Overcoming Artificial Multipoles in Intramolecular Symmetry-Adapted Perturbation Theory

Intramolecular symmetry-adapted perturbation
theory (ISAPT)
is
a method to compute and decompose the noncovalent interaction energy
between two molecular fragments A and B covalently
connected via a linker C. However, the existing ISAPT
algorithm displays several issues for many fragmentation patterns
(that is, specific assignments of atoms to the A/B/C subsystems), including an artificially repulsive
electrostatic energy (even when the fragments are hydrogen-bonded)
and very large and mutually cancelling induction and exchange-induction
terms. We attribute those issues to the presence of artificial dipole
moments at the interfragment boundary, as the atoms of A and B directly connected to C are missing
electrons on one of their hybrid orbitals. Therefore, we propose several
new partitioning algorithms which reassign one electron, on a singly
occupied link hybrid orbital, from C to each of A/B. Once the contributions from these link orbitals
are added to fragment density matrices, the computation of ISAPT electrostatic,
induction, and dispersion energies proceeds exactly as normal, and
the exchange energy expressions need only minor modifications. Among
the link partitioning algorithms introduced, the so-called ISAPT(SIAO1)
approach (in which the link orbital is obtained by a projection onto
the intrinsic atomic orbitals (IAOs) of a given fragment followed
by orthogonalization to this fragment’s occupied space) leads
to reasonable values of all ISAPT corrections for all fragmentation
patterns, and exhibits a fast and systematic basis set convergence.
This improvement is made possible by a significant reduction in magnitude
(even though not a complete elimination) of the unphysical dipole
moments at the interfragment boundaries. We demonstrate the utility
of the improved ISAPT partitioning by examining intramolecular interactions
in several pentanediol isomers, examples of linear and branched alkanes,
and the open and closed conformations of a family of N-arylimide molecular
torsion balances.