Solvent effects state-specific

Abstract The computational study of excited states of molecular systems in the condensed phase implies additional complications with respect to analogous studies on isolated molecules. Some of them can be faced by a computational modeling based on a continuum (i.e., implicit) description of the solvent. Among this class of methods, the polarizable continuum model (PCM) has widely been used in its basic formulation to study ground state properties of molecular solutes. The consideration of molecular properties of excited states has led to the elaboration of numerous additional features not present in the PCM basic version. Nonequilibrium effects, state-specific versus linear response quantum mechanical description, analytical gradients, and electronic coupling between solvated chromophores are reviewed in the present contribution. The presentation of some selected computational results shows the potentialities of the approach. 

The electrostatic solvait effects discussed in the preceding paragraphs are not the only possible modes of interaction of solvent with reactants and transition states. Specific structural effects may cause either the reactants or the transition state to be particularly stroi ly solvated. Figure 4.12 shows how such solvation can affect the relative energies of the ground state and transition state and cause rate variations from solvent to solvent. 

The followmg types of studies will not be presented individually but may have contnbuted supportmg data to coverage by compound type conformational analyses [23 24, 25, 26 27], fluoropolymers [28, 29, 30 31, 32], solid-state NMR [ii], and solvent effects [34 35, 36, 37] Many excellent articles with m-depth NMR interpretation of one specific compound or of a small, structurally related group of compounds can be found in the chemical hterature A few of these, not incorporated elsewhere in this secUon are referenced here carbonyl fluondes [JS 39 40], fluoropropanes [41 42, 43], fluorocyclopropanes [44, 45 46], fluorobutanes [47], perfluorocyclobutanone [48], fluorohexanes [49], and vinyl fluondes [50, 51 52, 53, 54]... 

However, for hydroxylic solvents such as methanol or water, specific solvent effects exist, the dielectric continuum result in eq. 17 is no longer applicable, and variations in XQ are appreciable. Even so, eq. 14 still applies in that for a series of excited states like (bpy)0sL 2+ > plots of lnknr vs. Eem remain linear and have the same slope as the plots for polar organic solvents. The difference is that the lines are parallel but offset, because the term appears in the intercept and xo is non-negli-gible for the hydroxylic solvents. 

The analysis of the transient fluorescence spectra of polar molecules in polar solvents that was outlined in Section I.A assumes that the specific probe molecule has certain ideal properties. The probe should not be strongly polarizable. Probe/solvent interactions involving specific effects, such as hydrogen-bonding should be avoided because specific solute/solvent effects may lead to photophysically discrete probe/solvent complexes. Discrete probe/solvent interactions are inconsistent with the continuum picture inherent in the theoretical formalism. Probes should not possess low lying, upper excited states which could interact with the first-excited state during the solvation processes. In addition, the probe should not possess more than one thermally accessible isomer of the excited state. 

The repertoire of reactions possible with organolithium compounds is well documented in the literature 4). The application of these functionalization reactions to polymers is also described in the anionic polymer review literature 314 316). Unfortunately, many of the reported applications of these functionalization reactions to anionic polymers have not been well characterized. Accordingly, one is faced with the situation in which a variety of useful chain end functionalization reactions is potentially possible, but whose application to polymers is not well defined in terms of specifics such as side reactions, yields, solvent effects, etc. The following discussion of representative functionalization reactions is not meant to be exhaustive, but can be regarded as typical of the state-of-the-art in this area. 

The water-promoted hydrolyses of a bicyclic amide, l-azabicyclo[2.2.2]octan-2-one (87), and a planar analogue, l,4-dimethylpiperidin-2-one (88), were studied using density functional theory in conjunction with a continuum dielectric method to introduce bulk solvent effects. The aim of these studies was to reveal how the twisting of the C-N bond affects the neutral hydrolysis of amides. The results predict important rate accelerations of the neutral hydrolysis of amides when the C-N bond is highly twisted, the corresponding barrier relaxation depending on the specific reaction pathway and transition state involved.85... 

A simple but effective strategy ( corrected LR, or cLR) aimed at overcoming this intrinsic limit of the nonlinear effective solute Hamiltonian when applied to LR approaches has been first proposed by Caricato et al. [33], With such a strategy, the state-specific solvent response is recovered within the linear response approach. As a result, the LR-SS differences in vertical excitation energies are greatly reduced (still keeping the computational feasibility of LR schemes). 

The requirement needed to incorporate the solvent effects into a state-specific (multireference) method is fulfilled by using the effective Hamiltonian defined in Equation (1.159). The only specificity to take into account is that in order to calculate Va we have to know the density matrix of the electronic state of interest (see the contribution by Cammi for more details). Such nonlinear character of Va is generally solved through an iterative procedure [35] at each iteration the solvent-induced component of the effective Hamiltonian is computed by exploiting Equation (1.157) with the apparent charges determined from the standard ASC equation with the first order density matrix of the preceding step. At each iteration n the free energy of each state K is obtained as... 

In this contribution we have presented some specific aspects of the quantum mechanical modelling of electronic transitions in solvated systems. In particular, attention has been focused on the ASC continuum models as in the last years they have become the most popular approach to include solvent effects in QM studies of absorption and emission phenomena. The main issues concerning these kinds of calculations, namely nonequilibrium effects and state-specific versus linear response formulations, have been presented and discussed within the most recent developments of modern continuum models. 

As reported in the Introduction, the basic PCM model has been proposed for describing solvent effects on molecules in the ground state. More specifically, the basic model has the following characteristics [1] ... 

Another important area of dynamic studies in biological samples is the effect of hydration upon molecular mobility in proteins and carbohydrates. The reason for these studies is primarily that protein dynamics, in particular, are crucial to their function, and so examining factors, such as the degree of hydration, that affect their dynamics is very important. However, it is obviously near-impossible to study dynamics in aqueous solution as a function of degree of hydration, and, since most proteins are not soluble in nonaqueous solvents, solid-state studies must be used. The motions at three methionine (Met) residues in Streptomyces subtilisin inhibitor (SSI) were studied with 2H NMR using a sample in which the Met residues at two crucial enzyme recognition sites (PI and P4) were specifically deuterated, along with one in the hydrophobic core.114 The motions of the Met side-chains were then examined... 

Not only classic (C.K. Ingold, 1953) but also recent solvent effect theories (Parker, 1969) claim that the influence of the solvent on the rate of reaction is a consequence of specific solvation of initial, transition and final states and of any intermediate. If the lifetime of the transition state is too short ( 10-12 — 10-13 sec), however, the reorientation of the solvent will lag behind (Bell, 1965 Jones, 1969b). Consequently, the solvation of the transition state will resemble that of the initial state. 

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