Electric field gradient calculation

All the data reported in the literature seem to confirm that the NH3-HCI complex possesses C3V symmetry (see Figure 2). Table 4 shows the geometrical parameters of the complex reported in the pertinent literature. Bacskay et al [26,27] confirm the C3V symmetry of the complex both at the MP2 and SCF level. A moderate variation from the C3V symmetry, however, results from EFG (Electric Field Gradient) calculations [22]. 

H. M. Petrilli, P. E. Blochl, P. Blaha and K. Schwarz, Electric-field-gradient calculations using the projector augmented wave method. Phys. Rev. B, 1998,57,14690-14697. 

Gajhede, M. (1985). Ab initio electric field gradient calculations for a series of oxygen-containing boron compounds. Chem. Phys. Lett. 120, 266-71. 

Mineeva RM (1978) Relationship between Mdssbauer spectra and defect structure in biotites from electric field gradient calculations. Phys Chem Minerals 2 267-277 Mizutani T, Fukushima Y, Kobayashi T (1991) Synthesis of 1 1 and 2 1 iron phyllosihcates and characterization of their iron state by Mdssbauer spectroscopy. Clays Clay Minerals 39 381-386 Moon N, Coffin CT, Steinke DC, Sands RH, Dnnham WR (1996) A high-sensitivity Mdssbaner spectrometer facilitates the study of iron proteins at natural abundance. Nncl Instr Meth Phys Res B 119 555-564... 

Table 4.10 Change of picture effect on the electronic contribution to electric field gradients calculated in DKH2-SCF approximation [a.u.]. Reproduced from Ref. [15] with kind permission of Acta Phys. Slovaca...

Kjaer el al. have performed a benchmark study of a combined multipole spin-spin coupling constant polarizability/reaction field (MJP/RF) approach to the calculation of both specific and bulk solvation effects on coupling in solvated molecule. The MJP/RF approach was based on the expansion of couplings of the solvated molecule in terms of coupling dipole and quadrupole polarizabilities and hyperpolarizabilities derived from single ab initio calculations, and on taking into account solvent electric field and electric field gradient calculated by molecular dynamics (MD)... 

F. Aquino, N. Govind, J. Autschbach. Electric Field Gradients Calculated from... 

K Schwarz, H Ripphnger, P Blaha. Electric field gradient calculations of various borides. Z Natur-forsch 51a 527a, 1996. 

Aquino F, Govind N and Autschbach J 2010 Electric field gradients calculated from two-component relativistic density functional theory inclnding spin-orbit coupling. J. Chem. Theory Comput. 6, 2669-2686. 

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... 

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,... 

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. 

To calculate the nuclear quadrupole moment from the measured quadrupole splitting, it is necessary to know the electric field gradient, q, at the Te nucleus as well as the asymmetry parameter, rj. These can be calculated in the Townes and Dailey approximation (4) by knowing the chemical bonding in Te. 

The relativistic coupled cluster method starts from the four-component solutions of the Drrac-Fock or Dirac-Fock-Breit equations, and correlates them by the coupled-cluster approach. The Fock-space coupled-cluster method yields atomic transition energies in good agreement (usually better than 0.1 eV) with known experimental values. This is demonstrated here by the electron affinities of group-13 atoms. Properties of superheavy atoms which are not known experimentally can be predicted. Here we show that the rare gas eka-radon (element 118) will have a positive electron affinity. One-, two-, and four-components methods are described and applied to several states of CdH and its ions. Methods for calculating properties other than energy are discussed, and the electric field gradients of Cl, Br, and I, required to extract nuclear quadrupoles from experimental data, are calculated. 

One method of determining nuclear quadrupole moment Q is by measuring the quadrupole coupling constant, given by eqQ/h, where e is the charge of the electron and q the electric field gradient due to the electrons at the atomic nucleus. The extraction of Q depends on an accurately calculated q. As a test of our finite-field relativistic coupled cluster approach, preliminary results for Cl, Br, and I are presented. 

Numerous X-ray investigations have unravelled the solid state structure of contact and solvent-separated ion pairs. It was therefore considered to be of interest to evaluate also the potential of solid state NMR as a tool for the investigation of this structural problem. In addition to the study of chemical shifts discussed above (Section II.B), the quadrupole coupling constant of the nuclide Li, x( Li), was expected to be an ideal sensor for the bonding situation around the lithium cation because, due to its dependence on the electric field gradient, the quadrupolar interaction for this spin-3/2 nucleus is strongly influenced by local symmetry, as exemplified in Section II.C.3. This is also shown with some model calculations in Section ILF. 

Finally, more sophisticated quantum-chemical programs like WIEN95 or the well-known program GAUSSIAN98 allow the calculation of the electric field gradient and the quadrupole parameters, but involving more computer time. Results obtained on this basis for a number of systems are collected in Table 17 They compare quite well... 

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