Collective Coulomb interactions effect

Real proteins are built up both from hydrophobic and polar amino acid residues, some of the latter can be charged. Many of the conformational and collective properties of proteins are due to a complex interplay between short-range (hydrophobic) effects and long-range (Coulomb) interactions. Electrostatic effects can also determine some of the unique solution properties of globular proteins. We have already discussed the results of simulations... 

Having obtained the zero frequency limit of the dynamic polarizability i.e., a = Iin, o7 (—wja ), we use a simplified approach to evaluate the screened dynamic response. This is necessary, since the expression given above, Eq. (40), for the polarizability neglects the induced collective effects essentially due to direct and exchange terms of the Coulomb interaction. To treat this screening approximately, we have used the simplified approach of Bertsch et al. [96] to include the induced electron interaction in the Ceo molecule, by a simple RPA type correction [92,95]... 

Under these conditions, the Coulomb interaction between the electrons involved in the collective wave function is introduced by the bias of the Hartree-Fock mean-field approximation. As previously seen in the introduction, an assumption concerning the starting magnetic configuration is required Anderson chose a ferromagnetic configuration. This aspect could have been questionable but Kondo showed that there is no pernicious effect [64]. Then the secular problem may be solved self-consistently. The Hg-and field wave function cpi r) is assumed to be a solution of the Hartree-Fock equations ... 

The few known stability constants of Tl(II) complexes are collected in Table II (85, 86). When the values of the corresponding equilibrium constants are compared for Tfi, Tl , and Tl (cf. Tables I-III) it can be noted that the coordination of thallium(II) is intermediate between (T1(I) and Tl(III). The stability of the chloro complexes follows the order TfiCl " < TFC1 " acid strength of the hydrated thallium ions. Coulombic interactions of the differently charged metal ions are probably the main reason for this effect, but other properties (polarizability, lone-pair effect) certainly play a role. It is probably safe to assume also that the softness... 

The electrostatic potential energy between two ions given by Equations 3.19 and 3.20 is called the Debye-Hiickel potential energy. The collective effect of the ions in the solution is to screen the Coulomb interaction between a pair of ions given by Equation 3.5 resulting in the screened electrostatic interaction given by Equation 3.19. 

N. Single Spherical Collector Efficiencies. Four collection mechanisms are considered in the present analysis inertial impaction, interception. Brownian movement and Coulombic forces. Although in our previous analysis the electrical forces were considered to be of the induced nature (13), there is evidence that it is the Coulombic forces which dominate the electrical interactions between the particle and collector (, ], 22). Taking the net effect as the simple summation of each collection mechanism results in the single spherical collector efficiency equation. 

Intermolecular interaction A collective term for the attractive (and repulsive) forces that control the association of two or more molecular entities. Intermolecular interactions include electrostatic (Coulombic) forces, van der Waals forces including dispersion (London) forces, hydrogen bonding interactions, Lewis acid—Lewis base interactions, electron-donor—electron-acceptor interactions, and the hydrophobic (solvophobic) effect. The same types of interactions can also occur between parts of the same molecular entity (intramolecular interactions). Although some interactions are weak relative to a covalent bond, others are not. The term includes a range of bonding characters from predominantly covalent, polar covalent, or ionic. 

The forces between non-reacting molecules are known collectively as van der Waals forces. Any pair of atoms or molecules—or even different parts of the same molecule—will interact through van der Waals forces. Like the forces at work in chemical bonds, the van der Waals forces arise from either the Coulomb force or exchange force (the quantum-mechanical effect that separates electrons with the same value of m. Section 4.3). Also like the forces in chemical bonds, the result may be an attraction or a repulsion. 

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