  The diagonal nonadiabatic term arising from the Born--Oppenheimer
wave-function ansatz contains contributions from a vector and scalar potential.
The former is provably zero when the wave function can be taken to be real
valued, and the latter, known as the diagonal Born--Oppenheimer correction
(DBOC), is typically small in magnitude. Therefore, unless high accuracy is
sought, the diagonal nonadiabatic term is usually neglected when calculating
molecular properties. In the presence of a magnetic field, the wave function is
generally complex, and the geometric vector potential gives rise to a screening
force that is qualitatively important for molecular dynamics. This screening
force is written in terms of the Berry curvature and is added to the bare
Lorentz force acting on the nuclei in the presence of the field. In this work,
we derive analytic expressions for the Berry curvature and DBOC using both
first and second quantization formalisms for the case of generalized and
restricted Hartree--Fock theories in a uniform magnetic field. The Berry
curvature and DBOC are calculated as a function of the magnetic field strength
and the bond distance for the ground-state singlets of H$_2$, LiH, BH, and
CH$^+$. We also examine the stability and time-reversal symmetry of the
underlying self-consistent field solutions. The character of the DBOC and Berry
curvature is found to depend upon the magnetic field and varies between
molecules. We also identify instances of broken time-reversal symmetry for the
dissociation curves of BH and CH$^+$.
