Solvent effects cavity field

J. B. Foresman, T. A. Keith, K. B. Wiberg, J. Snoonian and M. J. Frisch, Solvent Effects. 5. The Influence of Cavity Shape, Truncation of Electrostatics, and Electron Correlation on Ab Initio Reaction Field Calculations, J. Phys. Chem., submitted (1996). [Discusses the IPCM SCRF model.]... 

Fig. 2.2 Self-Consistent Reaction Field (SCRF) model for the inclusion of solvent effects in semi-empirical calculations. The solvent is represented as an isotropic, polarizable continuum of macroscopic dielectric e. The solute occupies a spherical cavity of radius ru, and has a dipole moment of p,o. The molecular dipole induces an opposing dipole in the solvent medium, the magnitude of which is dependent on e.

All of the interaction mechanisms described above are expected to produce electric fields in the solute cavity. In the case of specific interactions and reaction field effects these electric fields are expected to have some specific orientation with respect to the solute coordinate system. Dispersion forces and Stark effects are not expected to have any specific orientation with respect to the solute. Magnetic field effects seem unlikely to be important in light of the well-known invariance of coupling constants to changes of the external magnetic field. However, it is conceivable that a solvent magnetic reaction field might... 

Since the development of the Onsager model, there have been a number of elaborations on the model [4,5]. For example, the spherical cavity has been replaced by molecularly-shaped cavities. The state of the art within the field of solvent effects described by continuum solvent models is now implemented in, e.g., the Gaussian program package. 

Most of the quantum chemical calculations of the nuclear shielding constants have involved two classes of solvation models, which belong to the second group of models (n), namely, the continuum group (i) the apparent surface charge technique (ASC) in formulation C-PCM and IEF-PCM, and (ii) models based on a multipolar expansion of the reaction filed (MPE). The PCM formalism with its representation of the solvent field through an ASC approach is more flexible as far as the cavity shape is concerned, which permits solvent effects to be taken into account in a more accurate manner. 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

In Equation (2.183) new surface charges, qex, have been introduced these charges can be described as the response of the solvent to the external field (static or oscillating) when the volume representing the molecular cavity has been created in the bulk of the solvent. We note that the effects of qex in the limit of a spherical cavity coincide with that of the cavity field factors historically introduced to take into account the changes induced by the solvent molecules on the average macroscopic field at each local position inside the medium more details on this equivalence will be given in Section 2.7.4. 

The OWB equations obtained in this semiclassical scheme analyse the effective polarizabilities in term of solvent effects on the polarizabilities of the isolated molecules. Three main effects arise due to (a) a contribution from the static reaction field which results in a solute polarizability, different from that of the isolated molecules, (b) a coupling between the induced dipole moments and the dielectric medium, represented by the reaction field factors FR n, (c) the boundary of the cavity which modifies the cavity field with respect the macroscopic field in the medium (the Maxwell field) and this effect is represented by the cavity field factors /c,n. 

Organometallic systems such as porphyrines have been investigated because of the possibility to fine tune their response by functionalization[105-107]. Systems of increased the dimensionality have been of particular interest [108-111], Concomitant to the large effort to establish useful structure-to-properties relationships, considerable effort has now been put to investigate the environmental effects on TPA[112-114], For example, the solvent effect has been studied for a small linear push-pull chromophore using a self-consistent reaction field (homogeneous solvation) method employing a spherical cavity and an internal force field (IFF) method[l 12] in another study the polarizable continuum model has been employed to calculate the relevant quantities to obtain the TPA cross-section in the limit of a two-state model[113] Woo et al. made a critical study of experimental comparison of TPA cross-sections in different solvents[114]. 

The solvent effects are often described within a semiempirical selfconsistent reaction field theory (SCRF)248. In this theory the free energy of solvation is obtained from a set of selfconsistent equations describing the interaction of the solute (denoted by S) with the solvent modeled by a polarizable continuum characterized by a dielectric constant e. In the SCRF formalism, as developed by Rivail and collaborators249- 250 the solute-solvent system is modeled by a polarizable continuum (characterized by a dielectric constant e) in which the solvent molecule is immersed within an ellipsoidal cavity251,252. The Hamiltonian describing the solute in the cavity is given by,... 

