Abstract
Full multiple spawning (FMS) offers an exciting framework for the development of strategies to simulate the excited-state dynamics of molecular systems. FMS proposes to depict the dynamics of nuclear wavepackets by using a growing set of traveling multidimensional Gaussian functions called trajectory basis functions (TBFs). Perhaps the most recognized method emanating from FMS is the so-called ab initio multiple spawning (AIMS). In AIMS, the couplings between TBFs-in principle exact in FMS-are approximated to allow for the on-the-fly evaluation of required electronic-structure quantities. In addition, AIMS proposes to neglect the so-called second-order nonadiabatic couplings and the diagonal Born-Oppenheimer corrections. While AIMS has been applied successfully to simulate the nonadiabatic dynamics of numerous complex molecules, the direct influence of these missing or approximated terms on the nonadiabatic dynamics when approaching and crossing a conical intersection remains unknown to date. It is also unclear how AIMS could incorporate geometric-phase effects in the vicinity of a conical intersection. In this work, we assess the performance of AIMS in describing the nonadiabatic dynamics through a conical intersection for three two-dimensional, two-state systems that mimic the excited-state dynamics of bis(methylene)adamantyl, butatriene cation, and pyrazine. The population traces and nuclear density dynamics are compared with numerically exact quantum dynamics and trajectory surface hopping results. We find that AIMS offers a qualitatively correct description of the dynamics through a conical intersection for the three model systems. However, any attempt at improving the AIMS results by accounting for the originally neglected second-order nonadiabatic contributions appears to be stymied by the hermiticity requirement of the AIMS Hamiltonian and the independent first-generation approximation.
Highlights
Simulating the dynamics of a molecule following photoexcitation in an excited electronic state is a dantesque task due to the breakdown of the Born–Oppenheimer approximation, as it implies that one should explicitly account for nonadiabatic effects resulting from the coupling between electronic motion and nuclear motion.1,2 An accurate description of such processes would require an exact solution of the molecular time-dependent Schrödinger equation (TDSE), a task only achievable for the smallest molecular systems
Armed with equations for the ab initio multiple spawning (AIMS) Hamiltonian matrix elements accounting for nonadiabatic couplings (NACs), diagonal Born–Oppenheimer corrections (DBOCs), and GP effects while preserving the hermiticity of the Hamiltonian matrix, we propose to unravel the effects of these different contributions by studying the nonadiabatic dynamics of a nuclear wavepacket evolving through a conical intersection for two-dimensional, two-state model systems
Let us first start by investigating the excited-state population decay for the three different models, comparing the quantum dynamics (QD) results to the decays predicted by trajectory surface hopping (TSH) and AIMS within the SPA0 [Eqs. (8) and (9)]
Summary
Simulating the dynamics of a molecule following photoexcitation in an excited electronic state is a dantesque task due to the breakdown of the Born–Oppenheimer approximation, as it implies that one should explicitly account for nonadiabatic effects resulting from the coupling between electronic motion and nuclear motion. An accurate description of such processes would require an exact solution of the molecular time-dependent Schrödinger equation (TDSE), a task only achievable for the smallest molecular systems, . As AIMS proposes to perform nonadiabatic dynamics in the adiabatic representation of the electronic states, one may inquire about the inclusion of geometric-phase (GP) effects in its formalism. No work has tested the quality of the AIMS approximations to describe the nonadiabatic dynamics through conical intersections and the influence of the missing NACs, DBOCs, and GP terms mentioned above. We propose a thorough discussion of the original coupling elements in AIMS and how one could include the missing NACs, DBOCs, and geometric phase while preserving the hermiticity of the AIMS Hamiltonian (Sec. II). While preserving the philosophy of the AIMS approximations, we test the inclusion of NACs, DBOCs, and GP effects in the coupling terms (Sec. IV C), before questioning the use of Born–Huang (BH) vs Born–Oppenheimer PESs for the dynamics of the TBFs (Sec. IV D).
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