Size-extensivity corrections in configuration interaction methods

Abstract

Limited configuration interaction methods suffer from size-extensivity errors. The origin and behavior of these errors is discussed and new versions of single and multireference corrections are presented. Accuracy of the new and various other size-extensivity corrections used in the literature is discussed and compared in a series of model calculations and calculations on small molecules. None of the commonly used multireference corrections restores the size extensivity of multireference configuration interaction calculations. Our correction behaves correctly for the special case of a reference state composed from all singly and doubly excited configurations. Formulas for size extensivity corrections in the variational-perturbation method are given and discussed.

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

“…ECISD is a truncated CI, which is known to be size-inconsistent. 25 Hence, this gives a large ∆ SC of 5.18 mE h for AB, which nonetheless is slightly smaller than that of conventional CISD for AA (7.84 mE h ). Furthermore, it is worth mentioning that, for BB, the error in SUHF is compensated by ECISD.…”

“…The size-extensivity of each method can be studied using n non-interacting Be atoms (n > 1), 25 where all the atoms experience broken-symmetry. The correlation energy per atom (with respect to HF) is plotted for each method in Figure 4, in which we set N grid = 7 to perform precise spin-projection.…”

“…In both SR-CI and MR-CI, the introduction of size-consistent corrections by Davidson 21,22 and others 23,24 partially mitigates the size-inconsistency error by approximating quadruple excitations. 25 The generalization of the Davidson correction to ECISD (ECISD+Q) was shown to drastically improve the accuracy of ECISD; nonetheless, ECISD+Q is neither size-extensive nor variational with respect to the CI coefficients. The lack of the latter property is also troublesome, because the analytical gradient of ECISD+Q is not straightforward to compute, hindering the geometric optimization and computation of molecular properties (i.e., density matrix).…”

Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures

“…33,34 Generally, a variety of the Davidson corrections require the CI coefficient C 0 of the reference wave function, e.g., the simplest one being ∆E Q = (1 − C 2 0 )∆E SD . 32 In ECISD, on the other hand, this equation is not directly applicable because our reference wave functionP|Φ⟩ permeates the singles and doubles spaces throughP, as manifested by the fact ⟨Φ a i |P|Φ⟩ 0. The role of C 2 0 in the Davidson corrections for (MR)CISD is that it carries the information about the weight that the reference state occupies in the space spanned by |Ψ⟩.…”

“…However, since ECISD truncates the full-CI (FCI) expansion at doubles and neglects simultaneous double excitations, its correlation energy obviously does not have the proper scaling with respect to the system size. 32 To correct this, we consider, in analogy with regular CISD and MRCI, an a posteriori treatment of approximate quadruple excitations using the Davidson correction scheme. 33,34 Generally, a variety of the Davidson corrections require the CI coefficient C 0 of the reference wave function, e.g., the simplest one being ∆E Q = (1 − C 2 0 )∆E SD .…”