Vincent McKoy

Nonempirical Calculations on Excited States: The Ethylene Molecule

A series of nonempirical calculations are reported on the excited states of the ethylene molecule using a recent minimum basis set LCAO MO SCF wavefunction. For the lowest excited singlet state of ethylene (^1B_(3u)) the coupling between the π electrons and σ electrons is significant: the excitation energy being decreased from 11.98 to 10.17 eV and the oscillator strength from 1.03 to 0.73. This coupling has little effect on the triplet state. In the next higher approximation (the random‐phase approximation) the excitation energy is further decreased to 9.44 eV and the transition moment to 0.51. With the use of accurate LCAO MO SCF wavefunctions, it is felt that the methods presented here will provide a basis for the theoretical interpretation of electronic spectra.

Electron-Molecule and Photon-Molecule Collisions

Application of the Close-Coupling Method to Electron-Molecule Scattering.- The Coupled-Channels Integral-Equations Method in the Theory of Low-Energy Electron-Molecule Scattering.- Roundtable on Numerical Methods.- Contribution of the Variable Phase Method to the Frame Transformation Theory of Rotational Excitation of Molecules by Electron Impact.- The R-Matrix Method for Electron-Molecule Scattering: Theory and Computation.- The T-Matrix Method in Electron-Molecule Scattering.- Roundtable on L2-Methods.- The Separable Approximation in Multichannel Electron-Molecule Collisions.- Nonempirical Polarization in Low-Energy Electron-Molecule Scattering Theory.- R-Matrix Calculations for Electron Scattering by Diatomic Molecules.- Discussion on Electron-Molecule Scattering.- Polarization Potentials for Electron Scattering.- Vibrational Excitations of Low-Energy e-CO Scattering.- Improved Hybrid Theory Calculation of e-N2 Vibrational Excitation.- Stieltjes-Tchebycheff Moment-Theory Approach to Molecular Photoionization Studies.- The Continuum Multiple-Scattering Approach to Electron-Molecule Scattering and Molecular Photo ionization.- Molecular Resonance Phenomena.- Stieltjes-Moment-Theory Technique for Calculating Resonance Widths.- Progress Toward the Application of Complex Coordinte and Complex Basis Function Techniques to Molecular Resonance Calculations.- Discussion on Photoionization and Molecular Resonances.- A Modification of the Langhoff Imaging Technique.- Workshop on L2-Methods.- Workshop on Single-Center Techniques.

Theory of Dissociation Pressures of Some Gas Hydrates

Dissociation pressures of some gas hydrates have been evaluated using the Lennard‐Jones 12–6, 28–7, and Kihara potentials in the Lennard‐Jones‐Devonshire cell model. The Lennard‐Jones 28–7 potential gives the least satisfactory results. The Lennard‐Jones 12–6 potential works satisfactorily for the monatomic gases and CH4 but poorly for the rodlike molecules C2H6, CO2, N2, O2, C2H4. This failure may be due to (i) distortions of the hydrate lattice, (ii) neglect of molecular shape and size in determining the cavity potential (iii) barrier to internal rotation of the molecule in its cavity. A crude model for the lattice shows that it is not distorted. The Kihara potential predicts better dissociation pressures for the hydrates of the rodlike molecules. Unlike the previously used Lennard‐Jones 12–6 potential, it depends on the size and shape of the interacting molecules. The absence of lattice distortions, improved dissociation pressures through the use of the Kihara potential and the restriction of the motio...

Applications of the Schwinger variational principle to electron-molecule collisions and molecular photoionization

In this article we present a detailed overview of our studies of molecular photoionization and electron-molecule collisions in which we have used Schwinger-like variational principles and several important extensions of these principles. The various variational functionals and formulations, the interrelationships between these formulations, and a detailed discussion of the numerical and computational procedures which have been used in applications are presented.

