  We present a many-body expansion (MBE) formulation and implementation for
efficient computation of analytical energy gradients from OSV-MP2 theory based
on our earlier work (Zhou et al. J. Chem. Theory Comput. 2020, 16, 196-210).
The third-order MBE(3) expansion of OSV-MP2 wavefunction was developed to adopt
the orbital-specific clustering and long-range termination schemes, which
avoids term-by-term differentiations of the MBE energy bodies. We achieve
better efficiency by exploiting the algorithmic sparsity that allows to prune
out insignificant fitting integrals and OSV relaxations. With these
approximations, the present implementation is benchmarked on a range of
molecules that show an economic scaling in the linear and quadratic regimes for
computing MBE(3)-OSV-MP2 amplitude and gradient equations, respectively, and
yields normal accuracy comparable to the original OSV-MP2 results. The
MPI-3-based parallelism through shared memory one-sided communication is
further developed for improving parallel scalability and memory accessibility
by sorting the MBE(3) orbital clusters into independent tasks that are
distributed on multiple processes across many nodes, supporting both global and
local data locations in which selected MBE(3)-OSV-MP2 intermediates of
different sizes are distinguished and accordingly placed. The accuracy and
efficiency level of our MBE(3)-OSV-MP2 analytical gradient implementation is
finally illustrated in two applications: we show that the subtle coordination
structure differences of mechanically interlocked Cu-catenane complexes can be
distinguished when tuning ligand lengths; and the porphycene molecular dynamics
reveals the emergence of the vibrational signature arising from softened N-H
stretching associated with hydrogen transfer, using an MP2 level of electron
correlation and classical nuclei for the first time.
