Charge-quadrupole term

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 ... 

In accordance with the traditional chemical view, the negative point charges are located on the corresponding nuclei A and B, the q values are then perfectly determined. But, in general, the third relationship involving the quadrupole term will not be satisfied. The dipole and the quadrupole term can only be reproduced completely if the electronic charges are located at points other than the nuclear positions. Furthermore, for determining zx and it will be necessary to have recourse to the equation for the octupolar term, which will thus also be reproduced. 

My own criterion for evaluating charge density results is to compare the electrostatic physical properties with other experiments.28 1 tried to work up the numbers reported by Matthews et al.21 for a permanent dipole moment, but the information is insufficient since the local atomic axes are not reported. A coordinate system, defined with respect to the unit cell axes, should be supplied moreover, it is convenient for the reader if all population coefficients are rotated into this defined system. Of course, if rotational invariance is violated in the representation, then there is no sense to any of the results. I was also interested in determining the local electric field gradients on the N atoms of the tetracyano-ethylene oxide molecule, but the authors have prejudged the result by arbitrarily setting three of the five local quadrupole terms to zero. 

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 existence of an electric quadrupole interaction is one of the most useful features of Mossbauer spectroscopy. The theory is closely related to that used in nuclear quadrupole resonance spectroscopy [14, 15). Any nucleus with a spin quantum number of greater than / = 4 has a non-spherical charge distribution, which if expanded as a series of multipoles contains a quadrupole term. The magnitude of the charge deformation is described as the nuclear quadrupole moment Q, given by... 

No experimental data are available for solutions of salts in non-polar or slightly polar solvents. It can be concluded, however, from rather too low values of that the contribution of higher electric moments of the molecules is rather important and cannot be neglected, and we have shown that the use of the Bora equations corresponds to only charge-dipole terms being taken into account. This supports the kind of approach used by Buckingham, who took into account the ion-quadrupole... 

This equation shows that even for uncharged molecules with no net dipole moment may be significant owing to the quadrupole term. A detailed treatment of the theory has been presented by Abraham and Bretschneider (1974). The reaction-field model has been tested for a number of conformational equilibria, and usually gives excellent results, but is limited to solutions in which no specific interaction exists between solute and solvent, such as hydrogen bonding and charge-transfer complex formation. Thus water and alcohols are excluded, and aromatic solvents such as benzene and toluene also often show anomalous behaviour. Solvent mixtures can in principle be treated by the theory but such a treatment is usually avoided. 

Figure 3.5 Charge penetration in base stacking for the GGiCC base pair step [at 35° Twist and 0.28 A Siide] as a function of Rise, the vertical separation between the base pairs. The difference between the distributed multipole analysis [DMA) value for electrostatics and the quantum mechanical symmetry-adapted perturbation theory [SAPTO/jun-cc-pVDZ) value for electrostatics may be taken as a measure of the charge penetration term. The DMA analysis includes terms up through order 5 [32pole-chai e, hexadecapole-dipole, octopole-quadrupole). Charge penetration rapidly increases in magnitude for smaller intermolecular distances.

Function e provides a critical test for the approximate charge distribution model related to real applications. As the first example, we used imidazole, which frequently models histidine residue. In the Table 3 we compare results obtained for four different molecular charge density models Mulliken [27], CHELP [28] and ESP [29] charges and CAMM (up to quadruples). In general, electrostatic potentials on solvent accessible surfaces described by CAMM series truncated at quadrupole term tend to perform slightly better s = 2-10% than those calculated using potential-derived atomic charges. 

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