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https://github.com/QuantumPackage/qp2.git
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195 lines
6.3 KiB
Org Mode
195 lines
6.3 KiB
Org Mode
# -*- mode:org -*-
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#+TITLE: CFG-CI
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#+AUTHOR: Vijay Gopal Chilkuri
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#+FILE: configurations.org
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#+EMAIL: vijay.gopal.c@gmail.com
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#+OPTIONS: toc:t
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#+LATEX_CLASS: article
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#+LATEX_HEADER: \usepackage{tabularx}
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#+LATEX_HEADER: \usepackage{braket}
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#+LATEX_HEADER: \usepackage{minted}
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* Configuration based CI
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Here we write the main functions that perform the functions necessary for
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the Configuration based CI.
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There are three main functions required for doing the CI
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- Convert wavefunction from determinant basis to configuration state function (CSF) basis
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- Apply the Hamiltonian to the wavefunction in CSF basis
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- Convert the converged wavefunction back to determinant basis
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** TODO[0/3] Convert basis from DET to CSF
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The conversion of basis is done by going via bonded functions (BFs).
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Importantly, all the CSFs of a chosen configuration (CFG) are kept.
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The advantage is that the sigma-vector can be performed efficiently
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via BLAS level 3 operations.
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- [ ] Write a function to calculate the maximum dimensions required
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Prototype array contains the \( <I|\hat{E}_{pq}|J> \) for all possible
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CFGs \( I, J\) and all \(4\) types of excitations for all possible model
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orbitals \(p,q\). Note that the orbital ids \(p,q\) here do not refer to
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the actual MO ids, they simply refer to the orbitals involved in that spefcific
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SOMO, for e.g. an excitation of the type [2 2 2 1 1 1 1 0] -> [ 2 2 1 1 1 1 1]
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implies an excitation from orbital \(3\) to orbital \(8\) which are the real MO ids.
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However, the prototype only concerns the SOMOs like so [2 1 1 1 1 0] -> [ 1 1 1 1 1 1]
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therefore \(p,q\) are model space ids \(1,6\).
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#+begin_src f90 :main no :tangle configurations_sigma_vector.irp.f
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BEGIN_PROVIDER [ integer*8, NSOMOMax]
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&BEGIN_PROVIDER [ integer*8, NCSFMax]
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&BEGIN_PROVIDER [ integer*8, NMO]
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implicit none
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BEGIN_DOC
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! Documentation for NSOMOMax
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! The maximum number of SOMOs for the current calculation.
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! required for the calculation of prototype arrays.
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END_DOC
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NSOMOMax = 8
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NCSFMax = 14 ! TODO: NCSFs for MS=0
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NMO = NSOMOMax ! TODO: remove this
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END_PROVIDER
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#+end_src
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The prototype matrix AIJpqMatrixList has the following dimensions
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\(\left(NSOMOMax, NSOMOMax, 4, NSOMOMax, NSOMOMax,NCSFMAx,NCSFMax\right)\) where the first two
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indices represent the somos in \(I,J\) followed by the type of excitation and
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finally the two model space orbitals \(p,q\).
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The dimensions for each Isomo, Jsomo pair are precalculated and stored in the AIJpqMatrixDimsList
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variable which is provided here.
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#+begin_src f90 :main no :tangle configurations_sigma_vector.irp.f
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BEGIN_PROVIDER [ double precision, AIJpqMatrixDimsList, (NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,2)]
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use cfunctions
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implicit none
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BEGIN_DOC
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! Documentation for AIJpqMatrixList
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! The prototype matrix containing the <I|E_{pq}|J>
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! matrices for each I,J somo pair and orb ids.
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END_DOC
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integer i,j,k,l
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integer*8 Isomo, Jsomo
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Isomo = 0
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Jsomo = 0
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integer*8 rows, cols
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rows = -1
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cols = -1
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integer*8 MS
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MS = 0
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print *,"NSOMOMax = ",NSOMOMax
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!allocate(AIJpqMatrixDimsList(NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,2))
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do i = 2, NSOMOMax, 2
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Isomo = ISHFT(1,i)-1
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do j = i-2,i+2, 2
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Jsomo = ISHFT(1,j)-1
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if(j .GT. NSOMOMax .OR. j .LE. 0) then
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cycle
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end if
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do k = 1,NSOMOMax
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do l = k,NSOMOMax
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call getApqIJMatrixDims(Isomo, &
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Jsomo, &
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MS, &
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rows, &
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cols)
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print *, i,j,k,l,">",Isomo,Jsomo,">",rows, cols
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! i -> j
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AIJpqMatrixDimsList(i,j,1,k,l,1) = rows
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AIJpqMatrixDimsList(i,j,1,k,l,2) = cols
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AIJpqMatrixDimsList(i,j,1,l,k,1) = rows
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AIJpqMatrixDimsList(i,j,1,l,k,2) = cols
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! j -> i
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AIJpqMatrixDimsList(j,i,1,k,l,1) = rows
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AIJpqMatrixDimsList(j,i,1,k,l,2) = cols
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AIJpqMatrixDimsList(j,i,1,l,k,1) = rows
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AIJpqMatrixDimsList(j,i,1,l,k,2) = cols
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end do
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end do
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end do
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end do
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END_PROVIDER
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#+end_src
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- [ ] Read the transformation matrix based on the number of SOMOs
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We go through all the possible SOMOs and build the matrix-elements \(<I|E_{pq}|I>\) and
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store it in the AIJpq container.
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#+begin_src f90 :main no :tangle configurations_sigma_vector.irp.f
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BEGIN_PROVIDER [ real*8, AIJpqContainer, (NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,NSOMOMax,NSOMOMax)]
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use cfunctions
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implicit none
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BEGIN_DOC
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! Documentation for AIJpqMatrixList
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! The prototype matrix containing the <I|E_{pq}|J>
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! matrices for each I,J somo pair and orb ids.
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END_DOC
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integer i,j,k,l, orbp, orbq, ri, ci
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orbp = 0
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orbq = 0
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integer*8 Isomo, Jsomo
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Isomo = 0
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Jsomo = 0
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integer*8 rows, cols
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rows = -1
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cols = -1
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integer*8 MS
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MS = 0
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real*8,dimension(:),allocatable :: meMatrix
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print *,"NSOMOMax = ",NSOMOMax
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!allocate(AIJpqMatrixDimsList(NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,2))
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do i = 2, NSOMOMax, 2
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Isomo = ISHFT(1,i)-1
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do j = i-2,i+2, 2
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Jsomo = ISHFT(1,j)-1
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if(j .GT. NSOMOMax .OR. j .LE. 0) then
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cycle
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end if
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do k = 1,NSOMOMax
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do l = k,NSOMOMax
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call getApqIJMatrixDims(Isomo, &
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Jsomo, &
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MS, &
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rows, &
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cols)
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! allocate matrix
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allocate(meMatrix(rows*cols))
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! fill matrix
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call getApqIJMatrixDriver(Isomo, &
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Jsomo, &
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orbp, &
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orbq, &
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MS, &
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NMO, &
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meMatrix, &
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rows, &
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cols)
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print *, i,j,k,l,">",Isomo,Jsomo,">",rows, cols
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! i -> j
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do ri = 1,rows
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do ci = 1,cols
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AIJpqContainer(i,j,1,k,l,ri,ci) = meMatrix(ri*(cols-1) + ci)
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end do
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end do
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end do
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end do
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end do
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end do
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END_PROVIDER
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#+end_src
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- [ ] Perform the conversion by matrix-vector BLAS level 2 call
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