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化学 Gaussian 校正因子
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The determination of vibrational frequencies by ab initio computational methods is becoming increasingly important in many areas of chemistry. One such area is the identification of experimentally observed reactive intermediates for which the theoretically predicted frequencies can serve as fingerprints. Another important area is the derivation of thermochemical and kinetic information through statistical thermodynamics. Ab initio harmonic vibrational frequencies (ö  are typically larger than the fundamentals (îÄ observed experimentally.A major source of this disagreement is the neglect of anharmonicity effects in the theoretical treatment. Errors also arise because of incomplete incorporation of electron correlation and the use of finite basis sets. Thus, for example, Hartree-Fock (HF) theory tends to overestimate vibrational frequencies because of improper dissociation behavior, a shortcoming that can be partially compensated for by the explicit inclusion of electron correlation.The overestimation of ab initio harmonic vibrational frequen-cies is, however, found to be relatively uniform, and as a result generic frequency scaling factors are often applied. Good overall agreement between the scaled theoretical harmonic frequencies and the anharmonic experimental frequencies can then usually be obtained. The determination of appropriate scale factors for estimating experimental fundamental frequencies from theoretical harmonic frequencies has received considerable attention in the literature. Semiempirical methods, such as AM1and PM3,are potentially attractive for the computation of vibrational frequen-cies because of their inherent low computational cost. However,there has been little systematic work reported on the performance of such methods for the prediction of vibrational frequencies. The most comprehensive study to date is an AM1 investigation by Healy and Holder on 42 common organic molecules in which the computed harmonic frequencies were found to differ from experiment by an average of 10.4%. We are unaware of any such study for the PM3 method. Pople et al.found that the harmonic vibrational frequencies calculated at HF/3-21G for a set of 38 molecules (477 frequencies) had a mean ö(3-21G)/îÄ(expt) ratio of 1.123, which suggested that this level of theory overestimates frequencies by about 12%. A scaling factor of 0.89 for theoretical HF/3-21G harmonic frequencies was proposed as being appropriate for predictive purposes. Hehre et al.4 determined from an HF/6-31G(d) study of 36 molecules a mean percentage deviation of theoretical harmonic frequencies from experimental fundamen-tals of about 13%, similar to the findings of Pople et al.3 for HF/3-21G. An HF/6-31G(d) theoretical frequency scaling factor of 0.8929 has been widely used in theoretical thermochemical studies. Hehre et al. also determined that the MP2-fu/6-31G(d) method gave mean percentage deviations of theoretical harmonic frequencies from experimental fundamentals of about 7%. Such an error indicates that an appropriate scale factor for MP2-fu/ 6-31G(d) theoretical frequencies would be 0.921. In a later study, DeFrees and McLean5 found somewhat larger scale factors (of 0.96 for first-row molecules and 0.94 for second-row molecules) by determining an average of the experimental/ theoretical frequency ratios for individual modes. Recently, we determined the scale factors for the HF/6-31G-(d) and MP2-fu/6-31G(d) methods using a set of 122 molecules (1066 frequencies) and a least-squares approach.6 We computed an optimum HF/6-31G(d) frequency scale factor of 0.8953, very similar to the previous standard value of 0.8929, and recom-mended that the standard value remain unchanged. A scale factor appropriate for frequencies computed at the MP2-fu/6-31G(d) level of theory (0.9427) was also determined, which lies between the values proposed by Hehre and DeFrees. We also found that, even after removing some exceptionally poorly predicted frequencies for O3 and NO2, the overall root-mean-square (rms) error for the MP2-fu/6-31G(d) method was only slightly smaller than the overall rms error for the HF/6-31G(d) level of theory. Some work has been presented in the literature on harmonic vibrational frequencies determined with more sophisticated correlated methods.These studies have, however, been generally limited to small polyatomic molecules. Procedures such as QCISD, CCSD, and CCSD(T) have been shown by several researchers to provide excellent agreement with experi-mental harmonic frequencies when used in conjunction with a variety of basis sets (double zeta plus polarization and larger).15-18 While the computational cost of such procedures is very expensive relative to that for HF or MP2, recent and continuing improvements in raw computer speed together with more efficient programs make these methods increasingly feasible. The advent of density functional theory (DFT) has provided an alternative means of including electron correlation in the study of the vibrational frequencies of moderately large molecules. Of the myriad of DFT functionals that are available today, perhaps the most prominent are B-LYP and B3-LYP. B-LYP uses a combination of the Becke exchange functional (B) coupled with the correlational functional of Lee, Yang, and Parr (LYP),while the hybrid B3-LYP procedure uses Becke's three-parameter exchange functional (B3), as slightly modified by Stephens et al.,in combination with the LYP correlation functional. |
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