An Attempt to Test the Quantum Theory of X-Ray Scattering by Ralph Decker Bennett

By Ralph Decker Bennett

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We emphasize the deterministic aspect because the time-displaced procedure relies on this property. The time-displaced basis (TDB) method incorporates information about the PES in the region spanned by the wavefunction at previous times without resorting to interpolation. It can significantly reduce the number of matrix element evaluations (normally scaling quadratically with the number of basis functions) without compromising the quality of the results. As we will show, under certain assumptions it is possible to reduce the scaling of the procedure from quadratic to linear in the number of basis functions.

In some cases the orbitals determined from the SA-CASSCF have been used in an internally contracted multireference single and doubleexcitation configuration interaction treatment (MRSDCI) [197,198]. All the calculations used the MOLPRO [193] electronic structure code, and symmetry was never imposed on the electronic wavefunction. The calculations have followed the time ordering observed in the AIMS simulations, where one finds that immediately following the excitation the C–C bond stretches and subsequently the molecule begins to twist and pyramidalize.

Attempts at hydrogen migration are also observed, but only rarely have we seen the molecule decay to the ground electronic state via a hydrogenmigration conical intersection. The corresponding electronic dynamics involves three electronic states: N, V, and Z in Mulliken notation. The excited-state dynamics can be characterized as consisting of electron transfer between the two methylene units. The intramolecular electron transfer dynamics is punctuated by quenching back to the ground electronic state each time that the excited-state molecule reaches one of the excited-state minima, since these ab initio quantum molecular dynamics 485 Figure 11.

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