Solvation approaches

Karelson et al. [268] used the AMI D02 method with a spherical cavity of 2.5 A, radius to study tautomeric equilibria in the 3-hydroxyisoxazole system (the keto tautomer 13 is referred to as an isoxazolone). AMI predicts 13 to be 0.06 kcal/mol lower in energy than 14 in the gas phase. However, the AMI dipole moments are 3.32 and 4.21 D for 13 and 14, respectively. Hydroxy tautomer 14 is better solvated within the D02 model, and is predicted to be 2.6 kcal/mol lower in energy than 13 in a continuum dielectric with e = 78.4. Karelson et al. note, however, that the relative increase in dipole moment upon solvation is larger for 13 than for 14 (aqueous AMI dipole moments of 5.05 and 5.39 D, respectively). This indicates that the relative magnitude of gas-phase dipole moments will not always be indicative of which tautomer will be better solvated within a DO solvation approach — the polarizability of the solutes must also be considered. In any case, the D02 model is consistent with the experimental observation [266] of only the hydroxy tautomer in aqueous solution. 

Born s idea was taken up by Kirkwood and Onsager [24,25], who extended the dielectric continuum solvation approach by taking into account electrostatic multipole moments, Mf, i.e., dipole, quadrupole, octupole, and higher moments. Kirkwood derived the general formula ... 

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. 

Applications of continuum solvation approaches to MCSCF wavefunctions have required a more developed formulation with respect to the HF or DFT level. Even for an isolated molecule, the optimization of MCSFCF wavefunctions represents a difficult computational problem, owing to the marked nonlinearity of the MCSCF energy with respect to the orbital and configurational variational parameters. Only with the introduction of second-order optimization methods and of the variational parameters expressed in an exponential form, has the calculation of MCSCF wavefunction became routine. Thus, the requirements of the development of a second-order optimization method has been mandatory for any successful extension of the MCSCF approach to continuum solvation methods. In 1988 Mikkelsen el ol. [10] pioneered the second-order MCSCF within a multipole continuum model approach in a spherical cavity. Aguilar et al. [11] proposed the first implementation of the MCSCF method for the DPCM solvation model in 1991, and their PCM-MCSCF method has been the basis of many extensions to more robust second-order MCSCF optimization algorithms [12],... 

An ab initio version of the Mpller-Plesset perturbation theory within the DPCM solvation approach was introduced years ago by Olivares et al. [26] following the above intuitive considerations based on the fact that the electron correlation which modifies both the HF solute charge distribution and the solvent reaction potential depending on it can be back-modified by the solvent. To decouple these combined effects the authors introduced three alternative schemes ... 

Still within a continuum solvation approach [22,41], a unified treatment of the local field problem has recently been formulated within PCM for (hyper)polarizabilities [47] and extended to several optical and spectroscopic properties, including IR, Raman, VCD and VROA spectra [8,9,11,12],... 

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... 

This feature of the continuum solvation approach is present in several widely distributed computational codes. We shall, however, make reference in the following portion to the codes we have developed, collectively indicated with the acronym PCM (polarizable continuum model), because we have used PCM in the calculations reported in the following section and as PCM contains the richest collection of procedures useful for the study of photophysical and photochemical phenomena [1],... 

In spite of the fact that Stern had already distinguished between ions adsorbed on the electrode surface and those in the diffuse layer, it was Grahame11 who developed a model that is constituted by three regions (Fig. 3.8). The difference between this and the Stern model is the existence of specific adsorption (Section 3.4) a specifically adsorbed ion loses its solvation, approaching closer to the electrode surface—besides this it can have the same charge as the electrode or the opposite charge,... 

The review begins with a very brief summary of some early results achieved with an overly simplified solvation approach. The next section describes a number of variants of a more sophisticated continuum technique, and how the results differ. Attention then shifts to larger, biologically important systems such as amino acids, their functional side chains, and thence to dipeptides. The last major section deals with the phenomenon of H-bond cooperativity and how this property might differ for CH-0 as compared to OH-O H-bonds. In a number of places, there is some discussion as to how one might introduce specific interactions with a small number of discrete solvent molecules, within the general framework of the continuum approach. 

Padova, J. Solvation approach to ion-solvent interaction J. Chem. Phys. 1964, 40, 691-694. 

No systematic study of the effect of different solvation models has been performed. A few reports have compared specific cases such as the study of cationic and anionic alanines, which shows a significant improvement in the chemical shift prediction using polarized continuum method (PCM) or better stiU a hybrid solvation approach (Section 1.4.3). However, the linear scaling correction discussed below can often account for the systematic solvent effect and so sometimes one can get away without any solvent computation at all. 

The computed activation and reaction energies with the transition state geometrical parameters are reported in Table 1. In the same table onr results are compared with analogous results obtained recently by Traong et al. with a different continuum solvation approach, namely that known by the acronym GCOSMO, and at density functional (DF) level of the QM theory [20]. For the reaction in aqneons solution, the available experimental data are also reported. An experimental enthalpy change for the... 

The use of focused model must be accompanied by a sound strategy to test qualities, defects and potentialities. This may be performed by examining the outcomes of the model at its best, in its most complete and detailed form. The main aim of this review is to give an overview on how a specific continuum solvation approach, the Polarizable Continuum Model (PCM), has pursued this sjrstematic research effort. 

A further important methodological aspect of solvation methods is the computation of analytical derivatives of the solvation free energy with respect to various parameters. Here, in particular, we are focussing on PCM methods, and thus below we shdl report the derivative procedures developed for such methods, however we wemt to stress that it is possible to obtain the same quantities also for other alternative solvation approaches. ... 

Indeed this is the basis of the Abraham solvation approach. In that study the set of probes was deliberately selected to provide a broad range of interactions, whereas Reichardt s dye has a strongly hydrogen bond accepting phenoxide oxygen, which is anionic and will strongly and exclusively interact with the cation of the IL [56] and emphasize its role. 

Here we illustrate an explicit solvation approach for estimating the effect of water on the relative stability of surface intermediates. We calculate the interaction energy between an adsorbate and a shell of water molecules according to ... 

From a computational point of view, for a given theoretical level, piuely continuum solvation approaches are by far less expensive than explicit models. Such a feature is especially relevant if one is compelled to exploit QM techniques, such as those usually required to study problems in the field of computational spectroscopy. In this case, in fact, the modem implementations of continuum solvation models are able to keep the cost of the calculation for solvated systems basically the same as the corresponding calculation for the isolated system [149]. 

Reaction Field Ejfects Exactly as for isolated molecules, the evaluation of vibrational frequencies and normal modes for solvated molecules requires the evaluation of energy derivatives with respect to nuclear coordinates calculated at the equilibrium nuclear configuration. Within the continuum solvation approach, the energetic quantity to be differentiated is the free energy [174]. The QM analogues for vibrational intensities depend on the spectroscopy under study, but in any case derivative methods are needed... 

C. Cappelli, Continuum solvation approaches to vibrational properties, in Continuum Solvation Models in Chemical Physics Theory and Applications, B. Mennucci, R. Cammi, Eds., Wiley, Chichester, 2007, p. 167. 

Cappelli, C. (2007) Continuum Solvation Approaches to Vibrational Properties, John Wiley Sons, Ltd, Chichester, p. 167. 

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