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Working on building the prototype matrix AIJpq #143.

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# -*- mode:org -*-
#+TITLE: CFG-CI
#+AUTHOR: Vijay Gopal Chilkuri
#+FILE: configurations.org
#+EMAIL: vijay.gopal.c@gmail.com
#+OPTIONS: toc:t
#+LATEX_CLASS: article
#+LATEX_HEADER: \usepackage{tabularx}
#+LATEX_HEADER: \usepackage{braket}
#+LATEX_HEADER: \usepackage{minted}
* 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_src f90 :main no :tangle configurations_sigma_vector.irp.f
BEGIN_PROIDER[ integer, NSOMOMax]
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
END_PROVIDER
#+end_src
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 \(p,q\).
- [ ] Read the transformation matrix based on the number of SOMOs
#+begin_src f90 :main no
BEGIN_PROIDER[ double precision, AIJpqMatrixList, (NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,NCSFMax,NCSFMax)]
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
do i = 1,NSOMOMax
do j = i-1,i+1
if(j > NSOMOMax || j ==0) then
continue
end if
end do
end do
END_PROVIDER
#+end_src
- [ ] Perform the conversion by matrix-vector BLAS level 2 call

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BEGIN_PROIDER[ integer, NSOMOMax]
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
END_PROVIDER