The Isolated Solvated Electron in Dilute Solutions

The accumulated evidence for the electrolytic nature of dilute metal solutions is overwhelming—metal atoms introduced into a variety of nonaqueous solvents spontaneously dissociate into localized excess electrons and positive ions (37, 39, 164). 

Following a variational solution of the ground (Is) and first excited state (2p) of the electron in this potential well, various other polarization terms are added and a variety of characteristics for the solvated electron (optical transition energy, heat of solution, etc.) can be calculated (101,105). For illustrative purposes, we shall utilize this simple model because of its obvious transparency in relating certain (macroscopic) features of solvent properties to the energy levels and wave functions for the solvated electron in polar solvents. 

All attempts (74,89) to find a sensible, quantitative relation between the wavelength of maximum absorption ( max) and typical macroscopic properties of the solvent (i.e., dielectric constant) have so far failed (146). However, the size of the solvent cavity in which the electron is trapped also plays a decisive role (101) in determining the transition energy [Eqs. (2), (3)], and the solvent dependence of A.max might well indicate a variation in cavity size from solvent to solvent. In this spirit, Dorfman and Jou (48) have evaluated cavity radii on the basis of the simple Jortner model for the solvated electron. The values are shown in Fig. 3, which shows a plot of the optical transition energy max versus 

The cavity radii in water and alcohol are around 0.9-1.5 A, and in ammonia and the various amines and ethers between 2.5 and 4 A. 

Considerably more elaborate treatments (1, 40,105) for calculating the electronic energy levels and wave functions for the excess electron have since been developed and attempt to introduce certain microscopic features of the local molecular environment. Such calculations for electrons in ammonia were first reported by Copeland, Kestner, and Jortner (40). The reader is referred to the paper by Baneijee and Simons (1) and the recent review by Brodsky and Tkarevsky (9) for comprehensive discussions of the current theoretical descriptions for solvated electrons in disordered condensed media (see also Ref. 171). 

---

In the weak-interaction model (85) developed in the previous section to explain ion-pairing in metal-ammonia solutions, aggregation interactions involving Ms+ and es are relatively weak, and leave the isolated solvated electron properties virtually intact. However, a major difficulty (29,54,134) arises with the type of model when one considers the precise nature of the corresponding electron spin-pairing interaction in ammonia solutions. It is worth expanding on this issue because it probably remains one of the fundamental dilemmas of metal-ammonia solutions in the dilute range (54). 

---