Ehrenfest methods

Though it has been successfully applied, for example to describe energy transfer processes at metal surfaces, the Ehrenfest method fails when it becomes important to monitor different paths for different electronic states rather than a trajectory determined by an average over the different surfaces. This problem is particularly serious if one is interested in studying state specific nuclear pathways, such as those present in scattering events, or those determining low probability products in a chemical reaction. 

In mean-field or Ehrenfest methods, " the forces result from the contribution of two terms the first is related to the nonadiabatic coupling, the second is an average of the gradients of the potentials of the populated electronic states. Therefore, the forces acting on the nuclei depend directly on the population of the electronic states. The electronic problem and the nuclear dynamics have to be solved simultaneously. The time step must be sufficiently small to account for the time variation of the electronic wave functions. In this case, the solution of the TDSE can be propagated as ... 

Keywords Ehrenfest method CASSCF Coupled electron-nuclear dynamics Charge migration Charge transfer... 

We apply our second-order Ehrenfest method to a model system benzene radical cation. Ionization of the neutral from the degenerate HOMO/HOMO-1 leads to the Jahn-Teller [15] effect in the cation. There is a peaked conical intersection between the two lowest-energy eigenstates Dq and Dy at geometries with D h symmetry. Figure 1 represents the surrounding moat of the conical intersection seen from above. It contains several valence bond (VB) resonance structures three equivalent quinoid structures... 

The Ehrenfest method has been extensively discussed in the literature [16-26]. In this section, we review the Ehrenfest formalism following the elegant derivation of Tully [27]. Our aim is to explicitly state the approximations underlying the method and to discuss their implications. 

The first approximation made in the Ehrenfest method is thus the factorisation of the total wavefunction into a product of electronic and nuclear parts. One deficiency of the ansatz (2) is the fact that the electronic wavefunction does not have the possibility to decohere the populated electronic states in P(r,t) share the same nuclear wave-packet x(R, t) by definition of the total wavefunction. Decoherence here is defined as the tendency of the time-evolved electronic wavefunction to behave as a statistical ensemble of electronic states rather than a coherent superposition of them [26]. The neglect of electronic decoherence could lead to non-physical asymptotic behaviors in case of bifurcating paths. It is not expected to be a problem here as we are interested in relatively short timescale dynamics. 

The Ehrenfest method is obtained by taking the classical limit of Eqs. (3) and (4). To do that in Eq. (4), the nuclear wavefunction is (exactly) rewritten in a polar coordinate system in terms of an amplimde A and a phase S which are both considered to be real and positive ... 

We now describe our CASSCF implementation of the Ehrenfest method that allows the electronic wavefunction to be made of multiple states. An approximate second-order method with a numerical fit procedure is used for the propagation of the nuclei. 

We apply our second-order Ehrenfest method to study the coupled electron-nuclear dynamics of benzene upon... 

Saita K, Shalashilin DV (2012) On-the-fly ab initio molecular dynamics with multiconfigurational ehrenfest method. J Chem Phys 137(22) 22A506... 

Shalashilin DV (2010) Nonadiabatic dynamics with the help of multiconfigurational ehrenfest method improved theory and fully quantum 24d simulation of pyrazine. J Chem Phys 132(24) 244111... 

---