G. Das

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.

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.

Theoretical Study of the 1Σ+, 3Σ+, 3Π, 1Π States of NaLi and the 2Σ+ State of NaLi+

Ab initio calculations have been performed for the NaLi molecule at a series of internuclear distances. The Hartree–Fock and extended Hartree–Fock optimized valence configuration (OVC) approximations of Das and Wahl are compared for the 1Σ+ ground‐state potential curve. In each approximation, the NaLi molecule is found to be bound relative to the separated atoms. The OVC wavefunctions are tabulated as a function of internuclear distance and contour diagrams of the total density for the OVC wavefunction and of the difference densities between the ground‐state molecular OVC wavefunction and the atomic and molecular Hartree–Fock wavefunctions are given. The OVC calculations are compared with a further approximation in which Φ0 is frozen to be the Hartree–Fock configuration at each internuclear distance. The comparison suggests that a better approximation would be one in which only the core orbitals are frozen at the Hartree–Fock level and all valence and correlating orbitals optimized to self‐consistency. In...

A pseudopotential study of the iron‐series transition metal hydrides

Using a modified Phillips–Kleinman pseudopotential method, the nature of binding in the iron‐series transition metal hydrides is studied. While no (or limited types of) atomic correlation terms are considered, the wave functions contain all important molecular correlation effects. The spectroscopic constants derived theoretically agree well in all cases with those available experimentally. The agreement with some previous theoretical results, however, is poor.

Calculated long‐range interactions and low energy scattering in He+H, Ne+H, Ar+H, Kr+H, and Xe+H

The van der Waals (VDW) forces in rare‐gas hydride systems are evaluated through the use of the multiconfiguration self‐consistent field (MCSCF) method. For Kr–H and Xe–H, a pseudopotential variant of the MCSCF method is used. For each system, a potential energy curve is fit to the calculated potential energies, the VDW well depth and equilibrium position are determined, and the low energy total elastic cross sections are computed as a function of relative velocity. The calculated cross sections are in good to excellent agreement, for He–H, Ar–H and Xe–H, and in fair agreement, for Ne–H and Kr–H, with the most recent experimental measurements.

Ground and excited states of the diatoms CN and AlO

Multiconfiguration self‐consistent field (MCSCF) wavefunctions are obtained for the ground and some low‐lying valence excited states of the same symmetry for the diatomic systems CN and AlO. The spectroscopic constants of these states as well as their dipole moments as a function of the internuclear separation are also calculated and compared with previous theoretical and experimental results.

Calculated long‐range interactions and low energy scattering of Ar–H

The long‐range interaction potential in Ar–H is evaluated through the use of the multi‐configuration‐self‐consistent‐field (MCSCF) method. The values of C6 and C8 obtained by analysis of the dispersion terms in this potential agree with previous calculations and estimates. The potential is used to calculate the total elastic cross sections for low energy hydrogen‐argon scattering. These results support only one of the two conflicting experimental measurements reported in the literature.

Pseudopotential study of some prominent band systems of the spectra of the I2 molecule

Using pseudopotential multiconfiguration self‐consistent field (MCSCF) techniques several states of the I2 molecule are studied to explain some important band systems of the spectra of iodine vapor. Spectroscopic parameters of the states X 1Σg+, D 1Σg+, B 3Π0 +u, 3Π1u, 3Π2u, 3Π0 +g, 3Π1g, 3Π2g are evaluated and compared with known experimental data. Attempts are made to resolve questions in regard to the assignments of molecular states to the above band systems as well as those pertaining to the position and symmetries of various curves that have remained only partially answered over the years.

A modified pseudopotential approach to the heavy‐atomic molecular systems: Application to the X 2Σ1/2+, A 2Π1/2, and the A 2Π3/2 states of the HgH molecule

A new approach to the problem of quantitatively describing interactions in heavy‐atomic molecular systems is presented. In this approach the core electrons are removed from the Hamiltonian by using the exact numerical relativistic Hartree–Fock core potential. Both the local and nonlocal terms of this potential are represented in terms of a given basis set suitable to the valence electrons. Two categories of core‐orthogonality constraints are distinguished: those pertaining to outer core orbitals which can be qualitatively described by the given basis set and those pertaining to the inner core orbitals which cannot be thus described. While explicit descriptions for the former are used as orthogonality constraints, approximate ’’pseudopotential’’‐type terms are introduced into the Fock operators to represent the latter’s orthogonality effects. Estimates of the core distortion and relativistic contributions are considered. Application to the lowest 2Σ1/2+, 2Π1/2, and 2Π3/2 states of the HgH molecule is descr...