Theoretical Chemistry 1968-1976

The major theme in the theoretical chemistry effort during this period is change. At the beginning, its major focus was part of the program studying isotope effects. By the end, there was an independent theoretical effort with concentrations on electronic structure and molecular dynamics. The theoretical effort concerning isotope effects during this period is covered here.

Electronic Structure of Molecules

Prior to the 1960s theoretical chemistry was largely a pencil-and-paper endeavor. Lengthy calculations of molecular properties were either impractical, performed approximately, or made heroically on mechanical calculators. The arrival of electronic computers made calculations feasible, and the feasibility stimulated growth of new theoretical methods. Molecules are composed of atoms, and atoms are composed of nuclei and electrons. Analysis of molecular symmetry and molecular bonding requires, among other things, careful description of the electrostatic interactions among the nuclei and electrons constituting a molecule. The first barrier encountered is that if one considers all the pairwise interactions among nuclei and each electron, along with those between each pair of electrons, there is no closed-form solution to the electrostatic equations. Methods for approximating these interactions were a topic of intense interest. A series of papers was published examining and testing methods for approximating so-called "molecular orbitals".1,2

1. "Semi-Empirical MO Theory and Molecular Geometry. I. Analytical Procedures for Extended Hckel Methods" S. Eherenson, J. Amer. Chem. Soc. 91 3693 (1969).

2.  "Semi-Empirical MO Theory and Molecular Geometry. II. Analytical Procedures for Charge Redistribution Methods" S. Eherenson, J. Amer. Chem. Soc. 91 3702 (1969).

Solvation of Molecules in Solutions

The ability to make sophisticated electronic structure calculations, either ab initio or semiempirical, prompted a wave of calculations describing species too complex to be studied previously. Molecules in water solution are hydrated; that is, solute molecules and ions are coordinated to shells of solvent molecules. This ligation has profound effects with respect to solute reactivity, and understanding solute-solvent interactions is key to resolving effects in radiation chemistry, inorganic chemistry, radiation chemistry, and a myriad of other fields.

Ab initio molecular orbital calculations using Gaussian orbital basis sets were carried out for a large variety of structures of the hydrated proton and hydroxyl ion, H30+(H20)n, and OH-(H2O)n, n = 0, 4. Calculated solvation enthalpies, based on energy-optimized structures, were calculated to be within a few kilocalories of experimental values (after corrections for zero-point energy differences were made), and the experimentally observed similarities of enthalpies for isoelectronic cations and anions were reproduced. Preliminary calculations indicated no sharp discontinuities in solvation enthalpy associated with the transition from the inner to the outer solvation shell, in agreement with available cation data. Among the structural principles derived from the calculations were: (1) the general energetic preference for chain structures, with branching when possible, although cyclic species may be the favored structures for some of the larger hydrates; (2) an increase in interoxygen distances upon successive hydration; (3) a general tendency for bridging protons either to occupy asymmetric positions or to be associated with symmetric potentials characterized by essentially flat central regions; and (4) the reluctance of the hydronium ion and the hydroxyl ion to serve as a proton acceptor and a proton donor, respectively. Rules such as these, together with other features of the potential energy surfaces and charge distributions, lead to a comprehensive and apparently internally consistent picture of the hydrates of H+ and OH-. In the context of this picture, a detailed discussion of various static and dynamic properties of these complexes was given. General agreement was found with the previously suggested structure for the inner solvation shell of the proton (H904+), while a new alternative structure was proposed for the hydroxyl ion inner solvation shell (H704-). Although the calculations were most directly related to the isolated species for which they were carried out, their relevance to higher hydration processes and to condensed phase ion properties was emphasized.3

3. "Ab Initio Studies on the Structures and Energetics of Inner and Outer Shell Hydrates of H+ and OH-" M.D. Newton and S. Eherenson, J. Am. Chem. Soc. 93 4971 (1971).

Reactive and Nonreactive Scattering by Monte Carlo Methods

This period saw a true burgeoning of experimental and theoretical efforts in reactive and nonreactive scattering. Molecular beam experimental techniques, combined with the advent of new lasers and computers, made the whole field of chemical physics expand rapidly. Specifically, calculations of state-to-state gas-phase chemical reaction channels and rates became possible, popular, and useful. There was great interest in hydrogen halide chemical lasers to be used for isotope separation, laser-induced chemistry, and defense-related purposes. Therefore, in order to understand hydrogen halide chemically pumped lasers, and to advance the theory of such reactions, a detailed picture of the the chemical and physical processes leading to reaction, vibrational population inversion, or vibrational deactivation was necessary.

Accurate three-dimensional quantum mechanical calculations of reaction dynamics were still in the future, but the "Quasiclassical Trajectory" (QCT) method proved to be very successful to explain experimental results and to predict new behavior. In this method, continuous, classical (nonquantized) multidimensional potential energy surfaces are constructed that represent the energetic interactions among a set of potentially reactive atoms or molecules. Random initial conditions are chose, and atoms and molecules are computationally propagated across the surfaces, conserving energy and angular momentum as "exact" solutions to the classical equations of motion. Symmetry restrictions and quantum effects are added later. Accumulation of repeated calculations lead to a statistical prediction of reaction behavior.

For the reasons cited above, an important model system for experimentalists and theorists alike was the reaction between F atoms and hydrogen molecules (F + H2). For this very exothermic reaction, vibrational and rotational energy distributions among the products and state-resolved reaction rates were predicted using the QCT method. These calculations require a potential surface on which the reaction proceeds. The most successful surface, both from a scientific and scientifically popular point of view, is the "M5" surface4 developed in the BNL Chemistry Department.

A good example of the utility of QCT methods was a study of translationally excited (hot) 18F atoms with HD.5 During this period, pioneering work was being done in the Chemistry Department in this "hot atom" system. Understanding the mechanisms of reactions like this one became important because the Department introduced the synthesis and use of  18F-labeled  fluorodeoxyglucose in positron emission tomography (PET). Product yields, as reflected by "excitation functions" for the various channels in reactions of hot 18F atoms with ground-state HD were calculated. The production of H18F and D18F and dissociation into 18F+H+D were reported as a function of the center-of-mass collision energy over the range 0.165.0 eV. The calculated excitation functions for H18F and D18F cross at ~7 eV indicating an inversion in the intramolecular isotope effect with increasing collision energy. Features of these excitation functions and the calculated product energy distributions were discussed in terms of simple mechanistic models. The trajectory results, on the average, correlated well with the predictions of the spectator stripping model from epithermal collision energies up to the limiting energy where this model would lead only to dissociation. The high-energy tail of the abstraction excitation functions, however, was shown to be attributable to a mechanism which is the antithesis of spectator stripping. In these high-energy collisions, the nearer atom of the HD collides violently with the fluorine atom and recoils away. The training "abandoned atom" is left behind in the vicinity of the fluorine atom, with which it subsequently reacts.

4. "Applications of Classical Trajectory Techniques to Reactive Scattering" J.T. Muckerman in Theoretical Chemistry, Theory of Scattering: Papers in Honor of Henry Eyring, D. Henderson, ed. 6A p.1, Academic Press, London (1981).

5. "Classical Dynamics of the Reaction of Fluorine Atoms with Hydrogen Molecules. III. The Hot-Atom Reactions of 18F with HD" J.T. Muckerman, J. Chem. Phys. 57 3388 (1972).

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Last Modified: June 28, 2012