Dynamic behaviors of interactions: application of normal coordinates of internal vibrations to AIM dual functional analysis.

A method to evaluate the dynamic nature of interactions is proposed based on the AIM dual functional analysis. Normal coordinates of internal vibrations (NIV) are employed to generate the perturbed structures necessary for the analysis. H(b)(r(c)) are plotted versus H(b)(r(c))-V(b)(r(c))/2 [= (variant Planck's over 2pi(2)/8m)nabla(2)rho(b)(r(c))] at bond critical points for the purpose. The plots are represented by the polar (R, theta) coordinate. Each plot for an interaction shows a specific curve, which is expressed by (theta(p), kappa(p)): theta(p) corresponds to the tangent line for the plot from the y-direction, and kappa(p) is the curvature. Although (R, theta) values correspond to the static nature of interactions, (theta(p), kappa(p)) values show the dynamic nature. The applicability of NIV is examined exemplified by the charge-transfer interactions as the first step to analyze the dynamic behaviors of interactions with NIV. The (theta(p), kappa(p)) values evaluated with NIV are very close to those obtained by the partial-optimization method (POM), where the distances or angles in question are fixed suitably, if the internal vibrations are substantially located on the interactions in question. The magnitudes of differences in theta(p) and kappa(p) between those evaluated with NIV and POM are < or = 2 degrees and < or = 2 au(-1), respectively, for usual interactions. The treatment is demonstrated to be applicable to a wide range of interactions.