System polarization response calculation

The restricted-unrestricted approach not only improves results from the unrestricted approach, but also allows to rigorously describe the effect of spin polarization for tlie hyperfine coupling constants as well as to provide ways to analyze the behavior of spin polarization (response term in RU approach, see fheory part) in problematic cases. The RU approach therefore provides a higher degree of control over the calculation and its analysis compared to the unrestricted formalism. It can consequently be recommended for investigations of hyperfine coupling constants in various molecular systems. 

A different appro aeh to the caleulation of the dieleetrie eonstant via eomputer simulations is given by the polarization response method, i.e., to determine the polarization response of a liquid to an applied electric field Eq. If

is the average system dipole moment per unit volume along the direction of Eq, can be calculated using the following expression ... 

At about the same time as this work was published, Znamenskiy and Kobrak simulated the absorption spectrum of betaine-30, a commonly used solvatochromic probe molecule, in [C4inim][PF6]. They investigated the interactions responsible for the solvatochromic shift. Because this shift is used experimentally to assess solvent polarity, the calculations can thus provide a direct window into the nature of polarity in ionic Hquid systems. To conduct the study, a single molecule of betaine-30 was immersed in a Hquid containing 200 ion pairs. Twelve independent 1-ns runs were then carried out, and from that the absorption spectrum was computed. They observe two distinct time scales one on subpicosecond time scales and one that is on the order of 100 ps. This result is consistent with previous simulation studies as well as time-resolved fluorescence spectroscopy experiments. Although the actual absorption spectra computed do not agree quantitatively with experimental results, the qualitative features do. 

The treatment of electrostatics and dielectric effects in molecular mechanics calculations necessary for redox property calculations can be divided into two issues electronic polarization contributions to the dielectric response and reorientational polarization contributions to the dielectric response. Without reorientation, the electronic polarization contribution to e is 2 for the types of atoms found in biological systems. The reorientational contribution is due to the reorientation of polar groups by charges. In the protein, the reorientation is restricted by the bonding between the polar groups, whereas in water the reorientation is enhanced owing to cooperative effects of the freely rotating solvent molecules. 

For comparison of the SWV responses provided for systems of one and two polarized interfaces, Fig. 7.23 shows the/sw — E curves corresponding to the direct and to the reverse scans (solid line and empty circles, respectively) for both kinds of membrane systems, calculated for sw = 50 mV by using Eq. (7.44). The peaks obtained when two polarized interfaces are considered are shifted 8 mV with respect to those obtained for a system with a single polarized one, which implies that the half-wave potential for the system with two polarized interfaces can be easily determined from the peak potential by... 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

---