Polarizability atomic 97

The energy of a polarizable atom 1 in a field E is again given by Eq. VI-10,... 

Conformational Adjustments The conformations of protein and ligand in the free state may differ from those in the complex. The conformation in the complex may be different from the most stable conformation in solution, and/or a broader range of conformations may be sampled in solution than in the complex. In the former case, the required adjustment raises the energy, in the latter it lowers the entropy in either case this effect favors the dissociated state (although exceptional instances in which the flexibility increases as a result of complex formation seem possible). With current models based on two-body potentials (but not with force fields based on polarizable atoms, currently under development), separate intra-molecular energies of protein and ligand in the complex are, in fact, definable. However, it is impossible to assign separate entropies to the two parts of the complex. 

The electrostatic interaction between independent polarizable atoms is simply the sum of the charge-charge interactions between the four charge sites (i.e. two atoms and their respective Drude particles) ... 

When the Drude particles are treated adiabatically, a SCF method must be used to solve for the displacements of the Drude particle, d, similarly to the dipoles Jtj in the induced dipole model. The implementation of the SCF condition corresponding to the Born-Oppenheimer approximation is straightforward and the real forces acting on the nuclei must be determined after the Drude particles have attained the energy minimum for a particular nuclear configuration. In the case of N polarizable atoms with positions r, the relaxed Drude particle positions r + d5CF are found by solving... 

Ren PY, Ponder JW (2003) Polarizable atomic multipole water model for molecular mechanics simulation. J Phys Chem B 107(24) 5933-5947... 

Jiao D, King C, Grossfield A, Darden TA, Ren PY (2006) Simulation of Ca2+ and Mg2+ solvation using polarizable atomic multipole potential. J Phys Chem B 110(37) 18553—18559... 

The concept of dipole hardness permit to explore the relation between polarizability and reactivity from first principles. The physical idea is that an atom is more reactive if it is less stable relative to a perturbation (here the external electric field). The atomic stability is measured by the amount of energy we need to induce a dipole. For very small dipoles, this energy is quadratic (first term in Equation 24.19). There is no linear term in Equation 24.19 because the energy is minimum relative to the dipole in the ground state (variational principle). The curvature hi of E(p) is a first measure of the stability and is equal exactly to the inverse of the polarizability. Within the quadratic approximation of E(p), one deduces that a low polarizable atom is expected to be more stable or less reactive as it does in practice. But if the dipole is larger, it might be useful to consider the next perturbation order ... 

Allnatt). Polarizabilities, Atomic, Beam Measurements of (Bederson 11 1... 

Interestingly, inclusion of readily polarizable atoms do exert an effect likewise to lengthening a conjugated chain. Examples ... 

Dipole-induced dipole interaction energies are proportional to the product of the square of the dipole moment and the polarizability a of the atom/group with which the ion interacts, divided by the product of the square of dielectric constant D and the sixth power of the distance between the dipole and the polarizable group. Dispersion interactions have energies that are proportional to the product of polarizabilities i and 2. divided by the sixth power of the distance between two polarizable atoms (or groups of atoms). 

There are three common modes of polarizability in organic molecules, which are, in order of increasing resonant frequency, orientation polarizability, atomic polarizability, and electronic polarizability. ... 

The lipophilicity of perfluorocarbons is remarkably enhanced by introducing a more polarizable atom into the compound such as bromine or hydrogen (C8F18 CST +37 CC, C8F17Br CST —24.5 C, C8F17H CST +21.3 C). Thus, Rt —RH diblock compounds such as C6F13C3H7 or C8Fl7C8Hl7 are mostly totally miscible with hydrocarbons at room temperature.21... 

As mentioned above, for the H2-He pair two principal induction mechanisms exist multipole and overlap induction. Multipolar induction occurs mainly in the electric quadrupole field of H2 which polarizes the colli-sional partner (He). Qualitatively, the nature of the partner X is of little significance as long as it is polarizable. Quantitatively, one expects highly polarizable species (like Xe) to give rise to much stronger rotational lines than more weakly polarizable atoms (like He). Mainly for that reason, the rotational lines of H2-He are much weaker than those of H2-H2. (Another reason is that for H2-H2, molecule 1 induces a dipole in 2 and 2 induces one in 1, thereby doubling the intensities.)... 

To conclude this article, it is hoped that the discussion of relevant issues and opportunities for chemists presented here will sufficiently stimulate the interest of the chemical community. Their active participation is vital for building our understanding of optical nonlinearities in molecular systems as well as for the development of useful nonlinear optical materials. It is the time now to search for new avenues other than conjugation effects to enhance third-order optical nonlinearities. Therefore, we should broaden the scope of molecular materials to incorporate inorganic and organometallic structures, especially those involving highly polarizable atoms. 

Having electrons that are easily displaced toward a positive charge. Polarizable atoms can begin to form a bond at a relatively long distance, (p. 238)... 

In the water trimer induction nonadditivity provides a dominant contribution, which effectively overshadows all the other terms. Its mechanism is simple. For instance, in a cyclic water trimer the multipoles of A inductively alter the multipoles at B, which, in turn, inductively alter the multipoles at C, which then alter those on A, and so on, until the self-consistency is reached. Various formulations of this simple model were implemented in the simulations since the 1970s [84-87,63,64,50]. To include the many-body induction effects of point charges interacting with a set of polarizable atomic centers the following classical electrostatics equation is solved iteratively... 

The combination of a moderately polarizable atom with a tt-electron system can lead to a relatively high polarizability. 

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