Transformation of ab initio force fields in calculations of molecular vibrations using regundand vibrational coordinates

Abstract

539.19A technique was suggested to transform ab initio molecular force fields calculated using a set of independent vibrational coordinates into a form corresponding to a complete set of regundand coordinates and reflecting the molecular symmetry. Conditions necessary for the appropriate transformations to be possible are formulated. The possibility of transforming the force field for the simplest fragment containing regundand coordinates was demonstrated using ethylene as an example.Keywords: force field, vibrational spectrum, sets of regundand and independent vibrational coordinates.Introduction. The increased processing power of modern computers enables the acceleration and improvement of ab initio methods for calculating molecular force fields [1]. This includes the expansion of the basis set of functions [2] and consideration of increasingly finer effects from the interaction of electrons with each other and the nucleus [3][4][5][6][7]. However, vibrational spectra of only comparatively small molecules can be analyzed using the currently most accurate ab initio methods. Force constants that are calculated in several quantum-chemical programs using a set of independent vibrational coordinates cannot be translated into calculated force fields for more complicated molecules. It is well known that force fields that are constructed for a set of regundand natural coordinates do not have the aforementioned shortcomings and reflect fully the molecular symmetry. Such fields, similar to the empirical ones used earlier, can be readily translated to molecules of arbitrary complexity and can be used rather reliably to interpret vibrational spectra by using slight variations of the off-diagonal force constants. Therefore, finding the force field for a set of regundand coordinates by using the force-constant matrix for a set of independent coordinates is a very timely problem.Calculation Methods. Designating the force-constant matrix for a set of regundand natural coordinates by K and the corresponding matrix for a set of independent ones by k, it can be confirmed that if K is known then k can always be found unambiguously if matrix A that expresses a set of regundand natural coordinates through a set of independent ones is defined [8]. We will attempt to utilize the pseudo-inverse matrix A −1 to solve the inverse problem. Let [α reg ] = A[α ind ]. In the simplest instance for a planar configuration of four atoms (Fig. 1), the coordinates of the three bond angles are related by the obvious relationship:

Features of the Interaction of Hydroxyl and Methyl Tops in the Ethanol Molecule: 2D-Calculation of the Torsion Energy Levels

“…The calculated proportionality coeffi cient between F iφ and G ii was 13.047. It is noteworthy that the published program [24] was used several times before [25][26][27][28][29] to scale the force fi elds in natural coordinates that were calculated using it [14]. Each time the reproducibility of the vibrational frequencies for the unscaled force fi eld obtained using the programs [14, 24] was checked and confi rmed.…”