Nonadiabatic Potential Energy Surfaces for a Molecule on a Surface as Found by Constrained Complete Active Space Theory

Abstract

In order to study electron-transfer mediated chemical processes on a metal surface, one requires not one but two potential energy surfaces (one ground state and one excited state) as in Marcus theory. In this letter, we report that a novel, dynamically weighted, state-averaged constrained CASSCF(2,2) (DW-SA-cCASSCF(2,2)) can produce such surfaces for the Anderson impurity model. Both ground and excited state potentials are smooth, they incorporate states with a charge transfer character, and the accuracy of the ground state surface can be verified for some model problems by renormalization group theory. Future development of gradients and nonadiabatic derivative couplings should allow for the study of nonadiabatic dynamics for molecules near metal surfaces.

A Dynamically Weighted Constrained Complete Active Space Ansatz for Constructing Multiple Potential Energy Surfaces within the Anderson-Holstein Model

“…As a result, as we change the Fermi level, we will likely see instabilities of the excited states. Indeed, these instabilities are shown in ref . Note that this unstable structure can be easily removed, however, if we simply give some weight to the excited state so that the latter is chosen robustly.…”

“…In ref , we analyzed the Anderson Hamiltonian for both one-site and two-site cases. Here we write out two sets of Anderson Hamiltonians for the one-site and two-site models separately.…”

“…The usual frameworks would be GW methods, − embedding methods, − constrained DFT, − and/or ΔSCF . That being said, recently we introduced an orthogonal approach. Namely, we showed early data suggesting that a small CASSCF­(2,2) calculation (if properly constrained) could function as an excellent method, balancing accuracy and computational speed.…”

“…Namely, we showed early data suggesting that a small CASSCF­(2,2) calculation (if properly constrained) could function as an excellent method, balancing accuracy and computational speed. The key insight presented in ref is that, when constructing such a CASSCF­(2,2) approach, one must be sure ( i ) to constrain the two active orbitals so that their total population has some overlap with the molecule on the surface; and ( ii ) to use state-averaging so as to balance the gap between the ground and excited state and make smooth surfaces. If one implements these guidelines, ref demonstrates that the resulting algorithm can seemingly perform quite well (at least for those models tested).…”

“…Second, for the sake of completeness, we will then provide step-by-step instructions delineating exactly how to solve the equations just described, and we will benchmark the convergence of our proposed optimization. Third and finally, going beyond ref , we will investigate the couplings to the bath that arise from the infinite continuum of states. These couplings are needed if we wish to run fully nonadiabatic dynamics that are compatible with Marcus’s electrochemical rate expression and achieve electronic equilibration to the correct temperature, e.g., as in the FSSH-ER dynamics.…”