Arnold C. Wahl

Extended Hartree—Fock Wavefunctions: Optimized Valence Configurations for H2 and Li2, Optimized Double Configurations for F2

As a step beyond the Hartree—Fock technique in the search for better energies, wavefunctions, and the general description of molecular formation and dissociation, a configuration‐mixing method of the following nature is developed and illustrated for H2, Li2, and F2. The wavefunction Ψ= ∑ kAkΦk consists of several optimized configurations obtained by replacing one of the σ‐orbitals of the primary configuration (in our case the Hartree—Fock) by orbitals of different kinds. All the orbitals involved are orthonormalized, insuring orthonormalization of the configurations themselves. The present method determines energetically the optimum combination of both the mixing coefficients Ak and the linear orbital parameters by the solution of SCF‐type equations and insures dissociation of the molecule to two Hartree—Fock atoms. A program based upon this formalism has been constructed by the authors for the IBM 7094 computer and is capable of handling homonuclear diatomic molecules using as many as ten configurations ...

Electronic Structure of Diatomic Molecules. III. A. Hartree—Fock Wavefunctions and Energy Quantities for N2(X1Σg+) and N2+(X2Σg+, A2Πu, B2Σu+) Molecular Ions

The problem of the convergence of a sequence of Hartree—Fock—Roothaan wavefunctions and energy values to the true Hartree—Fock results is examined for N2(X1Σg+). This critical study is based on a hierarchy of Hartree—Fock—Roothaan wavefunctions which differ in the size and composition of the expansion basis set in terms of STO symmetry orbitals. The concluding basis set gives a total Hartree—Fock energy of −108.9956 hartree and Re(HF)=2.0132 bohr for N2(X1Σg+).Results are also presented from direct calculations for three states of the N2+ molecular ion (X2Σg+, A2Πu, B2Σu+) which are also thought to be very close approximations to the true Hartree—Fock values. The results give EHF=−108.4079, −108.4320, and −108.2702 hartree and Re(HF)=2.0385, 2.134, and 1.934 bohr for the X2Σg+, A2Πu, and B2Σu+ states of N2+, respectively. Extensive calculations for various R values establish that the X2Σg+ and A2Πu states are reversed in order relative to experiment, a short‐coming ascribed to the Hartree—Fock approximation.

The electronic structure of nitrogen dioxide. I. Multiconfiguration self‐consistent‐field calculation of the low‐lying electronic states

Traditional spectroscopic analysis of the complex and irregular absorption spectrum of NO2 has provided a relatively small amount of information concerning the nature of the excited states. An extensive ab initio investigation has been undertaken, therefore, to provide a basis for interpretation of the experimental results. Multiconfiguration self‐consistent‐field (MC–SCF) wavefunctions have been computed for the low‐lying X 2A1, A 2B2, B 2B1, C 2A2, 4B2, 4A2, and 2Σ+g electronic states of NO2. The minima of the A 2B2, B 2B1, and C 2A2 states have all been found to be within 2 eV of the minimum of the X 2A1 ground state; for these states, C2v potential surfaces have been constructed for purposes of a spectral interpretation. The 4B2, 4A2, and 2Σ+g states are all more than 4 eV above the minimum of the ground state and have been examined in less detail. The study described here significantly improves on previous NO2 ab initio calculations in three important areas: (1) The double‐zeta‐plus‐polarizatio...

Analytic Self‐Consistent Field Wavefunctions and Computed Properties for Homonuclear Diatomic Molecules

The analytic and computational framework for Hartree—Fock—Roothaan calculations on homonuclear diatomic molecules is presented. Several approaches to calculating the wavefunction are sketched as well as methods of computing molecular properties from the wavefunction. Emphasis is given to the efficient organization of these calculations for existing digital computers. Typical results obtained through the application of the programs and techniques developed are presented for the fluorine molecule.

