On the number of significant mode-mode anharmonic couplings in vibrational calculations: Correlation-corrected vibrational self-consistent field treatment of di-, tri-, and tetrapeptides

A computational study is made of the number of important anharmonic mode-mode couplings in the context of vibrational calculations for di-, tri-, and tetrapeptides. The method employed is the correlation-corrected vibrational self-consistent field (CC-VSCF) algorithm, which includes correlation effects between different vibrational modes. It is found that results of good accuracy can be obtained in calculations that include only N log N mode-mode coupling terms, where N is the number of modes. This simplification significantly accelerates CC-VSCF calculations for large molecules. A criterion based on the characteristics of the normal-mode displacements is employed to predict a priori unimportant coupling terms. The criterion is tested statistically using Spearman's rank correlation coefficient. The results are illustrated by calculations for several di-, tri-, and tetrapeptides using semiempirical PM3 potential surfaces. These results are analyzed and a statistical model for error estimation is given. The decrease in the number of included coupling from N2 to N log N opens possibilities of anharmonic vibrational calculations for large peptides.