An application of chemometric techniques to analyze the effects of the wave function modifications on the intermolecular stretching frequencies of the hydrogen-bonded complexes

Factorial design and principal component models are used to determine how ab initio H-bond stretching frequencies depend on characteristics of the molecular orbital wave functions of acetylene–HX, ethylene–HX and cyclopropane–HX π-type hydrogen complexes with X=F, Cl, CN, NC and CCH. The results obtained for the three sets of complexes show that factorial design and principal component analyses complement each other. Factorial design calculations clearly show that these frequencies are affected mostly by inclusion of electron correlation on the calculation level. On average, their values are increased by about 25 cm−1 due to a change from the Hartree–Fock (HF) to Möller–Plesset 2 (MP2) level. Valence, diffuse and polarization main effects as well as valence–diffuse, diffuse–correlation and polarization–correlation interaction effects are also important to better describe a factorial model to the H-bond stretching frequencies of these hydrogen complexes. This simplified model has been successful in reproducing the complete ab initio results, which correspond to two hundred and forty calculations. Principal component analyses applied only to hydrogen-bonded complexes whose experimental frequencies are known, has revealed that the six-dimensional original space can be accurately represented by a bidimensional space defined by two principal components. Its graphical representation reveals that the experimental intermolecular stretching frequencies are in closest agreement with the MP2/6–31+G and MP2/6–311+G ab initio results.