Theory of solvatochromic shifts

If solvent (or environment) relaxation is complete, equations for the dipole-dipole interaction solvatochromic shifts can be derived within the simple model of spherical-centered dipoles in isotropically polarizable spheres and within the assumption of equal dipole moments in Franck-Condon and relaxed states. The solvatochromic shifts (expressed in wavenumbers) are then given by Eqs (7.3) and (7.4) for absorption and emission, respectively  

To understand solvation dynamics, it is necessary to recall some aspects of dielectric relaxation in the framework of the simple continuum model, which treats the solvent as a uniform dielectric medium with exponential dielectric 

When a constant electric field is suddenly applied to an ensemble of polar molecules, the orientation polarization increases exponentially with a time constant td called the dielectric relaxation time or Debye relaxation time. The reciprocal of td characterizes the rate at which the dipole moments of molecules orient themselves with respect to the electric field. 

A single Debye relaxation time td has been measured for a number of common liquids, called Debye liquids. However, for alcohols, three relaxation times (tDi tD2 TD3) are generally found  

Consequently, the time evolution of the center gravity (expressed in wave-numbers) of the fluorescence spectrum of a fluorophore in a polar environment should be written in the following general form  

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There are single- and multiparameter approaches for determining the polarity and separation of contribution of different interactions to the total effect of polarity on spectroscopic characteristics. They are based on different theories of solvatochromic shifts of absorption and fluorescence bands. 

The assumptions made in theories of solvatochromic shifts, together with the uncertainty over the size and shape of the cavity radius, explain why the determination of excited-state dipole moments is not accurate. Examples of values of excited state dipole moments are given in Table 7.3. 

This external or outer-sphere parameter A0 can be expressed according to a modified form of the Born equation to take into account only the solvent s orientation polarization. (As in the theory of solvatochromic shifts, it is assumed that the induction polarization can follow electronic motion.)... 

An integral equation formalism (lEF) has been developed as particularly suitable for the description of solvent effects on spectral transition energies within the PCM model. The respective theoretical equations have been applied for the calculation of solvatochromic shifts of several carbonyl-group containing molecules at the self-consistent field (SCF), configuration interaction (Cl) and multiconfiguration self-consistent (MC SCF) field level of theory. The calculated spectral shifts accompanying the transfer of a solvatochromic compound from the gas phase to water were comparable with the experimental data. In Table 11.1.4, the results of calculations are presented for three carbonyl compounds, formaldehyde, acetaldehyde and acetone. 

Solvatochromic Shifts of Ions. There is at the present time no theory of the solvatochromic shifts of ions except for the effect of the change of volume in different electronic states. This follows from the Born equation, and a being the ionic radii in states i and f (initial and final). 

R. Cammi and J. Tomasi, Nonequilibrium solvation theory for the polarizable continuum model - a new formulation at the SCF level with application to the case of the frequency-dependent linear electric-response function, Int. J. Quantum Chem., (1995) 465-74 B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798-807 R. Cammi, L. Frediani, B. Mennucci, J. Tomasi, K. Ruud and K. V. Mikkelsen, A second-order, quadratically... 

Figure 6. Qustering of CHFj about (dimethylamino)benzonitrile at 50 C based on solvatochromic shifts in fluorescence (A data from ref. 26, — Onsager reaction field theory).

Kauffman and coworkers118 119 tried to fit the solvatochromic shifts of l-(9-anthryl)-3-(4-/V,/V-dimcthylanilino)propanc (83), relative to the hydrocarbon homomorph with the dimethylamino group replaced by H, to the dielectric non-ideality of solvent mixtures involving hexane with ethanol, tetrahydrofuran and dichloromethane. The shifts were not linear with the mole fraction of the polar component, and Suppan s theory of dielectric enrichment was applied to the data. It was found that the dielectric enrichment that can be calculated from the relative permittivities of the components and of the mixtures is not sufficient to account for the observed solvatochromic shifts, but that preferential solvation of the probe by the polar component is superimposed on this dielectric effect. Earlier,... 

The drastical enhancement of the TPA cross section in the presence of the solvent for the two-photon polymerization initiator [4-trans-[p-(N,N-Di- -butylamino)-p-stilbenyl vinyl piridinc (DBASVP) has been illustrated in a recent work by Wong et al. [112]. The DBASVP is the typical D-tt-A molecule exhibiting the positive solvatochromism (scheme 7). Hence, the lowest excited state of the DBASVP molecule has been found to be a CT state, which completely dominates the linear absorption spectrum. Wong et al. have combined the time-dependent density functional theory and the polarized continuum model (PCM) to evaluate the solvatochromic shift, TPA cross-section, and oxidation potential of the DBASVP molecule in different solutions. 

