A critical assessment of coupled cluster method in quantum chemistry

Simple closed-form expressions are derived for the “same vacuum” renormalization terms that arise in state-specific multireference coupled cluster (MRCC) theories. Explicit equations are provided for these coupling terms through the triple excitation level of MRCC theory, and a general expression is included for arbitrary-order excitations. The first production-level code (PSIMRCC) for state-specific and rigorously size-extensive Mukherjee multireference coupled cluster singles and doubles (MkCCSD) computations has been written. This code is also capable of evaluating analogous Brillouin-Wigner multireference energies (BWCCSD), including a posteriori size-extensivity corrections. Using correlation-consistent basis sets (cc-pVXZ, X=D,T,Q), MkCCSD and BWCCSD were tested and compared on two classic multireference problems: (1) the dissociation potential curve of molecular fluorine (F2) and (2) the structure and vibrational frequencies of ozone. Comparison with experimental data shows that the Mukherjee metho...

Coupling term derivation and general implementation of state-specific multireference coupled cluster theories

The recently developed new approach to the many-electron correlation problem in atoms and molecules, termed the method of moments of coupled-cluster (CC) equations (MMCC), is reviewed. The ground-state MMCC formalism and its extension to excited electronic states via the equation-of-motion coupled-cluster (EOMCC) approach are discussed. The main principle of all MMCC methods is that of the non-iterative energy corrections which, when added to the ground- and excited-state energies obtained in the standard CC calculations, such as CCSD or EOMCCSD, recover the exact, full configuration interaction (CI) energies. Three types of the MMCC approximations are reviewed in detail: (i) the CI-corrected MMCC methods, which can be applied to ground and excited states; (ii) the renormalized and completely renormalized CC methods for ground states; and (iii) the quasi-variational MMCC approaches for the ground-state problem, including the quadratic MMCC models. It is demonstrated that the MMCC formalism provides a new ...

Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches

Standard multireference (MR) coupled cluster (CC) approaches are based on the effective Hamiltonian formalism and generalized Bloch equation. Their implementation, relying on the valence universal or state universal cluster Ansatz, is very demanding and their practical exploitation is often plagued with intruder state and multiple solution problems. These problems are avoided in the so-called state selective or state specific (SS) MR approaches that concentrate on one state at a time. To preserve as much as possible the flexibility and generality offered by the general MR CC approaches, yet obtaining a reliable and manageable algorithm, we propose a novel SS strategy providing a size-extensive CC formalism, while exploiting the MR model space and the corresponding excited state manifold. This strategy involves three steps: (i) The construction of a variational configuration interaction (CI) wave function within the singly (S) and doubly (D) excited state manifold, (ii) the cluster analysis of this CI wave...

Reduced multireference CCSD method: An effective approach to quasidegenerate states

The necessity to account for many-electron correlation effects in atomic and molecular electronic structure calculations was realized in the sixties, when the first attempts to compute dissociation or activation energies of simple chemical processes (e. g., Wahl, 1964; Schaefer, 1971, 1972) and various molecular properties (e. g., Huo, 1965) were made. The initial hope that the configuration interaction (CI) approach limited to doubly excited configurations, originating from a single reference state, will provide a satisfactory description of correlation effects soon had to be given up (see, e. g., Bender and Davidson, 1968, 1969; Barr and Davidson, 1970; Davidson, 1974). By that time the basic structure of correlated wavefunctions (Hubbard, 1957, 1958) and the problem of size extensivity (Brueckner, 1955; Goldstone, 1957; Primas, 1965) were well understood [although this term was employed only later (Bartlett and Purvis, 1978)], thanks to the developments in solid state (e. g., Gell-Mann and Brueckner, 1957; Quinn and Ferrell, 1958) and nuclear (e. g., deShalit and Feshbach, 1974; Eisenberg and Greiner, 1972) physics. In particular, the linked cluster theorem of the many-body perturbation theory (MBPT) and the connected cluster structure of the exact wavefunctions (Hubbard, 1958b) were firmly established. The exponential ansatz for the wave operator, implied by Hubbard’s (1958b) work, was exploited in the context of the nuclear correlation problem by Coester (1958) and Coester and Kummel (1960).

Coupled Cluster Theory

Recently developed explicit form of a spin-adapted multi-reference linear coupled cluster (MRCC) formalism for the two-dimensional model space involving closed-shell-type configurations [B. Jeziorski and J. Paldus, J. Chem. Phys. 88, 5673 (1988)] has been extended by including quadratic terms in both the direct and the coupling part of the MRCC equations. The formalism has been applied to the H4 model system studied earlier by Jankowski and Paldus [Intern. J. Quantum Chem. 18, 1243 (1980)]. In the quasidegenerate region, where the single reference LCCSD approximation breaks down, the two-reference LCCSD method performs very well providing good results for both states. However, in the non-degenerate region, the linear multireference approach is plagued with intruder state problems, since the second reference state interacts strongly with other excited configurations. The inclusion of the quadratic terms in the MRCC equations resolves the intruder state difficulty. We also find that the MRCC equations possess multiple solutions capable of describing not only the two lowest states but also various other pairs of states, as long as they contain a significant contribution from the reference configurations.

Spin-Adapted Multi-Reference Coupled Cluster Formalism Including Non-Linear Terms and its Application to the H4 Model System

A brief description of basic models and methods that are currently exploited in molecular electronic structure calculations indicates the desirability of extending the single-reference coupled-cluster (CC) approach to the multi-reference (MR) case. The recently developed explicit formalism of orthogonally spin-adapted, state-universal (or Hilbert space) MR-CC theory for the special case of closed-shell type references is applied to a simple four-electron model system formed by two interacting hydrogen molecules. Varying the geometry of the nuclear framework from the square configuration to a linear one this model simulates the breaking of a single chemical bond and enables a continuous transition to be made between the degenerate and non-degenerate regimes. The simplicity of the model enables a comparison with the exact solution, obtained by the full configuration interaction method. In this way the performance of the MR-CC approach at both linear and non-linear levels of approximation, nature and multiplicity of MR-CC solutions and the role played by the intruder states can be examined in considerable detail.

L. Pylypow

Papers

Spin-Adapted Multi-Reference Coupled Cluster Formalism Including Non-Linear Terms and its Application to the H4 Model System

Extension of Coupled Cluster Methodology to Open Shells: State Universal Approach