Thomas R. Tuttle

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.

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.

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.

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.

A new model of solvated-electron systems. Spectral behaviour

A new adiabatic model of infinitely dilute solvated-electron systems is described in which the solvent is accorded a dual role suggested by the experimental behaviour of the optical absorption bands attributed to solvated electrons. A small, finite number of solvent molecules and an excess electron, designated as a solvent–anionic-complex, are treated as adiabatic particles; the remaining solvent molecules, comprising a macroscopic solvating system, are treated as averageable particles. As a result, the solvated-electron absorption spectrum is determined by the intrinsic properties of the solvated solvent–anionic-complex.A basic consequence of the present model is its implication of spectral shape stability of the solvated-electron absorption band when the latter results only from a single band of discrete–continuum transitions of the electron. Under such circumstances, a linear solvated-electron–solvent energy relationship is implied.

Shape stability of solvated-electron optical absorption bands. Part 3.—Linear solvated-electron–solvent energies relationship

A new, fundamental linear relationship between the mean energy of a solvated electron and the mean energy of a representative solvent molecule of the system is derived for solvated-electron optical absorption bands which exhibit spectral shape stability. In simplified form, [ωav(T)+ 4Neff(T)text-decoration:overlineEsolv(T)] is independent of temperature T, where (in atomic units)ωav(T) is the mean absorption frequency of the band, text-decoration:overlineEsolv(T) is the equilibrium-averaged molecular energy of the solvent and Neff(T) is an effective number of solvent molecules about which localization of a solvated electron presumably occurs. Temperature-independent, possibly solvent-dependent values of Neff ranging from 0.4 to 1.0 are obtained from available data for a number of solvents. When spectral shape stability obtains it further follows that the energy of the solvent must decrease in the threshold absorption process occurring at the zero of absolute temperature.

OPTICAL ABSORPTION SPECTRA OF ALKALI METAL SOLUTIONS IN AMINES AND ETHERS

The optical spectra of solutions of alkali metals in amine and ether solvents are studied in the range from about 250 mμ to about 2 000 mμ. Spectra of the following combinations of metal and solvent are obtained: lithium in ethylamine and ethylenediamine; sodium in ethylenediamine; potassium in ethylamine, ethylenediamine, tetrahydrofuran and 1,2-dimethoxyethane; rubidium in ethylenediamine; caesium in ethylamine. Results of salt addition experiments are also reported. Evidence is presented to show that the band commonly observed in solutions of all the alkali metals in the range from 600 mμ. to 720 mμ arises from a species containing sodium in solution. Because the experimental results obtained differ appreciably from some previously reported, the experimental techniques and procedures are presented in some detail. Three solvated species, in addition to the solvated metal cation, are postulated to explain the optical and spin resonance properties of the metal solutions.

Spectral-moment constrained density matrices of maximum entropy for solvated electrons

A single-particle density matrix for a solvated electron that pertains to its motion relative to its mean location has been obtained by maximizing its entropy subject to a constraint on the value of its Heisenberg Product. The latter quantity is the product of the mean dispersion-in-position and the mean dispersion-in-momentum of the solvated electron, which are determined by the inverse-first and first moments, respectively, of the solvated electrons optical absorption spectrum. The resulting density matrix is expressible as a canonical distribution function of a spherical-harmonic oscillator in equilibrium, with spectrally determined distribution modulus and force constant of the potential.

Optical absorption spectra of dilute sodium solutions in liquid methylamine

Abstract Optical absorption spectra of infinitely dilute sodium in methylamine are obtained at –50, –70 and –90°C. These spectra differ qualitatively from corresponding solvated electron spectra and are assumed to be intrinsic absorption bands attributable to solvated sodium anions. The notion of extended shape stability is applied in accounting for the thermal behavior of the band shapes.

Partial molal absorption spectroscopy: application to solvated electrons

Measured solvated-electron absorbances in ammonia–methylamine mixtures have been analysed to obtain the partial molal absorption spectra of the two different solvated-electron species presumed to coexist in an equimolar solvent mixture. Each of the latter spectra appears to be essentially a shifted version of the solvated-electron absorption spectrum obtained in the pertinent pure solvent, which serves to establish its identity. Seen here for the first time, these spectra provide the most direct evidence yet available attesting to the actual coexistence of the two kinds of solvated electrons.