Treatment of the solvent effect in

Analyzing the SPP, SB and SA scales in the light of spectroscopic data that are sensitive to the nature of the solvent poses no special problem thanks to the vertical nature of the transitions, where the cybotactic region surrounding the chromophore is hardly altered. The papers where the SPP, SA and SB scales were reported discuss large sets of spectroscopic data in terms of the nature of the solvent. Some additional comments are made below. 

Recently, Fawcet and Kloss, analyzed the S=0 stretching frequencies of dimethyl sulfoxide (DMSO) with a view to elucidating the behavior of 20 solvents and the gas phase. 

They found the frequency of this vibration in DMSO to be shifted by more than 150 cm and to be correlated to the Gutmann acceptor number (AN) for the solvents. Based on our analysis, the frequency shift reflects the acidity and, to a lesser extent, the polarity of the solvent, according to the following equation  

This fit is very good, taking into account that it encompasses highly polar solvents such as DMSO itself, highly acidic solvents such as trifluoroacetic acid (SPP=1.016, SA=1.307), and highly non-polar and non-acidic solvents such as the gas phase. 

Giam and Lyle determined the solvent sensitivity of the F NMR shifts on 4-fluoropyridine relative to benzene as an internal reference in 31 of the solvents listed in Table 10.3.1.If DMF is excluded on the grounds of its odd value, the chemical shifts for flie remaining 30 solvents are accurately described by the following function of solvent acidity and polarity  

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A scheme for the treatment of the solvent effects on the electronic absorption spectra in solution had been proposed in the framework of the electrostatic SCRF model and quantum chemical configuration interaction (Cl) method. Within this approach, the absorption of the light by chromophoric molecules was considered as an instantaneous process. Tliere-fore, during the photon absorption no change in the solvent orientational polarization was expected. Only the electronic polarization of solvent would respond to the changed electron density of the solute molecule in its excited (Franck-Condon) state. Consequently, the solvent orientation for the excited state remains the same as it was for the ground state, the solvent electronic polarization, however, must reflect the excited state dipole and other electric moments of the molecule. Considering the SCRF Hamiltonian... 

First, in our treatment of the solvent effects throughout this chapter we have noted several times that the solvent could be either a pure liquid, say water, or any mixture of liquids, including any number and concentration of solutes. Therefore the modifications that were carried out in this chapter already include, implicitly, the solute and the solvent effects. In every place where a coupling work was written as W(a w), one should reinterpret not as pure solvent, but as the entire solvent, including any number of components. 

In any case, it is clear that proper treatment of the solvent effect, both static and dynamical, is fundamental for reliable evaluation of the CT transition s stability in the condensed phase. When using continuum solvation models, a state-specific approach combined with an accurate description of the excited-state electron density (averaging procedures of the excited-state density such as those usually employed in CASPT2 should be avoided) is mandatory, since LR-PCM/TD-DFT strongly underestimates the stability of transition with even partial CT character. 

Several studies have combined force fields calculated in the presence of a dielectric continuum, most often the PCM [166, 167, 282, 283] or the COSMO model [284] in order to get an approximate treatment of the solvent effects on the ROA spectra. To the best of our knowledge, the only smdies in which the PCM has been apphed to all quantities determining the ROA spectrum are those of Pecul and co-workers [285, 286]. 

The complexity of an exact treatment of the solvent effects on intramolecular electron transfer has precluded such an analysis until now. Thus one has to use, for some time still further, macroscopic models such as the dielectric continuum model. Such models have indeed good predictive properties but they fail to describe specific solvent effects such as the donor ability or the H bonding ability. Even the more sophisticated quantum model, in its present form, is an oversimplification since the solvent motion is described by a single vibrational mode. The quantum model has some success because the vibronic levels corresponding to solvent modes are so closely spaced that in fact they can be approximated by a continuum. There is no doubt however that the progress in computing ability will allow in the future the simulation of the exact behaviour of the solvent in these reactions. 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

In connection with electronic strucmre metlrods (i.e. a quantal description of M), the term SCRF is quite generic, and it does not by itself indicate a specific model. Typically, however, the term is used for models where the cavity is either spherical or ellipsoidal, the charge distribution is represented as a multipole expansion, often terminated at quite low orders (for example only including the charge and dipole terms), and the cavity/ dispersion contributions are neglected. Such a treatment can only be used for a qualitative estimate of the solvent effect, although relative values may be reasonably accurate if the molecules are fairly polar (dominance of the dipole electrostatic term) and sufficiently similar in size and shape (cancellation of the cavity/dispersion terms). 

Summing up, small molecules are more sensihve to surface effects to influence their conformation than large biopolymers. Hence, we are convinced that conformational analyses in soluhon without explicit treatment of the solvent are arhficial and have to be taken with greatest caution. 

Hybrid MPC-MD schemes are an appropriate way to describe bead-spring polymer motions in solution because they combine a mesoscopic treatment of the polymer chain with a mesoscopic treatment of the solvent in a way that accounts for all hydrodynamic effects. These methods also allow one to treat polymer dynamics in fluid flows. 

