Selected Configuration Interaction in a Basis of Cluster State Tensor Products

Abstract

Selected configuration interaction (SCI) methods are currently enjoying a resurgence due to several recent developments which improve either the overall computational efficiency or the compactness of the resulting SCI vector. These recent advances have made it possible to get full CI (FCI) quality results for much larger orbital active spaces compared to conventional approaches. However, due to the starting assumption that the FCI vector has only a small number of significant Slater determinants, SCI becomes intractable for systems with strong correlation. This paper introduces a method for developing SCI algorithms in a way which exploits local molecular structure to significantly reduce the number of SCI variables. The proposed method is defined by first grouping the orbitals into clusters over which we can define many-particle cluster states. We then directly perform the SCI algorithm in a basis of tensor products of cluster states instead of Slater determinants. While the approach is general for arbitrarily defined cluster states, we find significantly improved performance by defining cluster states through a Tucker decomposition of the global (and sparse) SCI vector. To demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), we present numerical results for a diverse set of examples: (1) modified Hubbard model with different inter-and intracluster hopping terms, (2) less obviously clusterable cases of bond breaking in N 2 and F 2 , and (3) ground state energies of large planar π-conjugated systems with active spaces of up to 42 electrons in 42 orbitals. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems.

Reinforcement Learning Configuration Interaction

“…Further work to explore the transfer of data between different Hamiltonians in order to improve efficiency should also be explored. Additional investigations of perturbative corrections on top of the RLCI-learned wave function may also yield robust convergence to the FCI limit with compact wave function references, as has been observed in other sCI methods 5,18,[54][55][56]…”

Reinforcement Learning Configuration Interaction

“…Other improvements of the RLCI method include modifying the action space to allow more than one determinant to be added or removed from the state, optimizing the learning rate and the discount factor, and gaining a better understanding of the trade-off between exploration and exploitation. Additional investigations of perturbative corrections on top of the RLCI-learned wave function may also yield robust convergence to the FCI limit with compact wave function references, as has been observed in other sCI methods 3,16,[46][47][48]…”

“…We note that there is no orbital optimization in either the RLCI or HCI methods presented here, which may prove beneficial in cases such as these. Or, there may simply be limits to how well determinant-based methods can compress the wave function and other wave function ansätze, such as matrix 45 or tensor 16 product states may prove more efficient. Utilizing configuration state function (CSFs) may also additionally compress the wave function, though the RLCI will lose some of the computational advantages of a determinant-based approach.…”

Reinforcement Learning Configuration Interaction

“…Other improvements of the RLCI method include modifying the action space to allow more than one determinant to be added or removed from the state, optimizing the learning rate and the discount factor, and gaining a better understanding of the trade-off between exploration and exploitation. Additional investigations of perturbative corrections on top of the RLCI-learned wave function may also yield robust convergence to the FCI limit with compact wave function references, as has been observed in other sCI methods 5,18,[54][55][56] Graphical TOC Entry…”