Fermi resonance in CO₂: A combined electronic coupled-cluster and vibrational configuration-interaction prediction

The authors present a first-principles prediction of the energies of the eight lowest-lying anharmonic vibrational states of CO₂, including the fundamental symmetric stretching mode and the first overtone of the fundamental bending mode, which undergo a strong coupling known as Fermi resonance. They employ coupled-cluster singles, doubles, and (perturbative) triples [CCSD(T) and CCSDT] in conjunction with a range of Gaussian basis sets (up to cc-pV5Z, aug-cc-pVQZ, and aug-cc-pCVTZ) to calculate the potential energy surfaces (PESs) of the molecule, with the errors arising from the finite basis-set sizes eliminated by extrapolation. The resulting vibrational many-body problem is solved by the vibrational self-consistent-field and vibrational configuration-interaction (VCI) methods with the PESs represented by a fourth-order Taylor expansion or by numerical values on a Gauss-Hermite quadrature grid. With the VCI, the best theoretical estimates of the anharmonic energy levels agree excellently with experimental values within 3.5 cm ^-1 (the mean absolute deviation). The theoretical (experimental) anharmonic frequencies of the Fermi doublet are 1288.9 (1285.4) and 1389.3 (1388.2) cm^-1.