A molecular perspective on Tully models for nonadiabatic dynamics.

Over the past decades, an important number of methods have been developed to simulate the nonadiabatic dynamics of molecules, that is, the dynamics of molecules beyond the Born-Oppenheimer approximation. These nonadiabatic methods differ in the way they approximate the dynamics emanating from the time-dependent molecular Schrödinger equation. In 1990, Tully devised a series of three one-dimensional model systems to test the approximations of the method called trajectory surface hopping. The Tully models were designed to probe different scenarios of nonadiabatic processes, such as single and multiple nonadiabatic (re)crossings. These one-dimensional models rapidly became the testbed for any new nonadiabatic dynamics strategy. In this work, we present a molecular perspective to the Tully models by highlighting a correspondence between these simple one-dimensional models and processes happening during the excited-state dynamics of molecules. More importantly, each of these nonadiabatic processes can be connected to a given exemplary molecular system, and we propose here three molecules that could serve as molecular Tully models, reproducing some of the key features of the original models but this time in a high-dimensional space. We compare trajectory surface hopping with the ab initio multiple spawning for the three molecular Tully models and highlight particular features and differences between these methods resulting from their distinct approximations. We also provide all the necessary information - initial conditions and all required parameters for the dynamics as well as the electronic structure - employed in our simulations such that the molecular Tully models can become in the future a unified and standardized test for ab initio nonadiabatic molecular dynamics methods. The molecular Tully models also offer an exciting link between the world of low-dimensional model systems for nonadiabatic dynamics and the excited-state dynamics of molecular systems in their full dimensionality.