Ab Initio Nonadiabatic Quantum Molecular Dynamics

Abstract

The Born-Oppenheimer approximation underlies much of chemical simulation and provides the framework defining the potential energy surfaces that are used for much of our pictorial understanding of chemical phenomena. However, this approximation breaks down when the dynamics of molecules in excited electronic states are considered. Describing dynamics when the Born-Oppenheimer approximation breaks down requires a quantum mechanical description of the nuclei. Chemical reaction dynamics on excited electronic states is critical for many applications in renewable energy, chemical synthesis, and bioimaging. Furthermore, it is necessary in order to connect with many ultrafast pump-probe spectroscopic experiments. In this review, we provide an overview of methods that can describe nonadiabatic dynamics, with emphasis on those that are able to simultaneously address the quantum mechanics of both electrons and nuclei. Such ab initio quantum molecular dynamics methods solve the electronic Schrödinger equation alongside the nuclear dynamics and thereby avoid the need for precalculation of potential energy surfaces and nonadiabatic coupling matrix elements. Two main families of methods are commonly employed to simulate nonadiabatic dynamics in molecules: full quantum dynamics, such as the multiconfigurational time-dependent Hartree method, and classical trajectory-based approaches, such as trajectory surface hopping. In this review, we describe a third class of methods that is intermediate between the two: Gaussian basis set expansions built around trajectories.

Different flavors of nonadiabatic molecular dynamics

“…However, approximations can be devised to simplify the equations and allow for the nonadiabatic dynamics of molecules on‐the‐fly, leading to direct dynamics vMCG (DD‐vMCG), Ab Initio MCE (AIMCE), or Ab Initio Multiple Spawning (AIMS) . All three methods were successfully applied to problems in photochemistry and photophysics (see Reference for a list of the different molecular applications).…”

“…This section aims at offering some selected examples of the types of photophysical and photochemical processes described by these techniques. For a more extended list of applications, the reader can refer to References (for quantum dynamics), References (for traveling Gaussian techniques), or References (for mixed quantum/classical methods).…”

“…Last but not least, Full Multiple Spawning (FMS) 64,65 proposes to represent the nuclear amplitudes by a linear combination of frozen, classically-driven multidimensional Gaussians ( Figure 6). To overcome the challenge of having enough TBFs to support the nuclear dynamics, FMS introduces a spawning algorithm that allows for the addition of TBFs during the dynamics, that is, an adaptive size of the Gaussian basis, when the system reaches a region of strong nonadiabaticity 66,67 (Figure 6). Importantly, vMCG, MCE, and FMS can formally reproduce a numerically exact solution of the time-dependent Schrödinger equation in the limit of a large number of TBFs (and an accurate calculation of their respective couplings).…”

Curve crossing in a manifold of coupled electronic states: direct quantum dynamics simulations of formamide

“…A different approach is ab initio multiple spawning (AIMS). [14][15][16] In this, the nuclear wavepacket is described by a superposition of Gaussian basis functions, known as Gaussian wavepackets (GWPs). The expansion coefficients solve the full TDSE while the GWPs follow classical trajectories making them suitable for direct dynamics.…”

Instanton formulation of Fermi’s golden rule in the Marcus inverted regime

“…3 Due to the great interest in these phenomena, the study of nonadiabatic transitions is an important topic for research. Hence, there exists a plethora of different algorithms to simulate nonadiabatic dynamics, [4][5][6][7][8][9] from computationally expensive, but accurate methods based on wavefunction propagation [10][11][12][13] to heuristically motivated, pragmatic methods such as trajectory surface hopping. [14][15][16] Simulating the direct dynamics of a chemical reaction, however, is not usually a practical way to obtain information about the reaction rate, because the typical time scales of chemical reactions are long.…”