Electronic current density fields

Theoretical calculation of NMR chemical shifts is usually done by first considering the electronic current density which is induced by the external magnetic field. Once this current has been calculated the chemical shift can be obtained by application of the Biot-Savard law, which describes the magnetic field created by it. The strength of this field at the position of an atom represents the NMR chemical shielding of this atom. 

When the electronic current density j(r) has been calculated, the Biot-Savart law for the induced magnetic field reads ... 

Electronic Current Density in the Presence of Static Electric and Magnetic Fields. 

Electron-joule heating is the product of the electron current density, J, and the electric field intensity, E it has the following form as developed by Nighan [78] ... 

When a molecule is immersed in an external electromagnetic field, the electron distribution gets polarized and electronic current densities arise. The relative phenomenology can be investigated within the framework of response theory in both the classical and quantum case [1-3]. 

Gaussian distribution [Eqs. (52)], to its respective steady-state value in the time-independent field. The magnitude of the reduced electron current density increases in a nonmonotone manner from its initial value of zero to its steady-state value in the respective field. 

Fig. 8.60 Scaling of the electron current density j in Al/Alq3/Ca diodes with the inverse layer thickness d at room temperature for a mean electric field strength F = 5 10 V/cm. From [38].

Figure 6.1 shows two current-carrying (CC) electrodes connected to a tissue volume. In the electrode wires, the flow of electrons is confined to the wires. When the electrode dimensions are smaller than the tissue volume dimension, the ionic current spreads out from a source electrode so that the current density falls with distance from the electrode. Voltage and current in the electrode wires are measured and define the immittance. However, in the tissue volume, the current flow must he defined with hoth magnitude and direction, and the parameter is current density J [A/m ], a spatial vector. The current density field J(x,y,z) cannot easily be measured and the current density field is often unknown. 

The changes in the film material with the current density, field, and temperature at which the films are made (in dilute, aqueous solution) and the changes which occur on subsequent annealing at temperatures of up to 200 C or so, represent large proportional changes in the concentration of mobile ions, that is, according to the usual theory, in the concentration of defects (interstitial metal ions and anion and cation vacancies). However, the absolute variations in terms of numbers of defects are probably small. Thus the variations in properties, which are not directly functions of defect concentrations, such as refractive index and density, are of the order of 1 %— not large for ordinary formation conditions—whereas the variations in those properties, such as ionic conductivity, electronic conductivity, and rate of dissolution in which are directly dependent on the concentra-... 

Fig. 8.5 Snapshots of electron current density and time derivative electron density from pure electronic component without that conveyed by nuclear motion, for the collisions of Na + Cl. The pulse width is 4.84 fs (corresponding to the second panel from the left, middle row in Fig. 8.4). The time dependent behavior of external electronic field and state population dynamics are given in the panels (a) and (b), respectively. The snapshots at 15 and 25 fs are shown in (c) and (d), respectively. The arrows denote electron flux density. The red sold and blue dashed contour lines in (c) and (d) show the positive and negative values of the pure electronic component of time derivative of the electron density. Here pure electronic means only the time derivative of electronic wave function was utilized in the evaluation both in flux and time derivative density.

Lazzeretti, P. Malagoli, M. Zanasi, R. Electronic current density (383) induced by magnetic fields and magnetic moments in molecules. 

The electronic current density induced by a static magnetic field... 

Employing Eqs. (35)-(37), the first-order electronic current density induced by the external magnetic field can be written as a sum of paramagnetic and diamagnetic contributions. 

The magnetic resjwnse of diamagnetic atoms, molecules and clusters, i.e., typical quantum mechanical systems, can be effectively interpreted and visualized via the laws of classical electrodynamics, allowing for functions of position r which describe the electronic charge density p(r), a scalar property, and the electronic current density J(r), a vector field, evaluated by quantum mechanical methods. 

In a number of instances, the MLL formulation is quite useful, e.g., it yields powerful tools for studying molecular magnetic response, which can be rationahzed via the electronic current density induced by a spatially uniform, time-independent external magnetic field B and by intramolecular magnetic dipoles rtij, I = 1,2... N at the nuclei. The practical advantages of deahng with a vector function of position in real space, instead of a complex wave function depending on 6n space-spin coordinates for an n particle problem, are evident. 

Electron Current Density Induced by Magnetic Fields and Nuclear Magnetic Dipoles... 

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