ct9b01200_si_001.pdf (246.91 kB)
Iterative Configuration Interaction with Selection
journal contribution
posted on 2020-03-16, 16:35 authored by Ning Zhang, Wenjian Liu, Mark R. HoffmannEven when starting with very poor
initial guess, the iterative
configuration interaction (iCI) approach [J. Chem. Theory
Comput. 12, 1169 (2016)] for strongly correlated
electrons can converge from above to full CI (FCI) very quickly by
constructing and diagonalizing a very small Hamiltonian matrix at
each macro/micro-iteration. However, as a direct solver of the FCI
problem, iCI is computationally very expensive. The problem can be
mitigated by observing that a vast number of configurations have little
weights in the wave function and hence do not contribute discernibly
to the correlation energy. The real questions are as follows: (a)
how to identify those important configurations as early as possible
in the calculation and (b) how to account for the residual contributions
of those unimportant configurations. It is generally true that if
a high-quality yet compact variational space can be determined for
describing static correlation, a low-order treatment of the residual
dynamic correlation would then be sufficient. While this is common
to all selected CI schemes, the “iCI with selection”
scheme presented here has the following distinctive features: (1)
the full spin symmetry is always maintained by taking configuration
state functions (CSF) as the many-electron basis. (2) Although the
selection is performed on individual CSFs, it is orbital configurations
(oCFGs) that are used as the organizing units. (3) Given a coefficient
pruning-threshold Cmin (which determines
the size of the variational space for static correlation), the selection
of important oCFGs/CSFs is performed iteratively until convergence.
(4) At each iteration, for the growth of the wave function, the first-order
interacting space is decomposed into disjoint subspaces so as to reduce
memory requirement on the one hand and facilitate parallelization
on the other hand. (5) Upper bounds (which involve only two-electron
integrals) for the interactions between doubly connected oCFG pairs
are used to screen each first-order interacting subspace before the
first-order coefficients of individual CSFs are evaluated. (6) Upon
convergence of the static correlation for a given Cmin, dynamic correlation
is estimated using the state-specific Epstein–Nesbet second-order
perturbation theory (PT2). The efficacy of the iCIPT2 scheme is demonstrated
numerically using benchmark examples, including C2, O2, Cr2, and C6H6.