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 x are then computed from the third and fourth derivatives.
e e
The second approach invokes a purely empirical linear correlation between x e e and the harmonic frequencies . The third and fourth empirical approaches e suppose that the effective harmonic and anharmonic force constants are Ε½ . proportional with an additive constant in the fourth approach . Experimental values for x are compared with empirical predictions and with semiempirical e e Ε½ . Ε½ . estimates based upon HartreeαFock HF , MΓΈllerαPlesset MP2 , and local, Ε½ . nonlocal, and hybrid density-functional theories DFT , using the small 6-31G* basis set. Ab initio values of and bond lengths r are also compared against e e Ε½ . experiment. The U MP2 results are the worst and include several anomalies. The other semiempirical methods yield results of comparable accuracy for x e e of hydrides, although the DFT methods are markedly better for and r and e e for x of nonhydrides. The empirical estimates are nearly as good as the e e
Ε½ . semiempirical ones. We conclude that: 1 both empirical and semiempirical approximations are useful for predicting stretching anharmonicity constants
x to precisions of f 5 cm y1 for hydrides and f 1.5 cm y1 for e e Ε½ . 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 Ε½ . of vibrational constants calculated at the UMP2 level: a the calculated values of