Normal-Mode Vibrational Analysis of Weakly Bound Oligomers at Constrained Stationary Points of Arbitrary Order

Following the full realization of
the importance of noncovalent
interactions, finding and characterizing stationary points (SP), of
various order, for weakly bound oligomers have become important tasks
for computational chemists. An efficient algorithm and an associated
computer code, called oligoCGO, are described,
facilitating constrained geometry optimization of oligomers of arbitrary
structure and complexity and normal-mode vibrational analysis at nonstationary
geometries. To minimize the adverse effects of nonzero forces on harmonic
vibrational analyses at constrained stationary points (cSP), two residual
gradient correction (RGC) schemes are proposed. RGC1, for
which a rigorous justification is given, is based on ignoring the
remaining forces in internal-coordinate space. RGC2 modifies
the geometry of the cSP in a single Newton step and recalculates the
Cartesian Hessian at this updated geometry. As demonstrated by 10
examples related to the water–water, water–methane,
and methane–methane dimers as well as the methane trimer, without
RGC the harmonic analysis of cSPs may result in even qualitatively
incorrect results when compared to reference values obtained at the
nearby unconstrained SPs (uSP). Both RGC protocols work exceedingly
well, and the corrected harmonic wavenumbers of the cSPs are very
close to their uSP counterparts.