Application of the equations‐of‐motion method to the excited states of N2, CO, and C2H4

We have used the equations‐of‐motion method to study various states of N2, CO, and ethylene. In this approach one attempts to calculate excitation energies directly as opposed to solving Schrodingers equation separately for the absolute energies and wavefunctions. We have found that by including both single particle‐hole and two particle‐hole components in the excitation operators we can predict the excitation frequencies of all the low‐lying states of these three molecules to within about 10% of the observed values and the typical error is only half this. The calculated oscillator strengths are also in good agreement with experiment. The method is economical, requiring far less computation time than alternative procedures.

Equations‐of‐motion method including renormalization and double‐excitation mixing

The equations‐of‐motion method is discussed as an approach to calculating excitation energies and transition moments directly. The proposed solution [T. Shibuya and V. McKoy, Phys. Rev. A 2, 2208 (1970)] of these equations is extended in two ways. First we include the proper renormalization of the equations with respect to the ground state particle‐hole densities. We then show how to include the effects of two‐particle‐hole components in excited states which are primarily single‐particle‐hole states. This is seen to be equivalent to a single‐particle‐hole theory with a normalized interaction. Applications to various diatomic and polyatomic molecules indicate that the theory can predict excitation energies and transition moments accurately and economically.

Theory of resonantly enhanced multiphoton processes in molecules

In this paper we formulate a theory for the analysis of resonant enhanced multiphoton ionization processes in molecules. Our approach consists of viewing the (n+m) photon ionization process from an isotropic initial state as m‐photon ionization out of an oriented, excited state. The orientation in this resonant state, which is reached by n‐photon excitation from the initial state, is nonisotropic, and is characteristic of this absorption process. The ionization simply probes this anisotropic population. The calculation of the REMPI process thus consists of determining the anisotropy created in the resonant state and then coupling this anisotropic population to ionization out of it. While the former is accomplished by the solution of appropriate density matrix equations, the latter is done by coupling these density matrix elements to angle‐resolved ionization rates out of this state. An attractive feature of this approach is that the influence of saturation effects, and other interactions, such as collisions, on the photoelectron properties is easily understood and incorporated. General expressions are derived for photoelectron angular distributions. Based on these, several properties of the angular distributions that follow purely on symmetry considerations are discussed. One of the new features that emerge out of this work is the saturation induced anisotropy in REMPI. In this effect higher order contributions to the angular distributions appear since saturation influences different ionization channels differently thereby creating an additional anisotropy in the excited state.

Application of the RPA and Higher RPA to the V and T States of Ethylene

We have applied our proposed higher random‐phase approximation (HRPA) to the T and V states of ethylene. In the HRPA, unlike the RPA, one solves for the excitation frequencies and the ground‐state correlations self‐consistently. We also develop a simplified scheme (SHRPA) for solving the equations of the HRPA, using only molecular integrals sufficient for the usual RPA calculations. The HRPA removes the triplet instability which often occurs in the RPA. The excitation energy for the N → T transition is now in good agreement with experiment. The N → V transition energy increases by 15% over its RPA Value. The N → V oscillator strength changes only very slightly. These results are also useful in explaining the appearance and ordering of states obtained in recent direct open‐shell SCF calculations.

Ionic rotational selection rules for (n + 1) resonant enhanced multiphoton ionization

We derive a selection rule for production of ionic rotational states in resonant enhanced multiphoton ionization (REMPI) of diatomic molecules. This selection rule enables a separation of both the particular symmetry components of the ionic rovibronic state and the even (gerade) and odd (ungerade) partial wave components of the electronic continuum even in heteronuclear molecules. The extreme sensitivity of the ionic rotational spectra to the symmetry of states allows one to influence the population of ionic rotational states through careful choices of REMPI schemes.

Assignments in the electronic spectrum of water

To explain the inelastic feature at 4.5 eV in the spectrum of water and to study its spectrum in some detail, we have carried out several calculations on the excited states of water using the equations‐of‐motion method. We conclude that the calculated vertical excitation energy of 6.9 eV for the ^3B_1 state corresponds to the strong feature at 7.2 eV observed in low‐energy electron scattering spectrum. The 4.5 eV inelastic process almost certainly does not correspond to a vertical excitation of water at the ground state geometry. The other excitation energies and oscillator strengths agree well with experiment.