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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]

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Abstract: 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 0.0022Å, 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 +0.0027Å, 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 0.0014Å, respectively) and correspond to the calculated points in closest proximity to the experimental one. [Copyright &y& Elsevier]

MP2/6-31++G** and B3LYP/6-31++G** ab initio molecular orbital calculations have been performed in order to obtain molecular geometries, binding energies and vibrational properties of the C2H2—HF, C2H(CH3)—HF and C2(CH3)2—HF H-bonded complexes. As expected, the more pronounced effects on the structural properties of the isolated molecules due to complexation was verified for the C≡C and H—F bond lengths, which are directly involved in the H-bond formation. These bond distances increased after complexation. BSSE uncorrected B3LYP binding energies are always lower than the corresponding MP2 values. However, the opposite trend has been verified after BSSE correction by the counterpoise method since it is much lower at B3LYP than at MP2 level. The binding energies for these complexes as well as for the HF acid submolecule modes (the HF stretching and vibrational frequency modes) showed an increasing hydrogen-bonding strength with increasing methyl substitution. The splitting in the HF in-plane and out-of-plane bending modes reflects the anisotropy in the hydrogen-bonding interaction with the π system of the C≡C bond. The H—F stretching frequency is shifted downward after complexation and it increases with the methyl substitution. The IR intensities of the HF acid submolecule fundamentals are adequately interpreted through the atomic polar tensor of the hydrogen atom using the charge–charge flux-overlap model. The skeletal stretching modes of the Alkyne submolecule are decreased in the complex. The new vibrational modes arising from complexation show several interesting features. [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 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]

DFT calculations with B3LYP and PBE1PBE functionals and 6–311++G(d,p) basis set have been performed in order to obtain molecular geometries, binding energies and vibrational properties of the RCN⋯HF H-bonded complexes with R = NH2, CH3O, CH3, OH, SH, H, Cl, F, CF3, C≡N and NO2. As expected, it has been verified as a red-shift of the HF stretching frequency (νHF), in conformity with the elongation of the bond after complexation. On the other hand, the C≡N stretching frequency (νC≡N) is blue-shifted and corresponds to a shortening of the bond. The binding energies (ΔEc), including BSSE and ZPVE corrections, show a linear correlation with several structural, electronic and vibrational properties. In particular, an important linear dependence between the binding energy and the calculated dipole moment of the free R-C≡N molecule (μRCN) has been found. This result suggests that μRCN can be a useful quantity in order to predict the ability of this fragment to form a hydrogen-bond. The IR intensities of stretching and bending modes of complexed H-F acid fragment are adequately interpreted through the atomic polar tensor of the hydrogen atom in H-F using the modified CCFO model for infrared intensities. The new vibrational modes arising from complexation show several interesting features. [Copyright &y& Elsevier]