Ab Initio Multiple Spawning:  Photochemistry from First Principles Quantum Molecular Dynamics

Abstract

The ab initio multiple spawning (AIMS) method is a time-dependent formulation of quantum chemistry, whereby the nuclear dynamics and electronic structure problems are solved simultaneously. Quantum mechanical effects in the nuclear dynamics are included, especially the nonadiabatic effects which are crucial in modeling dynamics on multiple electronic states. The AIMS method makes it possible to describe photochemistry from first principles molecular dynamics, with no empirical parameters. We describe the method and present the application to two molecules of interest in organic photochemistrysethylene and cyclobutene. We show that the photodynamics of ethylene involves both covalent and ionic electronic excited states and the return to the ground state proceeds through a pyramidalized geometry. For the photoinduced ring opening of cyclobutene, we show that the disrotatory motion predicted by the Woodward-Hoffmann rules is established within the first 50 fs after optical excitation.

Nonequilibrium Fermi golden rule for electronic transitions through conical intersections

“…On the other hand, fully quantum treatment of electrons and nuclei is impractical for systems with a large number of degrees of freedom (DOF). Some intermediate solutions have been devised in the past decades, to name a few: mixed quantumclassical techniques 3,4 (e.g., surface hopping), wave packet methods [5][6][7] , semi-classical 8 and general path-integral based approaches 9,10 . Although all these techniques alleviate burden of the full quantum consideration, they require numerical simulations and still can be quite computationally expensive owing to multiple potential energy surface (PES) calculations involved at every dynamical step.…”

Exact Factorization of the Time-Dependent Electron-Nuclear Wave Function

“…To make numerical calculations feasible, the description usually involves approximations such as classical dynamics for nuclei with electron-nuclear coupling provided by Ehrenfest dynamics or surfacehopping [1], or even just static nuclei [2]. Quantum features of the nuclear dynamics (e.g., zero-point energies, tunneling, and interference) are included approximately in some methods [3,4], while numerically exact solutions of the time-dependent Schrödinger equation (TDSE) for the coupled system of electrons and nuclei have been given for very small systems like H + 2 [5]. Clearly, the full electron-nuclear wavefunction contains the complete information on the system, but it lacks the intuitive picture that potential energy surfaces (PES) can provide.…”

GPU-Accelerated State-Averaged Complete Active Space Self-Consistent Field Interfaced with Ab Initio Multiple Spawning Unravels the Photodynamics of Provitamin D3

“…Ab initio nonadiabatic molecular dynamics represents a compromise between efficiency and accuracy that includes surface crossing (nonadiabatic) effects while determining the required potential energy surfaces from simultaneous solution of the electronic Schrödinger equation. [12][13][14][15][16][17][18][19][20][21] Quantum mechanical effects related to surface crossing can be described either by a swarm of classical trajectories that can hop between electronic states -trajectory surface hopping (TSH) [22][23][24] -or by an expansion of the nuclear wavefunctions in terms of frozen Gaussians following classical trajectories called "trajectory basis functions" -Full Multiple Spawning (FMS) [12][13][25][26][27] and related methods. 19,[28][29][30] The propagation of trajectories substantially reduces the cost of the nuclear propagation compared to grid-based solution of the time-dependent Schrödinger equation.…”