Grid-Based Ehrenfest Model To Study Electron–Nuclear Processes

Abstract

The two-dimensional electron-nuclear Schrödinger equation using soft-core Coulomb potentials has been a cornerstone for modeling and predicting the behavior of one-active-electron diatomic molecules, particularly for processes where both bound and continuum states are important. The model, however, is computationally expensive to extend to more electron or nuclear coordinates.Here we propose to use the Ehrenfest approach to treat the nuclear motion, while the electronic motion is still solved by quantum propagation on a grid. In this work we present results for a one-dimensional treatment of H + 2 , where the quantum and semi-classical dynamics can be directly compared, showing remarkably good agreement for a variety of situations. The advantage of the Ehrenfest approach is that it can be easily extended to treat as many nuclear degrees of freedom as needed. * Electronic address: isola@quim.ucm.es 1 arXiv:1905.13702v1 [physics.chem-ph]

Control defeasance by anti-alignment in the excited state

“…For the aligned molecules (in a effectively 1-dimensional treatment) the model gives results that are in agreement with those of full quantum (electron and nuclear) calculations with the same Hamiltonian [33]. But we expect, as explained in the paper, the validity of the results to be far more general, as well as the process of anti-alignment.…”

“…In particular, the average results obtained from an ensemble of trajectories (weighted by a Wigner distribution) using the Ehrenfest approximation for a 1-D model of H + 2 with a softcore Coulomb potential are very similar to those obtained by solving the quantum 1 + 1D (electron-nuclear) TDSE, both when we start in a superposition of electronic states in the absence of the field, and when we start in the excited state (or the dressed electronic state) in the presence of the field [33].…”

“…The electron motion is correlated to the vibrational motion such that the electron moves away with the proton against the field, reaching a classical turning point and returning to the initial position. This was shown in a fully-quantum (1 + 1)-D model for a molecule aligned with the field [35,36] and reproduced with a 1D Ehrenfest model of the electron moving in the molecular axis [33]. Figure 2 depicts the results using the 2D-Ehrenfest model for an ensemble of 200 molecules initially aligned with a field of E 0 = 0.02 a.u.…”

“…In our example, the narrower initial distribution (σ = a 0 /2) reaches larger bond distances. This is because it corresponds to a broader initial momentum distribution [33]. For the same reason the dephasing is somehow stronger for this distribution and the decay of the oscillation is larger than for the σ = a 0 / √ 2 case.…”

Anti-alignment driven dynamics in the excited states of molecules under strong fields

“…But because all these structures lie far from equilibrium, it becomes increasingly important to study the dynamics of the molecule considering all its degrees of freedom. It is in this context that we have recently developed simplified models to solve the electronic and nuclear (vibration and rotation) motion of H + 2 in strong fields [32]. These models used soft-core Coulomb potentials [33][34][35] in a plane (instead of a line) where the nuclear motion was treated using the Ehrenfest ansatz.…”