On the necessity of <i>f</i> basis functions for bending frequencies

Abstract

The calculation of out-of-plane bending vibrations for π-bonded systems appears to be extraordinarily sensitive to the choice of a one-particle basis set. Ab initio predictions are reported for acetylene, an extreme example, at the self-consistent field (SCF), singles and doubles configuration interaction (CISD), nth order Mo/ller–Plesset perturbation theory (MPn,n=2–4), coupled-pair functional (CPF), and singles and doubles coupled cluster (CCSD) levels of theory. It is found that the addition of a set of f basis functions to the carbon atom changes the value of the SCF πg frequency by +45 cm−1, and the value of all correlated πg frequencies by more than +100 cm−1. Evidence is presented that this behavior is present in other π-bonded systems. It is concluded that basis sets consisting of triple zeta plus two sets of polarization functions plus one set of f functions (TZ2P+f ) can predict highly accurate (∼1% average error) harmonic frequencies with the MP2, CPF, and CCSD methods, for a large number of molecules.