Polarizability of an Ion in a Molecule. Applications of Rittner's Model to Alkali Halides and Hydrides Revisited

Abstract

An attempt is made to estimate the polarizability of an ion in an ionic diatomic molecule. The method is applied to alkali halide and hydride diatoms. In this connection, the applicability of Rittner's model to these test molecules is examined critically. A new phenomenological form of the repulsive part of Rittner's model is suggested. It is argued that the polarizability of an ion can be used as an index of the gas-phase chemical hardness of an ion in a molecule.Determination of the static electric dipole polarizability (hereinafter referred to simply as polarizability) R of an ion in a molecule is an old and important problem. It was realized long ago that R of an ion in a molecule is not the same as that in the free state. In 1934 Fajans 1 introduced a principle that states that R is diminished in the field of positive charge and increased in the field of negative charge. This statement was theoretically quantified later by Ruffa in 1963. 2 In the past there have been a number of attempts to estimate the R of an ion in a molecule. For a recent brief review on these efforts, see ref 3. Coker has found that in alkali halide crystals polarizability of an anion decreases while that of a cation increases. 4 Coker has also tried to find a relation between the R value of a free ion and that of the ion in a crystal. Here we are not interested in finding the R of an ion in a crystal lattice but that in an isolated molecule.A possible way of checking whether the R of an ion in a molecule has been estimated correctly is to work out Rittner's model 5 for a diatomic molecule AB in detail. In 1951, to explain bonding in specifically the alkali halide diatomics and to estimate their various spectroscopic constants theoretically, Rittner developed a model where an AB molecule is described as a cation-anion pair (polarizable charged spheres) held together by electrostatic attraction but prevented from collapse by a repulsive potential. In this model, the dipole moment µ and the ionic bond dissociation energy W are given by eqs 1 and 2, respectively. In eq 2 C is the van der Waals constant, φ(r) is the repulsive energy resulting from the overlap of the electron clouds of the two ions A + and B -, the last term represents the zero-point energy, and the superscripts + and -designate cation and anion, respectively. Using the derivatives of W with respect to r (of various orders) and some standard relations, 3,6 one can calculate the rotational-vibrational coupling constant (R e ), vibrational anharmonicity constant (ω e x e ), and other higher order spectroscopic constants, γ e and e (these notations are standard as used by Huber and Herzberg 7 ). This model, which because of its nature is likely to hold in rather ionic diatomics, has been examined by many workers in the past using mainly the alkali halide diatoms as the testing grounds 3,6,8-12 (in only one study 3 have the hydrides of the alkali metals been considered). As a general result, a simplification of Rittner's model by omitting the product terms R + R -, which arise ...

Equilibrium interfacial tension and the influence of extreme dilutions of uni-univalent salts: An expression of the “Jones–Ray effect”

“…This matter has been confirmed by the molecular dynamic simulation technique [39]. The ionic radii and polarizability of I À are 0.216 nm and 8.283 Á 10 À3 nm 3 and those for Cl À are 0.181 nm and 4.369 Á 10 À3 nm 3 , respectively [40]. The special situation at 50.0°C may be due to the ion hydration weakening which leads ions like K + to approach the interface.…”

Complete basis set extrapolated potential energy, dipole, and polarizability surfaces of alkali halide ion-neutral weakly avoided crossings with and without applied electric fields

“…Gas phase alkali halides represent a set of prototypical systems to study charge transfer and have been the subject of numerous theoretical [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] and experimental [33][34][35][36][37] studies. These systems are dominated by ionic character at close separation and are well characterized as neutral atoms at large separation.…”

Atomic Charges in Highly Ionic Diatomic Molecules

“…The atomic charges are assumed to be 1.0 e in Rittner models for all the alkali halide molecules, as done in other literature studies. 28,30−33 In the point charge model, results with q = 1 e (“-×-”) and the NPA atomic charges (“-▷-”) at the HF/6-311+G(3df) level are also given for comparison. Compared with the experimental data (“-■-”), the predictions with the point charge model (“-×-” and “-▷-”) are too large and the results from the original Rittner model (“-●-”) are obviously small for dipole moments.…”

“…However, for a large part of the molecules, the predicted atomic charges with the same relationships were far larger than the expected values. To improve the quality of predictions, the above-mentioned Rittner relationships had been widely investigated, 30−33 including the assumption of the polarizabilities for species in molecules were functions of the potentials between ions in molecules and so on. 31,32 This made the polarizabilities of species in molecules not detectable; therefore, the corresponding atomic charges were not functions of complete experimental variables.…”