Effects of wave function modifications on calculated carbon-hydrogen bond lengths

The two-level factorial design (FD) and principal component analysis (PCA) chemometric techniques were used to investigate the carbon-hydrogen bond lengths dependence on the basis set size and quantum chemistry method, for H-C≡CH, H-C≡CF, H-C≡CCH3, H-C≡CCN, H-C≡CCl and H-C≡CCCH molecular systems. The calculations were performed by using Hartree-Fock (HF), Møller-Plesset 2 (MP2) and Density Functional Theory (DFT) with B3LYP exchange-correlation functional methods. The effects concerning basis set size include the number of valence and polarization functions as well as the cooperative effect between them, at all computational levels. The increase in the number of valence functions decreases the calculated C-H bond lengths by approximately 0.0022 Å, while the inclusion of polarization functions at HF and B3LYP levels increases the C-H bond length, in contrast to the behavior obtained at MP2 level. The effect of the inclusion of diffuse functions is non-significant, at all three computational levels. Moreover, the valence-polarization interaction effects are not significant, except at the MP2 calculational level, in which such effects lead to an increase in the calculated C-H bond lengths. When the computational level changes from HF→B3LYP and B3LYP→MP2 the calculated C-H bond length values increase (on average) by +0.0100 and +0.0027 Å, respectively. Algebraic models (one for each level of calculation) successfully employed to reproduce the calculated values for H-C≡N bond length, a system not included in the training set. The HF/6-31G(d,p) and HF/6-31++G(d,p) results yield the lowest standard errors (0.0015 and 0.0014 Å, respectively) and correspond to the calculated points in closest proximity to the experimental one.