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1. Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states

   https://doi.org/10.1063/5.0186984  

   Villaseco_Arribas, Evaristo; Maitra, Neepa T; Agostini, Federica (February 2024, The Journal of Chemical Physics)

   Advances in coherent light sources and development of pump–probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron–nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. This work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes. 

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2. Nuclear gradient expressions for molecular cavity quantum electrodynamics simulations using mixed quantum-classical methods

   https://doi.org/10.1063/5.0109395  

   Zhou, Wanghuai; Hu, Deping; Mandal, Arkajit; Huo, Pengfei (September 2022, The Journal of Chemical Physics)

   We derive a rigorous nuclear gradient for a molecule-cavity hybrid system using the quantum electrodynamics Hamiltonian. We treat the electronic–photonic degrees of freedom (DOFs) as the quantum subsystem and the nuclei as the classical subsystem. Using the adiabatic basis for the electronic DOF and the Fock basis for the photonic DOF and requiring the total energy conservation of this mixed quantum–classical (MQC) system, we derived the rigorous nuclear gradient for the molecule–cavity hybrid system, which is naturally connected to the approximate gradient under the Jaynes–Cummings approximation. The nuclear gradient expression can be readily used in any MQC simulations and will allow one to perform the non-adiabatic on-the-fly simulation of polariton quantum dynamics. The theoretical developments in this work could significantly benefit the polariton quantum dynamics community with a rigorous nuclear gradient of the molecule–cavity hybrid system and have a broad impact on the future non-adiabatic simulations of polariton quantum dynamics. 

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3. Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states

   https://doi.org/10.1063/5.0177778  

   Tao, Zhen; Bian, Xuezhi; Wu, Yanze; Rawlinson, Jonathan; Littlejohn, Robert G; Subotnik, Joseph E (February 2024, The Journal of Chemical Physics)

   We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, “Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions,” J. Chem. Phys. 122, 084113 (2005) and V. Krishna, “Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit,” J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree–Fock with spin–orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born–Oppenheimer approximation when using ab initio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results. 

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4. Different flavors of exact-factorization-based mixed quantum-classical methods for multistate dynamics

   https://doi.org/10.1039/d3cp03464j  

   Villaseco_Arribas, Evaristo; Vindel-Zandbergen, Patricia; Roy, Saswata; Maitra, Neepa T (October 2023, Physical Chemistry Chemical Physics)

   Coupled electron–ion dynamicsviathe exact factorization approach gives improved mixed quantum classical methods due to trajectory-coupling. 

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5. Rare Events Sampling Methods for Quantum and Classical Ab Initio Molecular Dynamics

   https://doi.org/10.1021/acs.jpca.3c07385  

   Iyengar, Srinivasan S; Schlegel, H Bernhard; Sumner, Isaiah; Li, Junjie (July 2024, The Journal of Physical Chemistry A)

   We provide an approach to sample rare events during classical ab initio molecular dynamics and quantum wavepacket dynamics. For classical AIMD, a set of fictitious degrees of freedom are introduced that may harmonically interact with the electronic and nuclear degrees of freedom to steer the dynamics in a conservative fashion toward energetically forbidden regions. A similar approach when introduced for quantum wavepacket dynamics has the effect of biasing the trajectory of the wavepacket centroid toward the regions of the potential surface that are difficult to sample. The approach is demonstrated for a phenol-amine system, which is a prototypical problem for condensed phase-proton transfer, and for model potentials undergoing wavepacket dynamics. In all cases, the approach yields trajectories that conserve energy while sampling rare events. 

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