Polarizable dielectric continuum

Figure 6 Singly occupied molecular orbital (SOMO) of a propeller-like trimer radical anion of acetonitrile obtained using density functional theory. The structure was immersed in a polarizable dielectric continuum with the properties of liquid acetonitrile. Several surfaces (on the right) and midplane cuts (on the left) are shown. The SOMO has a diffuse halo that envelops the whole cluster within this halo, there is a more compact kernel that has nodes at the cavity center and on the molecules.

The structure of this contribution is as follows. After a brief summary of the theory of optical activity, with particular emphasis on the computational challenges induced by the presence of the magnetic dipole operator, we will focus on theoretical studies of solvent effects on these properties, which to a large extent has been done using various polarizable dielectric continuum models. Our purpose is not to give an exhaustive review of all theoretical studies of solvent effects on natural optical activity but rather to focus on a few representative studies in order to illustrate the importance of the solvent effects and the accuracy that can be expected from different theoretical methods. 

According to Onsager, a reaction field is the electric field arising from an interaction between an ideal nonpolarizable point dipole and a homogeneous polarizable dielectric continuum in which the dipole is immersed [80]. The reaction field is the electric field felt by the solute molecule due to the orientation and/or electronic polarization of the solvent molecules by the solute dipole. 

The second approach to the approximate description of the dynamic solvation effects is based on the semiempirical account for the time-dependent electrical polarization of the medium in the field of the solute molecule. In this case, the statistical averaging over the solute-solvent intennolecular distances and configurations is presumed before the solution of the SchrOdinger equation for the solute and correspondingly, the solvent is described as a polarizable dielectric continuum. The respective electrostatic solvation energy of a solute molecule is given by the following equation[13]... 

Cossi, M., Rega, N., Scalmani, G., and Barone, V. (2001). Polarizable dielectric continuum model of solvation with inclusion of charge penetration effects,/. Chem. Phys. 114, pp. 5691-5701. 

Ao varies with (l/Z)op - 1/DS) and for polar solvents Dop 4 Ds, e.g. Dop = 2.028 and Ds = 8.9 for dichloromethane. As a consequence, dielectric continuum theory predicts electron transfer rates to be enhanced in solvents like CH2C12 which are electronically relatively highly polarizable. 

In more recent work, Johnston and co-workers (17,18,20,27,32) showed quantitatively that the local fluid density about the solute is greater than the bulk density. In these papers, results were presented for CQ2, C2H4, CF3H, and CF3C1. Local densities were recovered by comparison of the observed spectral shift (or position) to that expected for a homogeneous polarizable dielectric medium. Clustering manifests itself in deviation from the expected linear McRae continuum model (17,18,20,27,32,56,57). These data were subsequently interpreted using an expression derived from Kirkwood-Buff solution theory (20). Detailed theoretical... 

To begin to elucidate such issues and to create a theoretical framework for them, we have focused [4-9] on a model of a protonated Schiff base (PSB) in a nonequilibrium dielectric continuum solvent. A key feature for the Sj-Sq Cl in PSBs such as retinal which plays a key role in the chromophore s cis-trans isomerization is that a charge transfer is involved, implying a strong electrostatic coupling to a polar and polarizable environment. In particular, there is translocation of a positive charge [92], discussed further below. Charge transfer also characterizes the earliest events in the photoactive yellow protein photocycle, for example [93],... 

The mutual polarization process between the solute and the polarizable medium is obtained by solving a system of two coupled equations, i.e., the QM Schrodinger equation for the solute in presence of the polarized dielectric, and the electrostatic Poisson equation for the dielectric medium in presence of the charge distribution (electrons and nuclei) of the solute. The solute occupies a molecular shaped cavity within the dielectric continuum, whose polarization is represented by an apparent surface charge (ASC) density spread on the cavity surface. The solute-solvent interaction is then represented by a QM operator, the solvent reaction potential operator, Va, corresponding to the electrostatic interaction of the solute electrons and nuclei with the ASC density of the solvent. 

The collective properties of bulk material typically reflect the behavior of tens of thousands of molecules in a volume of at least 106 A3 [123], The description of the electrostatic and response properties of such volumes is obviously beyond any discrete approach and one has to resort to experimental information, i.e., the dielectric constant. In the Introduction we argued that if sufficient solvation shells are included in a calculation, the effect of an enveloping continuum can be neglected. Nevertheless we give here, for completeness sake, an explicit formulation of the coupling between a set of point charges and polarizabilities and a dielectric continuum. 

Before details of QMSTAT are formulated in the sections below, a brief overview is given. The molecular system in QMSTAT in divided into three parts One region described with a quantum chemical method, one region of water molecules described with a polarizable force-field and a dielectric continuum that encompasses the other two regions, see Figure 9-1. To refer to the discussion in the first paragraph,... 

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). 

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