A systematic theoretical study of the harmonic vibrational frequencies for polyatomic molecules: The single, double, and perturbative triple excitation coupled-cluster [CCSD(T)] method

Abstract

Analytic gradient methods have been used to predict the harmonic vibrational frequencies and the infrared (IR) intensities of HCN, HNC, CO2, CH4, NH4+, C2H2, H2O, H2CO, and NH3 at the single, double, and perturbative triple excitation coupled-cluster [CCSD(T)] level of theory. All studies were performed using a double zeta plus polarization (DZ+P) basis set with a contraction scheme of (9s5p1d/4s2p1d) for C, N, and O and (4s1p/2s1p) for H. The results of previous studies using the same basis set with self-consistent field (SCF), single and double excitation configuration interaction (CISD), and the single and double excitation coupled-cluster (CCSD) methods are included to allow a detailed comparison. The theoretical harmonic frequencies of all nine molecules are compared to the 28 (out of a total of 35 possible) known experimental harmonic vibrational frequencies. IR intensities are also compared to known experimental values. The absolute average error in frequencies for the CCSD(T) method with respect to experiment was 2.4%. Values of 9.1%, 3.7%, and 2.3% have been reported previously for the SCF, CISD, and CCSD methods, respectively. The CCSD(T) method is the only one for which a significant number of the theoretical vibrational frequencies lie below experiment. If the absolute errors for two frequencies that are known to be described inadequately with the DZP basis set are not included in the averages, they become 8.6% (SCF), 3.6% (CISD), 1.7% (CCSD), and 1.5% [CCSD(T)]. The establishment of an average error for the DZP CCSD(T) method should improve the reliability in the prediction of unknown experimental frequencies.