Polarizability atomic contributions

These are three examples of the use of atomic properties to obtain quantitative structure-activity relationships (QSAR) or structure-function relationships. One should bear in mind that all properties have an atomic basis, making a multitude of new relationships possible. The atomic contribution to the polarizability, for example, is definable and shown to be transferable [26-28], offering the possibility of improving the use of an electrostatic potential map from zero- to first-order estimates of energies of interaction. 

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... 

Equation (118) yields a partition of the molecular polarizability into gross atomic contributions. One could also introduce a different additive scheme defining net atomic contributions and bond, or pair, contributions a -. 

In several cases, the polarizability distribution can be found by chemical intuition. For instance, in the case of naphthalene, which is made up of two identical fragments, the polarizability can be decomposed into two equivalent parts. Also, group or atom contributions can be deduced from a variety of schemes such as Stone s approach [74], the theory of atoms in molecules [75], the localization of molecular orbitals into chemical functions [76], atom/ bond additivity [77], the use of the acceleration gauge for the electric dipole operator [78], quantum mechanically determined induction energies [79], or calculated molecular quadrupole polarizabilities and their derivatives with respect to molecular deformations [80]. Several of these models consider charge... 

Here the superscripts (BC) and (LJ) refer to the Buckingham-Corner and Lennard-Jones potentials, respectively is the distance between the m-th atom of the molecule and the s-th atom of the surface. The coefficients C, D, B, Q depend on microscopic characteristics, such as static polarizability, ionization potential, etc. For a detailed discussion of atom-atom interaction potentials, the reader is referred to [12]. The subscripts M and S denote atomic species of the adsorbed molecule and the adsorbent surface note that in summations like (11), it is implied that for any value of m (or s) there is the definite M (or S) value which corresponds to a particular atomic species. Therefore, the internal summation in equation (11) can be performed to give the sum of atomic contributions ... 

This expression is known as the Clausius Mossotti relation. To simplify, the polarizability of the crystal can be taken as the sum of the electronic and atomic contributions. The electronic polarizability, aeiec, corresponds to the coupling of the electronic cloud of the otherwise immobile atoms with the electromagnetic wave, and it is a high-frequency process, whose contribution can be considered more or less frequency-independent below Es. The atomic... 

In this approach, the solute-solvent interactions are modeled using polarizability and the molar volume of the solute. Polarizability, O, is in turn modeled by Ketelaar s method (13). where an atomic contribution scheme is employed. Molar volume is in turn modeled by molecular connectivity indices, %, which are calculated using slightly modified algorithms (9), originally proposed by Kicr and Hall (14.15). These indices encode information on the molecular topology and its hctcroatom content. They have been shown to correlate well with the solutes molar volume, and... 

In words y is the atomic contribution to the polarizability of a solvent molecule multiplied by the ratio of the molecular volume of solute to the molecular volume of solvent. Alternatively yi is the value which y would have if the atomic contributions to the polarizabilities of solute and solvent molecules were in the ratio of their volumes. 

The integration of this density over the basin of an atom gives the corresponding atomic contribution to the polarizability, and the polarizability, like all properties, is determined by a sum of atomic contributions. The polarizability density includes the interaction of the density at a point r with the effects of the external field at all points within the molecule. The mean polarizability a is defined as the average of the three principal components of the polarizability tensor ... 

What are the four atomic contributions to the electric polarizability How can their characteristic frequency be changed in materials ... 

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