An application of chemometric techniques to analyze the effects of wave function modifications on the binding energies of hydrogen-bonded complexes

Factorial design and principal component models are used to determine how ab initio H-bond energies depend on characteristics of the molecular orbital wave functions of HCN–HX linear complexes and acetylene–HX T-shaped complexes, with X=F, NC, Cl, CN and CCH. The results obtained for the two sets of complexes show that factorial design and principal component analyses complement each other. The H-bond energies of the HCN–HX linear complexes are affected mostly by adding polarization functions and by MP2 treatment, which have opposite signs. When polarization functions are introduced in the basis set the calculated H-bond energies decrease by  ≈4 kJ·mol−1. In contrast, when the level of calculation is changed from Hartree–Fock to MP2, the energies are increased by nearly the same amount on average. The principal component analysis shows that for the HCN–HX linear complexes the ab initio results are grouped into four well-separated classes: (I) HF calculations with polarization functions (HF/6-nG** and HF/6-n++G**), with n=31 or 311; (II) MP2 calculations without polarization functions (MP2/6-nG and MP2/6-n++G); (III) MP2 calculations including polarization functions (MP2/6-nG** and MP2/6-n++G**) and (IV) HF results without polarization functions (HF/6-nG and HF/6-n++G). The ab initio results of the group (III) are those that show a better agreement with the available experimental values. The change from the Hartree–Fock to the MP2 level is the most significant effect for the acetylene–HX complexes, increasing the calculated H-bond energy values by about 4.5 kJ·mol−1 on average. Here the ab initio results can be essentially grouped into two classes: HF or MP2 calculations. The H-bond energies calculated from the factorial models for the two sets of complexes are found to deviate only 6.5% from the full ab initio values.