Consequently, it is also apparent that the solvent effect can be described on the basis of mathematical relationships between parameters which fall within the relationships defined as free energy correlations. In fact, the more parameters that are included in the mathematical treatment (multi-parameter equations), the better the description of the solvent effect that results. However, we will consider here only those parameters which take into account the solvent effect on redox potentials. 

In order for a solvated ion to migrate under an electric field, it must be prevented from forming close ion pairs with its counterions by the solvating solvent. The effectiveness of the solvent molecule in shielding the interionic Coulombic attraction is closely related with its dielectric constant. The critical distance for the ion pair formation q is given by eq 4 according to Bjerrum s treatment, with the hypothesis that ion-pair formation occurs if the interionic distance is smaller than... 

The theoretical treatment of the hydrophobic effect is limited to pure aqueous systems. To describe chromatographic separations in RPC Horvath and Melander developed the solvophobic theory [47]. In this theory, no special assumptions are made about the properties of solute and solvent, and besides hydrophobic interaction electrostatic and other specific interactions are included. The theory has been valuable to describe the retention of nonpolar [48], polar [49], and ionizable [50] solutes in RPC. The modulation of selectivity via secondary equilibria (variation of pH, ion pair formation [51]) can also be described. On the other hand, it is not a problem to find examples of dispersive interactions in literature, e.g., separation of carotinoids with a long chain (C30) RP gives a higher selectivity compared to standard RP C18 cyclohexanols are preferentially retarded on cyclohexyl-bonded phases compared to phases with linear-bonded alkyl groups. 

In addition, the SM2/AM1 model together with the SCRF method [101-103] was used to assess solvent effects on relative N- and O- acidity of2- and 4-[(2,4, 6-trinitrophenyl)amino] benzioic acids. The authors stated that SCRF appears superior to SM2/AM1 but that the poorer performance of the latter might be due to limitations of the underlying quantum mechanical - semiempirical - method rather than to the approximate treatment of the solvent [104],... 

Equation (3.21) shows that the potential of the mean force is an effective potential energy surface created by the solute-solvent interaction. The PMF may be calculated by an explicit treatment of the entire solute-solvent system by molecular dynamics or Monte Carlo methods, or it may be calculated by an implicit treatment of the solvent, such as by a continuum model, which is the subject of this book. A third possibility (discussed at length in Section 3.3.3) is that some solvent molecules are explicit or discrete and others are implicit and represented as a continuous medium. Such a mixed discrete-continuum model may be considered as a special case of a continuum model in which the solute and explicit solvent molecules form a supermolecule or cluster that is embedded in a continuum. In this contribution we will emphasize continuum models (including cluster-continuum models). 

In general, any satisfactory theoretical calculation of a nuclear coupling constant requires reliable calculation of the molecular wavefunction. As a consequence, a realistic approximation to the actual charge distribution in the carbohydrate molecule must presumably enter any theoretical model that attempts to provide a quantitative interpretation of solvent effects. The simplest treatments, and those that have been proposed most frequently to account for the solvent effect in the absence of specific effects, are those in which the solvent is treated as a continuum surrounding the solute molecule. Several different models where the solvent dependence of coupling interactions is related to the polarity of the medium have been proposed.78-79 The solvation theory80,81 has been successfully used within the FPT formalism to interpret the effect of solvent on Jc H and 3/CH. On the basis of this model, the Hamiltonian of a particular molecule includes the solvent-solute interaction term //so,v ... 

Furthermore, such a C3 -> C4 ring expansion could even be induced by lithium chloride. Thus, the cyclopropylcarbinol 228, prepared by addition of acetylenic Grignard reagents to the cyclopropanecarboxaldehyde 171a in 80-90% yield1101, was transformed into the tosylate 229 upon successive treatment with one equivalent of methyllithium in ether at 0 °C and with one equivalent of tosyl chloride at —40 °C, lithium chloride being formed as by-product. The formation of tosylate 229 appeared, however, to be strongly dependent upon the nature of the solvent effectively, the same... 

For many physical organic chemists, the Menschutkin reaction was a kind of guinea pig , which has been extensively used for the study of solvent effects on chemical reactivity. A comprehensive review of this reaction has been given by Abboud el al. [786], More recent theoretical treatments of the solvent influence on Menschutkin reactions can be found in references [787-789]. 

Further examples of Diels-Alder cycloaddition reactions with small or negligible rate solvent effects can be found in the literature [531-535], The thermolysis of 7-oxabicyclo[2.2.1]hept-5-ene derivatives is an example of a solvent-independent retro-Diels-Alder reaction [537]. For some theoretical treatments of the solvent influence on Diels-Alder cycloaddition reactions, which, in general, confirm their small solvent-dependence, see references [536, 797-799]. 

In an earlier work, the same group had used Hartree-Fock calculations in calculating An for the most stable isomer of some chiral organic molecules in vacuum.In the more recent work, ° they extended the study in several directions. At first, they applied the B3LYP density-functional method, whereby also correlation effects were included. Second, they compared gas-phase results with those obtained for a solution, whereby they applied the polarizable-continuum method for the treatment of the solvent. And third, for some of the larger molecules they included the effects of having a mixture of more different stable structures in an approach very similar to that we discussed above in section III I for the calculation of the optical rotation. 

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