Nuclear quadrupole moment determination

Finally, some special features may be found in the same column. These include references to a change of spectrum with temperature, to antiferromagnetic behavior, if it has been found or substantiated by EPR measurements, the ratio of HFS splitting constants for two isotopes, nuclear quadrupole moments determined from EPR and alike. For some polycrystalline samples, the half width d/fj of the line has been included. 

Belpassi, L., Tarantelli, F., Sgamellotti, A., Gdtz, A.W. and Visscher, L. (2007) An indirect approach to the determination of the nuclear quadrupole moment by four-component relativistic DFT in molecular calculations. Chemical Physics Letters, 442, 233-237. 

One method of determining nuclear quadrupole moment Q is by measuring the quadrupole coupling constant, given by eqQ/h, where e is the charge of the electron and q the electric field gradient due to the electrons at the atomic nucleus. The extraction of Q depends on an accurately calculated q. As a test of our finite-field relativistic coupled cluster approach, preliminary results for Cl, Br, and I are presented. 

The quantity pv C is the unpaired w-electron spin density at the carbon atom to which the hydrogen atom in question is bonded p c is defined as 1 times the fractional number of unpaired it electrons on the carbon atom, with the sign being determined by whether the net unpaired spin at the carbon atom is in the same or opposite direction as the spin vector of the molecule. The term -electron spin density is somewhat misleading in that pn is not an electron probability density (which is measured in electrons/cm3), but rather is a pure number. The semiempirical constant Q (no connection with nuclear quadrupole moments) is approximately —23 G. 

The determination of correlation times requires particular attention and is not a problem that can be easily resolved. It is necessary to consider not only the overall molecular tumbling, but also internal rotation motions, which can modulate the interaction between the nuclear quadrupole moment and the electric field gradient. In any case, it must be considered that % depends on the square root of and, even if in most cases it is not possible to measure or calculate precise values of t , the uncertainties introduced in the values of x may often be accepted. 

The quadrupole splitting A Eg is the first Mossbauer parameter that could be predicted with reasonable accuracy by electronic structure calculations. The quadrupole sphtting can be related to the EFG at the Mossbauer nucleus according to equation (12). Since the nuclear quadrupole moment Q is very difficult to determine by experiment alone, the combination of Mossbauer spectroscopy and density functional calculations is currently the most accurate approach to estimate Q. A linear regression of measured quadrupole splittings and calculated electric field gradients has been performed by Blaha et al. for a large series of compounds... 

A seminal paper dealt with NQls in metals and compounds for the purpose of the determination of nuclear quadrupole moments using reference moments. ... 

Dufek, P, Blaha, P, Schwarz, K. Determination of the nuclear-quadrupole moment of 57Fe. Phys Rev. Lett. 1995, 75, 3545-8. 

It follows that by increasing the constant of vibronic coupling the relative contribution of Jahn-Teller nuclear vibrations to the effective quadrupole moment determining the birefringence is increasing. Therefore ( ",)(r, ft) [to be distinguished from the reduction parameters (r, /3)] can be called the parameter of vibronic amplification of the vibrational contributions to the quadrupole moment. 

J. Bieron, C. Froese Fischer, I. P. Grant, Large-scale multiconfigurational Dirac-Fock calculations of the hyperfine structure constants and determination of the nuclear quadrupole moment of Ti, Phys. Rev. A 59 (1999) 4295-4299. 

The constant factor (b, I Bj b, I) is determined by the condition that 2 2,o and -42,o have the same expectation value in the substate with the maximum spin projection, i.e. Mj = +/. The only constant which is necessary is denoted (eQ) and is termed the nuclear quadrupole moment—see Table 3.2. 

Q Nuclear quadrupole moment in units of femtometers squared (1 fm = 10 barn). Because the determination of quadrupole moments requires knowledge of the electron configuration... 

An overview of relativistic state-of-the-art calculations on electric field gradients (EFG) in atoms and molecules neccessary for the determination of nuclear quadrupole moments (NQM) is presented. Especially for heavy elements four-component calculations are the method of choice due to the strong weighting of the core region by the EFG operator and the concomitant importance of relativity. Accurate nuclear data are required for testing and verification of the various nuclear models in theoretical nuclear physics and this field represents an illustrative example of how electronic structure theory and theoretical physics can fruitfully interplay. Basic atomic and molecular experimental techniques for the determination of the magnetic and electric hyperfine constants A and B axe briefly discussed in order to provide the reader with some background information in this field. 

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