allocate matrix
            allocate(meMatrix(rows*cols))

            ! fill matrix
            call getApqIJMatrixDriver(Isomo,           &
                 Jsomo, &
                 orbp,                     &
                 orbq,                     &
                 MS,                       &
                 NMO,                      &
                 meMatrix,                 &
                 rows,                     &
                 cols)
           print *, i,j,k,l,">",Isomo,Jsomo,">",rows, cols
            ! i -> j
           do ri = 1,rows
               do ci = 1,cols
                  AIJpqContainer(i,j,1,k,l,ri,ci) = meMatrix(ri*(cols-1) + ci)
               end do
            end do
         end do
      end do
   end do
end do
END_PROVIDER

Perform the conversion by matrix-vector BLAS level 2 call

6.3 KiB Raw Blame History

CFG-CI

Configuration based CI

TODO[0/3] Convert basis from DET to CSF

6.3 KiB

Raw Blame History

TODO`[0/3]` Convert basis from DET to CSF