Single‐Configuration Wavefunctions and Potential Curves for Low‐Lying States of He2+, Ne2+, Ar2+, F2−, Cl2− and the Ground State of Cl2

Wavefunctions, orbital energies, and potential curves for He2+, Ne2+, Ar2+, F2−, and Cl2− have been calculated in the molecular‐orbital, self‐consistent‐field approximation over a range Re ≲ R < ∞ for the ground state and those excited states which dissociate into an atom and an ion in their ground states. The ground state potential curve for Cl2 has been calculated for R ∼ Re. Dissociation energies and other parameters obtained from the calculated potential curves are compared with corresponding parameters obtained from elastic differential scattering measurements and resonant electron capture in noble gases, measurements of afterglow line profiles in dissociative recombination radiation in neon and argon, optical absorption spectra of VK centers, and endoergic charge transfer studies of halogen ions and molecules. A formal analysis and discussion of the sources of correlation error in the calculated potential curves and a discussion of the expansion errors are also given.

The Method of Optimized Valence Configurations: A Reasonable Application of the Multiconfiguration Self-Consistent-Field Technique to the Quantitative Description of Chemical Bonding*

Publisher Summary This chapter discusses the method of optimized valence configurations, which is reasonable application of the multi-configuration self-consistent field technique to the quantitative description of chemical bonding. It is the purpose of this chapter to review and bring up to date the conceptual features, the analysis, and results obtained by the application of the method of Optimized Valence Configurations to diatomic molecules. Several significant conclusions can be drawn from the experience obtained in developing this method, and in assessing its relationship to other schemes. (1) It is possible to quantitatively separate the “molecular” aspects of the changing correlation energy of two approaching atoms from the remaining correlation. (2) The number of significant configurations representing extra molecular correlation is small and readily obtainable by a sequence of limited multi-configurational self-consistent-field computations, followed by a single configuration interaction involving all new orbitals thus obtained while those configurations representing atomic correlation are indeed numerous, but are easily accounted for by a suitable perturbation technique. (3) An excellent initial guess for excited starting orbitals can be obtained by maximization of the exchange integral between the orbital of the Hartree-Fock configuration being correlated and the excited orbital.

New Techniques for the Computation of Multiconfiguration Self‐Consistent Field (MCSCF) Wavefunctions

New techniques are described for obtaining MCSCF wavefunctions and energies via the expansion method. These include (i) a simple but generalized algorithm for obtaining symmetrized configurations and the corresponding vector‐coupling coefficients for diagonal and off‐diagonal matrix elements referred to the symmetry species of a diatomic molecule; (ii) a new iterative scheme which leads to a fast convergence of the MCSCF process provided the starting conditions are properly chosen, and (iii) a method to ensure such proper starting conditions in regard to the form of the initial orbitals.

Interaction Energy Curves of LiHe and NaHe (X 2Σ+, A 2Π, B 2Σ+) and X 1Σ+ Ions

Hartree–Fock interaction energy curves have been calculated for the X 2Σ+, A 2Π, and B 2Σ+ states of neutral LiHe and NaHe as well as for the ground state X 1Σ+ ions over a range of distances from 3 to 10 a.u. Since it is intended to apply these results to scattering problems, the variation of the dipole and quadrupole moments and the electronic transition probabilities with internuclear distance were also obtained. Both Slater‐type functions and Gaussian‐type functions were used as variational trial functions with the intention of gauging the efficacy of the Gaussian basis. Except for situations involving small energy minima the Gaussian basis yielded results accurate relative to the Slater basis. The features of the Hartree–Fock interaction energy curves can be summarized as follows:(1) The X 2Σ+ interaction energy is purely repulsive for both molecules to the accuracy of the present calculation.(2) The A 2Π and X 1Σ+ curves are strikingly similar for both Li and Na confirming the penetration of the He ...

Study of the ground state potential curve and dipole moment of OH by the method of optimized valence configurations

Accurate theoretical potential and dipole moment curves are presented for the X2Πi state of the hydroxyl radical. The theoretically determined dissociation energy is 4.53 eV as compared to the experimental value of 4.63 eV. The computed dipole moment at the experimental equilibrium internuclear separation is 1.674 D, which is in excellent agreement with the most reliable experimental value of 1.66±0.01 D. A detailed, general prescription for constructing optimized valence configuration wavefunctions for diatomic hydrides is presented with OH as a specific example.

Abinitio vertical spectra and linear bent correlation diagrams for the valence states of CO2 and its singly charged ions

Correlated and uncorrelated ab initio vertical spectra are reported for the valence states of CO2, CO2+, and CO2−. Calculations with polarized and unpolarized basis sets are compared at each level. Ground state quadrupole moments are computed. Linear molecule to bent molecule SCF correlation diagrams are also reported.