Dynamic Core Polarization

Bond lengths R (A), binding energies D. (eV) and vibrational constants a>e (cm ) of the homonuclear halogen dimers from dl-electron (AE) Douglas-Kroll-HeB (DKH) and valence-only energy-consistent pseudopotential (EC-PP) Hartree-Fock self-consistent field (SCF) calculations. The effects of static and dynamic core-polarization at the valence-only level are modelled by a core-polarization potential (CPP). 

Positive pair-binding energies, and hence the effective attractive interaction between electrons, arc necessarily a core polarization effect. If all of the 60 valence electrons were treated as an inert Fermi sea, the net interaction between two electrons added to a given molecule would necessarily be repulsive there is no bound-state solution to the Cooper problem with purely repttlsive interactions. It is the dynamic interactions with the valence electrons that are crucial in producing overscreening of the purely bare repulsive interaction. Although the first-order term does not involve any virtual excitations, the second-order theory includes important core-polarization effects. 

Although the frozen-core approximation underlies all ECP schemes discussed so far, both static (polarization of the core at the Hartree-Fock level) and dynamic (core-valence correlation) polarization of the core may accurately and efficiently be accounted for by a core polarization potential (CPP). The CPP approach was originally used by Meyer and co-workers (MUller etal. 1984) for all-electron calculations and adapted by the Stuttgart group (Fuentealba et al. 1982) for PP calculations. The... 

The frozen-core approximation is one basic assumption underlying all ECP schemes described so far. Especially for main group elements, where a large-core ECP approximation works fairly well if not too high accuracy is desired, the polarizability of the cores (Fig. 14) has nonnegligible effects for elements from the lower part of the periodic table. Within the ECP approach it is indeed possible to account for both static (polarization of the core at the HF level) and dynamic (core-valence correlation) polarization of the cores in an efficient way. Meyer and coworkers [202] proposed in the framework of AE calculations the... 

Arakawa T, Timasheff SN (1984) Mechanism of protein salting in and salting out by divalent cation salts balance between hydration and salt binding. Biochemistry 23 5912-5923 Armstrong BD, Choi J, Lopez C, Wesener DA, HubbeU W, Cavagnero S, Han S (2011) Site-specific hydration dynamics in the nonpolar core of a molten globule by dynamic nuclear polarization of water. J Am Chem Soc 133 5987-5995... 

A novel analytieal tool for the selective detection of local water inside soft mol. assemblies (hydrophobic cores, vesicular bilayers, and micellar structures) suspended in bulk water has been presented. Through the use of dynamic nuclear polarization (DNP), the NMR signal of water is ampUfied, as it interacts with stable radicals that possess about 658 times higher spin polarization. Stable nitroxide radicals covalently attached along the hydrophobic tail of stearic acid molecules that incorporate themselves into surfactant-based micelle or vesicle structures have been used, allowing to study the local water content and fluid viscosity inside oleate micelles and vesicles and Triton X-100 micelles to serve as model systems for soft molecular assembhes. ... 

A practical instrument for many-electron open shell system is still the MCDF method. There are several modifications of it implemented into computational codes of Desclaux [57], developed further by Indelicato [36], of Grant [58] and Frose-Fisher [59]. Based on the Cl technique, the MCDF method accounts for most of the correlation effects while retaining a relatively small number of configurations. It can treat a large number of open shell configurations and can be applied to elements with any number of valence electrons. It omits, however, dynamic correlation, since excitations of the type (nj) n j) cannot be handled, and some core polarization, which makes it less accurate than the DC(B) CC methods. An average error for IP of heavy elements is about 1 eV. Calculations for many heaviest and superheavy elements were performed with the use of the AL version [23-31], as well as with a more accurate OL one [36]. 

Dynamic models for ionic lattices recognize explicitly the force constants between ions and their polarization. In shell models, the ions are represented as a shell and a core, coupled by a spring (see Refs. 57-59), and parameters are evaluated by matching bulk elastic and dielectric properties. Application of these models to the surface region has allowed calculation of surface vibrational modes [60] and LEED patterns [61-63] (see Section VIII-2). 

Molecules that possess both hydrophilic and hydrophobic structures may associate in aqueous media to form dynamic aggregates, commonly known as micelles. The properties of micellar structures have been discussed in great detail [66-69], but thejr main pharmaceutical application lies in their ability to provide enhanced solubility to compounds lacking sufficient aqueous solubility [70], The ability of a micelle to solubilize compounds of limited aqueous solubility can be understood from consideration of the schematic drawing of Fig. 10a. Above the critical micelle concentration, these molecules orient themselves with the polar ends in interfacing with the aqueous solution and the nonpolar ends at the interior. A hydrophobic core is formed at the interior of the micelle, and hydrophobic solute molecules enter and occupy this region. 

Example 12.1. The CMC of C12E7 is 0.083 mM at room temperature. By SANS and dynamic light scattering the mean hydrocarbon core radius was found to be 1.70 nm at a surfactant concentration of 2 mM [532], The mean aggregation number is 64. If we divide the total surface area of the core by the number of surfactants, we get the area per molecule at the core radius. It is 47r (1.7 nm)2 /64 = 0.57 nm2. The cross-sectional area of polyethylene oxide is below 0.2 nm2. So, more than half the core area is exposed to aqueous or at least to a polar medium. 

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