Evolutionary algorithm based configuration interaction approach

Abstract

A stochastic configuration interaction method based on evolutionary algorithm is designed as an affordable approximation to full configuration interaction (FCI). The algorithm comprises of initiation, propagation and termination steps, where the propagation step is performed with cloning, mutation and cross-over, taking inspiration from genetic algorithm. We have tested its accuracy in 1D Hubbard problem and a molecular system (symmetric bond breaking of water molecule). We have tested two different fitness functions based on energy of the determinants and the CI coefficients of determinants. We find that the absolute value of CI coefficients is a more suitable fitness function when combined with a fixed selection scheme.Keywords: genetic algorithm, evolutionary algorithm, configuration interaction Majority of the electronic structure methods that have been developed and used over the last few decades starts with the independent orbital approximation, i.e. the assumption that a single Slater determinant is a qualitatively correct starting point for a calculation. This qualitatively correct reference is typically corrected for dynamic correlation with post Hartree Fock (HF) methods such as Moller-Plesset perturbation theory (MP2) or coupled cluster singles and doubles (CCSD). However, the assumption of a single Slater determinant as a reference is not qualitatively correct, especially in situations where there are significant orbital degeneracies or neardegeneracies, e.g., bond breaking or di-and tri-radicals. Such systems are referred to as strongly correlated systems and the electronic correlation in these systems are referred to as static correlation, as opposed to dynamic correlation. It is important to note that we are not differentiating between true correlation due to orbital degeneracies and that required to treat proper spin symmetry (non-dynamic and static correlations). 1 Full configuration interaction (FCI) is the most rigorous method to treat correlation, both static and dynamic. However, FCI involves exact diagonalization of the full Hamiltonian in its Hilbert space and is therefore, not affordable for reasonable system sizes and basis sets. 2 Therefore, approximate methods such as CASSCF 3 and RASSCF 4 etc have been developed where only a subset of the orbital space is treated exactly to reduce the computational cost. But these methods also involve an exact diagonalization, albeit over a smaller sub-space. On the other hand, density matrix renormalization group (DMRG) 5-9 have been developed to circumvent the exact diagonalization problem and therefore, the associated exponential scaling. While DMRG has been remarkably successful in the case of pseudo-linear systems, more general 2D and 3D systems are complicated due to problems in orbital ordering. 10,11 However, there have been a) http://academic.ncl.res.in/debashree.ghosh b) Electronic mail: debashree.ghosh@gmail.com developments towards using tensor networks to alleviate this problem. 12,13 Antisymmetrized geminal power (AGP) wavefunctions ha...

Selected Configuration Interaction in a Basis of Cluster State Tensor Products

“…More general tensor networks have also been explored. − For systems whose strong correlation occurs among a relatively small subset of Slater determinants (as opposed to a single-particle subset defining an active-space), one might choose to perform a configuration interaction (CI) calculation using only the important Slater determinants. This is the physical motivation for so-called “selected CI” methods which have a long history in the field − but which have seen a resurgence during the past few years. − …”

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