Electron charge distribution in type H2A molecules and calculation of their geometric, force, and electrooptic parameters

Abstract

UDC 539.19 Simpler methods based on specific models of the electronic charge distribution in a molecule [1, 2] are used in conjunction with complex quantum chemical methods in the calculation of molecular constants. One of the best known examples of this kind is the valence shell electron pair repulsion method (VSEPR) [1] which has achieved considerable success in the qualitative description of molecular geometries. In the VSEPRmethod a model of the molecule is set up in the form of spherical atomic cores betweenwhichthe spheres of the electron pairs arelocated and, moreover, the whole of the charge due to an electron pair lies within such a sphere. This model contradicts the true electronic charge distribution in a chemical bond since it is well known that, in the hydrogen molecules, for example, only a part of the electron cloud is concentrated in the region between the atoms while the residual part is localized around the atoms. In the present work, by taking H2A molecules as the examples, it has been shown that, by taking account of the localization of the electronic charge of a bond not only in the region between the atoms but also around the atoms, it is not only possible to obtain qualitative data concerning the geometry of a molecule but also quantitative data. Additionally, it turns out that it is possible to calculate the force constants and electrooptic parameters of molecules. we shall represent the electron cloud of a single bond as consisting of three parts, one of which surrounds the first atom, the second of which surrounds the second atom, and thethird of which is localized Between the two atoms. We shall denote the fractional aprt of each of the two ele~r which participate inthe formation of the tkird part of the electron cloud of the i-th bond by a i. Then the charse inthe thirdpart of the electron cloud which is localized in the region between the atoms is equal to -2~ie , where e is the electronic charge and the charges in the first and second parts are equal to +ale. We shall also represent the electron cloud of a lone pair of electrons in the form of two parts, one of which is localized aroundthe atom while the other is localized around a point situated at a certain distance from the atom. We shall denote the fractional participation of each of the two lone pair electrons in the formation of the second part of the electron cloud by e. Then, the charges on these parts are equal to +2ee and -2ee respectively. We shall not introduce the following simplification. We shall replacethe complex electronic charge distribution in the separate parts of the bonds by point charges which are localized at the centers of the atoms (charges of +~i e) and on the lines linking the atoms, i.e., on the bonds at a distance r i from the central atom A (a charge of -2~ie). We shall also replace the complex electronic charge distribution in the lone pairs by point charges localized on atom A (a charge of +2ee) and at a distance p from atom A (a charge of -2ee). The magnitudes of these point charges vary as the atoms vibrate. We shall assume thatthe magnitude of the point charges vary according tothe exponential law ~i ~--- ~ exp (-- q~/cr), (I) where a are the values of the parameters a i in the equilibrium position, qi i s the change in the bondlength as the atoms vibrate, and ~ is a parameter which characterizesthe degree of the change in the magnitude of the charge as the atoms vibrate. C oulombic forces act between allthe point charges. However, according to Earnshaw's theorem, C oulombic forces alone cannot ensure a stable state for the system. Hence, it is necessary to take account of the repulsive forces between the neighboring parts of the electron cloud. The potential due to the repulsive forces is usually represented in the form Ur~ ~ A/r~. (2)