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In this paper the authors address the problem of internal consistency in trajectory surface hopping methods, i.e., the requirement that the fraction of trajectories running on each electronic state equals the probabilities computed by the electronic time-dependent Schrodinger equation, after averaging over all trajectories. They derive a formula for the hopping probability in Tully's "fewest switches" spirit that would yield a rigorously consistent treatment. They show the relationship of Tully's widely used surface hopping algorithm with the "exact" prescription that cannot be applied when running each trajectory independently. They also bring out the connection of the consistency problem with the coherent propagation of the electronic wave function and the artifacts caused by coherent Rabi-type oscillations of the state probabilities in weak coupling regimes. A real molecule (azobenzene) and two ad hoc models serve as examples to illustrate the above theoretical arguments. Following a proposal by Truhlar's group [Zhu et al., J. Chem. Phys. 121, 7658 (2004) Zhu et al., J. Chem. Theory Comput. 1, 527 (2005)], they apply a decoherence correction to the state probabilities, in conjunction with Tully's algorithm, and they obtain satisfactory results in terms of internal consistency and of agreement with the outcomes of quantum wave packet calculations.

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.

The Newton-X program is a general-purpose program package for excited-state molecular dynamics, including nonadiabatic methods. Its modular design allows Newton-X to be easily linked to any quantum-chemistry package that can provide excited-state energy gradients. At the current version, Newton-X can perform nonadiabatic dynamics using Columbus, Turbomole, Gaussian, and Gamess program packages with multireference configuration interaction, multiconfigurational self-consistent field, time-dependent density functional theory, and other methods. Nonadiabatic dynamics simulations with a hybrid combination of methods, such as Quantum-Mechanics/Molecular-Mechanics, are also possible. Moreover, Newton-X can be used for the simulation of absorption and emission spectra. The code is distributed free of charge for noncommercial and nonprofit uses at www.newtonx.org

No abstract

We have simulated the photoisomerization dynamics of azobenzene, taking into account internal conversion and geometrical relaxation processes, by means of a semiclassical surface hopping approach. Both n-->pi* and pi-->pi* excitations and both cis-->trans and trans-->cis conversions have been considered. We show that in all cases the torsion around the N==N double bond is the preferred mechanism. The quantum yields measured are correctly reproduced and the observed differences are explained as a result of the competition between the inertia of the torsional motion and the premature deactivation of the excited state. Recent time-resolved spectroscopic experiments are interpreted in the light of the simulated dynamics.

In this paper we set up a method called overlap decoherence correction (ODC) to take into account the quantum decoherence effect in a surface hopping framework. While keeping the standard surface hopping approach based on independent trajectories, our method allows to account for quantum decoherence by evaluating the overlap between frozen Gaussian wavepackets, the time evolution of which is obtained in an approximate way. The ODC scheme mainly depends on the parameter σ, which is the Gaussian width of the wavepackets. The performance of the ODC method is tested versus full quantum calculations on three model systems, and by comparison with full multiple spawning (FMS) results for the S(1)→S(0) decay in the azobenzene molecule.

In this work, the advantages of a locally diabatic propagation of the electronic wave function in surface hopping dynamics proceeding on adiabatic surfaces are presented providing very stable results even in challenging cases of highly peaked nonadiabatic interactions. The method was applied to the simulation of transport phenomena in the stacked ethylene dimer radical cation and the hydrogen bonded 2-pyridone dimer. Systematic tests showed the reliability of the method, in situations where standard methods relying on an adiabatic propagation of the wave function and explicit calculation of the nonadiabatic coupling terms exhibited significant numerical instabilities. Investigations of the ethylene dimer radical cation with an intermolecular distance of 7.0 Å provided a quantitative description of diabatic charge trapping. For the 2-pyidone dimer, a complex dynamics was obtained: a very fast (<10 fs) initial S(2)∕S(1) internal conversion; subsequent excitation energy transfers with a characteristic time of 207 fs; and the occurrence of proton coupled electron transfer (PCET) in 26% of the trajectories. The computed characteristic excitation energy transfer time of 207 fs is in satisfactory agreement with the experimental value of 318 fs derived from the vibronic exciton splittings in a monodeuterated 2-pyridone dimer complex. The importance of nonadiabatic coupling for the PCET related to the electron transfer was demonstrated by the dynamics simulations.