Point-charge model quadrupole moments

The point-charge model can be improved by considering the effects of higher multipole moments in eq. (46). Dipole and quadrupole contributions (terms with k - and 2 in eq. (46)) have been evaluated for PrCL (Hutchings and Ray, 1963). It is possible to include the dipole contributions to the crystal field in a self-consistent manner (Morrison, 1976) in that treatment, point charge and dipole contributions to the electric field at various lattice sites are evaluated, and the dipole moments at these sites... 

M. Pempointner, M. Seth, P. Schwerdt-feger. A point-charge model for the nuclear quadrupole moment Coupled-cluster, Dirac-Fock, Douglas-KroU, and nonrelativistic Hartree-Eock calculations for the Cu and F electric field gradients in CuF. /. Chem. Phys., 108(16) (1998) 6722-6738. 

Terms up to order 1/c are normally sufficient for explaining experimental data. There is one exception, however, namely the interaction of the nuclear quadrupole moment with the electric field gradient, which is of order 1/c. Although nuclei often are modelled as point charges in quantum chemistry, they do in fact have a finite size. The internal structure of the nucleus leads to a quadrupole moment for nuclei with spin larger than 1/2 (the dipole and octopole moments vanish by symmetry). As discussed in section 10.1.1, this leads to an interaction term which is the product of the quadrupole moment with the field gradient (F = VF) created by the electron distribution. 

In the simplest case, the model is based on the concept of an idealised 7i-system that consists of a positively charged o framework (-t-le) sandwiched between two regions of 7i-electron density (2 x -V2e). This situation is illustrated in Figure 2.6. Point charges are used to represent these regions, the distance between them being governed by the experimental value of the quadrupole moment of benzene. 

U. Dinur and A. T. Hagler, J. Chem. Phys., 91, 2959 (1989). Determination of Atomic Charges and Point Dipoles from Derivatives of the Molecular Dipole and Quadrupole Moments and from Energy Second Derivatives. II. Applications to Model Systems. 

Overall, the QM results indicate both a large quadrupole and out-of-plane character in the charge distribution of a water molecule in the liquid phase. Only SSDQOl has multipoles consistent with both features, although somewhat too little for the former and too much for the latter. Furthermore, it was shown that multisite models require at least six points to reproduce moments consistent with the QM results [55], as has also been found for polarizable multisite models [37, 57]. On the other hand, it was also shown [55] that multipole models are able to reproduce electrostatic potentials due to the QM charge distribution with moments up to the octupole. 

In order to understand ionic distributions in the EDL a realistic description of hydration or, more generally, solvation phenomena is necessary, which in protic liquids implies an adequate description of the hydrogen-bond network. Theory and computer simulation of bulk liquids showed that the most efficient way to include these properties into the models is via distributed charge models in which the intramolecular charge distribution is represented by several point charges. The point charges are adjusted to reproduce experimental dipole and/or quadrupole moments of the molecule, the bulk structure... 

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 relaxation of the quadrupolar Xe nucleus is predominantly due to the interaction between the nuclear electric quadrupole moment and the fluctuating EFG at the nuclear site. The origin of the EFG contributing in a solution is, however, still partly an open question. Various models, both electrostatic and electronic, have been developed. The electrostatic models assume the EFG to be due to solvent molecules represented by point charges, point dipoles or quadrupoles, or a dielectric continuum. In the electronic approach, EFG is considered to be a consequence of the deformation of the spherical electron distribution of Xe. The deformation arises from the collisions between xenon and solvent molecules. It is obvious (evidence is provided, for example, by i Xe NMR experiments in liquid-crystal solutions, and by first principles calculations) that neither of these approaches alone is sufficient. In typical isotropic solvents, the Xe ranges from 4 ms to -40 ms. 

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