Field gradient definition

The operators for the potential, the electric field, and the electric field gradient have the same symmetry, respectively, as those for the atomic charge, the dipole moment, and the quadrupole moment discussed in chapter 7. In analogy with the moments, only the spherical components on the density give a central contribution to the electrostatic potential, while the dipolar components are the sole central contributors to the electric field, and only quadrupolar components contribute to the electric field gradient in its traceless definition. 

In the above formula, Q is the nuclear coordinate, p, and I/r are the ground state and excited electronic terms. Here Kv is provided through the traditional Rayleigh-Schrodinger perturbation formula and K0 have an electrostatic meaning. This expression will be called traditional approach, which has, in principle, quantum correctness, but requires some amendments when different particular approaches of electronic structure calculation are employed (see the Bersuker s work in this volume). In the traditional formalism the vibronic constants P0 dH/dQ Pr) can be tackled with the electric field integrals at nuclei, while the K0 is ultimately related with electric field gradients. Computationally, these are easy to evaluate but the literally use of equations (1) and (2) definitions does not recover the total curvature computed by the ab initio method at hand. 

Now we note that A = 0 tor a state, and neglect the mixing of excited electronic states by putting q = 0. We also note the definition of the electric field gradient at the nucleus, r/o, given in equation (8.28). With these simplifications the result is... 

Confining attention to the molecule-fixed q = 0 component, and making use of the definition (8.28) of the electric field gradient qx at nucleus 1, we obtain the final result... 

The remaining matrix element in (8.382) leads to definitions of the q = 0, 2 components of the electric field gradient tensor (actually, its negative), which are... 

We have already restricted our attention to the p = 0 components, and we now further limit ourselves to the q = 0 components of (9.16) since the q = 1, 2 terms involve mixing of excited electronic states. The q = 0 term leads to the definition of the (negative of the) electric field gradient e/ at the 14N nucleus, i.e. 

Everything is general so far but, as in previous cases, we confine attention to the q = 0 component (the molecule-fixed axial component) and make use of the definition of the electric field gradient at nucleus 1,... 

A nuclear quadrupole interaction is by definition anisotropic (parameters P, rj) as is an electronic quadrupole interaction (i.e., zfs parameters D, E), since these are described by a nonzero field gradient. Both of these effects have been briefly mentioned above, but the most important manifestation of anisotropy in ENDOR is with respect to g valnes and to hyperfine coupling interactions. 

Definitions the electric field gradient, the asymmetry parameter of the electric field gradient and the deuterium quadrupole coupling constant. 

DEFINITIONS-.THE ELECTRIC FIELD GRADIENT, THE ASYMMETRY PARAMETER OF THE ELECTRIC FIELD GRADIENT AND THE DEUTERIUM QUADRUPOLE COUPLING CONSTANT. 

Virtually all NMR experiments can described in terms of a pulse sequence, which, as the name suggests, is a notation which describes the series of radiofrequency (rf) or field-gradient pulses used to manipulate nuclear spins and so tailor the experiment to provide the desired information. Over the years, a largely (although not completely) standard pictorial format has evolved for representing these sequences, not unlike the way a musical score is used to encode a symphony. As these crop up repeatedly throughout the text, the format and conventions used in this book deserve explanation. Only the definitions of the various... 

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