Electrostatic interactions polarizability

Consider the interaction of a neutral, dipolar molecule A with a neutral, S-state atom B. There are no electrostatic interactions because all the miiltipole moments of the atom are zero. However, the electric field of A distorts the charge distribution of B and induces miiltipole moments in B. The leading induction tenn is the interaction between the pennanent dipole moment of A and the dipole moment induced in B. The latter can be expressed in tenns of the polarizability of B, see equation (Al.S.g). and the dipole-mduced-dipole interaction is given by... 

Electrostatic terms other than the simple charge interactions above are commonly included in molecular mechanics calculations. particularly dipole-dipole interactions. More recently, second-order electrostatic interactions like those describing polarizability have been added to some force fields. 

The alkali metals tend to ionize thus, their modeling is dominated by electrostatic interactions. They can be described well by ah initio calculations, provided that diffuse, polarized basis sets are used. This allows the calculation to describe the very polarizable electron density distribution. Core potentials are used for ah initio calculations on the heavier elements. 

The concepts of electronegativity, hardness, and polarizability are all interrelated. For the kind of qualitative applications we will make in discussing reactivity, the concept that initial interactions between reacting molecules can be dominated by either partial electron transfer by bond formation (soft reactants) or by electrostatic interaction (hard reactants) is a useftxl generalization. 

Hogeveen138 measured apparent acidity constants of substituted /i-phenylthio-, /J-phenylsulfinyl- and / -phenylsulfonyl-acrylic acids (cis and trans) in 50% v/v ethanol. The p values for transmission through SCH=CH, SOCH=CH and S02CH=CH were 0.531, 0.389 and 0.320 respectively for the cis acids and 0.652, 0.282 and 0.331 for the trans acids. These results were discussed in considerable detail and compared with those of pertinent related systems. Little importance was attached to the small differences between p values for cis/trans isomers, and the relative transmissions were taken as the mean p values 0.59,0.34 and 0.33. The superior transmission of SCH=CH was attributed to greater polarizability. The values for pKJtrans) — pKJcis) of isomeric acids were also discussed. For the sulfonyl acids this is almost constant at 0.1 unit for the sulfinyl adds there is some variation about a mean value of 0.26 unit, and for the thio adds there is also some variation about a mean value of — 0.15 unit. The differing behavior of the three systems in this respect was explained in terms of hypothetical conformations and electrostatic interactions therein. 

More realistic treatment of the electrostatic interactions of the solvent can be made. The dipolar hard-sphere model is a simple representation of the polar nature of the solvent and has been adopted in studies of bulk electrolyte and electrolyte interfaces [35-39], Recently, it was found that this model gives rise to phase behavior that does not exist in experiments [40,41] and that the Stockmeyer potential [41,42] with soft cores should be better to avoid artifacts. Representation of higher-order multipoles are given in several popular models of water, namely, the simple point charge (SPC) model [43] and its extension (SPC/E) [44], the transferable interaction potential (T1PS)[45], and other central force models [46-48], Models have also been proposed to treat the polarizability of water [49],... 

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) ... 

It is also interesting to note that metal ions having low polarizability (Al3+ Be2+ etc.) are those that are acidic (as shown in Eq. (9.17)). Also, in Chapter 7 we discussed how the polarization of ions leads to a lattice energy that is higher than that predicted on the basis of electrostatic interactions alone. The polarizability data shown in the table make it easy to see that certain ions are much more polarizable than others. Although we will not visit again all of the ramifications of electronic polarizability, it is a very useful and important property of molecules and ions that relates to both chemical and physical behavior. 

In general, polarizability increases as the orbital increases in size negative electrons orbit the positive nucleus at a greater distance in such atoms, and consequently experience a weaker electrostatic interaction. For this reason, London dispersion forces tend to be stronger between molecules that are easily polarized, and weaker between molecules that are not easily polarized. 

The electrostatic interaction energy between the solute (represented by the charge distribution Q) and the polarizable medium represented by the induced charge distribution QP° e) becomes ... 

For instance, in structure 12-e, the C-X and C-0 dipole moments are additive, leading to a destabilization of the molecule by increasing the energy. In structure 12-a, offset of the C-X and C-0 dipole moments minimizes electrostatic interactions, thus leading to a more stable conformation. This electrostatic model was supported by the observed increase of the percentage of the equatorial conformation of 2-methoxy tetrahydropyran (14) when moving from a non-polar to a polar solvent (Table 3).12 In this model, the polar groups are not polarizable and lead to dipole/dipole (hard/hard) interactions. 

The rationalization of the conformational anomeric effect solely based on electrostatic interactions fails to account for these solvent effects. Another interpretation based on bond polarizability in 1,1-dialkoxyalkyl systems calls electronic transfer from a non bonding electron pair of one oxygen atom to the empty cr c 0 orbital from the other alkoxy substituent (Fig. 10).16... 

The charge delocalization or the polarizability difference explains the selectivity behaviour in cases of high polarizability differences (complex versus aqueous metal ion) or in a homologous series of ions (either inorganic cations or ammonium cations). The smaller hydration status of all types of interlamellarly adsorbed cations is ascribed to the mutual stabilization by charge delocalization over the planar oxygens and exchangeable cations and is caused by the electrostatic interaction forces. 

According to the hard and soft acids and bases (HSAB) principle, developed by Pearson in 1963232,233, Lewis acids and Lewis bases are divided into two groups hard and soft. Pearson correlated the hardness of acids and bases with their polarizability, whereby soft acids and bases are large and easily polarizable, and vice versa. A selected list of Lewis acids ordered according to their hardness in aqueous solution is presented in Table 18. The HSAB principle predicts strong association of like partners. Hard acid-soft base complexes mainly result from electrostatic interactions, while soft acid-soft base complexes are dominated by covalent interactions. 

A more refined but still debated in the literature notion is Pearson s Hard and Soft Acids and Bases (HSAB) principle [9,41], which quantifies energy changes to second order according to which hard (soft) acids (electron pair acceptors) prefer to interact with hard (soft) bases (electron pair donors). Soft likes soft relates to covalent bonds being facilitated by high polarizabilities, while hard likes hard relates to a creation of predominantly electrostatic interactions. 

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