Concordant Mode Approach (CMA): Vibrational Analysis of New and Upgraded Intermolecular Benchmarks for Noncovalent Bonding

The Concordant Mode
Approach (CMA) is a novel method
that offers
tremendous potential for increasing the system size and the level
of theory attainable in quantum chemical computations of molecular
vibrational frequencies. To investigate the extension of CMA to intermolecular
vibrations, computations with coupled cluster singles and doubles
with perturbative triples theory [CCSD(T)] using two augmented correlation-consistent
polarized-valence triple-ζ basis sets (aug-cc-pVTZ or h-aug-cc-pVTZ)
were performed on 17 prototypical loosely bound complexes of hydrogen-bonded,
dispersion, and mixed character. These Level A results provide new
and upgraded benchmarks for noncovalent bonding and a severe test
for CMA vibrational analyses. The Level A target frequencies were
recovered remarkably well using second-order Møller–Plesset
perturbation theory (MP2) with h-aug-cc-pVTZ for generating the underlying
(Level B) normal modes of the CMA scheme. Employing this Level B within
the lowest-rung CMA-0A method reproduces the 435 benchmark frequencies
with a mean absolute error (MAE) of 0.23 cm–1 and
a corresponding standard deviation (σ) of 0.84 cm–1; strikingly, the corresponding subset of 106 interfragment frequencies
exhibits MAE = 0.34 cm–1 and σ = 0.90 cm–1. Subsequent application of the higher-rung CMA-2A
scheme eliminates all outliers and reduces the overall MAE to a minuscule
0.08 cm–1 with the inclusion of only 3.0% of the
off-diagonal couplings not accounted for by CMA-0A. Accordingly, the
highly efficient CMA methodology proves to be robust even for vibrations
on flat potential energy surfaces.