Propagation techniques, electronic states

Prony analysis, electron nuclear dynamics (END), molecular systems, 344-349 Propagation techniques, electronic states,... 

Calculations of core hole states and core electron binding energies have mostly concerned state-by-state optimization using open-shell Hartree-Fock, multiconfiguration self-consistent field, and configuration interaction techniques, while propagator techniques have been of restricted use owing to the relaxation problem ... 

Early semiempirical calculations laid the foundations for subsequent ab initio methods which can now not only describe the electronic structure of optically accessible excited states, but also model the wavepacket propagation on the resulting potential energy surfaces. These models are supported by ultrafast studies using femptosecond (fs) pulsed lasers with a variety of detection systems. Many systems use indirect detection of excited-state processes because many excited states are unbound and not amenable to spectroscopic techniques. 

When dealing with non-adiabatic dynamics, a fruitful strategy to approximate the fully quantum propagation involves taking a classical limit for the evolution of the nuclear degrees of freedom in the presence of a set of quantum states. This kind of approach profits from the powerful simulation techniques available for evolving classical degrees of freedom, with the added benefit that the dimensionality of the quantum part of the problem is reduced to that of the electronic subset. 

The limit with respect to rj is taken because of integration techniques required in a Fourier transform from the time-dependent representation. Indices r and s refer to general, orthonormal spin-orbitals, r x) and os(x), respectively, where x is a space-spin coordinate. Matrix elements of the corresponding field operators, al and as/ depend on the N-electron reference state, N), and final states with N 1 electrons, labeled by the indices m and n. The propagator matrix is energy-dependent poles occur when E equals a negative VDE, Eq(N) — En(N — 1), or a negative VAE, Em(N +1) — Eq(N). 

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