Champagne et al.206 have studied solvent effects, through a continuum model, on the a and response functions of polyacetylene chains in the TDHF approximation. They find large increases in the values which they relate to the solvatochromic shifts in the lowest optically allowed transition. Density functional theory has also been assessed207 in connection with the calculation of the same response functions, but has been found to be inadequate due to the inability of the exchange/correlation potentials to satisfactorily represent the effects of the ends of the polymer. Schmidt and Springborg208 have calculated the static hyperpolarizability of polyacetylene and polycarbonitrile in DFT in the presence of external fields. 

Ayachit and Tonannavar [184] have critically examined Suppan s method and developed two improvements intended to resolve the uncertainty concerning the direction of excited-state dipole moments. Kurbako et al. [18S] have developed a new solvent shift approach based on a theory of universal intermolecular interactions. Abe has proposed a method of estimating the angle between ground- and excited-state dipole moments based on improved solvatochromic... 

Mulder, W.H. Parkanyi. C. Theory of the salt effect on solvatochromic shifts and its potential application to the determination of ground-state and excited-state dipole moments. J. Phys. Chem., A 2002. 106. 11932-11937. 

Lin, Y. L., Gao, J. L. (2007). Solvatochromic Shifts of the N ->Pi Transition of Acetone from Steam Vapor to Ambient Aqueous Solution A Combined Configuration Interaction QM/MM Simulation Study Incorporating Solvent Polarization, / Chem. Theory Comp., 3, 1484-1493. 

The SCRF methodology has been employed also for the prediction of the solvatochromic shifts on emission spectra. A satisfactory agreement was obtained between the calculated and experimental fluorescence energies of p-N,N-dimethylaminobenzonitrile in different solvents. Finally, the solvent-induced shifts in the vibrational spectra of molecules have been also calculated using the SCRF theory The SCRF approach has been also implemented for the treatment of solute-continuum solvent systems at the ab initio Hartree-Fock level of theory In addition, a general SCRF... 

The fundamental principles developed for gas-phase or liqnid-phase reactions may be applied to supercritical phase reactions as well. When the reaction medium density is gas-like, the concepts developed for gas-phase reactions (such as kinetic theory of gases) may be applied. For liquid-like reaction mixtures (ie, dense supercritical reaction media), principles of liqnid-phase kinetics have been applied. Parameters such as the solvent s solubility parameter, dielectric constant or solvatochromic shift, routinely used to interpret liquid-phase reactions, have been employed to understand the effect of a given supercritical solvent on chemical reaction (42,43). In the vicinity of the critical point, supercritical reaction media admit some unique phenomena such as local enhancement of density (the so-called clustering phenomenon) and sensitive pressure effects on reaction rate and equilibrium constants. 

Recently, Rosch and Zerner published a paper describing a perturbation method with the use of sum rules to examine the solute-solvent dispersion contribution in solvatochromic shift within the INDO-SCRF model.2 2,278 jhe method makes use of separate calculation of the solute and solvent in the continuum solvent and combines the results to evaluate dispersion interactions. The theory was successfully applied to acetone, benzene, naphthalene, and chrysene in cyclohexane, which all show large red absorption shifts relative to the gas phase spectra. Within the same spirit, the method may be applied to correct the results predicted by combined QM-CI/MM simulations. 

Lin YL, Gao J (2007) Solvatochromic shifts of the n tc transition of acetone from steam vapor to ambient aqueous solution a combined configuration interaction QM/MM simulation study incorporating solvent polarization. J Chem Theory Comput 3 1484—1493... 

Much of the work on solvation effects has concentrated on modeling the shift of the centre of an electronic absorption or emission band that occurs on solvation, i.e.. the solvatochromic shift. According to the Franck-Condon principle the centre of such a band corresponds to the vertical excitation energy (from an initial to final electronic state) at a fixed nuclear geometry. Solvation of a chromophore thus implies that while the system in its initial electronic state is in equilibrium with its environment, it is not so in its vertically excited state. On excitation of the solute the electronic polarization of the solvent is assumed to relax instantaneously while the ori-entational/distortional polarization is thought of as remaining frozen, a view which may be somewhat simplistic. Within the reaction-field model application of the above theory to a solvated dipole results in a solvent shift of... 

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