The quantum-Ehrenfest method with the inclusion of an IR pulse: Application to electron dynamics of the allene radical cation

Abstract

We describe the implementation of a laser control pulse in the Quantum-Ehrenfest method, a molecular quantum dynamics method that solves the time-dependent Schrödinger equation for both electrons and nuclei. The oscillating electric fielddipole interaction is incorporated directly in the one-electron Hamiltonian of the electronic structure part of the algorithm. We then use the coupled electron-nuclear dynamics of the -system in allene radical cation (•CH2=C=CH2) + as a simple model of a pump-control experiment. We start (pump) with a two-state superposition of two cationic states. The resulting electron dynamics corresponds to the rapid oscillation of the unpaired electron between the two terminal methlylenes. This electron dynamics is in turn coupled to the torsional motion of the terminal methylenes. There is a conical intersection at 90 o twist where the electron dynamics collapses because the adiabatic states become degenerate. After passing the conical intersection the electron dynamics revives. The IR pulse (control) in our simulations is timed to have its maximum at the conical intersection. Our simulations show that the effect of the (control) pulse is to change the electron dynamics at the conical intersection and, as

Attochemistry: Is Controlling Electrons the Future of Photochemistry?

“…We underline that there exist several other variants of on-the-fly coupled Gaussian trajectory-based methods that are in principle quantum mechanically exact: in particular, the Quantum-Ehrenfest method of Robb was already applied in the present context. 54 However, this method uses classical trajectories as basis, which does not guarantee convergence to the exact result.…”

“…The theoretical studies summarized above treat quantum mechanically the nuclear motion by solving numerically (on a grid) the time-dependent Schrödinger equation, at the expense of taking into account a few nuclear coordinates only. Using Quantum-Ehrenfest dynamics, Robb et al studied such coupled electron–nuclear dynamics under the influence of a control IR pulse in the allene radical cation in a more approximate way but taking into account the 15 nuclear degrees of freedom of that compound . In the Quantum-Ehrenfest method, the nuclear wavepacket is described by a linear combination of Gaussian basis functions.…”

“…Early schemes proposed for the control of formation of electronic superpositions typically relied on CEP-controlled IR pulses , because of the limitations of attosecond pulses at this time . Consequently, state-of-the-art theoretical studies have involved incorporation of CEP laser pulses into the already complex coupled electron–nuclear dynamics. , The very first studies focused on the control of dissociation of diatomics upon ionization, while recent studies aim at controlling the outcome (branching ratio) of a passage through a CI in more interesting molecular systems. Using this approach, the time it takes for the molecular wavepacket to reach the CI must be well-known in order to determine when to apply the IR pulse to build up the superposition.…”

“…In addition, the effect of the IR pulse on the electron dynamics itself must also be considered. Strong field IR pulses can have significant effects on potential energy surfaces, and it can be difficult to determine if the final results originate in the electron dynamics because of the complex superposition itself or because of the alteration of the dynamics by the pulse itself. ,, On the other hand, as suggested by a number of groups, ,,, the altering of the potential energy surfaces and dynamics by the IR pulse is another possible route to control the electron dynamics and reactivity. Finally, using IR pulses to control or induce CIs in molecules is another potential route to light-induced control of molecular reactions, which could be combined with attosecond schemes. ,− …”

“…Using Quantum-Ehrenfest dynamics, 53 Robb et al studied such coupled electron−nuclear dynamics under the influence of a control IR pulse in the allene radical cation in a more approximate way but taking into account the 15 nuclear degrees of freedom of that compound. 54 In the Quantum-Ehrenfest method, the nuclear wavepacket is described by a linear combination of Gaussian basis functions. The amplitudes of the Gaussian functions are determined quantum mechanically by solving the time-dependent Schrodinger equation.…”