Sidney Golden

Generalizations of the Hohenberg-Kohn theorem: I. Legendre Transform Constructions of Variational Principles for Density Matrices and Electron Distribution Functions

Given a general, N-particle Hamiltonian operator, analogs of the Hohenberg-Kohn theorem are derived for functions that are more general than the particle density, including density matrices and the diagonal elements thereof. The generalization of Liebs Legendre transform ansatz to the generalized Hohenberg-Kohn functional not only solves the upsilon-representability problem for these entities, but, more importantly, also solves the N-representability problem. Restricting the range of operators explored by the Legendre transform leads to a lower bound on the true functional. If all the operators of interest are incorporated in the restricted maximization, however, the variational principle dictates that exact results are obtained for the systems of interest. This might have important implications for practical work not only for density matrices but also for density functionals. A follow-up paper will present a useful alternative approach to the upsilon- and N-representability problems based on the constrained search formalism.

Species and Composition of Dilute Alkali‐Metal—Ammonia Solutions

Dilute solutions of the alkali metals in liquid ammonia are assumed to consist of the following constituents: M+, the solvated metal cation; S, the solvent; M−, the solvated metal anion; S−, the solvent anion (solvated electron); the ion pairs M+·M− and M+·S−. These species are assumed to be in equilibrium via M++2S−⇌M−+2S and M++A−⇌M+·A−, where A− is either M− or S−. For simplicity, the activity coefficient of each species is assumed to be given by the extended theory of Debye and Huckel, with a fixed value of 5.5 A for the interionic size parameter; the ion‐pairing theory of Fuoss, with the same value for the interionic size parameter, is also assumed. The only adjustable parameter then remaining for a complete characterization of the composition of dilute alkali‐metal—ammonia solutions is the redox equilibrium constant.With generally good results being obtained, the foregoing model has been applied to account for the following properties of alkali‐metal—ammonia solutions which are more dilute than abou...

Shape stability of solvated-electron optical absorption bands. Part 1.—Experimental basis

Optical absorption bands of solvated electrons in seven different polar liquids under a range of different conditions are analysed to demonstrate a relative constancy of the spectral profile, termed spectral shape stability, in each of the liquids. As a consequence, average spectral profiles characteristic of each liquid are defined and shown to be appreciably different for chemically different liquids, thus serving to distinguish these liquids and their solvated electrons from each other. Spectral shape stability and deviations from it for pure liquids and the characterization of chemically different liquids and their solvated electrons by average spectral profiles are discussed briefly.

The Quantum Mechanics of Chemical Kinetics of Homogeneous Gas Phase Reactions I. General Considerations

From the zeroth order Born‐Oppenheimer approximation to the wave functions of a molecular system and the first order time‐dependent perturbation theory of quantum mechanics it has been possible to deduce: (1) the adiabatic hypothesis; (2) the dependence of the rate of homogeneous gas phase chemical reactions upon the composition of reaction mixtures; (3) the condition for zero net rate of reaction, which corresponds precisely to the statistical mechanical condition for equilibrium; (4) the dependence of the chemical reaction rate upon the temperature.Heuristic considerations transcribe the quantum mechanical result into terms of the collision theory and the activated complex theory of chemical reactions.

Nature of solvated electron absorption spectra

A fundamental many-particle theory of temperature-dependent spectral moments is developed for the enhanced optical absorption bands attributed to solvated electrons in various polar solvents. Several new results are obtained (expressed in atomic units): (1)n0ƒ= 1, where n0 is a mean index of refraction of the solvent and ƒ is the empirical oscillator strength of the band; (2)〈∣Δre∣2〉=(1/ω)av, where 〈∣Δre∣2〉 is an equilibrium-averaged dispersion-in-position of the solvated electron and (1/ω)av is the mean reciprocal absorption frequency of the band; (3)µe–¾ωav, where µe is the standard chemical potential of the solvated electron and ωav is the mean absorption frequency of the band; (4)ωth⩽¾ωav, where ωth is the (vertical) photoejection threshold frequency of the solvated electron.For solvated-electron spectra in ammonia, water and a number of other solvents, no more than about 25 % of the pertinent absorption band can be ascribed to bound–bound transitions involving excited states with energies less than that of the photoejection threshold of the solvated electron.

