Coupled-pair Many-electron Theory Research Articles

Approximate account of the connected quadruply excited clusters in the coupled-pair many-electron theory

In nondegenerate systems, the tetraexcited clusters are well approximated by products of disconnected pair clusters and the connected quadruply excited component is negligible. In contrast, when the reference state becomes quasidegenerate with the lowest biexcited configuration(s), the connected quadruply excited clusters become very important. To extend the applicability of the coupled-pair many-electron theory to such situations, we approximate the connected tetraexcited contribution in the form suggested by the unrestricted Hartree-Fock-type wave function, or one of its projected versions, such as the alternant molecular-orbital method. We show that the incorporation of the connected quadruply excited clusters into the coupled-pair equations effectively cancels certain nonlinear terms, originating from disconnected quadruple excitations, so that the resulting equations are very similar (up to a numerical factor) to the approximate coupled-pair theory, in which only those nonlinear terms which factorize with respect to the hole-electron pairs are considered. This fact shows in turn why various approximate coupled-pair approaches can often provide better results than the full coupled-pair many-electron theory.

Quasilinearized form of the CPMET method for closed-shell molecules

A diagrammatic version of the quasilinearized (QL) form of the coupled-pair-many-electron-theory (CPMET) equations for closed-shell molecules is suggested. Using the Feynman–Goldstone diagrammatic technique, a special type of one- and two-particle effective interactions is introduced, and then the CPMET equations can be formally rewritten in a form very similar to the linear coupled-cluster approach (CCA) of Coester, Kümmel, and Čížek. The QL–CPMET facilitates the formulation of the coupled-electron-pair-approximation (CEPA) methods.

Symmetry-adapted coupled-pair approach to the many-electron correlation problem. II. Application to the Be atom

The analytic forms of both the $\mathrm{LS}$-adapted coupled-pair many-electron theory (CPMET) and its linear version (LCPMET) are applied to the ground state of the Be atom in order to examine the reliability of the analytic coupled-pair approaches. Using CPMET within a ($7s,7p,4d,3f,3g$) set of orbitals, we obtain 97% of the experimental correlation energy. Special attention is paid to the convergence properties for both radial and angular correlation effects. By means of the partial-wave analysis of the various pair energies it is shown that the difference between LCPMET and CPMET is primarily due to the quasidegeneracy of the Be ground state. The role of different types of coupling terms for pair clusters is also examined yielding a basis for an understanding of various approximate coupled-pair theories. The results are compared with other calculations and the role of monoexcited and triexcited clusters is briefly discussed.

Symmetry-adapted coupled-pair approach to the many-electron correlation problem. III. Approximate coupled-pair approaches for the Be atom

Various approximations to the orthogonally spin- and orbital-symmetry-adapted coupled-pair many-electron theory (CPMET) are suggested and discussed. These approximations include methods of the well-known coupled-electron-pair-approximation (CEPA) type and methods consisting of truncating the number of pair clusters considered in the nonlinear part of the CPMET. To enable assessment of the reliability of our approximate approaches in the presence of quasidegeneracy effects, calculations of the correlation energy are performed for the Be-atom ground state.

Symmetry-adapted coupled-pair approach to the many-electron correlation problem. I.LS-adapted theory for closed-shell atoms

The orthogonally spin- and orbital-symmetry-adapted ($\mathrm{LS}$-coupled) coupled-pair many-electron theory and its extended version involving monoexcited and biexcited cluster coefficients is derived in a form suitable for application to closed-shell atomic systems. A diagrammatic approach, based on second quantization, the time-independent Wick theorem, and the graphical methods of spin algebras, is employed.

Size consistency in multi-reference double excitation CI calculations

The problem of size consistency in a multi-reference CI calculation is discussed using the method of quasi-degenerate many-body perturbation theory suggested by Brandow [1, 2]. The multi-reference form of linear coupled pair many-electron theory (CPMET), the coupled electron pair approximation (CEPA) and the Davidson correction are derived. It is shown that these methods are easily implemented in quantum chemical calculations.

A note on the lower-bound nature of the linearized CPMET

It is shown by a simple demonstration that the energy calculated from the linearized version of the coupled-pair many-electron theory (L-CPMET) of Čížek is the same as that would be obtained from the lower-bound equation of the wave operator for pair correlations as derived by Goscinski and Sinanoǧlu. A possible extension of L-CPMET retaining the lower-bound character is also indicated.

Orthogonally-spin-adapted coupled-cluster theory for closed-shell systems including triexcited clusters

The orthogonally-spin-adapted form of the nonlinear system of equations for the extended coupled-pair many-electron theory, which involves the monoexcited, biexcited, and triexcited states and cluster components, is derived. A diagrammatic approach, based on second quantization, the time-independent Wick theorem, and the graphical methods of spin algebras, is employed. The advantages of using the orthogonally-spin-adapted states and cluster components, rather than the nonorthogonally-spin-adapted ones which have been previously employed, particularly in the triexcited case, are also discussed. It is also shown that the formulas for the direct configuration-interaction method can easily be obtained in compact form from the linear part of the system of extended coupled-pair equations.

Many‐body perturbation theory, coupled‐pair many‐electron theory, and the importance of quadruple excitations for the correlation problem

AbstractMany‐body (diagrammatic) perturbation theory (MBPT), coupled‐pair many‐electron theory (CPMET), and configuration interaction (CI) are investigated with particular emphasis on the importance of quadruple excitations in correlation theories. These different methods are used to obtain single, double, and quadruple excitation contributions to the correlation energy for a series of molecules including CO2, HCN, N2, CO, BH3, and NH3. It is demonstrated that the sum of double and quadruple excitation diagrams through fourth‐order perturbation theory is usually quite close to the CPMET result for these molecules at equilibrium geometries. The superior reliability of the CPMET model as a function of internuclear separation is illustrated by studying the 1∑ potential curve of Be2. This molecule violates the assumption common to nondegenerate perturbation theory that only a single reference function is important and this causes improper behavior of the potential curve as a function of R. This is resolved once the quadruple excitation terms are fully included by CPMET.

Correlation Problems in Atomic and Molecular Systems. IV. Extended Coupled-Pair Many-Electron Theory and Its Application to the BH3Molecule

The equations of the coupled-pair many-electron theory (CPMET) are extended to incorporate the effect of both unlinked and linked triexcited clusters. The minimal basis correlation energy of the B${\mathrm{H}}_{3}$ molecule in the ground state is calculated using the ordinary as well as extended CPMET in various degrees of approximation, and the relative importance of linked and unlinked triexcited clusters is studied. The results afford an unambiguous conclusion for closed-shell systems that, in contrast to the situation with tetraexcited states, unlinked triexcited clusters are negligible relative to the linked ones. It is shown that the extended CPMET reproduces the full configuration-interaction results to a very high degree of accuracy.

Correlation problems in atomic and molecular systems III. Rederivation of the coupled‐pair many‐electron theory using the traditional quantum chemical methodst

AbstractThe equations of the coupled‐pair many‐electron theory (CPMET) for the closed shell systems are rederived both in the spin‐orbital and orbital forms without the use of second quantization, Wick's theorem or the technique of Feynman‐like diagrams. Only the Slater rules are used for the calculation of necessary matrix elements. A comparison with earlier papers shows clearly the usefulness and conceptual simplicity of the mathematical methods of quantum field theory both in the derivation of the CPMET, in spin‐orbital form, and in the process of excluding spin variables.