Chapter 6 - The State-Specific Expansion Approach to the Solution of the Polyelectronic Time-Dependent Schrödinger Equation for Atoms and Molecules in Unstable States

Abstract

Abstract Important problems in chemical physics require the ab initio computation of the nonstationary many-electron wavefunction that solves the time-dependent Schrödinger equation (TDSE) for time-independent and, especially, for time-dependent Hamiltonians. This chapter reviews the state-specific expansion approach (SSEA) to the solution of a variety of time-dependent many-electron problems (TDMEPs) in atoms and small molecules. Because of its structure, the SSEA places emphasis on the efficient computation of state-specific wavefunctions in the discrete and in the continuous spectrum. Therefore, the review covers, apart from the methodology of solving the TDSE, the theory for the solution of the many-electron problem in two broad subjects of modern research: One which refers to isolated discrete and resonance states and one which refers to the series of states just below and just above the fragmentation threshold. Thus, it is also concerned with the theory of the quantum defect and of related issues. The applications which are mentioned or are discussed briefly involve either the ab initio computation of the time-resolved decay of autoionizing states or, especially, prototypical TDMEPs of absorption of one or of many photons by atoms, by negative ions, and by diatomics. In the latter case, we demonstrate how the “multipolar” interaction expressing the full atom–field interaction (and not just the electric dipole approximation) can be incorporated into a practical computational methodology.