On a quantum mechanical theory of absolute reaction rates

The phenomenologica l laws which descr ibe the t e m p o r a l evo lu t ion of a r eac t ing chemica l sys tem are sufficiently well known to requi re l i t t l e a t t e n t i o n here to be given to the i r expos i t ion (1). Bo th the concen t r a t i on dependence of the k ine t i c equa t ions and the t e m p e r a t u r e coefficients of the r a t e cons tan t s of these equa t ions are now genera l ly unde r s t ood in the l igh t of the molecu la r processes occurr ing dur ing the course of chemica l change. To be sure, quest ions not fu l ly answered remain . I n the r e a l m of t heo re t i ca l i nves t iga t ions these refer genera l ly to de ta i l s of the sor t necessar i ly i nvo lved in p roduc ing q u a n t i t a t i v e l y precise, abso lu te theor ies of r eac t ion ra tes . To inves t iga t e such quest ions in a u l t i m a t e sense, a t h e o r y of abso lu te reac t ion ra tes mus t be based upon q u a n t u m mechanics . However , such a t h e o r y m a y assume a form more-orless express ib le in c lass ica l mechan ica l t e rms when classical mechanics furnishes an a d e q u a t e desc r ip t ion of the sys t em

Model potentials and the optical spectra of solvated electrons

Optical absorption spectra attributed to solvated electrons in ammonia, water, ethylenediamine and methanol are fitted by calculated photoejection spectra using a number of different model potentials. Theoretical spectra resulting from several spherically symmetric potentials yield excellent and in some cases indistinguishable representations of the experimental spectra. As a result, the optical spectra data are shown to provide only an insufficient basis for distinguishing between these different model potentials.

Continuous Representations in the Statistical Theory of Electronic Energies

The use of continuous bases of representation other than a plane‐wave basis is considered in the theory developed originally by Thomas and Fermi. The bases considered here are the sets of eigenfunctions of Hamiltonians corresponding to a particle subjected to a field of force which varies inversely as the cube of the distance to some fixed point. Variation of the strength of the interaction varies the basis continuously. Calculations of the energy of the hydrogen atom is carried out, with results that are appreciably closer to the quantum‐mechanical result than is obtained with the original Thomas—Fermi theory. Numerical results suggest the possible existence of a statistical analog of the Rayleigh—Ritz variation principle.

Shape stability of solvated-electron optical absorption bands. Part 2.—Theoretical implication

The enhanced optical absorption bands attributable to solvated electrons in polar solvents often merely shift in frequency with essentially unaltered shape when the temperature and/or density of the solution are changed. The resulting spectral shape stability is examined in terms of a fundamental many-particle theory of temperature-dependent spectral moments developed recently to deal with solvated-electron absorption bands. When spectral shape stability is extrapolatable to the zero of absolute temperature the solvated-electron absorption band is found to be equivalent to one in which the radiative transitions have an essential bound–continuum nature.The theory is expressed in terms of a continuum formalism built upon an energy band structure for solvated-electron systems. Expressions for the absorption line shape are obtained which are formally similar to those obtained from various single-particle theories in which bound–unbound transitions of the absorbing particle successfully account for the shape.An extended spectral shape stability is conjectured which appears to accommodate some cases in which overall spectral shape stability does not obtain.

CONTINUOUS REPRESENTATIONS IN THE STATISTICAL THEORY OF ELECTRONIC ENERGIES. THE H2(+) ION.

A version of the statistical theory of electronic energies, arising from a consideration of alternative partitionings of the Hamiltonian, has been applied to the H2+ ion, yielding electronic energies ∼6% greater in magnitude than the exact theoretical values at several values of the internuclear separation. The binding energy at the theoretical equilibrium separation was calculated to be 0.1024 a.u. compared to the experimental value of 0.1026 a.u.