Molecular quadrupole-moment parameter

Mhin et al. [148] used a molecular quadrupole-moment parameter to describe the electrostatic interaction of polychlorinated dibenzo-p-dioxins at the Ah receptor active site. Their analysis suggests that the most potent molecules have a high polarizability across the lateral direction. 

The uncertainties in the molecular quadrupole moments in Tables 1 and 2 calculated with Eq. (11), (12), or (13) depend in most cases on the uncertainties in the magnetic susceptibility anisotropies as the g values are normally the more accurate Zeeman parameter. It is evident from Table 1 that the determination of the sign of the electric dipole moment is a marginal experiment as the standard deviations are normally as large as the measured moments. Nevertheless, most of the di-... 

Table II.1. Molecular quadrupole moments calculated with the molecular Zeeman parameters and Eq. (II. 1) H. The experimental uncertainties follow from standard error propagation and do not reflect systematic errors introduced, for instance, through the neglect of vibrations. Also listed for comparison are values calculated from atom dipoles and values calculated from INDO-wavefunc-tions 10). Only the quadrupole moments of the most abundant isotopic species are listed in each case. The values are given in units of 10 28 esu cm and are referred to the principal axis system of the moment of inertia tensor. The structure references are given in Refs. 9) and i )...

Donkersloot and Walmsley (1970) discussed calculations for the q = 0 lattice modes of a-N. They used two potential models. First these authors assumed an atom-atom potential with 6-12 terms similar to that of Kuan, Warshel, and Schnepp (1969), but they adopted a more restrictive procedure for the evaluation of the parameters. Second, Donkersloot and Walmsley assumed an explicit charge distribution (monopole model), which was compatible with the experimental value of the molecular quadrupole moment. Neither of these models reproduced the librational mode frequencies satisfactorily. 

Rotational g-values, magnetic susceptibilities and anisotropies, paramagnetic and diamagnetic contribntions, molecular quadrupole moments, electronic charge distributions, spin-rotation and spin-spin coupling parameters, nuclear g-values from the rotational Zeeman effect and nuclear magnetic shieldii parameters from the rotational Zeeman effect as well as indirectly via the paramagnetic contribution to the... 

Proceeding along these lines, equation (8) then implies that the atomic dipole moments must sum up to zero, otherwise there will be a contribution to the total molecular dipole moment from these atomic dipoles, contrary to equation (8). Similar considerations imply that in order for the atomic charges and dipoles to exactly reproduce the molecular quadrupole moment, and avoid the introduction of atomic quadrupole parameters, then the sum of the atomic quadrupoles must also be zero. 

For a set of atomic parameters q, m, Vq, Vwi that satisfy the set of constraints described above, namely equations (8) and (11), and the exact reproduction of the molecular quadrupole moment by the atomic charges and dipoles, equations (12) and (13) are accurate to the same order as equations (6) and (7). It is just that for force field calculations and molecular modeling the former equations are more useful. (In fact, the use of atomic moments often yields more accurate energies than the truncated series in equation (6) because the atomic charges and dipoles automatically generate all higher-order molecular multipoles, and sometimes with good accuracy. In such cases the molecular potential may be more accurate with the use of atomic parameters than with the use of just two molecular multipoles.)... 

Curran et al. [ 16] conclude their analysis of the 1A NF spectrum by comparing the magnitudes of the magnetic hyperfine, quadrupole and dipole moment parameters with predictions from self-consistent field calculations due to O Hare and Wahl [19]. The agreement is satisfactory, and one supposes that contemporary calculations would be in even better agreement with experiment. One of the main purposes of the measurements and spectral analysis described in this section is to provide accurate benchmarks for theoretical calculations, and also physical insight into the nature of the molecular bonding. 

The binary and ternary radial correlation parameters occurring in equations (221) and (222) are defined by (151) and (152), respectively. Fluctuations of molecular fields. As in the case of pure liquids, fluctuations of molecular fields in solutions contribute to the effects und consideration. In particular, they lead to non-zero values of the constant in non-dipolar substances. For instance, if the molecules of the various components are axially symmetric and if they possess permanent quadrupole moments, we obtain for the binary correlations, in a first approximation ... 

Apart from this n-vector model allowing for a -component order parameter, there is also the need to consider order parameters of tensorial character. This happens, for example, when we consider the adsorption of molecules such as N2 on grafoil. For describing the orientational ordering of these dumbbell-shaped molecules, the relevant molecular degree of freedom which matters is their electric quadrupole moment tensor,... 

Since the nuclear quadrupole moments for almost all nuclei are known, the study of the nuclear quadrupole coupling constant and the asymmetry parameter furnishes valuable information on molecular structure and symmetry. 

The quantity (e2 qQ) is the known quadrupole coupling constant and is made up of the electronic charge e, electric field gradient q and nuclear quadrupole moment Q. ra is a correlation time for molecular motion, rj is an asymmetry parameter and I is the nuclear spin quantum number. 

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