  Non-adiabatic coupling matrix elements (NACMEs) are important in quantum
chemistry, particularly for molecular dynamics methods such as surface hopping.
However, NACMEs are gauge dependent. This presents a difficulty for their
calculation in general, where there are no restrictions on the gauge function
except that it be differentiable. These cases are relevant for complex-valued
electronic wave functions, such as those that arise in the presence of a
magnetic field or spin-orbit coupling. Additionally, the Berry curvature and
Berry force play an important role in molecular dynamics in a magnetic field,
and are also relevant in the context of spin-orbit coupling. For methods such
as surface hopping, excited-state Berry curvatures will also be of interest.
With this in mind, we have developed a scheme for the calculation of
continuous, differentiable NACMEs as a function of the molecular geometry for
complex-valued wave functions. We demonstrate the efficacy of the method by
using the H$_2$ molecule at the full configuration-interaction (FCI) level of
theory. Additionally, ground- and excited- state Berry curvatures are computed
for the first time using FCI theory. Finally, Berry phases are computed
directly in terms of diagonal NACMEs.
