Solvent effects equilibrium geometries

The molecular mechanics calculations discussed so far have been concerned with predictions of the possible equilibrium geometries of molecules in vacuo and at OK. Because of the classical treatment, there is no zero-point energy (which is a pure quantum-mechanical effect), and so the molecules are completely at rest at 0 K. There are therefore two problems that I have carefully avoided. First of all, I have not treated dynamical processes. Neither have I mentioned the effect of temperature, and for that matter, how do molecules know the temperature Secondly, very few scientists are interested in isolated molecules in the gas phase. Chemical reactions usually take place in solution and so we should ask how to tackle the solvent. We will pick up these problems in future chapters. 

Also, because such derivatives are to be evaluated at the equilibrium geometry, a key point is the determination of that geometry on the solvated PES, which leads to the so-called indirect solvent effects , which still requires a viable method to calculate free energy gradients (and possibly hessians). The problem of the formulation of free energy derivatives within continuum solvation models is treated elsewhere in this book and for this reason it will not considered here. Instead, it is worth remarking in this context another implication of such a formulation, i.e. that a choice between a complete equilibrium scheme or the account for vibrational and/or electronic nonequilibrium solvent effects [42, 43] should be done (see below). 

Both effects 1 and 2 may be more or less obscured by the presence of heteroatoms on nitrogen or other polar groups which may also present solvent-dependent interactions. For instance when different rotamers are present, changing solvent may also affect the rotamer populations (or the equilibrium geometry of a single rotamer) and thus modify the inversion barrier. Such effects may occur, for instance, in hydroxylamine 86> and hydrazine 76> derivatives. 

Another consequence of the stronger interactions upon ionization is that the equilibrium geometry of the ionized complex may differ significantly from that of the neutral states. Broadened ionization onsets are frequently attributed to the spectral superposition of ionization into several vibrational levels for which Franck-Condon factors are more favorable.261 As a result, the adiabatic ionization potential may be considerably lower than the vertical potential, and the observed ionization onsets may occur above the adiabatic potential. Another factor to be considered is the conformation-dependent effect,213 due to the different conformations of the solvent molecules. The most populated form of a complex may involve a less stable form of the solvent. After photoionisation, the lowest-energy dissociation channel in the complex ion leads to the most stable form of isolated solvent, which has to be taken into account for the estimate of the binding energy. 

Preferred geometry of the benzene oxide-oxepin system can be predicted by molecular orbital methods. Thus benzene oxide la is predicted to be markedly non-planar (with the epoxide ring at an angle of 73° to the benzene ring), while the oxepin lb has been predicted to prefer a shallow boat structure (MINDO/3) or a planar structure ab initio) As previously mentioned, the proportion of each tautomer present at equilibrium is both temperature and solvent-dependent. Molecular orbital calculations have been used to rationalize the solvent effects, both in terms of the more polar character of the arene oxide that is favored in polar solvents and the strengthening of the oxirane C-C bond upon coordination of the oxygen atom lone pair in polar solvents. Thus values in the range 1.5-2.0 D and 0.76-1.36 D for the dipole moments of arene oxide la and oxepin lb have been calculated. 

A short overview of the quantum chemical and statistical physical methods of modelling the solvent effects in condensed disordered media is presented. In particular, the methods for the calculation of the electrostatic, dispersion and cavity formation contributions to the solvation energy of electroneutral solutes are considered. The calculated solvation free energies, proceeding from different geometrical shapes for the solute cavity are compared with the experimental data. The self-consistent reaction field theory has been used for a correct prediction of the tautomeric equilibrium constant of acetylacetone in different dielectric media,. Finally, solvent effects on the molecular geometry and charge distribution in condensed media are discussed. 

A molecule at equilibrium geometry possesses maximum hardness and minimum polarizability values when compared with the corresponding values for any other geometry obtained through a nontotally symmetric distortion. In the internal rotation process, the most stable isomer is associated with the maximum r] and minimum a values, and the least stable isomer is associated with the minimum r] and maximum a values. For several chemical reactions, it has been observed that the reaction proceeds in the direction that produces the hardest and least polarizable species [28,187,188], It has been observed that a system is the hardest and the least polarizable in its ground state [189,190] and for the most stable species along the reaction path [191,192]. Chemical periodicity [118,193], improvement of basis set quality [194,195], and solvent effects [196] have also been studied in this connection. 

Moreover, the calculation of 7 " can be partitioned into several contributions for studies in vacuo the partition is generally done in terms of electronic and vibrational contributions. Here we consider it convenient to make reference to the in vacuo case, adding a further term, the geometry relaxation contribution, measuring the effects on the electronic polarizability due to the changes in the equilibrium geometry induced by the solvent. 

Of considerable significance to any discussion of electronic spectroscopy is the Franck-Condon principle the time taken for an electronic transition is short compared with the times taken for nuclear movements. This means that the Franck-Condon excited state of a molecule, i.e. that existing momentarily after excitation, has the same nuclear geometry as the ground state from which the transition occurred. Further, the solvent molecules around the excited molecules also remain in the same position during the transition. Only after the transition is completed will the excited molecule in the Franck-Condon excited state and its solvation sphere (if any) rearrange into their new equilibrium (excited state) positions. This has an important bearing on the interpretation of solvent effects. 

The previous derivation is limited at the S( I level, fhe correction of these results by correlation effects will modify the molecular energy. By modifying the molecular electron distribution, it is expected to modify the solute-solvent interaction free energy and therefore the equilibrium geometry of the solute. 

Among the several possible environmental effects, in this paper we focus our attention almost exclusively on the influence of the solvent on e hfs, which is the most thoroughly studied by the experiments [8,22]. The solvent can influence the magnetic properties of a nitroxide both polarizing the electron density and modifying the equilibrium geometry. In the past, experimentalists and theoreticians have considered mainly the former aspect. However, since these factors can affect in opposite direction the hfs of nitroxides, it is very important to perform geometry optimizations of nitroxides in solution. Moreover, it is necessary to take into account both the effect of the bulk properties of the solvent (e.g. the dielectric constant) and the influence of specific interactions between the solvent molecules and the nitroxide. As a consequence, the computational recipes must be sufficiently flexible to treat both aspecific and specific solute-solvent interactions. 

For NMR and EPR parameters, the PCM description affects the computation at several levels. First, the reaction field alters both the equilibrium geometry and the electronic distribution of the solute. Second, inclusion of the PCM operator introduces additional terms in the GIAO differentiation. Almost all the existing continuum-based approaches have been used to reproduce solvent effects on magnetic properties and their performances have also been critically compared [58-60]. 

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