Cavity ellipsoidal

A drawback of the SCRF method is its use of a spherical cavity molecules are rarely exac spherical in shape. However, a spherical representation can be a reasonable first apprc mation to the shape of many molecules. It is also possible to use an ellipsoidal cavity t may be a more appropriate shape for some molecules. For both the spherical and ellipsoi cavities analytical expressions for the first and second derivatives of the energy can derived, so enabling geometry optimisations to be performed efficiently. For these cavil it is necessary to define their size. In the case of a spherical cavity a value for the rad can be calculated from the molecular volume ... 

Rinaldi D, M F Ruiz-Lopez and J L Rivail 1983. Ab Initio SCF Calculations on Electrostatically Solvate Molecules Using a Deformable Three Axes Ellipsoidal Cavity. Journal of Chemical Physics 78 834 838. 

For spherical or ellipsoidal cavities, eq. (16.44) can be solved analytically, but for molecular shaped surfaces, it must be done numerically, typically by breaking it into smaller fractions which are assumed to have a constant a. Once o-(rs) is determined, the associated potential is added as an extra term to the Hamilton operator. 

Hydration-free enthalpies of different conformers of formamide and allyl vinyl ether were studied using the ellipsoidal cavity model and the BLYP functional170,177. A very good agreement between the MP2/SCRF and the DFT(BLYP)/SCRF results was shown for the... 

The solvated H3N. . . HBr complex was studied by Ruiz-Lopez et al.m using the ellipsoidal cavity in the DFT(B88/P86)/SCRF calculations which demonstrated that the solvent stabilizes the ionic pair structure. The authors found only one conformational minimum of the complex, which electronic structure corresponded to that of anionic pair. 

Foresman et al.175 applied the DFT(B3LYP)/SCRF calculations to obtain the polar solvent effect on conformational equilibria in furfuraldehyde and on the C-C rotational barrier of (2-nitrovinyl)amine. The authors demonstrated that the poor results obtained using either spherical or ellipsoidal cavities can be significantly improved upon performing the SCRF calculations for the cavity of molecular shape. 

These problems were partially solved through the inclusion of multipole expansions in ellipsoidal cavities [23] or through the use of the polarizable continuum method... 

The dynamics of carbon-halogen bond reductive cleavage in alkyl halides was studied by MP3 ab initio calculations, using pseudopotentials for the halogens and semidiffuse functions for the heavy atoms [104], The effect of solvent was treated by means of the ellipsoidal cavity dielectric continuum model. Both a concerted (i.e., a one-step) and a stepwise mechanism (in which an anion radical is formed at first) were... 

Nevertheless, the use of spherical-cavity SCRF models finally led to a dead end, because no meaningful spherical cavities can be defined for non-spherical molecules. Even the attempt to overcome this problem by an extension of the Onsager model to ellipsoidal cavities did not really solve the problem, because this introduces additional fit parameters, while only a small portion of real molecules can still be considered as approximately ellipsoidal. Thus, the need for molecular-shaped SCRF models became more and more obvious. 

Figure 12 A similar representation of (10)4-(chloroform) but projected on to the ac plane. The ellipsoidal cavities that make up the vertical columns are alternately orthogonal.

For continuum solvation, give an example of a molecule for which a good approximation might be (a) a spherical cavity, (b) an ellipsoidal cavity. 

The OWB model describes the solute as a classical polarizable point dipole located in a spherical or ellipsoidal cavity in an isotropic and homogeneous dielectric medium representing the solvent. In the presence of a macroscopic Maxwell field E, the solute experiences an internal (or local) field E given by a superposition of a cavity field Ec and a reaction field ER. In terms of Fourier components E -n, Ec,n, ER,n of the fields we have... 

D. Rinaldi, M. F. Ruiz-Lopez and J. L. Rivail, Ab initio SCF calculations on electrostatically solvated molecules using a deformable three axes ellipsoidal cavity, J. Chem. Phys., 78 (1983) 834-838. 

The effects of solvation have been studied by an implementation of an ellipsoid cavity model into Kohn-Sham theory [94]. The lowering of the activation energy by water solvation of the allyl vinyl ether has been calculated to be 0.3 kcal/mol by this method. This value is considerably lower than the results from other calculations on the same system using cavity models [95], free energy perturbation [96], or QM/MM calculations [97] as well as the values... 

Onsager 0 equations (Section 5.10), one can extract the dipole moments of polar molecules and the polarizability of any solute molecule. One needs a capacitance cell whose electrodes are as close to each other as practical (for higher capacitances) and reasonable solubilities. If the shape of the solute is very different from the sphere used in the Debye model, then the ellipsoidal cavity has been treated theoretically [13] and applied to hypsochromism [14]. 

Figure 35a shows the crystal structure of the bistren derivative 20 alone, which discloses an elongated ellipsoidal cavity [71]. It appears, at the first sight, that the... 

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). 

As shown in Figure 1,4a, most molecules are not spherical, and so use of a spherical cavity large enough to enclose the whole molecule may mean that solvent will be quite far away from the molecule in some directions. The Kirkwood-Westheimer model uses an ellipsoidal cavity, which comes closer to mimicking a true molecular surface. 

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