Interactions between molecules dipole-quadrupole

Finally, the interaction between the dipole and quadrupole of donor and acceptor molecules [13] is generally much weaker than the dipole-dipole interaction. The dipole—quadrupole term [/ (r) r-8] is typically 10—100 times weaker than the dipole—dipole term, though if the acceptor absorption spectrum is symmetry-forbidden (and so weak) but not spin-forbidden, the dipole transition moment for the acceptor is small [127]. Such is the case for energy transfer between rare-earth ions in tungstates typically separated by 1.7 nm [146]. The kinetics of dipole—quadrupole energy transfer are discussed in Chap. 4, Sect. 2.6. 

R l term would be nonzero only if both partners were charged, with nonzero monopoles (i = /—()). An R 2 term appears in the interaction between the monopole of one O = 0) and the dipole of the other ( / = 1). The first term that occurs in the case of a pair of neutral molecules, as in the water dimer, is R 3 which corresponds to the interaction between the dipole moments of the two molecules (i = j = 1). Any nonzero monopole quadrupole terms would appear in this term as well. Dipole-quadrupole interactions die off as R 4, which would also contain charge-octapole interactions, should they exist. Just as the continuation of the multipole expansion to higher orders progressively improves the approximation of the true charge distribution of each monomer, the continuation of the R n summation yields a progressively better approximation to the true electrostatic interaction energy. 

The leading term in the electrostatic interaction between the dipole moment of molecule A and the axial quadrupole moment of a linear, spherical or symmetric top B is... 

Generally speaking, compounds exhibiting the Sc phase have transverse components of permanent electric dipole moments. A number of molecular statistical models (including hard rod theories for systems composed of oblique cylinders) have been developed. " Goossens " has proposed a model composed of ellipsoidal molecules with attractive interactions arising from anisotropic dispersion forces as well as permanent quadrupole moments. His calculations show that the interaction between the permanent quadrupole moments can produce a tilting of the molecules, but a detailed comparison of the predictions with experimental data has yet to be made. 

The first energy component UoiDi results from the dipole-dipole interactions between molecules of the same kind i. The second one Ua-other stems from the interactions of the dipole i with all other sources of electrostatic coupling, the non-dipolar multipoles of the species i (charges, quadrupoles, etc.) as well as all multipoles (including dipoles) of the other species. 

The range of systems that have been studied by force field methods is extremely varied. Some force fields liave been developed to study just one atomic or molecular sp>ecies under a wider range of conditions. For example, the chlorine model of Rodger, Stone and TUdesley [Rodger et al 1988] can be used to study the solid, liquid and gaseous phases. This is an anisotropic site model, in which the interaction between a pair of sites on two molecules dep>ends not only upon the separation between the sites (as in an isotropic model such as the Lennard-Jones model) but also upon the orientation of the site-site vector with resp>ect to the bond vectors of the two molecules. The model includes an electrostatic component which contciins dipwle-dipole, dipole-quadrupole and quadrupole-quadrupole terms, and the van der Waals contribution is modelled using a Buckingham-like function. 

In this expansion the dipole-dipole term is the most prominent if donor-acceptor distance R is not too small. The dipole-dipole term represents the interaction between the transition dipole moments Md and MA of donor and acceptor molecules, respectively. The square of these transition dipoles is proportional to the oscillator strengths fy> and fA for radiative transitions in the individual donor and acceptor molecules (equation 3.73). Higher order terms such as electric dipole-electric quadrupole, electric-dipole-magnetic dipole, become important at close approach and may be effective in crystals and highly ordered array of chromophores. 

One of the simplest orientational-dependent potentials that has been used for polar molecules is the Stockmayer potential.48 It consists of a spherically symmetric Lennard-Jones potential plus a term representing the interaction between two point dipoles. This latter term contains the orientational dependence. Carbon monoxide and nitrogen both have permanent quadrupole moments. Therefore, an obvious generalization of Stockmayer potential is a Lennard-Jones potential plus terms involving quadrupole-quadrupole, dipole-dipole interactions. That is, the orientational part of the potential is derived from a multipole expansion of the electrostatic interaction between the charge distributions on two different molecules and only permanent (not induced) multipoles are considered. Further, the expansion is truncated at the quadrupole-quadrupole term. In all of the simulations discussed here, we have used potentials of this type. The components of the intermolecular potentials we considered are given by ... 

The first two contributions (4>D + sorbate-sorbent systems. The last three contributions arise from charges (which create electric fields) on the solid surface. (This is a simplified view, because an adsorbate molecule with a permanent dipole can also induce a dipole in the sorbent if the sorbent is a conductor (Masel, 1996)). For activated carbon, the nonspecific interactions dominate. For metal oxides and ionic solids, the electrostatic interactions often dominate, depending on the adsorbate. For adsorbate with a quadrupole, the net interaction between a uniform field and the quadrupole is zero. However, the quadrupole interacts strongly with the field gradient, hence the term (pPQ. 

The electrostatic interactions between the adsorbed molecule and the adsorbent framework depend on the structure and composition of the adsorbed molecule and the adsorbent itself. For example, for H20, H2S, S02, and NH3 (molecules with a high dipole moment), and C02 (a molecule with a high quadrupole moment), the electrostatic, attractive interactions are stronger than the dispersion interactions [2], Alternatively, dispersion is the fundamental attractive force present during adsorption in all adsorbents, in the case of molecules like H2, Ar, CH4, N2, and 02. Given the... 

Dispersion and repulsion are the fundamental forces present during the adsorption of nonpolar molecules in silica because the dipole moment of this molecule is null, the quadrupole moment is very low, and interactions with the hydroxyl groups do not exist. In the case of polar molecules, dispersion and repulsion interactions are present. But, specific interactions between the silica surface and the polar molecule, such as the dipole interaction, and, fundamentally, the interactions with the hydroxyl groups [124-126] are responsible for a more intense interaction of the silica surface with the polar molecules in comparison to nonpolar molecules [4],... 

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