Jeremiah N. Silverman

The effect of molecular topology on π-molecular-orbital energies

Three models for constructing topologically related pairs of molecular isomers are discussed at length. The topological-effect-on-molecular-orbitals (TEMO) theorem is presented in detail and illustrated with experimental data; this theorem demonstrates that molecular topology imposes constraints in the form of general interlacing rules on the MO energy patterns of topologically related molecules. Further, non-empirical SCF MO calculations have been performed for topologically related o- and p-divinylbenzenes, difluorobenzenes, benzoquinones, and benzoquinodimethanes in standard and optimized geometries using various basis sets. In most cases, the SCF π-MO eigenvalue patterns of topological related isomers are in complete agreement with the TEMO theorem, thus demonstrating the dominant influence of topology on the π-MO energies. A modified version of the generalized perturbationalvariational Rayleigh-Ritz (PV-RR) procedure is described which is used to study the occasional observed deviations from the TEMO predictions; this procedure had been combined with the concept of critical λ (i.e. the threshold value of the perturbation parameter λ at which the TEMO order of a pair of MO eigenvalues starts to invert), thus enabling us to analyze in quantitative detail the physical factors which compete with molecular topology in conditioning the ab initio MO energy patterns.

Topological effect on mo energies: On the MO energies of topologically related benzoquinones☆

Abstract Non-empirical HF SCF MO calculations have been performed for the topologically related o-and p-benzoquinones. The SCF π-MO eigenvalues obtain

Complex Stark eigenvalues via analytic continuation of real high-order perturbation series

Abstract We have calculated complex Stark eigenvalues for the ground state of the H atom for field strengths 0.025–1.0 au by combining a procedure due to Reinhardt for the analytic continuation of real large-order eigenvalue (polarizability) perturbation series with the perturbational-variational Rayleigh-Ritz (PV-RR) method for generating such series; the analytic continuation is accomplished by shifting the origin of the real series into the complex plane where the divergent series involved are summed by Pade approximants. The method yields results for hydrogenic Stark resonances of good accuracy over a wide range of field strengths with slight computational effort. PV-RR implements large-order perturbation theory with the variational method, thus rendering feasible the extension of the technique to larger systems.

Accurate eigenvalues of three- through ten-electron atomic isoelectronic sequences from low-order Z-dependent perturbation theory combined with variational constraints and screening

Abstract A method is developed, based on Rayleigh-Schrodinger perturbation theory combined with variational constraints and screening, for obtaining accurate atomic eigenvalues from third-order 1/ Z expansions. Application of the procedure to the ground states of the 3⩽ N ⩽V10 electron atomic sequences yields energies of 99.95–100.05% or greater accuracy, a marked improvement over those obtained from other third-order summations including Pade approximants. In the important test cases of the Be and Ne atoms, our results are found to exceed in accuracy all but the most elaborate ab initio calculations.

Energies and Widths of the Ground and Excited States of Hydrogen in a DC Field via Variationally-Based Large-Order Perturbation Theory

We have recently computed the energies and widths (complex eigenvalues) of the ground and many (more than 100) excited states of hydrogen in a dc field (the Stark effect) for numerous field strengths by combining a procedure for the analytic continuation of real large-order eigenvalue perturbation series with the perturbational-variational Rayleigh-Ritz (PV-RR) method for generating such series. The analytic continuation is accomplished by shifting the origin of the real eigenvalue series into the complex plane where the relevant divergent series are summed by a twofold application of Pade approximants. Our composite PV-RR method fills a gap in theory and results for the ground and highly excited states of the hydrogenic Stark effect; since the procedure implements large-order perturbation theory with the variational method, it is feasible to extend the technique to larger systems such as light atoms. After introducing the problem, this lecture briefly summarizes previous methods of calculating hydrogenic Stark resonances. Next, the theory of our procedure is outlined, including an explanation and illustration of our novel method of relieving zero-order degeneracy of excited Stark states. Our extensive calculations are then described, and selected results are reported and discussed. Finally, we present our conclusions.

Physical origins of high-order Born-Oppenheimer electronic polarizabilities: Application to a 30th-order perturbation study of H2+

Abstract A method is developed for investigating the physical origins of high-order Born-Oppenheimer (BO) electronic polarizabilities for diatomic molecules; the procedure is based upon resolution of the polarizabilities in each order into their kinetic, internal-potential, and field-potential energetic components. The energetic components of BO polarizabilities are subject to a priori constraints on their relative magnitudes and signs which are similar to but less restrictive than.those for non-Born-Oppenheimer (NBO) polarizabilities. The procedure, implemented via the perturbational-variational Rayleigh-Ritz formalism, is illustrated by a 30th-order polarizability study of the ground state of BO H2+. The BO results are compared to those for NBO H2+ and their differing behaviour is discussed. Other diatomic molecules are considered.