Solvent reaction field modelling

Jensen, L., Duijnen P.Th. van and Snijders J.G., A discrete solvent reaction field model for calculating molecular linear response properties in solution. J.Chem.Phys. (2003) 119 12998-13006. 

Jensen, L. and Duijnen P. Th. van, The Discrete Solvent Reaction Field model A Quantum me-chanics/Molecular mechanics model for calculating nonlinear optical properties of molecules in the condensed phase., in Atoms, molecules and clusters in electric fields. Theoretical approaches to the calculation of electric polarizability, G. Maroulis, Editor. 2006, Imperial College Press London, p. 1-43. 

The simplest SCRF model is the Onsager reaction field model. In this method, the solute occupies a fixed spherical cavity of radius Oq within the solvent field. A dipole in the molecule will induce a dipole in the medium, and the electric field applied by the solvent dipole will in turn interact with the molecular dipole, leading to net stabilization. 

Shang, H. S., and T. Head-Gordon. 1994. Stabilization of Helices in Glycine and Alanine Dipeptides in a Reaction Field Model of Solvent. J. Am. Chem. Soc. 116, 1528-1532. 

As discussed in Section 2, one key assumption of reaction field models is that the polarization field of the solvent is fully equilibrated with the solute. Such a situation is most likely to occur when the solute is a long-lived, stable molecular structure, e g., the electronic ground state for some local minimum on a Bom-Oppenheimer potential energy surface. As a result, continuum solvation models... 

A related methodology that makes use of the calculated surface charges at the cavity surface to estimate the interaction with the solvent has been described in Ref. [54] in addition, the reaction field model can be extended to include the effects of higher order multipoles [55], In the present implementation, only dipole effects are considered. 

As a first approximation, solvent effects can be described by models where the solvent is represented by a dielectric continuum, e.g., the Onsager reaction-field model. 

The quantum mechanical (QM) (time-independent) problem for the continuum solvation methods refers to the solution of the Schrodinger equation for the effective Hamiltonian of a molecular solute embedded in the solvent reaction field [1-5]. In this section we review the most relevant aspects of such a QM effective problem, comment on the differences with respect to the parallel problem for isolated molecules, and describe the extensions of the QM solvation models to the methods of modern quantum chemistry. Such extensions constitute a field of activity of increasing relevance in many of the quantum chemistry programs [6],... 

A further issue arises in the Cl solvation models, because Cl wavefunction is not completely variational (the orbital variational parameter have a fixed value during the Cl coefficient optimization). In contrast with completely variational methods (HF/MFSCF), the Cl approach presents two nonequivalent ways of evaluating the value of a first-order observable, such as the electronic density of the nonlinear term of the effective Hamiltonian (Equation 1.107). The first approach (the so called unrelaxed density method) evaluates the electronic density as an expectation value using the Cl wavefunction coefficients. In contrast, the second approach, the so-called relaxed density method, evaluates the electronic density as a derivative of the free-energy functional [18], As a consequence, there should be two nonequivalent approaches to the calculation of the solvent reaction field induced by the molecular solute. The unrelaxed density approach is by far the simplest to implement and all the Cl solvation models described above have been based on this method. 

The Cl relaxed density approach [18] should give a more accurate evaluation of the reaction field, but because of its more involved computational character it has been rarely applied in Cl solvation models. The only notably exception is the Cl methods proposed by Wiberg at al. in 1991 [19] within the framework of the Onsager reaction field model. In their approach, the electric dipole moment of the solute determining the solvent reaction field is not given by an expectation value but instead it is computed as a derivative of the solute energy with respect to a uniform electric field. 

Methods based on the solvent reaction field philosophy differ mainly in (i) the cavity shape, and (ii) the way the charge interaction with the medium is calculated. The cavity is differently defined in the various versions of models it may be a sphere, an ellipsoid or a more complicated shape following the surface of the molecule. The cavity should not contain the solvent molecules, but it contains within its boundaries the solute charge distribution. 

