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Inexpensive vibrational anharmonicities from estimated derivatives: Diatomic molecules
Author(s) -
Hassanzedeh Parviz,
Irikura Karl K.
Publication year - 1998
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/(sici)1096-987x(199808)19:11<1315::aid-jcc11>3.0.co;2-k
Subject(s) - anharmonicity , diatomic molecule , ab initio , morse potential , chemistry , computational chemistry , basis set , density functional theory , bond length , molecule , atomic physics , physics , quantum mechanics , organic chemistry
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 e x e are then computed from the third and fourth derivatives. The second approach invokes a purely empirical linear correlation between ω e x 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 e x 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 e x e of hydrides, although the DFT methods are markedly better for ω e and r e and for ω e x 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 e x 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 e x 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 〈 S 2 〉/ dR ≳0.05 Å −1 , suggests that calculated constants are too large. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1315–1324, 1998