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Two-level factorial designs (FD) have been used to determine the effects of wave function modifications on calculated CH and CC harmonic stretching frequencies of the H2CCHX and HCCX molecules with X;=H, CH3, F, Cl and CN. These modifications were treated at two levels, which consists in: (I) using either a double- or a triple-zeta valence basis set; (II) including or not diffuse functions in basis set, (III) including or not polarization functions in basis set, and (IV) performing a calculation with or without electron correlation beyond the Hartree–Fock level, i.e., MP2 or B3LYP. Our results have shown that valence (Val), diffuse (Dif), polarization (Pol) and electron correlation (Corr) main effects as well as the Pol/Corr second-order interaction effect are significant to build factorial models for these vibrational modes. When valence and diffuse functions are introduced in the basis set, the calculated HC and CC stretching frequencies are decreased in both the HCCX and H2CCHX molecules. As expected, by far the correlation principal effect is the most important on the frequency values. This effect provokes a decrease of −281.4cm−1 and −153.3cm−1 in the CC and CC vibrational frequencies, respectively, using the MP2 calculations, whereas this decrease for the HC oscillator is −156.1cm−1 and −116.1cm−1 in HCCX and H2CCHX, respectively. This same effect produces an important Pol/Corr interaction effect on HC and CC stretching frequencies, increasing their values by +45.3cm−1 and +18.4cm−1 in HCCX, respectively, whereas their corresponding values in H2CCHX are +43.9cm−1 and +11.0cm−1, respectively. Finally, algebraic models were then established to explain how calculated HC and CC stretching frequencies in HCCX and H2CCHX depend on the characteristics of the molecular orbital wave functions. [Copyright &y& Elsevier]

Two-level factorial design (FD) and principal component (PC) models are used to determine the effects of wave function modifications on calculated H&bond;C and C&tbond;C harmonic stretching frequencies for the H&bond;C&tbond;CH, H&bond;C&tbond;CF, H&bond;C&tbond;CCl, H&bond;C&tbond;CCCH, H&bond;C&tbond;CCN and H&bond;C&tbond;CCH3 molecules. Our results have shown that valence (val), diffuse (dif), polarization (pol), and electron correlation (corr) main effects as well as some second-order interaction effects are significant to build factorial models for these vibrational frequencies. For instance, when valence and diffuse functions are introduced in the basis set, the calculated H&bond;C and C&tbond;C stretching frequencies decrease. However, this reduction is much more accentuated when the electron correlation effect is introduced in the Hartree-Fock wave functions. By far, the corr main effect is the most important one on the H&bond;C and C&tbond;C frequency values. The MP2 electron correlation effect provokes an increment of -157.4 cm-1 and -283.8 cm-1 on the H&bond;C and C&tbond;C stretching frequencies, respectively, whereas the dif effect produces only a reduction of -9.1 cm-1 and -12.9 cm-1 on these frequencies, respectively. The inclusion of Møller–Plesset 2 perturbation in the Hartree-Fock wave functions also produces an important pol–corr interaction effect on the H&bond;C and C&tbond;C stretching frequencies, increasing their values by +45.2 cm-1 and +17.3 cm-1, respectively. Algebraic models were then established to explain how calculated H&bond;C and C&tbond;C stretching frequencies depend on characteristics of the molecular orbital wave functions. These models were successful in reproducing calculated H&bond;C and C&tbond;C frequency values for the H&bond;CN and CH3C&tbond;CCH3 molcules, which were not included in the training set. The principal component analysis has revealed that the calculated H&bond;C and C&tbond;C stretching frequencies can be adequately described by a single principal component. It is capable of explaining more than 99% of the total data variance. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [ABSTRACT FROM AUTHOR]

Two-level factorial design (FD) and principal component (PC) models are used to determine the effects of wave function modifications on calculated carbon–carbon triple bond lengths for the HC≡CH, HC≡CF, HC≡CCH3, CH3C≡CCH3 and HC≡CCCH molecules. Our results have shown that valence, diffuse and polarization main effects are significant at the three levels of calculation here employed: Hartree–Fock (HF), Møller–Plesset 2 (MP2) and density functional theory (DFT) with B3LYP exchange–correlation functional. The valence–polarization interaction effect is significant at only the HF and MP2 levels of calculation. When valence and polarization functions are introduced in the basis set, the calculated C≡C bond length values decrease, in contrast with the results obtained when diffuse functions are used. The latter increase the C≡C bond length by +0.0016 Å, at all levels of calculations. Changing the method from HF to B3LYP and from B3LYP to MP2 yields an increase (averaged values) of +0.0195 and +0.0169 Å, respectively, on the calculated CC bond length values. For each level of calculation it was possible to establish an algebraic model to explain how the calculated C≡C bond length values depend on the molecular orbital wave functions. Such algebraic models successfully reproduce calculated C≡C bond lengths for the HC≡CCN and HC≡CCl molecules, which were not included in our training set. Our FD and PC models lead to the B3LYP/6-31G(d,p) and B3LYP/6-311++G wave functions as the selected ones in order to better reproduce experimental C≡C bond lengths for all the seven molecules here studied (training and validation molecules). Their predicted values deviate by just 0.004 Å from the experimental ones. [Copyright &y& Elsevier]