While the treatment of conical intersections in molecular dynamics generally
requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation
is still adopted as a valid alternative in certain circumstances. In the
context of Mead-Truhlar minimal coupling, this paper presents a new closure of
the nuclear Born-Oppenheimer equation, thereby leading to a molecular dynamics
scheme capturing geometric phase effects. Specifically, a semiclassical closure
of the nuclear Ehrenfest dynamics is obtained through a convenient prescription
for the nuclear Bohmian trajectories. The conical intersections are suitably
regularized in the resulting nuclear particle motion and the associated Lorentz
force involves a smoothened Berry curvature identifying a loop-dependent
geometric phase. In turn, this geometric phase rapidly reaches the usual
topological index as the loop expands away from the original singularity. This
feature reproduces the phenomenology appearing in recent exact nonadiabatic
studies, as shown explicitly in the Jahn-Teller problem for linear vibronic
coupling. Likewise, a newly proposed regularization of the diagonal correction
term is also shown to reproduce quite faithfully the energy surface presented
in recent nonadiabatic studies.Comment: Third version with minor changes. To appear in Phys. Rev.
