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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. [ABSTRACT FROM AUTHOR]

For a system without spin–orbit coupling, the (i) nuclear plus electronic linear momentum and (ii) nuclear plus orbital electronic angular momentum are good quantum numbers. Thus, when a molecular system undergoes a nonadiabatic transition, there should be no change in the total linear or angular momentum. Now, the standard surface hopping algorithm ignores the electronic momentum and indirectly equates the momentum of the nuclear degrees of freedom to the total momentum. However, even with this simplification, the algorithm still does not conserve either the nuclear linear or the nuclear angular momenta. Here, we show that one way to address these failures is to dress the derivative couplings (i.e., the hopping directions) in two ways: (i) we disallow changes in the nuclear linear momentum by working in a translating basis (which is well known and leads to electron translation factors) and (ii) we disallow changes in the nuclear angular momentum by working in a basis that rotates around the center of mass [which is not well-known and leads to a novel, rotationally removable component of the derivative coupling that we will call electron rotation factors below, cf. Eq. (96)]. The present findings should be helpful in the short term as far as interpreting surface hopping calculations for singlet systems (without spin) and then developing the new surface hopping algorithm in the long term for systems where one cannot ignore the electronic orbital and/or spin angular momentum. [ABSTRACT FROM AUTHOR]

The recently developed real-time nuclear–electronic orbital (RT-NEO) approach provides an elegant framework for treating electrons and selected nuclei, typically protons, quantum mechanically in nonequilibrium dynamical processes. However, the RT-NEO approach neglects the motion of the other nuclei, preventing a complete description of the coupled nuclear–electronic dynamics and spectroscopy. In this work, the dynamical interactions between the other nuclei and the electron–proton subsystem are described with the mixed quantum–classical Ehrenfest dynamics method. The NEO-Ehrenfest approach propagates the electrons and quantum protons in a time-dependent variational framework, while the remaining nuclei move classically on the corresponding average electron–proton vibronic surface. This approach includes the non-Born–Oppenheimer effects between the electrons and the quantum protons with RT-NEO and between the classical nuclei and the electron–proton subsystem with Ehrenfest dynamics. Spectral features for vibrational modes involving both quantum and classical nuclei are resolved from the time-dependent dipole moments. This work shows that the NEO-Ehrenfest method is a powerful tool to study dynamical processes with coupled electronic and nuclear degrees of freedom. [ABSTRACT FROM AUTHOR]