Quadrupoles, induced dipoles and

The intermolecular forces of adhesion and cohesion can be loosely classified into three categories quantum mechanical forces, pure electrostatic forces, and polarization forces. Quantum mechanical forces give rise both to covalent bonding and to the exchange interactions that balance tile attractive forces when matter is compressed to the point where outer electron orbits interpenetrate. Pure electrostatic interactions include Coulomb forces between charged ions, permanent dipoles, and quadrupoles. Polarization forces arise from the dipole moments induced in atoms and molecules by the electric fields of nearby charges and other permanent and induced dipoles. 

The leading term in the interaction between positronium and a charged particle is the usual 1/R4 polarization potential, where R is the coordinate of the centre of mass of the positronium relative to the other particle. If, however, positronium interacts with a neutral atom or another positronium, the interaction is dominated by the van der Waals potential arising from the induced dipole-dipole and quadrupole-dipole terms, which has the long-range form... 

The calculated first hyperpolarizabilities (see Table 2-4) are surprisingly close to the experimental data, which is probably fortuitous because they were calculated without taking into account vibrational effect. These studies demonstrated also that the double-zeta basis set augmented by field-induced polarization functions, although sufficient for calculations of dipole and quadrupole moments of the studied molecules at the Kohn-Sham LDA level, is not sufficient in the case of hyperpolarizabilities. 

Weakly polar interactions in proteins and protein-ligand complexes are frequently phenomenologically analyzed and classified in terms of the interacting partners (36). This especially includes interactions with x-sys-tems, such as the NH-T, OH-T, or CH-ir interaction (37, 38), aromatic-aromatic interactions (parallel t-t stacking versus edge-to-face interaction), and the cation-T interaction (39). All of these can mostly be rationalized in terms of electrostatic interactions outlined above that is, they involve interactions between monopoles, dipoles, and quadrupoles (permanent and induced). A more distinct character can be attributed to metal complex-ation, which can play a significant role in individual cases of protein-ligand interactions, as for example in metalloenzymes (2,40, 41). 

One of the most important aspects in both experimental and theoretieal studies in molecular spectroscopy is, undoubtedly, the characterization of intensities induced by electromagnetic radiation. We are, of course, interested in obtaining information concerning infrared and Raman transitions which are driven by electric dipole and quadrupole operators, respectively. These transitions can be represented as... 

Equation 5 neglects interactions between quadrupoles, induced dipoles, and multiple bodies. An increase in temperature at constant density decreases the contribution of the fluid s dipole to the dielectric constant due to increased random motion. The polarizability is independent of temperature, although the polarizability of CO2 reportedly decreases by 10% under a pressure of 100 to 200 atm (14-15). Dielectric constant measurements for... 

The electrostatic interaction term 0, between solute and solvent is based on the continuum reaction field which takes into accoimt a reaction potential induced by the solute dipole and quadrupole (third step in Figure 12.2.7) in a continuum medium of dielectric constant e ... 

These equations indicate the way in which the thermodynamic properties of the system change with the composition. In a blend of polymers, new interactions can be created which are not present in the homopolymer system. For instance, polar groups can induce dipoles or quadrupoles that will increase the interaction energy between the polymer chains and can change the entropy of the system. Such interactions explain the unusual properties obtained when fluorine atoms are present in a polymer system. 

Similar measurements of d-f and d-g intervals in lithium Rydberg states by Cooke et yielded fine structure intervals in accordance with the hydrogenic theory. Ruff and co-workers measured n = 15-17 f-g intervals in Cs and determined values for the effective Cs dipole and quadrupole polarizabilities. To reach the Rydberg levels the first laser excited atoms from the 6si/2 ground state to the lp-i/2 state, from which they cascaded to the 5ds/2 level. The second laser then induced the 5ds/2-16/7/2 transition. This excitation technique was first used by Lundberg and Svanberg for lifetime measurements. ... 

This expression is governed by the same convergence provisos as apply to equation 2.1. It expresses the total field at a molecule as the sum of the laser field and the fields from the permanent (jj, ) and field- induced (aFj AF,. ) dipoles, quadrupoles etc. on other molecules. T(2)(rij) and T(3)(rij) give the field at i due to a dipole and quadrupole on j, respectively they are given by... 

At the simplest level the calculation can be regarded as including the intermolecular field-induced dipole contribution to the total moment of the sample. The potential model used has point charges on the three interaction sites - these are chosen to reproduce the dipole and quadrupole moment of the molecule< The intermolecular ( ) field is calculated as the field at the central carbon atom due to these charges on all the other molecules in the simulation (500 in total). The induced dipole is given by... 

The maximum attractive contributions from the ion-dipole, ion induced-dipole, and ion-quadrupole terms to the Hg - - HCl interaction potential... 

We consider first the effect of aqueous solvation on all intermolecular stabilizations that derive from the interaction of charged or dipolar species. Because of its small size and significant dipole and quadrupole, water interacts strongly with all ionic and dipolar species. A binding event of charged or dipolar compounds thus proceeds with a significant loss of favorable cohesive interactions between solutes and water. The effect is most profound for ionic interactions similar ameliorations of solute-solute interaction apply to multipole-multipole and dipole-induced dipole interactions. 

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