Potential gradient tensor

In this case p (r) is the external force and (r) is the corresponding system response. Alternatively we may find it convenient to express the charge distribution in tenns of point moments (dipoles, quadrupoles, etc.) coupled to the coiTesponding local potential gradient tensors, for example, H will contain terms of the form fi V and g VV (b , where fi and Q are point dipoles and quadrupoles respectively. 

The first derivative of the potential T at r = (0,0,0), taken as negative value, represents the ekctric field E, and the second derivative represents the electric field gradient tensor V at the nucleus,... 

When inserting into (4.5), the term ZeR will be multiplied with the elements of the electric field gradient tensor V. Fortunately, the procedure can be restricted to diagonal elements Vu, because V is symmetric and, consequently, a principal axes system exists in which the nondiagonal elements vanish, = 0. The diagonal elements can be determined by using Poisson s differential equation for the electronic potential at point r = 0 with charge density (0), AV = Anp, which yields... 

JJor chemists interested in modem theories of chemical bonding, the most useful data obtainable by the Mossbauer technique are the magnitude and sign of the electric quadrupole field gradient tensor and the magnitude of the shift, 8, (which we prefer to call the chemical isomeric. Cl, shift), of the center of the Mossbauer spectrum relative to some standard absorber. Although a considerable amount of chemical and structural information is potentially available from quadrupole data on iron compounds, relatively little use has been made of such data in the literature, and we will not discuss this parameter here. We will instead restrict ourselves to two main points review of the explanations put forth to explain Cl shift data in iron compounds, and a survey of some of the correlations and generalizations which have been found. 

Electric-field-gradient tensor, 230 Electric potential, 230 Electric quadrupole moment, 229-231, 365-366... 

For the potential Laplace s equation states = 0, from which it follows that for the electric gradient tensor,... 

Letting Vhe the potential at the nucleus in question due to all other charges, matrix elements taken of the electric field gradient tensor U are given by matrix elements of the second derivative of V directed along the space-fixed Z axis (= axis of quantization) ... 

Dft(a) tensors elements connect the chemical potential gradients and the heat-flux... 

The three components of an electric field vector are defined by the partial derivatives of the electrostatic potential with respect to the positional coordinates. The three principal values of the electric field gradient tensor are thus ... 

In the second approach we will use the fact that the moments are defined as derivatives of the energy of a molecule in the presence of an inhomogeneous electric field, Eqs. (4.19), (4.20) and (4.21). In order to apply these definitions we need to find an expression for the energy of a molecule in the presence of an inhomogeneous electric field. Here, we are using perturbation theory as developed in Section 3.2. The first step is thus to define the perturbation Hamiltonian operators and to derive explicit expressions for them in terms of components of the electric field a(Ro) and field gradient tensor a/3(Ro)- The electric field and field gradient enter the molecular Hamiltonian in the form of the scalar potential From Eq. (4.15) we can see... 

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