The applications of continuum models to the study of solvent induced changes of the shielding constant are numerous. Solvent reaction field calculations differ mainly in the level of theory of the quantum mechanical treatment, the method used for the gauge invariance problem in the calculations of the shielding constants and the approaches used for the calculations of the charge interaction with the medium. 

The solvent reaction field calculations involve several different aspects. We would like concentrate on the points required to make these models successful as well as on the facts that limit their accuracy. One of them is the shape of the molecular cavity, which can be modelled spherically or according to the real shape of the solute molecule. First, we discuss the papers in which spherical cavity models were applied. The studies utilizing the solute-shaped cavity models are collected the second group. Finally, the approaches employing explicit treatment of the first-solvation shell molecules combined with the continuum models are discussed. 

The methodology that uses the dielectric model is instead the simpler and in principle the more suitable for the study of chemical reactions involving large molecular systems. In 1998, Amovilli et al [13] developed a computer code in which the solvent reaction field, including all the basic solute-solvent interactions, has been considered for Complete Active Space Self Consistent Field (CASSCF) calculations. 

Gallicchio E, Linda Yu Zhang, Levy RM (2002) The SGB/NP Hydration Free Energy Model Based on the Surface Generalized Bom Solvent Reaction Field and Novel Nonpolar Hydration Free Energy Estimators. J. Comput. Chem. 23 517-529... 

There are various methods for treating solvation, ranging from a detailed description at the molecular level to reaction field models where the solvent is modelled as a continuum method.125... 

This demonstrates that especially for systems with very flat potential energy surfaces of polar bonds, the interpretation of precise X-ray data has to be carried out very carefully and all possible perturbations of the environment must be taken into account. The comparison with the structures of free molecules is not appropriate. On the other hand, the theoretical model for the correct interpretation of such structures in polar mediums must be expanded for example, with the calculation of an Onsager solvent reaction field. 

The experimental data reported in the Table for gas phase have been extracted from measurements in dioxane solution by applying the Onsager reaction field model to eliminate the solvent effect [37], By contrast, the cyclohexane experimental dipole moments have been obtained from those reported in Ref. [37] re-including the proper reaction field factors. Once recalled these facts, we note that the observed solvent-induced changes on both ground and excited state dipole moments are quantitatively reproduced by the calculations. 

In the reaction field model (Onsager, 1936), a solute molecule is considered as a polarizable point dipole located in a spherical or ellipsoidal cavity in the solvent. The solvent itself is considered as an isotropic and homogeneous dielectric continuum. The local field E at the location of the solute molecule is represented by (78) as a superposition of a cavity field E and a reaction field (Boettcher, 1973). 

We have shown above how the reaction field model can be used to estimate solute-solvent interactions in the absence of external fields. Now we introduce effective polarizabilities that connect the Fourier components of the induced dipole moment (33) with the macroscopic fields in the medium. In the linear case, the Fourier component / induced by an external optical field can be represented by the product of the macroscopic field amplitude " and an effective first-order polarizability a(-tu w) using (93). 

One reason for this at first sight unexpected result is the fact that probably 70... 90% of the solute/solvent interaction term is caused by London dispersion forces, which are more or less equal for the cis and trans isomers. Another important reason is that one has to take into account higher electric moments the trans isomer has a quadrupole moment, and the cis isomer also has moments of a higher order than two. Calculations of solute/solvent interactions of both diastereomers using a reaction field model led to the conclusion that the quadrupolar contribution of the trans isomer is comparable to the dipolar contribution of the cis isomer. It has been pointed out that the neglect of solute/solvent interactions implying higher electric moments than the dipole moment can lead to completely false conclusions [202],... 

The application of eight different reaction-field models to the solvent-induced shift of the carbonyl IR absorption band of 2-butanone, determined in 27 non-HBD solvents, has shown that in this group of solvents the dipolarity and polarizability are the dominating solvent properties responsible for the observed band shift (Avc o = —16 cm for -hexane —> sulfolane) [499]. Among the various reaction-field functions tested, a two-parameter equation with the Kirkwood-Bauer-Magat function /(fir) and the cross function f si,n ) was the most successful one. 

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