Use of noncanonical orbitals in many-body perturbation theory

A formalism for dealing with noncanonical Hartree–Fock spin orbitals is presented within the framework of many-body perturbation theory. A test calculation on the planar methyl radical is carried out which displays certain features of open-shell calculations and which demonstrates the viability of using noncanonical spin orbitals. Results are found to be in good agreement with a previous configuration interaction calculation.     

Application of the many-body perturbation theory to normal saturated hydrocarbons in the localized representation

The second-order energy corrections are calculated for some normal saturated hydrocarbons by using the many body-perturbation theory (MBPT) based on localized orbitals. The correlation energies are expressed as the sum of contributions from virtual orbital pairs. We have found that these contributions are transferable and have interesting structural features: the trans-coplanar effects are relatively large. Partitioning the correlation energies according to the order of neighbourhood we have found that the zero order effects are the largest but the first and second neighbour contributions are also important.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Application of many-body perturbation theory in the localized representation for the all-trans conjugated polyenes

Ab initio self-consistent field (SCF ) calculations are performed with the standard 6-31G* basis set for all-trans conjugated oligomers C_2n+2H_2n+4. The canonical occupied and virtual molecular orbitals (MO s) are separately localized by unitary transformations. Due to the localization, the perturbation operator is partitioned into two-particle and into single-particle terms; the MBPT is, therefore, a double-perturbation expansion in this case. By using the localized representation of the MBPT , the correlation energy contributions can be partitioned into local and nonlocal effects. It can be shown that the local effects are very important and well transferable, which makes possible the calculation of the correlation energy of larger molecules if the localized molecular orbitals (occupied and virtual) of smaller related molecules are known. © 1994 John Wiley & Sons, Inc.     

Finite-field many-body perturbation theory. Calculations of the dipole polarizability of the fluoride ion using electric-field-variant gaussian-type orbitals

The dipole polarizability of the fluoride ion, F^–, is calculated using finite-field many-body perturbation theory. The use of electric-field-variant basis sets in such calculations is investigated. Scaling of the zero-order Hamiltonian and the formation of Padé approximants are considered. Empirical and theoretical estimates of the polarizability of F^– are compared.Science Research Council Advanced Fellow.     

A constant-denominator perturbation theory using circulant orbitals

Molecular-orbital calculations, using the INDO procedures, were carried out on the tautomers of 1, 2, 4-triazole and its benzo-derivative as well as on 1, 2, 5-oxadiazole and its benzo-derivative. Calculations of the transition energy as well as the dipole moment helped to predict the predominant tautomer in an equilibrium mixture. The correspondence between the calculated and observed data is satisfactory. The results of calculations indicated some differences in the electronic structures of the tautomers of a compound.     

Iterative natural orbitals for configuration interaction using perturbation theory

Approximate natural orbitals are determined iteratively from CI expansions constructed using first-order perturbation theory in order to investigate the possibility of eliminating the complete transformation of MO integrals on each iteration. Results on LiH and H₂O are compared with fully variationally determined NO's to assess questions of convergence.     

Calculation of correlation energy by many-body diagrammatic perturbation theory

The many-body diagrammatic perturbation theory is used for calculation of the correlation energy of closed-shell molecular systems. We apply Brueckner's concept of the two-particle renormalized interaction defined by a non-linear diagrammatic expression containing all possible (diagonal and/or non-diagonal) particle-particle, hole-hole and particle-hole intermediate elementary processes. Then, a “second-order” simple diagrammatic expression for the correlation energy can be formed, where the correlation energy is approximated by all the diagrams with biexcited intermediate states. An illustrative numerical application for the LiH molecule is presented. This article is dedicated to the memory of our friends and colleagues Dr. Jarka Surá and Dr. Marta Černayová, who tragically died in July 1976.     

Electric dipole polarizability of the hydrogen molecule by many-body perturbation theory

Many-body perturbation theory is used to calculate the static electric dipole polarizability of the hydrogen molecule with a basis set of gaussian orbitals. Corrections complete through second order in electron correlation are calculated, and partial summation of certain classes of diagrams are extensively explored. The results are discussed in connection with the geometric approximation incorporating higher-order corrections.     

Finite-field many-body perturbation theory quadrupole polarizability of Be

Many-body perturbation theory is used for the calculation of the quadrupole polarizability of the Be atom within the finite-field perturbation scheme. The correlation corrections exhibit a considerable dependence on the f-type orbital exponents and the final results are in the range 287–294 au. The convergence of the correlation perturbation series is discussed.     

A note on the convergence of multiconfigurational many-body perturbation theory

The convergence of multiconfigurational many-body perturbation theory (MC MBPT ) is discussed in connection with the intruder state. Its convergence properties are first examined with a fictitious three-level system employing a Hermitian version of MC MBPT , which permits a general model space. It is then applied to the H₂—H₂ and N₂ systems. The results suggest that a more extensive model space is likely to embrace new intruder states and the space extension be executed with due caution.     

