GVB–RP: A reliable MCSCF wave function for large systems

We have developed a version of generalized valence bond (GVB) that overcomes the major weakness of the perfect pairing approximation without requiring a full transformation of the integrals at each step of the self‐consistent orbital optimization. The method, called generalized valence bond–restricted pairing (GVB–RP), describes properly the dissociation of up to triple bonds and provides smooth potential energy surfaces for most chemical reactions. The wave functions obtained are a good starting point for more sophisticated computational techniques. The applicability of the method is illustrated with a few simple examples including multiple‐bond dissociations, transition states for symmetry allowed, symmetry forbidden, and radical reactions, as well as reactions at a transition‐metal center. The cost of the method compares well with other self‐consistent correlated techniques. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 1–22, 1999     

Unrestricted perfect pairing: the simplest wave-function-based model chemistry beyond mean field

The perfect pairing (PP) approximation from generalized valence bond theory is formulated in an unrestricted fashion for both closed- and open-shell systems using a coupled cluster ansatz. In the model chemistry proposed here, active electron pairs are correlated, but the unpaired or radical electrons remain uncorrelated, leading to a linear number of decoupled cluster amplitudes which can be solved for analytically. The alpha and beta spatial orbitals are variationally optimized independently. This minimal treatment of electron-electron correlation noticeably improves upon symmetry-breaking problems and other pathologies in Hartree-Fock (HF) theory and may be computed using the resolution of the identity approximation at only a factor of several times more effort than HF itself. PP also generally predicts improved molecular structures over HF. This compact, correlated wave function potentially provides a useful starting point for dynamical correlation corrections.     

Electron pair localization function: a practical tool to visualize electron localization in molecules from quantum Monte Carlo data

In this work we introduce an electron localization function describing the pairing of electrons in a molecular system. This function, called "electron pair localization function," is constructed to be particularly simple to evaluate within a quantum Monte Carlo framework. Two major advantages of this function are the following: (i) the simplicity and generality of its definition; and (ii) the possibility of calculating it with quantum Monte Carlo at various levels of accuracy (Hartree-Fock, multiconfigurational wave functions, valence bond, density functional theory, variational Monte Carlo with explicitly correlated trial wave functions, fixed-node diffusion Monte Carlo, etc). A number of applications of the electron pair localization function to simple atomic and molecular systems are presented and systematic comparisons with the more standard electron localization function of Becke and Edgecombe are done. Results illustrate that the electron pair localization function is a simple and practical tool for visualizing electronic localization in molecular systems.     

Ab initio valence bond calculations. XI. Pyridine: Ground and ionized states

The ab initio valence bond method has been used to study the ground and the lowest vertical valence ionized states of pyridine. On the basis of our calculations the first two ionization potentials are assigned to π and n electron removals, respectively. The final wave functions have been interpreted in terms of valence bond structures by means of an appropriate population analysis.     

Quantum Monte Carlo with Jastrow-valence-bond wave functions

We consider the use in quantum Monte Carlo calculations of two types of valence bond wave functions based on strictly localized active orbitals, namely valence bond self-consistent-field and breathing-orbital valence bond wave functions. Complemented by a Jastrow factor, these Jastrow-valence-bond wave functions are tested by computing the equilibrium well depths of the four diatomic molecules C(2), N(2), O(2), and F(2) in both variational Monte Carlo and diffusion Monte Carlo. We show that it is possible to design compact wave functions based on chemical grounds that are capable of describing both static and dynamic electron correlations. These wave functions can be systematically improved by inclusion of valence bond structures corresponding to additional bonding patterns.     

MO theoretical studies of electron pair decorrelation processes. I. Pair correlation energy and single bond dissociation

The homolytic dissociation of a single bond involves the decorrelation of one electron pair. Thus, the contribution of electron correlation to dissociation energies is large. In the present paper a new procedure is presented which allows the computation of the (within the given basis) complete correlation energy of one optimized electron pair. The method which requires only modest computational effort has been applied to the calculation of dissociation energies of a number of bonds of different types. The results show that the correlation of the electron pair of the bond which is broken contributes about 50–80% to the change of the total correlation energy occuring during the dissociation process which amounts to 20–70 kcal/mol. The fraction of correlation contributed by the bond electron pair as well as the relative importance of the left-right correlation within the bond depend very much on the type of the bond. In the case of CC and CH single bonds our method yields dissociation energies which are low by only about 5 kcal/mol. Thus, the method seems to be well suited for the calculation of potential surfaces of non-concerted organic chemical reactions which involve diradicals as intermediates.     

Unrestricted-Hartree–Fock wave functions approximating low-lying covalent states of ring π systems

We show that spin projected unrestricted-Hartree–Fock (PUHF ) wave functions are able to well approximate some low-lying covalent states of ring π systems. The UHF wave functions belong to either the axial or torsional spin density wave class. Their spin structures are found to be approximations for the spin correlation structures of the corresponding exact wave functions. The PUHF wave functions become close to exact eigenstates with homopolar valence bond characters in the strong correlation limit.     

