Solvation coordinate

THF and DME are slightly polar solvents which are moderately good cation solvators. Coordination to the metal cation involves the oxygen lone pairs. These solvents, because of their lower dielectric constants, are less effective at separating ion pairs and higher aggregates than are the polar aprotic solvents. The crystal structures of the lithium and potassium enolates of methyl /-butyl ketone have been determined by X-ray crystal-... 

Fig. 3.7. Schematic two-dimensional energy plot for the singlet states as a function of solvation variable and the twist angle 6. The cases shown in Fig. 3.6 are represented from left to right along the solvation coordinate.

Figure 5. Schematic illustration of the potential energy surfaces involved in solvation dynamics showing the water orientational motions along the solvation coordinate together with instantaneous polarization P. In the inset, we show the change in the potential energy along the intramolecular nuclear coordinate. As solvation proceeds, the energy of the solute comes down, which causes a red shift in the fluorescence spectrum [9],...

Then zeolites rapidly appeared as most convenient matrices or solid solvents capable of accomodating and solvating coordination complexes of potential catalytic use. 

Coordination and solvation numbers refiect the simple idea that the solvation of ions or molecules consists of a coordination of solute and solvent molecules. The coordination number is defined as the number of solvent molecules in the first coordination sphere of an ion in solution [103], This first coordination sphere is composed only of solvent molecules in contact with or in bonding distance of the ion such that no other solvent molecules are interposed between them and the ion. This kind of solvation is sometimes termed primary or chemical solvation. Coordination numbers, determined by different experimental techniques [103], range in water from approx. 4 for Be to approx. 9 for Th" , although the majority of the values are close to 6 e.g. for AP ). 

When, as suggested by Bockris and Reddy, the number of water molecules that stay with the ion (SN) is distinguished from the number that simply surround the first shell (CN), m . will differ for molecules referred to as solvational coordinated water and for those referred to as nonsolvational coordinated water (NSC W). Then AH will be given by... 

In an ion-solvent interaction model (Fig. P2.1), solvated coordinated water has two sites capable of forming hydrogen bonds with water molecules in the SB region. Are these two sites identical in bonding For nonsolvated coordinated water, there are three sites for hydrogen bonds. Are these three identical Why (Xu)... 

The potential energies of Red and Ox (+ one electron in vacuum) are shown as a function of a generalized solvation coordinate p. I is the ionization energy in the gas phase I p) is the ionization energy for a given solvation structure. The energy of a solvation structure with respect to equilibrium is indicated by E p) - Red , and... 

Since there is a unique and continuous relationship between —I p) and the solvation coordinate p, there is also a unique and continuous relationship between the thermal deviations from equilibrium [Eox p) - ox d E-R dip) Redl Kp)-This means that the probability of nonequilibrium solvation can be expressed as a function of the vertical energy difference —I p) -... 

The solvent surrounding a polar molecule polarizes itself generating a reaction field at the chromophore position [51, 52]. The electronic polarization of the solvent is very fast and, as such, only results in a renormalization of the electronic states [84]. The slow orientational component of the solvent polarization, as occurring in polar solvents instead plays essentially the same role as internal vibrations, the main difference being that the relevant solvation coordinate is a very slow, actually overdamped coordinate [74, 85]. The similarity of polar solvation and vibrational coupling is not accidental in pp chromophores molecular vibrations induce a flux of electronic charge back and forth between the D and A sites and hence plays exactly the same role as an electric field [86]. Much as with the reaction field, the amplitude of the oscillations self-consistently depends on the molecular polarity. 

It should be noticed that an important contribution to understand solvatochromism and NLO response of molecules of the D-tt-A type has been given by Painelli et al. [95-100], These authors have developed a simple non-perturbative model for the description of the NLO response and low-energy spectral properties of numerous donor-acceptor systems. A polar molecule in solution is modeled in terms of the two electronic states linearly coupled to molecular vibrations and to so-called solvation coordinate. This coordinate describes orientational degrees of freedom of the surrounding solvent. 

Many X-ray diffraction studies of electrolyte solutions have been carried out in aqueous solutions [Gl, 4, 5]. Values of the most probable distance, between the oxygen atom in water and a number of monoatomic ions are summarized in table 5.1. In the case of the cations, this distance reflects the radius of the cation plus the effective radius of the water molecule measured in the direction of the lone pairs on oxygen. In the case of alkali metals, the effective radius of water increases from 122 pm for Li" " to 131 pm for Cs when the Shannon and Prewitt radii are assumed for the cations (see section 3.2), the average value being 127 pm. This result can be attributed to the observation that the coordination number for water molecules around an alkali metal or alkaline metal earth cation changes with cation size and electrolyte concentration. In the case of the Li" " ion, this number decreases from six in very dilute solutions to four in concentrated solutions [5]. Because of the electrostatic character of the interaction between the cation and water molecules, these molecules exchange rapidly with other water molecules in their vicinity. For this reason, the solvation coordination number should be considered as an average. 

The role of vibrational relaxation and solvation dynamics can be probed most effectively by fluorescence experiments, which are both time- and frequency-resolved,66-68 as indicated at the end of Sec. V. We have recently developed a theory for fluorescence of polar molecules in polar solvents.68 The solvaion dynamics is related to the solvent dielectric function e(co) by introducing a solvation coordinate. When (ai) has a Lorentzian dependence on frequency (the Debye model), the broadening is described by the stochastic model [Eqs. (113)], where the parameters A and A may be related to molecular... 

Figure 9.10. Diabatic free energy curves illustrating (a) photoinduced ET reaction and (b) back ET reaction in a ID solvation coordinate system. A resonant optical pulse brings a stationary nuclear wave packet from the ground potential surface to the donor surface, where it relaxes toward equilibrium with concomitant ET to the acceptor state.

Apparently in eqn (13.4) takes the Caldeira-Leggett s form for the coupling between the solvation coordinate xb and the secondary harmonic x -bath. Assume further that the solvation mode is subject to a Brownian oscillation in the original bath environment ... 

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