Extremely localized molecular orbitals: theory and applications

Orbitals that are extremely localized on molecular fragments represent a powerful tool for a number of purposes: to cite a few examples, they allow to reduce strongly the complexity of calculations on large systems and are easily transferable from one molecule to another, providing a suitable and efficient way to build up the electronic structure of large molecules. Recently, we have developed efficient algorithms to determine extremely localized molecular orbitals (ELMOs), which will be reviewed in this paper. As a rigorous localization is strictly connected to a reduction in the number of variational parameters, which reflects into an increased value of the associated energy with respect to the Hartree Fock value, we have developed a number of strategies to relax the wavefunction built up using transferred localized orbitals. The extreme localization has also been exploited in connection with the “Divide and Conquer” technique to determine the electron densities of large polypeptides assembled from orbitals computed on small model molecules. Moreover, we will discuss the recent application of the ELMOs in the framework of the hybrid QM/MM methods to describe the frontier region. We will also show that the ELMOs can be used to extract chemical interpretations from numerical results. A variety of applications will be presented.     

Systematic sequences of even-tempered Gaussian primitives in electron correlation studies using many-body perturbation theory

The use of systematic sequences of even-tempered Gaussian primitive functions in electron correlation studies using diagrammatic many-body perturbation theory is examined. The s limit electronic energy of the Be atom and the sp limit energy of the Ne atom have been computed as examples. The use of the Hartree extrapolation procedure to obtain empirical upper bounds for the basis set limit is investigated. The empirical lower bound for the basis set limit suggested by Schmidt and Ruedenberg is examined for calculations which include electron correlation.     

Excited-state energies from many-body perturbation theory with the excitation-adapted one-particle potential

Calculation of excited-state energies by many-body perturbation theory is discussed. A Hartree-Fock-type potential suitable for a given excited-state configuration is introduced. Advantages which follow from the excitation-adapted one-particle potential are examined. The theory resembles that for external perturbation effects and amounts to removing or minimizing the contribution of non-diagonal one-particle terms.     

Pseudopotential method for the direct construction of localized orbitals by multiconfiguration self-consistent field theory

The orbital equations for the direct construction of localized fixed orbitals by multiconfiguration self-consistent field theory (MCSCF-FXO) are transformed without approximation into pseudopotential form by a two-step process. First the utilization of a particular family of localization is shown to separate the set of orbital equations into two sets of coupled equations, one describing “valence” orbitals and one describing “core” orbitals. In addition we obtain by appropriate choice of localization potential three different sets of MCSCF-FXO orbitals, namely: maximally screened, “one-center” and “intermediate” orbitals. In the second step the orbital equations are transformed into pseudopotential form and explicit non-local pseudopotentials yielding and core orbitals are obtained. Finally, several different physically motivated approximations to the exact pseudopotentials, and the frozen-core approximation are discussed.     

On the use of spin graphs for spin adapting many-body perturbation theory

In connection with spin adaptation in many-body perturbation theory, this paper reexamines the use of spin graphs in view of a Hugenholtz-like representation where both the orbital and the spin parts coexist. Together with the idea of essentially distinct diagrams, this representation leads to an economic handling of spin adaptation. As a side issue, the appropriate generalization of the Epstein–Nesbet partitioning for spin-adapted perturbation theory is obtained. Compact formulas up to fourth order of the ground-state energy, and up to third order for excitation energies and ionization potentials are given.     

Applicability of multireference many-body perturbation theory to the Ne2+ molecule

The ground state as well as some low-lying excited states of the Ne₂⁺ molecule are calculated by means of the third-order multireference many-body perturbation theory with the “full” eight-orbital valence space using DZP and polarized valence TZ basis sets. The problem encountered with a large number of valence electrons is avoided by a proper definition of the Fermi vacuum. The calculated equilibrium distance of 1.721 Å and chemical dissociation energy D₀ = 1.283 eV are in good agreement with experimental results. A comparison with other ab initio techniques is also provided. © 1997 John Wiley & Sons, Inc.     

Third-order many-body perturbation theory for the ground state of the carbon monoxide molecule

Many-body perturbation calculations have been performed for the ground state of the carbon monoxide molecule at its equilibrium internuclear separation. The calculations are complete through third order within the algebraic approximation; i.e., the state functions are parameterized by expansion in a finite basis set. All two-, three-, and four-body terms are rigorously determined, and many-body effects are found to be very important. A detailed comparison is made with a previously reported configuration interaction study. Padé approximants to the energy expansion are constructed. The many-body perturbative wave function is used in the Rayleigh quotient to produce upper bounds to the electronic energy.