Parbury P. Schmidt

Continuous charge distribution models of ions in polar media. Part 5.—Quantum mechanical treatment of ionic and molecular solvation

This paper explores the possibility of establishing a computationally useful theory of ionic and molecular solvation based upon the direct use of quantum mechanically defined charge density components. The objective is to calculate free energies of solvation. The form of analysis proposed makes use of Ruedenbergs density matrix formulation with which the molecular electronic charge distribution is decomposed into quasiclassical and interference density components. Thus, the electrostatic source charges in a molecule contribute individually to the free energy. The various contributions, further, can be related to terms in a typical molecular orbital calculation. Formally, it appears possible at this stage to anticipate that general rules of solvation can be formulated, and that the rules of solvation should emerge in much the same form as the rules of bond energy additivity in thermochemistry. The concepts advanced in this paper are illustrated by the use of three transparent, simple molecular systems: H+2, H2, and H–2 in a structureless, continuum water solvent system.

Continuous charge distribution models of ions in polar media. Part 2.—Self and interaction energies for soft charged ring systems dissolved in a polar medium

This paper is concerned with the calculation of self and interaction energies for ring type charge distributions as representations of a class of ions (namely, radical ions of the aromatic ring type). The ionic systems are considered to be dissolved in a suitable polar solvent medium. The energy quantities are useful in the calculation of solvation energies. In particular, the interaction energy enters into the consideration of the repolarization energy for an electron transfer transition between donor and acceptor species.

Contribution of ionic effects to electron transfer reactions

This paper reports an initial effort to combine the theory of ionic conductivity, due to Friedman, with the theory of simple outer sphere electron transfer reactions. In this work the ions, which do not participate in the electron transfer transitions, are considered individually. The solvent is considered, as elsewhere, as a dielectric continuum. The calculations are carried out for extreme ionic dilution, a Debye–Huckel limit. The purpose of this work is to attempt to provide a more detailed account of the effect of ions present in the solution on the reaction rate. The effect which arises manifests itself through the reaction rate constant expression. Specifically, we find that as a result of the interaction between the electron transfer system and the ions in solution, transport coefficients associated with ionic mobilities in solution appear in the rate constant expression. The nature of the ionic effect is similar to the effect found when one considers either damping of the electron transfer transition state or damping of the energy states of the polarization modes of the dielectric continuum.

Continuous charge distribution models of ions in polar media. Part 6.—Reltationship between quantum and classical charge distributions

A formal relationship between the classical phenomenological charge distribution representations of ions and the quantum mechanical treatment is presented. This relationship is established by means of an expansion of the molecular electronic quantal charge density in terms of a complete set of orthonormal functions. Such an expansion is similar in form to a classical multipole expansion for an arbitrary charge distribution. The analysis reported provides a rigorous mathematical and an enhanced physical interpretation of the “effective Bohr radial” quantities introduced with the earlier phenomenological models.

Continuous charge distribution models of ions in polar media. Part 4.—Planar elliptic ring systems

This paper reports a continuation of our investigation into the solvation self and interaction energies of continuous charge distribution models of molecular ionic systems. In particular, the ring system considered previously is generalized by examining an elliptic modification. The previous work was suitable for the consideration of the self and interaction energies of benzenoid redical ions. This work is suitable for the consideration of naphthalenic and higher regular shaped radical ions.

Effect of damping mechanisms on electron transfer reactions

The application of an orthogonal expansion of the Lorentz distribution is made in order to investigate the effects of damping on electron transfer reactions. The results correct and extend an earlier work. It is possible with this approach to predict the conditions under which state and solvent mode damping become important.

Collective treatment of inner sphere reactions. Part 2.—Contributions from the ionic solvation surface

Molecular giant resonance and solvation sphere surface modes of oscillation were introduced and applied to the electron transfer reaction in two previous papers. The giant resonances are associated with relative ion-solvent motions in the first solvation sphere, and these degrees of freedom enter into the activation for the electron transfer transition. In this paper a similar analysis is applied to the surface modes. Surface oscillations are important. They provide a measure of the interaction between the solvated ion and the medium neighbouring it. We find that it is unlikely that surface reorganization plays any significant role in an outer sphere reaction. On the other hand, for the inner sphere reaction, for which gross chemical change takes place, these reorganization energy contributions can be significant. Several examples are considered.

Continuous charge distribution models of ions in polar media. Part 3.—The effects of tetragonal and octahedral distortion

In this paper the soft spherical charge distribution model of an ion introduced in Part 1 is modified to take into account tetragonal and octahedral distortion effects. These effects are associated with the solvation or coordination of an ion. The treatment introduced here therefore represents a generalization of the previous work. In particular, we find that a single charge distribution representation can be used both for cations and anions. The amount of tetragonal distortion introduced in each case is fixed by a simple relationship. For the alkali and alkaline earth cations and halide anions agreement with the experimental self energies is obtained.

Vibrational spectrum of an ion pair in a non-polar solvent

The vibrational spectrum of an ion pair dissolved in a low polarity solvent is investigated. The analysis presented is phenomenological and concentrates on one particular system: namely, an ion pair composed of a rigid charged ring, e.g., the benzene radical anion, and a spherical counter ion. The potential energy function for the system consists (1) of an electrostatic component which is formulated in terms of continuous charge distributions, and (2) a simple exponential, short ranged repulsion term. The complete interaction energy depends parametrically upon several parameters, and the adjustment of these parameters can be carried out based on physical arguments. Vibrational force constants, the associated frequencies, and the oscillator strengths for the first allowed dipole transitions are determined with the use of the harmonic term in a general Taylor expansion of the interaction energy. Stable force constants are found for a limited range of values of the ring radius, the equilibrium separation between the ring and counter ion, and the repulsion parameter. The vibrations of the spherical counter ion in the plane of the ring, which are of importance for coupled electron-ion transport processes, have predicted frequencies in the range of 30 to 550 cm–1.

Quantum collective model of ionic solvation

This paper contains a quantum hydrodynamic and collective surface mode treatment of the internal dynamics of a solvated ion. The theory developed is particularly useful for the consideration of the influence which internal solvation degrees of freedom have on electron transfer rate and reaction processes. The model consists of two inter-penetrating fluids: one ionic and one solvent. In addition, as the solvated ion occupies space within a continuum dielectric, the surface of the ion is considered as composed partly of the dielectric medium. Thus, surface quadrupole and higher multipole oscillations reflect distortions in the medium; these distortions can accommodate the movement of species to and from the ionic inner solvation sphere. As a result, it is possible to account for changes in coordination and bonding which take place in a number of electron transfer reactions. In addition, the theory shows a good agreement with the observed far infrared spectra of simple solvated ions. Isotope and solvent effects are predicted accurately.