Superposition of nonorthogonal Slater determinants towards electron correlation problems

Abstract

We propose variational and nonvariational methods based on the superposition of nonorthogonal Slater determinants. Properties of the reference functions are discussed. In the nonorthogonal con®guration interaction method, all the excited con®gurations of multiple determinants are integrated into a variational space. An ecient way to manipulate matrix elements over determinants of distinct vacuums is presented by introducing similarity transformed operator and bracket transformations. The method enables us to map a matrix multiplication in the nonorthogonal problem to an orthogonal one, and thus maintains a fundamental scaling property along with the amount of data processed in the corresponding orthogonal con®guration interaction method. Furthermore, we discuss a coupledcluster theory employing a vacuum-dependent wave operator, which is entirely size consistent as well as core extensive. These methods are applied to H 2 O nHen 0À2 and a single-bond dissociation of the HF molecule, compared with conventional methods including full and multireference con®guration interaction methods.

Black-Box Description of Electron Correlation with the Spin-Extended Configuration Interaction Model: Implementation and Assessment

“…Therefore, it is convenient to take the summations of indices as in eqs and to transform the Fock and two-electron integrals. This Hamiltonian transformation is similar to but different from the one used in the coupled-cluster theory with exp­( T̂ 1 ), , which does not contain redundant de-excitations, contrary to our R̂ g .…”

“…As mentioned, however, we noticed very few works along this line. One of us proposed such a scheme based on two spin-restricted nonorthogonal determinants with very accurate results . Yost et al recently developed a “perturb-then-diagonalize” scheme that uses the first-order wave functions of non-aufbau SCF states as a NOCI basis …”

Generalized nonorthogonal matrix elements: Unifying Wick’s theorem and the Slater–Condon rules

“…Matrix elements between nonorthogonal Slater determinants are increasingly common in emerging electronic structure methods. For example, capturing strong correlation using a linear combination of nonorthogonal Slater determinants is a relatively old idea [1][2][3][4] that has seen a renaissance in the past decade. [5][6][7][8][9][10][11][12][13][14] Similarly, nonorthogonal matrix elements arise in projected Hartree-Fock methods, 15,16 while the combination of geminal-based nonorthogonal functions is an area of ongoing research.…”

“…16,40,41 Computationally efficient nonorthogonal matrix elements become increasingly important in methods that use orthogonally excited configurations from nonorthogonal reference determinants. For example, including post-NOCI dynamic correlation in methods such as perturbative NOCI-MP2 [42][43][44] and NOCI-PT2, 14 or nonorthogonal multireference CI, 3,16,41,45 requires overlap, onebody, or two-body coupling terms between excitations from nonorthogonal determinants. The number of nonorthogonal matrix elements therefore grows rapidly, and repeated biorthogonalization of the occupied orbitals becomes prohibitively expensive.…”

Reaching Full Correlation through Nonorthogonal Configuration Interaction: A Second-Order Perturbative Approach

“…The primary obstacle to deriving dynamically correlated post-NOCI techniques is the lack of a common set of molecular orbitals for the NOCI reference determinants. While multireference CI and coupled-cluster (CC) extensions to NOCI were reported in ref , subsequent developments have focussed on adding dynamic correlation to the NOCI expansion in an approximate manner. For example, in the NOCI-MP2 approach, each reference determinant is individually perturbed using the second-order Møller–Plesset perturbation theory (MP2) before the NOCI eigenvalue problem is solved, leading to a “perturb-then-diagonalize” approach. − However, the original NOCI-MP2 algorithm was found to contain size consistency errors that required ad hoc alterations to the working equations .…”