Electronic distribution electric field gradients

Peripheral contributions become important when short interatomic distances are involved, as, for example, for the EFG at nitrogen nuclei and especially at nuclei of hydrogen atoms. Since hydrogen has only one electron, the electric field gradient is mainly due to the density farther from the nucleus, and has therefore been described as less sensitive to the precise charge distribution (Tegenfeldt and Hermansson 1985). 

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. 

Figure 4.54 The effect of an electric field gradient (EFG) creating asymmetry in the electron distribution round a gold nucleus, leading to a quadrupole splitting in the Mossbauer spectrum. (Reproduced with permission from Gold Bull., 1982,15, 53, published by World Gold Council.)...

The origin of the electric field gradient is twofold it is caused by asymmetrically distributed electrons in incompletely filled shells of the atom itself and by charges on neighboring ions. The distinction is not always clear, because the lattice symmetry determines the direction of the bonding orbitals in which the valence electrons reside. If the symmetry of the electrons is cubic, the electric field gradient vanishes. We look at two examples. 

In Formulas (19) and (20) the actual value of the quadrupole moment Q that occurs is not that of the bare nucleus, but the bare nucleus value multiplied by a parameter 1 — This is necessary because the electron distribution of the atom is distorted when the atom is in an electric field gradient, due to the interaction of the electrons with the field gradient. This distortion produces an additional gradient which is —7 times the... 

Although 1 is one of the best investigated molecules, there is, apart from data concerning its electron density distribution, very little information available on its one-electron properties. In principle, accurate data could be obtained by correlation-corrected ab initio methods, but almost nothing has been done in this direction, which of course has to do with the fact that experimental data on one-electron properties of 1 are also rare, and therefore, it is difficult to assess the accuracy and usefulness of calculated one-electron properties such as higher multipole moments, electric field gradients, etc. 

The three components of the electric field gradient tensor are related by Poisson s equation, as shown earlier. However, the electrons that have a finite probability density at the nucleus, the s and p1/2 electrons, have a spherically symmetric distribution around the nucleus and as such do not contribute to E2. Thus, in the computation of E2, the Un can be related by... 

The symmetry of the electron distribution about the nucleus, as reflected in the quadrupole splitting, can be divided into two parts (32, 53,54). First, the atomic electrons about the central nucleus may fill orbitals in such a manner that the resulting electron cloud produces an electric field gradient at the nucleus. Second, the electric charges external to the central atom from the neighboring atoms, ligands, or ions must also be considered in a calculation of the field gradient at the central atom nucleus. These two effects are expressed as ... 

Consider first the effect of the atomic electrons. A filled or half-filled electron shell has a spherically symmetric electron distribution, and as such gives rise to no electric field gradient (except through external deformation, i.e., Sternheimer antishielding). Thus, of all the atomic electrons, only the... 

Vanadium-51 is a spin 7/2 nucleus, and consequently it has a quadrupole moment and is frequently referred to as a quadrupolar nucleus. The nuclear quadrupole moment is moderate in size, having a value of -0.052 x 10 2S m2. Vanadium-51 is about 40% as sensitive as protons toward NMR observation, and therefore spectra are generally easily obtained. The NMR spectroscopy of vanadium is influenced strongly by the quadrupolar properties, which derive from charge separation within the nucleus. The quadrupole moment interacts with its environment by means of electric field gradients within the electron cloud surrounding the nucleus. The electric field gradients arise from a nonspherical distribution of electron density about the... 

The distribution of bonding, or valence, electrons is the largest contributor to the electric field gradient. In a molecular frame of reference, we can define three orthogonal components of the electric field gradient, Vxx, Vyy, and Vzz, where Vxx + Vyy + Vzz = 0 and, by convention, VXX < V l < VZZ. From these electric field gradient components, we define two parameters ... 

S has a moderate quadrupolar moment, eQ, arising from its non-spherical charge distribution. The interaction between the nuclear quadrupole moment and the electric field gradient, which is generated at the nucleus itself by the surrounding electronic distribution, is modulated by molecular reorientational motion and provides the only effective relaxation mechanism in liquid. The resulting relaxation times are on the order of milliseconds. 

S nuclear quadrupole coupling constants have been determined from line width values in some 3- and 4-substituted sodium benzenesulphonates33 63 and in 2-substituted sodium ethanesulphonates.35 Reasonably, in sulphonates R — SO3, (i) t] is near zero due to the tetrahedral symmetry of the electronic distribution at the 33S nucleus, and (ii) qzz is the component of the electric field gradient along the C-S axis. In the benzenesulphonate anion, the correlation time has been obtained from 13C spin-lattice relaxation time and NOE measurements. In substituted benzenesulphonates, it has been obtained by the Debye-Stokes-Einstein relationship, corrected by an empirically determined microviscosity factor. In 2-substituted ethanesulphonates, the molecular correlation time of the sphere having a volume equal to the molecular volume has been considered. 

In these studies, the parameters that could provide the most interesting information are likely to be the electric field gradient (nuclear quadrupole coupling constant) at the 33S nucleus and its asymmetry parameter. Indeed, modifications of the lattice structure in different cement matrixes are expected to influence the symmetry of the electronic distribution around the sulphur nucleus more than the chemical environment of sulphur. 

Quantum mechanical calculations of 33S nuclear quadrupole coupling constants are not an easy matter (not only for the 33S nucleus, but for all quadrupolar nuclei). Indeed, the electric field gradient is a typical core property, and it is difficult to find wave functions correctly describing the electronic distribution in close proximity to the nucleus. Moreover, in the case of 33S, the real importance of the Sternheimer shielding contribution has not been completely assessed, and in any case the Sternheimer effect is difficult to calculate. 

The quadrupole coupling constant is proportional to the electric-field gradient, eq, which measures the asymmetry of the electron density surrounding the nucleus. Since the core electrons and the valence-shell s electrons are spherically distributed, they contribute... 

Similar relations can be used in comparing two isotopes of the same element. By observation of the same transition frequency of the two isotopic nuclei in one compound, one can assume a constant electric field gradient (that is, no measurable influence of the nuclear mass and the nuclear charge distribution on the core electrons). 

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