On the nodal structure of single-particle approximation based atomic wave functions

The nodal structures of atomic wave functions based on a product of spatial orbitals, namely, restricted, unrestricted, and generalized valence bond wave functions, are shown to be equivalent. This result is verified by fixed node-diffusion Monte Carlo simulations for atoms up to Ne. Also for a molecular system, Li(2) at the equilibrium geometry, a multideterminantal generalized valence bond wave function does not improve the nodal surfaces of a restricted Hartree-Fock wave function.     

Character of the electronic ground state and of charge-transfer excited states in ionic solids: An ab initio cluster model approach

The electronic structure of the ground electronic state and of some special charge-transfer excited states in ionic solids is examined from the ab initio cluster model approach. Different ab initio wave functions, including a frozen orbital approach, the Hartree–Fock self-consistent field, and multireference configuration interaction wave functions, are considered and analyzed using different theoretical techniques. We explicitly consider some alkaline–earth oxides such as CaO, a more difficult case such as A1₂O₃, a transition-metal oxide such as NiO, and a system with a more complicated structure such as KNiF₃. Analysis of ab initio wave functions in terms of valence bond components shows that all these compounds are largely ionic, thus supporting the simple picture arising from the ionic model. However, the nature of the excited states is more complex. Alkaline–earth oxides lowest excited states are essentially described as charge-transfer excitations dominated by a single resonant valence bond structure and the calculated energy difference is comparable to the experimental optical gap. In the case of A1₂O₃, the electronic spectra presents excitonic features and the local charge-transfer excitation excited states provide a reasonable representation of these phenomena. Finally, several different valence bond structures are present in the lowest electronic states of KNiF₃. © 1994 John Wiley & Sons, Inc.     

Correlation effects in the low–lying excited states of the PPP models of alternant hydrocarbons. I. Qualitative rules for the effect of limited configuration interaction

Simple rules for an estimate of the correlation effects in the low-lying states of alternant hydrocarbons, as described by the Pariser–Parr–Pople Hamiltonian, are formulated. These rules are based on the alternancy and spin symmetry classification of states in both strongly and weakly correlated limits and on the valence bond characteristics of those states in the fully correlated limit. It is shown that the largest effect of the electron correlation will be found for the singlet “minus” states (using Pariser's classification of the alternancy symmetry species), a smaller effect for the triplet “plus” states, and a much smaller effect for the remaining states. These rules are exemplified by limited CI calculations including all monoexcited and all mono- and bi-excited configurations, respectively, for a number of π-electronic systems. In view of these rules the success of the PPP model in the monoexcited CI approximation may be understood.     

One-center expansion method with model potentials. I. Formulation and test calculations

The one-center expansion (OCE ) method is extended to evaluate molecular wave functions for molecules with heavy off-center nuclei. This extension is achieved through the use of model potentials (MP ) to approximate the highly bound core orbitals. The remaining diffuse valence charge distribution is then rather easy to simulate using OCE . The formulation of the method is described. New molecular integrals are solved to a high degree of accuracy. Successful results are reported for H₂O, H₂S, and N₂. The valence electron distributions and orbital energies are in good agreement with those obtained from more complete calculations. The method combines the computational economy of both OCE and MP procedures, resulting in a potentially useful package for further chemical applications.     

Symmetry breaking in benzene and larger aromatic molecules within generalized valence bond coupled cluster methods

The origin of symmetry breaking (SB) in benzene in generalized valence bond methods is investigated within a coupled cluster formalism that correlates all valence electrons. Retention of a limited number of pair correlation amplitudes (as in the perfect- and imperfect-pairing models) that incompletely describes interpair correlations leads to symmetry breaking as the orbitals and amplitudes are optimized. Local correlation models that are exact for one, two, and three interacting pairs at the doubles excitation level are compared against the exact pair correlation treatment, which correlates four interacting pairs at once in the connected double substitution operator. For simplicity, this comparison is performed with a second-order model of electron correlation, which is reasonably faithful to the infinite-order result. The significant SB known for the one-pair model (perfect pairing) is not eliminated at the two-pair level, but is virtually eliminated at the three-pair level. Therefore, a tractable hybrid model is proposed, which combines three-pair correlations at the second-order level and infinite-order treatment for the strong imperfect-pairing correlations involving one and two-pair correlations. This model greatly reduces SB in benzene and larger delocalized pi systems such as naphthalene and the phenalenyl cation and anion. The resulting optimized orbitals are localized in the sigma space but exhibit significant delocalization in the pi space. This means that correlation effects associated with different resonance structures are treated in a more balanced way than if the pi orbitals localize, leading to reduced SB.     

Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals

A method is presented for expressing the occupied self-consistent-field (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic minimal-basis-set orbitals that deviate as little as possible from free-atom SCF minimal-basis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the free-atom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed "quasiatomic minimal-basis-sets" is independent of the calculational atomic orbital basis used. The resulting resolution of molecular orbitals in terms of quasiatomic minimal basis set orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimal-basis orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence orbitals, which are useful for calculating electron correlation and the interpretation of reactions. The method is applicable to Kohn-Sham density functional theory orbitals and is easily generalized to valence MCSCF orbitals.     

A convenient decontraction procedure of internally contracted state-specific multireference algorithms

Internally contracted state-specific multireference (MR) algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F(2) ground state wave function.