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1. On the meaning of Berry force for unrestricted systems treated with mean-field electronic structure

   https://doi.org/10.1063/5.0093092  

   Bian, Xuezhi; Qiu, Tian; Chen, Junhan; Subotnik, Joseph E. (June 2022, The Journal of Chemical Physics)

   We show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons interacting via a two-body (Hubbard) interaction and a spin–orbit coupling, we show that a meaningful nonzero Berry force emerges whenever there is spin unrestriction—even though the Hamiltonian is real-valued and formally the on-diagonal single-surface Berry force must be zero. Moreover, if properly applied, this mean-field Berry force yields roughly the correct asymptotic motion for scattering through an avoided crossing. That being said, within the context of a ground-state calculation, several nuances do arise as far interpreting the Berry force correctly, and as a practical matter, the Berry force diverges near the Coulson–Fischer point (which can lead to numerical instabilities). We do not address magnetic fields here. 

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2. State-interaction pair density functional theory for locally avoided crossings of potential energy surfaces in methylamine

   https://doi.org/10.1039/C9CP02240F  

   Zhou, Chen; Gagliardi, Laura; Truhlar, Donald G. (June 2019, Physical Chemistry Chemical Physics)

   The strong couplings between electronic states in conical intersection regions are among the most challenging problems in quantum chemistry. XMS-CASPT2, a second-order multireference quasidegenerate perturbation theory, has been successful in describing potential energy surfaces near the conical intersections. We have recently proposed a less expensive method for this problem, namely state-interaction pair-density functional theory (SI-PDFT), which considers the coupling between electronic states described by multiconfiguration pair-density functional theory (MC-PDFT). Here we test the accuracy of SI-PDFT for closely coupled potential energy surfaces of methylamine along five different reaction paths for N–H bond fission. We choose paths that pass close to a conical intersection of the ground and first excited states. We find that SI-PDFT predicts potential energy curves and energy splittings near the locally avoided crossing in close proximity to those obtained by XMS-CASPT2. This validates the method for application to photochemical simulations. 

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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. How excitation wavelength affects excited state dynamics in o -nitrophenol: A theoretical perspective

   https://doi.org/10.1063/5.0274633  

   Abeygunewardane, Dakshitha; Weinacht, Thomas; Matsika, Spiridoula (July 2025, The Journal of Chemical Physics)

   The excited-state dynamics of o-nitrophenol have been explored using trajectory surface hopping nonadiabatic dynamics combined with floating occupation molecular orbital complete active space configuration interaction. We focus on the effect of excitation energy on the subsequent dynamics. The absorption spectrum of o-nitrophenol has two peaks, centered at 3.9 eV (∼320 nm) and 5.1 eV (∼240 nm), and we performed dynamics starting from each of these peaks. The results show that even though the relaxation time constants are similar for the two excitation windows, the underlying dynamics are different. When exciting to the low energy peak, the dynamics are dominated by intramolecular proton transfer followed by internal conversion to the ground state, while exciting to the high-energy peak leads to fast internal conversion to the first excited state and slower decay to the ground state. In this case, intramolecular proton transfer does not occur as frequently, and many trajectories decay to the ground state through conical intersections without proton transfer. By calculating spin–orbit coupling values along the trajectories, we also show that intersystem crossing is possible. Based on the Landau–Zener probability formula, we estimate that there is about a 30%–40% probability that intersystem crossing will occur within 1 ps. 

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5. Electronic frustration, Berry’s phase interference and slow dynamics in some tight-binding systems coupled to harmonic baths

   https://doi.org/10.1088/1751-8121/acbff2  

   Makri, Nancy (March 2023, Journal of Physics A: Mathematical and Theoretical)

   Abstract Conical intersections in two-state systems require a coordinate-dependent coupling. This paper identifies and investigates conical intersections in cyclic tight-binding system-bath Hamiltonians with an odd number of sites and a constant site-to-site coupling. In the absence of bath degrees of freedom, such tight-binding systems with a positive coupling parameter exhibit electronic frustration and a doubly-degenerate ground state. When these systems interact with a harmonic bath, the degeneracy becomes a conical intersection between the adiabatic ground and first excited states. Under weak system-bath coupling, overlapping wavefunctions associated with different sites give rise to distinct pathways with interfering geometric phases, which lead to considerably slower transfer dynamics. The effect is most pronounced in the presence of low-temperature dissipative baths characterized by a continuous spectral density. It is found that the transfer dynamics and equilibration time of a cyclic dissipative three-site system with a positive coupling exceeds that of a similar three-site system with a negative coupling, as well as that of cyclic four-site systems, by an order of magnitude. 

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