Final-state analysis

Final state analysis is where dynamical methods of evolving states meet the concepts of stationary states. By their definition, final states are relatively long lived. Therefore experiment often selects a single stationary state or a statistical mixture of stationary states. Since END evolution includes the possibility of electronic excitations, we analyze reaction products in terms of rovibronic states. 

Density functional theory, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems, 404-411 Density operator, direct molecular dynamics, adiabatic systems, 375-377 Derivative couplings conical intersections, 569-570 direct molecular dynamics, vibronic coupling, conical intersections, 386-389 Determinantal wave function, electron nuclear dynamics (END), molecular systems, final-state analysis, 342-349 Diabatic representation ... 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Electronic structure theory, electron nuclear dynamics (END) structure and properties, 326-327 theoretical background, 324-325 time-dependent variational principle (TDVP), general nuclear dynamics, 334-337 Electronic wave function, permutational symmetry, 680-682 Electron nuclear dynamics (END) degenerate states chemistry, xii-xiii direct molecular dynamics, structure and properties, 327 molecular systems, 337-351 final-state analysis, 342-349 intramolecular electron transfer,... 

Reactive collisions, electron nuclear dynamics (END), molecular systems, 338—342 final-state analysis, 343 -349... 

A. H. Zewail With regard to Prof. Marcus s comment, we have observed the coherence-in-products first in the IHgl system where the wavepacket is launched near the saddle point. The persistence of coherence in products is fundamentally due to (1) the initial coherent preparation (no random trajectories) and (2) the nature of the potential transverse to the reaction coordinate (no dispersion). The issue of vibrational adiabaticity in the course of the reaction, as you pointed out, must await complete final-state analysis for well-defined initial energy. However, we do know that for a given energy of the initial wavepacket a broad distribution of vibrational coherence (in the diatom) is observed. 

The final state analysis behaves exactly the same as without scaling (Eqs. (64)-(65)) (4). This approach is related to that of Mandelshtam and Taylor (32) by a simple transformation, relating the damped Chebychev recursion and the Faber-Chebychev recursion with damped Hamiltonian. 

---