Field gradient calculations

Bosa5ek et al. (168) used wide-line 27A1 NMR measurements of stationary samples to measure the EFG at the nuclear site in decationated zeolites. In zeolite Na-Y they measured a line half-width of Sv1/2 = 61 kHz (for vL = 16 MHz) which led, via theoretical considerations (173) to vD = 840 kHz the calculated field gradient was 2.9 V/A2. In hydrated samples this gradient was partially averaged by random reorientation of water molecules, giving <5v,/2 = 5.7 kHz and vQ = 256 kHz. 

There are higher multipole polarizabilities tiiat describe higher-order multipole moments induced by non-imifonn fields. For example, the quadnipole polarizability is a fourth-rank tensor C that characterizes the lowest-order quadnipole moment induced by an applied field gradient. There are also mixed polarizabilities such as the third-rank dipole-quadnipole polarizability tensor A that describes the lowest-order response of the dipole moment to a field gradient and of the quadnipole moment to a dipolar field. All polarizabilities of order higher tlian dipole depend on the choice of origin. Experimental values are basically restricted to the dipole polarizability and hyperpolarizability [21, 24 and 21]. Ab initio calculations are an imponant source of both dipole and higher polarizabilities [20] some recent examples include [26, 22] ... 

The PCM algorithm is as follows. First, the cavity siuface is determined from the van der Waals radii of the atoms. That fraction of each atom s van der Waals sphere which contributes to the cavity is then divided into a nmnber of small surface elements of calculable surface area. The simplest way to to this is to define a local polar coordinate frame at tlie centre of each atom s van der Waals sphere and to use fixed increments of AO and A(p to give rectangular surface elements (Figure 11.22). The surface can also be divided using tessellation methods [Paschual-Ahuir d al. 1987]. An initial value of the point charge for each surface element is then calculated from the electric field gradient due to the solute alone ... 

Once an approximation to the wavefunction of a molecule has been found, it can be used to calculate the probable result of many physical measurements and hence to predict properties such as a molecular hexadecapole moment or the electric field gradient at a quadrupolar nucleus. For many workers in the field, this is the primary objective for performing quantum-mechanical calculations. But from... 

Eckart, criteria, 264, 298 procedure, 267 Effective charge, 274, 276 Effective Hamiltonian, 226 Elastic model, excess entropy calculation from, 141 of a solid solution, 140 Electric correlation, 248 Electric field gradient, 188, 189 Electron (s), 200... 

The two-layer model is being progressively updated as fresh experimental results and correlations become available. The most satisfactory starting-point for anyone wishing to use the model to calculate pressure gradients for flow of solids-liquid mixtures in a pipeline is the text of SHOOK and Roc.o(52) which includes a worked example. However, there are many pitfalls to be avoided in this area, and there is no substitute for pracucal experience gained by working in the field. 

Malkin, L, Malkina, O.L. and Malkin, V.G. (2002) Relativistic calculations of electric field gradients using the Douglas—Kroll method. Chemical Physics Letters, 361, 231-236. 

In the stochastic theory of lineshape developed by Blume [31], the spectral lines are calculated under the influence of a time-dependent Hamiltonian. The method has been successfully applied to a variety of dynamic effects in Mossbauer spectra. We consider here an adaptation due to Blume and Tjon [32, 33] for a Hamiltonian fluctuating between two states with axially symmetric electric field gradients (efg s), the orientation of which is parallel or perpendicular to each other. The present formulation is applicable for states with the same... 

In the case of covalent compounds, crystal-field theory is a poor model for estimating electric field gradients because of the extensive participation of ligand atomic orbitals in the chemical bonds. MO calculations are a much better choice, since the corresponding interactions are considered, and realistic (noninteger) population numbers are obtained for the central metal as well as the ligand atomic orbitals. 

Marathe, V.R., Trautwein, A. Calculation of charge density, electric field gradient and internal magnetic field at the nuclear site using molecular orbital cluster theory. In Thosar,... 

Table 5.7 Breakdown of the contributions to the largest field gradient tensor element in a.u. from spin-polarized B3LYP DPT calculations (from [60])...

Other key properties of these complexes relevant for comparison with experiment are the nuclear quadrupole coupling constants. Theoretical NQCC values, as calculated via electric field gradients, are discussed exhaustively in several recent theoretical investigations [26,28,30,33,34] and in experimental work [4-11]. BH HLYP/aug-cc-pVTZ calculated NQCCs [30,34], as evaluated for XY- -NH3 complexes, are listed in Table 10. 

Reorientations produce characteristic maxima in the relaxation rate, which may be different for the various symmetry species of CD4. The measured relaxation rates exhibit dependence on two time constants at low temperatures, but also double maxima for both relaxation rates. We assume that molecules may move over some places (adsorption sites) on the cage walls and experience different local potentials. Under the assumption of large tunnelling splittings the T and (A+E) sub-systems relax at different rates. In the first step of calculation the effect of exchange between the different places was considered. Comparison with experimental data led to the conclusion that we have to include also a new relaxation process, namely the contribution from an external electric field gradient. It is finally quite understandable to expect that such effect appears when CD4 moves in the vicinity of a Na+ ion. 

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