  Drachmann's regularization approach is implemented for floating explicitly
correlated Gaussians (fECGs) and molecular systems. Earlier applications of
drachmannized relativistic corrections for molecular systems were hindered due
to the unknown analytic matrix elements of $1/r_{ix}1/r_{jy}$-type operators
with fECGs. In the present work, one of the $1/r$ factors is approximated by a
linear combination of Gaussians, which results in calculable integrals. The
numerical approach is found to be precise and robust over a range of molecular
systems and nuclear configurations, and thus, it opens the route towards an
automated evaluation of high-precision relativistic corrections over potential
energy surfaces of polyatomic systems. Furthermore, the newly developed
integration approach makes it possible to construct the matrix representation
of the square of the electronic Hamiltonian relevant for energy lower-bound as
well as time-dependent computations of molecular systems with a flexible and
high-precision fECG basis representation.
