Field gradient electric

The electrons at the Mossbauer atom and the surrounding charges on the ligands cause an electric potential V(r) at the nucleus (located at r = (0,0,0). The negative value of the first derivative of the potential represents the electric field, E = — VV, which has three components in Cartesian coordinates, E (3V73x, dVIdy, dVIdz). 

The EFG at the nucleus corresponds to the second derivative of the electric potential V r) at r = 0, that is, 

The trace vanishes because only p- and /-electrons contribute to the EFG, which have zero probability of presence at r = 0 (i.e. Laplace s equation applies as opposed to Poisson s equation, because the nucleus is external to the EFG-generating part of the electronic charge distribution). As the EFG tensor is symmetric, it can be diagonalized by rotation to a principal axes system (PAS) for which the off-diagonal elements vanish, = 0. By convention, the principal axes are chosen such that 

For a three- or fourfold axis of symmetry passing through the Mdssbauer nucleus as the center of symmetry, one can show that the FFG is symmetric, that is, = Vyy and therefore, r/ = 0. In a system with two mutually perpendicular axes of threefold or higher-symmetry, the EFG must be zero. 

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The electric field gradient is again a tensor interaction that, in its principal axis system (PAS), is described by the tluee components F Kand V, where indicates that the axes are not necessarily coincident with the laboratory axes defined by the magnetic field. Although the tensor is completely defined by these components it is conventional to recast these into the electric field gradient eq = the largest component,... 

Intramolecular quadrupolar 2 Reorientation of the electric field gradient principal axis Dominant for />1 (covalently bonded) [14]... 

Intermolecular quadrupolar 2 Fluctuation of the electric field gradient, moving multipoles Common for />1 In free Ions In solution [la... 

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 ... 

Electric field gradient q Exempli gratia (for example) e-g-... 

Electric-Field Gradients across the Glow Discharge... 

In Figure 6.4, the two electrodes are marked as cathode and anode, arising from the application of an external voltage between them. Before any discharge occurs, the electric-field gradient between the electrodes is uniform and is simply the applied voltage divided by the their separation distance, as shown in Figure 6.7. 

If the electrodes are moved closer together, the positive column begins to shorten as it moves through the Faraday dark space because the ions and electrons within it have a shorter distance through which to diffuse. Near the cathode, however, the electric-field gradient becomes steeper and electrons from the cathode are accelerated more quickly. Thus atom excitation through collision with electrons occurs nearer and nearer to the cathode, and the cathode glow moves down toward the electrode. 

Particularly in mass spectrometry, where discharges are used to enhance or produce ions from sample materials, mostly coronas, plasmas, and arcs are used. The gas pressure is normally atmospheric, and the electrodes are arranged to give nonuniform electric fields. Usually, coronas and plasmas are struck between electrodes that are not of similar shapes, complicating any description of the discharge because the resulting electric-field gradients are not uniform between the electrodes. 

The primary photochemical act, subsequent to near-uv light (wavelengths <400 nm) absorption by Ti02 particles, is generation of electron—hole pairs where the separation (eq. 3) into conduction band electrons (e g ) and valence band holes (/lyB ) faciUtated by the electric field gradient in the space charge region. Chemically, the hole associated with valence band levels is constrained at... 

Electrostatic precipitation Electric-field gradient a. Attraction h. Induction / /5,-n/K D 5,e,2 l5, + 2/l nDtV, / Surface accommodation... 

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... 

Just like the electric quadrupole moment, the electric field gradient matrix can be written in diagonal form for a suitable choice of coordinate axes. 

In a molecule, a given nucleus will generally experience an electric field gradient due to the surrounding electrons. The energy of interaction U between the nuclear quadrupole and the electric field gradient E is given by... 

It is usual to denote the electric field gradient at nuclear position N by q, which can be written as a 3 x 3 matrix... 

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