We consider photoinduced electronic transitions through conical intersections in large molecules.Starting from the linear vibronic model Hamiltonian and treating linear diabatic couplings within the second order cumulant expansion we have developed a simple analytical expression for the time evolution of electronic populations at finite temperature. The derived expression can be seen as a nonequilibrium generalization of the Fermi Golden Rule due to a nonequilibrium character of the initial photoinduced nuclear distribution. All parameters in our model are obtained from electronic structure calculations followed by a diabatization procedure. The results of our model are found to agree well with those of quantum dynamics for a test set of systems: fulvene molecule, bis-methylene adamantane cation and its dimethyl derivative.

Coupled electron-nuclear dynamics, implemented using the Ehrenfest method, has been used to study charge migration with fixed nuclei, together with charge transfer when nuclei are allowed to move. Simulations were initiated at reference geometries of neutral benzene and 2-phenylethylamine (PEA), and at geometries close to potential energy surface crossings in the cations. Cationic eigenstates, and the so-called sudden approximation, involving removal of an electron from a correlated ground-state wavefunction for the neutral species, were used as initial conditions. Charge migration without coupled nuclear motion could be observed if the Ehrenfest simulation, using the sudden approximation, was started near a conical intersection where the states were both strongly coupled and quasi-degenerate. Further, the main features associated with charge migration were still recognizable when the nuclear motion was allowed to couple. In the benzene radical cation, starting from the reference neutral geometry with the sudden approximation, one could observe sub-femtosecond charge migration with a small amplitude, which results from weak interaction with higher electronic states. However, we were able to engineer large amplitude charge migration, with a period between 10 and 100 fs, corresponding to oscillation of the electronic structure between the quinoid and anti-quinoid cationic electronic configurations, by distorting the geometry along the derivative coupling vector from the D 6h Jahn-Teller crossing to lower symmetry where the states are not degenerate. When the nuclear motion becomes coupled, the period changes only slightly. In PEA, in an Ehrenfest trajectory starting from the D 2 eigenstate and reference geometry, a partial charge transfer occurs after about 12 fs near the first crossing between D 1 , D 2 (N + -Phenyl, N-Phenyl + ). If the Ehrenfest propagation is started near this point, using the sudden approximation without coupled nuclear motion, one observes an oscillation of the spin density -charge migration -between the N atom and the phenyl ring with a period of 4 fs. When the nuclear motion becomes coupled, this oscillation persists in a damped form, followed by an effective charge transfer after 30 fs. © 2013 AIP Publishing LLC.

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This article describes the Ehrenfest method and our second-order implementation (with approximate gradient and Hessian) within a CASSCF formalism. We demonstrate that the second order implementation with the predictor-corrector integration method improves the accuracy of the simulation significantly in terms of energy conservation. Although the method is general and can be used to study any coupled electron-nuclear dynamics, we apply it to investigate charge migration upon ionization of small organic molecules, focusing on benzene cation. Using this approach, we can study the evolution of a non-stationary electronic wavefunction for fixed atomic nuclei, and where the nuclei are allowed to move, to investigate the interplay between them for the first time. Analysis methods for the interpretation of the electronic and nuclear dynamics are suggested: we monitor the electronic dynamics by calculating the spin density of the system as a function of time.