Inexpensive vibrational anharmonicities from estimated derivatives: Diatomic molecules

Four alternatives are compared for estimating vibrational anharmonicity constants without explicitly calculating the expensive fourth derivatives of the potential curves. In the first, semiempirical approach, fourth derivatives for 53 diatomic molecules are estimated from ab initio second and third derivatives by using the Morse model potential. Vibrational anharmonicities ω_ex_e are then computed from the third and fourth derivatives. The second approach invokes a purely empirical linear correlation between ω_ex_e and the harmonic frequencies ω_e. The third and fourth empirical approaches suppose that the effective harmonic and anharmonic force constants are proportional (with an additive constant in the fourth approach). Experimental values for ω_ex_e are compared with empirical predictions and with semiempirical estimates based upon Hartree–Fock (HF), Møller–Plesset (MP2), and local, nonlocal, and hybrid density-functional theories (DFT), using the small 6-31G* basis set. Ab initio values of ω_e and bond lengths r_e are also compared against experiment. The (U)MP2 results are the worst and include several anomalies. The other semiempirical methods yield results of comparable accuracy for ω_ex_e of hydrides, although the DFT methods are markedly better for ω_e and r_e and for ω_ex_e of nonhydrides. The empirical estimates are nearly as good as the semiempirical ones. We conclude that: (1) both empirical and semiempirical approximations are useful for predicting stretching anharmonicity constants ω_ex_e to precisions of σ≈5 cm⁻¹ for hydrides and σ≈1.5 cm⁻¹ for nonhydrides; and (2) MP2 theory is relatively unreliable for such calculations. In addition, we find the following tests to be useful when evaluating the reliability of vibrational constants calculated at the UMP2 level: (a) the calculated values of ω_e and ω_ex_e should not deviate substantially from the empirical relations; (b) harmonic frequencies and intensities calculated at the MP2 level should be smaller than those calculated at the corresponding HF level; (c) a large distance-dependence of the spin contamination, d〈S²〉/dR≳0.05 Å⁻¹, suggests that calculated constants are too large. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1315–1324, 1998