Methods to Calculate Electronic Excited-state Dynamics For Molecules on Large Metal Clusters with Many States: Ensuring Fast Overlap Calculations and a Robust Choice of Phase

We present an efficient set of methods for propagating excited-state dynamics involving a large number of electronic states based on a CIS electronic state overlap scheme. Specifically, (i) following Head-Gordon et al, we implement an exact evaluation of the overlap of singly-excited electronic states at different nuclear geometries using a biorthogonal basis, and (ii) we employ a unified protocol for choosing the correct phase for each adiabat at each geometry. For many-electron systems, the combination of these techniques significantly reduces the computational cost of integrating the electronic Schrodinger equation and imposes minimal overhead on top of the underlying electronic structure calculation. As a demonstration, we calculate the electronic excited-state dynamics for a hydrogen molecule scattering off a silver metal cluster, focusing on high-lying excited states where many electrons can be excited collectively and crossings are plentiful. Interestingly, we find that the high-lying, plasmon-like collective excitation spectrum changes with nuclear dynamics, highlighting the need to simulate non-adiabatic nuclear dynamics and plasmonic excitations simultaneously. In the future, the combination of methods presented here should help theorists build a mechanistic understanding of plasmon-assisted charge transfer and excitation energy relaxation processes near a nanoparticle or metal surface.