Keywords Solvent Effects, Self-consistent Reaction Field, Continuum, Cavity, Polarizable Contin-... 

Foresman JB, Keith TA, Wiberg KB, Snoonian J, Frisch MJ (1996) Solvent effects. 5. Influence of cavity shape, truncation of electrostatics, and electron correlation on ab initio reaction field calculations. J Phys Chem 100 16098-16104... 

Alternatively, reaction field calculations with the IPCM (isodensity surface polarized continuum model) [73,74] can be performed to model solvent effects. In this approach, an isodensity surface defined by a value of 0.0004 a.u. of the total electron density distribution is calculated at the level of theory employed. Such an isodensity surface has been found to define rather accurately the volume of a molecule [75] and, therefore, it should also define a reasonable cavity for the soluted molecule within the polarizable continuum where the cavity can iteratively be adjusted when improving wavefunction and electron density distribution during a self consistent field (SCF) calculation at the HF or DFT level. The IPCM method has also the advantage that geometry optimization of the solute molecule is easier than for the PISA model and, apart from this, electron correlation effects can be included into the IPCM calculation. For the investigation of Si compounds (either neutral or ionic) in solution both the PISA and IPCM methods have been used. [41-47]... 

Cobalt(II,III) sepulchrates have been used in the chemical education [415] and considerable number of the chemical and physicochemical studies as efficient quencher of the phosphorescence [416] and electronic excited states [417, 418], as a reductant in kinetic studies of redox reactions [419, 420], as a model for study of magnetodynamic [421], solvent [422] and pressure [423] effects on the outer-sphere electron-transfer reactions. Transfer chemical potentials (from solubility measurements) [424], electrochemical reduction potentials [425] and ligand-field parameters [426] for cobalt sepulchrates have been calculated. Solvent effect on Co chemical shift of cobalt(III) ion encapsulated in the sepulchrate cavity [427]... 

A primitive approach to treating the solvent effect was made with 6,6-diheterosub-stituted fulvenes by calculating the gas-phase barriers with the CNDO/2 method and the solvent stabilization of ground and transition states in the reaction field formalism with a spherical cavity. The result was found to be very sensitive to the cavity size and to the calculated ground-state and transition-state dipole moments, and no reliable numerical data could be obtained. The calculated gas-phase barriers were too high, although they fell in the correct order. 

The study of solvatochromic shifts is of great importance and has received enormous theoretical attention in recent years. Progress has been achieved in the use of the self-consistent reaction field and cavity models. These advances have also shown several limitations. It is thus of great interest to have alternative procedures to calculate solvent effects. In this respect the use of Monte Carlo/Molecular Dynamics simulations has been growing. In this paper we suggest a procedure to allow a full quantum mechanical calculation of the solute-solvent system. The basic idea is to treat the solute, the solvent and its interaction by quantum mechanics. First a Monte Carlo simulation is performed to characterize the liquid structure. These structures are then used in the quantum mechanical calculation. As a liquid has not one but a great number of structures equally possible within a... 

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. 

Recently, a new category of methods, the cavity model, has been proposed to account for the solvent effect. Molecules or supermolecules are embedded in a cavity surrounded by a dielectric continuum, the solvent being represented by its static dielectric constant. The molecules (supermolecules) polarize the continuum. As a consequence this creates an electrostatic potential in the cavity. This reaction potential interacts with the molecules (supermolecules). This effect can be taken into account through an interaction operator. The usual SCF scheme is modified into a SCRF (self consistent reaction field) scheme, and similar modifications can be implemented beyond the SCF level. Several studies based on this category of methods have been published on protonated hydrates. They account for the solvent effect on the filling of the first solvation shell (53, 69), the charges (69, 76) and the energy barrier to proton transfer (53, 76). 

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