Transition solvation effects

A number of types of calculations can be performed. These include optimization of geometry, transition structure optimization, frequency calculation, and IRC calculation. It is also possible to compute electronic excited states using the TDDFT method. Solvation effects can be included using the COSMO method. Electric fields and point charges may be included in the calculation. Relativistic density functional calculations can be run using the ZORA method or the Pauli Hamiltonian. The program authors recommend using the ZORA method. 

It should always be home in mind that solvent effects can modify the energy of both tile reactants and the transition slate. It is the difference in the two solvation effects that is the basis for changes in activation energies and reaction rates. Ihus, although it is conimon to express solvent effects solely in terms of reactant solvation or transition-slate solvation,... 

The neutral reactants possess permanent dipoles, the product is ionic, and the transition state must be intermediate in its charge separation, so an increase in solvent polarity should increase the rate. Except for selective solvation effects of the type cited in the preceding section, this qualitative prediction is correct. 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

These differences were explained by solvation effects in the liquid phase. The carbenium ions are more efficiently stabilized by solvation than carbonium ions, because the former have unsaturated trivalent carbon atoms. In this way, the energy barrier between the (solvated) carbenium ion and the carbonium ion transition state increases. 

The existence of critical solvation numbers for a given process to happen is an important concept. Quantum chemical calculations using ancillary solvent molecules usually produce drastic changes on the electronic nature of saddle points of index one (SPi-1) when comparisons are made with those that have been determined in absence of such solvent molecules. Such results can not be used to show the lack of invariance of a given quantum transition structure without further ado. Solvent cluster calculations must be carefully matched with experimental information on such species, they cannot be used to represent solvation effects in condensed phases. 

Note Added in Proof After we sent the manuscript to the publishers we became aware of CNDO studies on alkali ion solvation performed by Gupta and Rao 270> and Balasubramanian et al.271 >, which might be of some importance for readers interested in cation solvation by water and various amides. Another CNDO model investigation on the structure of hydrated ions was published very recently by Cremaschi and Simonetta 272> They studied CH5 and CH5 surrounded by a first shell of water molecules in order to discuss solvation effects on structure and stability of these organic intermediates or transition states respectively. 

The structure of the norbomyl ion under stable-ion conditions appears to be as elusive as that of the transition state reached during solvolysis. Theory suggests that the intrinsic energies of the classical and non-classical forms of the ion are extremely close and hence the structure to be found in solution will be governed by solvation effects. 

Temperature and pressure effects on rate constants for [Fe(phen)3] +/[Fe(phen)3] + electron transfer in water and in acetonitrile have yielded activation parameters AF was discussed in relation to possible nonadiabaticity and solvation contributions. Solvation effects on AF° for [Fe(diimine)3] " " " " half-cells, related diimine/cyanide ternary systems (diimine = phen, bipy), and also [Fe(CN)6] and Fe aq/Fe aq, have been assessed. Initial state-transition state analyses for base hydrolysis and for peroxodisulfate oxidation for [Fe(diimine)3] +, [Fe(tsb)2] ", [Fe(cage)] " " in DMSO-water mixtures suggest that base hydrolysis is generally controlled by hydroxide (de)hydration, but that in peroxodisulfate oxidation solvation changes for both reactants are significant in determining the overall reactivity pattern. ... 

Procedures " for distinguishing between the two means of facilitation include (1) Use of a reagent that does not bind as an affinity label. If facilitation is due to hyperreactivity, this reagent should also be more reactive. (2) Use of transition-state analysis. A favorable change in the entropy of activation (A ) would imply facilitation via affinity labeling whereas a more favorable change in the enthalpy of activation (AH ) implies hyperreactivity. However, a certain caution should always be exercised since other factors, e.g. differential solvation effects, can result in a certain degree of compensation between AH and AS. ... 

B3LYP/6-31G //HF/6-31G energies, including aqueous solvation effects, predicted this reaction to be exothermic by 5.1 kcalmoG with an a of just 4.4 kcalmoG, which is lower than the experimental values for substitution by iV-methylanilme in methanol With the likely degree of charge separation in the transition state, it is reasonable to suppose that a in aqueous solution (s = 80) would be lower than the in methanol (8 = 33). 

Moreover, the interpretation of experimental data on clusters in solution requires more elaborate theoretical models to include the solvation effects around the structure of a small metal cluster. New kinetic models must be developed to describe nucleation, which governs the phase transition from a solute to a small solid phase. 

The conclusion from these experiments is that the associated ions [RXY]-are stereochemically related to the SN2 transition state. Furthermore, little variation occurs in the stability of the associated ions for CH3C1, CH3Br and CH3I, and steric hindrance is apparently of small consequence in the enthalpic and entropic contributions of these equilibria. These data can be compared directly to the solution values for enthalpy and entropy of activation to show that solvation effects on both parameters are indeed responsible for the large variations in rates observed in solution. 

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