By Ben-nun M., Martinez T.J.

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Schematic illustration of the time evolution of a time-displaced basis. Basis states 1, 2, and 3 belong to one seed while 4, 5, and 6 belong to another. The basis set is shown at two time points, and the leading basis functions are shaded in gray. The arrows connecting basis functions indicate required new matrix elements at time t þ Át. For this specific example, 11 new matrix elements are evaluated at each point in time, compared to 21 if all basis functions had been chosen independently. (Figure adapted from Ref.

Indeed, one might then expect that classification of the cyclobutene and substituted cyclobutene ring-opening reactions that do and do not lead to the WH-predicted stereochemistry could be correlated with the effective mass of the substituents: The heavier the substituents, the more likely that the initial WH-directed impulse could be overcome by the detailed landscape of the excited-state potential energy surface. Further calculations and experiments—using, for example, deuterated cyclobutene—are needed to make progress in formulating such a theory.

The Li þ H2 problem was used to test the ab initio/interpolated extension of the AIMS method. F [125], the interpolation function is called on to represent the smooth regions of the potential energy surfaces, while ab initio quantum chemistry, in this case full configuration interaction, represents the regions near conical intersections and the nonadiabatic coupling between electronic states. The accuracy of the hybrid approach was investigated by (1) comparing various cuts of the potential energy surfaces, (2) comparing time traces of individual trajectories/basis functions, and (3) comparing averaged expectation values.