Beyond the Spectra and Dynamics of Diatomic Molecules

Whether the inactive region is a true continuum (e.g., photofragmentation) or a quasi-continuum comprised of an enormous density of rigorously bound eigenstates (polyatomic molecule dynamics, Section 9.4.14) is often of no detectable consequence. The dynamical quantities discussed in Section 9.1.4 (probability density, density matrix, autocorrelation function, survival probability, transfer probability, expectation values of coordinates and conjugate momenta) describe the active space dynamics without any reference to the detailed nature of the inactive space. 

A complex Heff model is constructed by associating an amplitude decay rate, Tj/2, with the zero-order energy, e3 — iTj/2, of each active-space basis state. The Tj values may be derived from a state-space Fermi Golden Rule treatment of the average squared interaction strength of the j-th active-space basis state with the approximately isoenergetic basis states in the inactive space (I) 

Each of the anharmonic coupling terms in the V(Q), e.g., kj xQjQK (where Qk is a coordinate in the inactive region of space), generates an explicitly 

Basis states are equally important in understanding frequency- and time-domain experiments. In the frequency domain, the pattern is comprised of the 

There is no best way to observe and understand molecular dynamics. Sometimes a mechanistic feature is sampled more transparently in the time or the frequency domain. The design of an experiment (quantum number pre-or post-selection, an ingeniously designed pluck) is far more important than whether the experiment is performed in the time- or frequency-domain. 

---