Péter R. Surján

Higher excitations in coupled-cluster theory

The viability of treating higher excitations in coupled-cluster theory is discussed. An algorithm is presented for solving coupled-cluster (CC) equations which can handle any excitation. Our method combines the formalism of diagrammatic many-body perturbation theory and string-based configuration interaction (CI). CC equations are explicitly put down in terms of antisymmetrized diagrams and a general method is proposed for the factorization of the corresponding algebraic expressions. Contractions between cluster amplitudes and intermediates are evaluated by a string-based algorithm. In contrast to our previous developments [J. Chem. Phys. 113, 1359 (2000)] the operation count of this new method scales roughly as the (2n+2)nd power of the basis set size where n is the highest excitation in the cluster operator. As a by-product we get a completely new CI formalism which is effective for solving both truncated and full CI problems. Generalization for approximate CC models as well as multireference cases is a...

A general state-selective multireference coupled-cluster algorithm

A state-selective multireference coupled-cluster algorithm is presented which is capable of describing single, double (or higher) excitations from an arbitrary complete model space. One of the active space determinants is chosen as a formal Fermi-vacuum and single, double (or higher) excitations from the other reference functions are considered as higher excitations from this determinant as it has been previously proposed by Oliphant and Adamowicz [J. Chem. Phys. 94, 1229 (1991)]. Coupled-cluster equations are generated in terms of antisymmetrized diagrams and restrictions are imposed on these diagrams to eliminate those cluster amplitudes which carry undesirable number of inactive indices. The corresponding algebraic expressions are factorized and contractions between cluster amplitudes and intermediates are evaluated by our recent string-based algorithm [J. Chem. Phys. 115, 2945 (2001)]. The method can be easily modified to solve multireference configuration interaction problems. Performance of the method is demonstrated by several test calculations on systems which require a multireference description. The problem related to the choice of the Fermi-vacuum has also been investigated.

Computing coupled-cluster wave functions with arbitrary excitations

An algorithm is presented for solving coupled-cluster (CC) equations by successive diagonalization of 2×2 matrices. It is more expensive than usual procedures, but it is capable of solving a CC problem where any arbitrary excitation is included in the cluster operator. Equation-of-motion coupled-cluster (EOMCC) excitation energies can also be determined by this method regardless of the type of excitations in the cluster operator and the space where the effective Hamiltonian is diagonalized. The algorithm is applied to the study of the convergence of CC and EOMCC series in some small bases.

An observable-based interpretation of electronic wavefunctions: application to “hypervalent” molecules

Abstract The quantum-mechanical definition of observables is extended to all properties that can be derived from experimentally measurable quantities with the help of universal operators. Even such an extended definition, however, does not cover several commonly used concepts such as atomic orbitais in molecules or Mulliken atomic charges. Principles of an observable-based interpretation of electronic wavefunctions are outlined. Such an approach avoids ill-defined properties and concepts, therefore minimizing arbitrariness inherent in the interpretation process. Currently known atomic and bond quantities that are observable are reviewed and applied to four “hypervalent” molecules containing sulfur atoms. It is found that the S-O bonds in the molecules under study have highly ionic character and bond orders close to unity. This clear-cut analysis demonstrates that the octet rule is not violated in “hypervalent” compounds with one or two S-O bonds.

Monomer geometry relaxation and the basis set superposition error

Abstract Possible generalizations of the Boys—Bernardi counterpoise correction scheme to the case of relaxed monomer geometries is discussed. It is emphasized that the monomer relaxation energy should be calculated in the basis of free monomers, because it becomes ambiguous in the supermolecule basis.

Two-body zeroth order Hamiltonians in multireference perturbation theory: The APSG reference state

A special version of multi-reference perturbation theory is investigated which differs from standard ones by using a zeroth order Hamiltonian that contains two-electron terms explicitly. The method is applicable to reference states that can be written as an antisymmetrized product of two or more electron functions. In that case the zeroth order Hamiltonian has a well defined physical meaning and the matrix elements that come about can be evaluated in an efficient manner. We implemented the theory for the antisymmetrized product of strongly orthogonal geminals wave function and, as a special case, for the generalized valence bond. Illustrative calculations on sample molecules show the reliability of the approach, as well as a significant improvement in many cases compared to MRPT versions based on one-body zeroth order Hamiltonians.

On the perturbation of multiconfiguration wave functions

A simple variant of perturbation theory is used to correct reference states of a general multiconfigurational character. The full solution of an active space is not required, and no iterative procedure is applied to construct the resolvent operator. The perturbed wave function is expanded in a complete set of determinants from which the reference function is projected out, and the overlap between projected determinants is handled by an explicit, analytic inversion of the overlap matrix.

An Introduction to the Theory of Geminals

Two-electron functions, called also geminals, have been around in quantum chemistry for some time. They represent a generalization of one-electron orbitals accounting for intra-orbital correlation effects. Geminal-based methods can be tailored to be variational as well as size-consistent and size-extensive. In spite of these appealing features, geminals became somewhat eclipsed in modern quantum chemistry because of their relative complexity and because the associated energies do not always cover a sufficient fraction of the correlation energy. However, several recent investigations revisit geminals and advocate the use of some extended geminal models which may turn out to offer useful alternatives to conventional approaches. In this paper, the formalism of two-electron functions will be reviewed in a simple fashion, focusing mainly on qualitative and conceptual points rather than technical details. After a short historical survey, the basic notions of geminals will be reviewed both in first- and second-quantized notations, the latter being especially advantageous when dealing with geminals. A few important points about the optimization of geminal-based wave functions will then be discussed, followed by a discussion about the inherent connection between geminals and the localization problem. We shall close with a few remarks on the prospect of geminal theories.

Localization and delocalization: Distinction between through space and through bond interactions

We propose a special perturbation formalism based on the local Brillouin theorem to study the effects causing delocalization (’’tails’’) of bond orbitals. Assuming a given one‐electron Hamiltonian, an explicit recursion relation is derived for the tails to any order. It permits to distinguish between the ’’through space’’ effects caused by the direct interaction of bonds, and the ’’through bond’’ ones which appear in higher orders. Application of the results to SCF‐type theories indicates that only through space interactions like vicinal ones are orientation sensitive.

Multiconfiguration perturbation theory: Size consistency at second order

A modified version of a previously elaborated multiconfiguration perturbation theory (MCPT) [Rolik et al. J. Chem. Phys. 119, 1922 (2003)] is presented. In the modified formulation size consistency is ensured at second order in energy, by omitting projectors from the zero order Hamiltonian operator. This MCPT formulation is abbreviated as SC2-MCPT (size consistent at second order). To ensure proper separability, we also require that energy denominators are constructed as differences of some one-particle energies. A similar choice for energy denominators also renders the well-known multireference Moller-Plesset (MRMP) energy size consistent at second order. The same thing applies to the related multireference perturbation theory by Witek, Nakano, and Hirao.