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The method developed in this work can be applied to a number of curve-crossing processes, ranging from intersystem crossing to electron transfer. We shall therefore use the terms "nonadiabatic" and "nonradiative" (somewhat loosely) interchangeably to refer to any process governed by a Hamiltonian of the form indicated in eq 1.
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Because the time-dependent SE is linear, no loss of generality is entailed by this "specialization". If the initial state has nuclear wavepacket components on both surfaces, then we can do the temporal propagation for each component separately and coherently add the results of the two calculations.
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46
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0009268852
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An important special case of this situation is when both potential energy surfaces separate into a sum of one-dimensional contributions (in the same coordinate system). Then provided that g factorizes in the same coordinate system and that the initial wavepacket state also factorizes in these coordinates, all the evolved nuclear wavepackets remain factorized for all times and can be calculated by independent one-dimensional propagations. This simplifies the computation immensely. This feature has been nicely exploited by: Ilk, G.; Makri, N. J. Chem. Phys. 1994, 101, 6708. However, in the general case, these conditions are not satisfied and a different approach appears to be required.
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These possibilities were pointed out by an anonymous referee
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These possibilities were pointed out by an anonymous referee.
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The integrated probability densities for electronic states 1 and 2 obtained by the GWD-PI method are each high by about 0.005 (roughly 1%). This method does not conserve probability automatically, so the deviation of the total probability to be in both electronic states from unity is a meaningful indicator of the accuracy of the approximation.
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