Factorial design analysis of the effects of wave function modifications on calculated HC and CC stretching frequencies in H2CCHX and HCCX

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 −281.4 cm−1 and −153.3 cm−1 in the CC and CC vibrational frequencies, respectively, using the MP2 calculations, whereas this decrease for the HC oscillator is −156.1 cm−1 and −116.1 cm−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 +45.3 cm−1 and +18.4 cm−1 in HCCX, respectively, whereas their corresponding values in H2CCHX are +43.9 cm−1 and +11.0 cm−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.