Direct semiclassical simulation of photochemical processes with semiempirical wave functions

Abstract

We describe a new method for the simulation of excited state dynamics, based on classical trajectories and surface hopping, with direct semiempirical calculation of the electronic wave functions and potential energy surfaces (DTSH method). Semiempirical self-consistent-field molecular orbitals (SCF MO’s) are computed with geometry-dependent occupation numbers, in order to ensure correct homolytic dissociation, fragment orbital degeneracy, and partial optimization of the lowest virtuals. Electronic wave functions are of the MO active space configuration interaction (CI) type, for which analytic energy gradients have been implemented. The time-dependent electronic wave function is propagated by means of a local diabatization algorithm which is inherently stable also in the case of surface crossings. The method is tested for the problem of excited ethylene nonadiabatic dynamics, and the results are compared with recent quantum mechanical calculations.

A general method to describe intersystem crossing dynamics in trajectory surface hopping

“…The equation can be derived similarly as in Ref. [181], but using P † cðt1DtÞ5cðtÞ instead of cðt1DtÞ5PcðtÞ. One advantage of eq.…”

“…(23) over the one in Ref. [181] is that the denominator in eq. (23) does not tend to zero when the population transfer becomes large, giving more accurate results.…”

“…If nonadiabatic couplings are not available, it is still possible to calculate the propagator matrix P using other schemes, see, for example, Refs. [55,181]. However, for the gradient transformation no alternative schemes without nonadiabatic couplings are available, and, as an approximation K MCH ij has to be neglected in eqs.…”

“…We note here that P MCH ðt1Dt; tÞ could also be calculated differently from eq. (20), for example using the local diabatization procedure of Granucci et al [181,182] The condition that the time step Dt is short enough can be fulfilled by choosing a shorter time step for the electronic propagation than for the nuclear propagation and linearly interpolating the electronic properties (see Appendix A for the corresponding equations).…”

“…Here we use a variant of the equation derived in Ref. [181], where the hopping probability h b!a is just a function of the old and new coefficients and the propagator matrix:…”