Yngve Öhrn

Molecular Electron Propagator Theory and Calculations

Publisher Summary This chapter describes that the electron propagator is being employed in molecular theory primarily for the calculation of electron binding energies as well as for photoionization cross sections and intensities related to various spectrometric processes. The usefulness of propagator theory is by no means limited to the realm of electron binding energies. All areas of spectrometry can be given a unified treatment and the solution of the equation of motion for the appropriate propagator yields a spectral density function and energy differences from which expectation values and spectra can be obtained. The chapter reviews some of the basic definitions and introduces the notations of the electron propagator. The decoupling problem is stated and general methods of approximation are discussed using a spin orbital basis. The direct pole-residue search is described and implemented. It is discussed for the solution of the working equations to produce the spectral representation of the electron propagator. The emphasis is placed on the calculation of relative intensities of lines in photoelectron spectra.

Atomic and molecular electronic spectra and properties from the electron propagator

Decoupling in terms of the superoperator formalism according to Pickup and Goscinski is employed to find tractable forms of the self‐energy operator leading to direct calculation of the electron propagator or Greens function. This is applied to the calculation of photoelectron line spectra, ground state total energies, and electronic properties of atoms and molecules. Numerical results for the helium atom and the nitrogen molecule are reported.

Derivation and Analysis of the Pariser–Parr–Pople Model

Second quantization formalism is used to derive the Pariser–Parr–Pople model for planar unsaturated molecules. The model is analyzed in detail in the atomic limit and the equivalence with an Heisenberg antiferromagnet is demonstrated by perturbation theory. An approximate Greens‐function method is developed and its properties in the same limit are derived and shown to be correct. The case of a linear chain is calculated explicitly and compared with other results. Limitations and difficulties in the establishment of the results are discussed.

Electron propagator calculations of the photoelectron spectrum for open shell molecules with applications to the oxygen molecule

An approximate self−energy for the electron propagator is derived using the Grand Canonical averaging procedure for open shell molecules. The connection between the overlap amplitudes and the photoionization cross section is discussed. A direct pole and residue search is employed to solve the Dyson equation with a second order self−energy for the oxygen molecule, yielding a theoretical photoelectron spectrum in good agreement with experimental x−ray induced spectra.

Higher‐order decoupling of the electron propagator

The decoupling of the electron propagator in the superoperator formalism is extended to include a description of processes corresponding to simultaneous electron ionization (or electron attachment) and double excitation, observed in electron spectrometry, by including products of five spin–orbital field operators in the inner projection basis. Although the terms thus introduced are fourth order in the electron interaction, an argument based on the self‐consistent solution of the second‐order equations suggests that these fourth‐order terms are more important than the third‐order terms. The argument is substantiated by numerical applications to the neon atom. A calculation using third‐order shifts is compared with a calculation using the suggested fourth‐order terms, but without third‐order terms.

On the Calculation of Some Atomic Integrals Containing Functions of r12, r13, and r23

Different forms of correlated atomic wavefunctions and their implications on the integrals occurring in calculations of variational solution to Schrodingers equation are briefly discussed. A scheme for computing the integral ∫ f1(r1)f2(r2)f3(r3)g1(r12)g2(r23)g3(r31)(dv) is described and applied to the case gi(rij) = rijk.

A limited basis molecular orbital calculation on H2O and H2O

An MO−SCF calculation on five states of H2O+ and on the ground state of H2O is shown to yield molecular geometries, force constants, ionization energies, and for the neutral ground state, relative infrared intensities in good agreement with experimental results, and, where available, with more sophisticated calculations.

Time‐dependent dynamics of electrons and nuclei

Using the time‐dependent variational principle with a group theoretical coherent state defining the wave functions for electrons and nuclei, a system of coupled, first‐order, nonlinear differential equations is obtained for a general molecular system. The equations form a classical Hamiltonian system within a generalized phase space that allows a systematic time‐dependent study of molecular processes. The approach is general and provides a computational framework for a variety of properties such as transition and excitation probabilities in atomic and molecular collisions, and molecular spectra such as vibrational spectra with anharmonicities. The basic approximation corresponding to the choice of a single determinantal wave function for the electrons and classical nuclei is analyzed. Illustrative applications to the p+H collision process and to vibrations of the H2O molecule exhibit good agreement with experiment and with other theoretical work.

Configuration interaction calculations of some observed states of NO−, NO, NO+, and NO2+

Minimal STO basis has been used in configuration interaction calculations on the molecule NO and some of its ions. Several observed states of these systems have been calculated with full potential energy curves, and comparisons have been made with results from photoelectron spectroscopy, double charge transfer spectroscopy, and photodetachment spectroscopy.

Elementary finite order perturbation theory for vertical ionization energies

The analysis of ionization energies in Rayleigh–Schrodinger perturbation theory and in propagator theory, previously known separately through third order in electron interaction, are compared in detail using elementary algebraic methods and their equivalence is explicitly shown. Relaxation terms are identified as the ΔESCF contributions and appropriate rules are described for their construction from the electron propagator diagrams of arbitrary order. Correlation terms are obtained separately. The transition operator method is analyzed and found to differ from ΔESCF in third order, contrary to earlier claims.