Theory and Computation of Nonstationary States of Polyelectronic Atoms and Molecules

Abstract

I present a theory of polyelectronic atomic and molecular nonstationary states decaying into free particle continua, which shows how to define and compute efficiently correlated wavefunctions, energies, energy shifts and transition rates for phenomena such as autoionization, multiphoton ionization, static and dynamic polarization, predissociation etc. The problem is formulated in a unified manner as a complex eigenvalue Schrodinger equation (CESE) which is derived rigorously for each state of interest starting from Fano’s basic equation of discrete -continuous spectra mixing. The form of the resulting resonance wave-function is ψ=aψ_o+bX_as, where ψ_o is the maximum square-integrable projec-tion of ψ, excluding the open channels. Knowledge of the exact asymptotic form of the resonance wavefunctions thus derived, allows the imposition of suitable perturbations of the asymptotic boundary conditions in the form of coordinate transformations, in order to render the resonance wavefunction normalizable. Thus, for short-range or Coulomb potentials, the corresponding coordinate transformation is r → ρ = re^iθ, first introduced for short-range potentials by Dykhne and Chaplik in 1961. For the LoSurdo-Stark potential, the herein derived resonance asymptotic form and subsequent analysis justifies previous choices of the coordinate rotation and translation transformations as well as of their combination r → ρ = re^iθ − z_o/F, where z_o is the complex eigenvalue and F is the field strength. Now, ψ_o and X_as are represented by different function spaces which are optimized separately, the first on the real axis once, yielding a real energy, E_o, and the second partly on the real axis for its bound part and partly in the complex energy plane. The second part of the computation depends only on the structure of the continuous spectrum and yields the energy shift, Δ, and the width, Γ. For Coulomb autoionization where the interaction operator is nonseparable, the state-specific calculation of ψ_o is based on the existence of a localized, self-consistent multiconfigurational zeroth order function satisfying the virial theorem and the physically correct orbital nodal structure. The remaining localized electron correlation is obtained variationally. Both the zeroth order and the localized correlation part exclude the open channels by construction and by satisfying orthogonality constraints to electronic structure dependent core orbitals. It is shown how this scheme can be used for the construction of diabatic or quasidiabatic states. X_as incorporates the interchannel couplings and a simple expression yields the partial widths to all orders. When the nonstationary state is caused by an external ac-field, the present theory is adapted to solving the ensuing many-electron, many-photon (MEMP) problem as a time-independent CESE where the computed multiphoton ionization rates and frequency-dependent hyperpolarizabilities constitute the Floquet averages over the field cycle. The following, field-free, examples are discussed: The inner-hole Auger state Ne⁺ 1s2s²2p^{6 2}S; the triply excited He⁻ 2s2p^{2 2}D and ⁴P resonances; the $He_2^ + {\mkern 1mu} {}^2\sum _g^ +$ diabatic spectrum. The formulation of the MEMP theory and its applications are relegated to the references.