Quadrupole splitting calculation

Table 1. The 72-atom model examined by different theoretical methods. The energy differences (AE in kcal/mol) are calculated with respect to the lowest SCF energy. q(Fe) stands for Mulliken population charges on the Fe atoms q(S) and SS(b.i.) are the Mulliken population charges and the bond index for the bridging S atoms, respectively AEq is the calculated Mossbauer quadrupole splitting constant [mm/sec]. The PUHF spin states are those projected from the UHF wavefunction with 5 = 5,. 

Principally, stmctural information can be obtained from the quadrupol splitting in the Mossbauer spectra of tin (IV)-compounds by the calculation of expectation regions... 

Quadrupole splitting in mm/sec, calculated with Q = 0.21 0.03 barns. Multicentre integrals have been neglected. The indicated error is due to the uncertainty in Q only. 

From a theoretical point of view, the calculation of the quadrupole splitting is relatively straightforward since it can be calculated directly from the elements of the EFG tensor at the iron nucleus (nucleus A ) as ... 

Once available, and supplemented by the nuclear contribution, the EFG tensor can be diagonalized. The numerically largest element (in atomic units) defines the value of q which is in turn used to calculate the quadrupole splitting parameter... 

Fig. 5.7 Comparison of calculated and measured Fe quadrupole splittings. Nuclear quadrupole moments of 0.158 bam (nonrelativistic DFT) and 0.156 bam (ZORA) were used in the calculations (taken from [25])...

Potzel and Kalvius were the first to investigate zinc compounds with Zn Mossbauer spectroscopy. The first measurements were carried out with Znp2 powder at 4.2 K [80]. The observed quadrupole splitting could not be explained by a simple lattice sum calculation. More detailed measurements were carried out at... 

Both Fe(ll)(TPP) and Fe(II)(OEP) have positive electric quadrupole splitting without significant temperature dependence which, however, cannot be satisfactorily explained within the crystal field model [117]. Spin-restricted and spin-unrestricted Xoi multiple scattering calculations revealed large asymmetry in the population of the valence orbitals and appreciable 4p contributions to the EFG [153] which then was further specified by ab initio and DFT calculations [154,155]. 

Table 5.4 A comparison of specific surface area ratio calculated from quadrupole splitting (Aq), spin-lattice relaxation rate (Rf, half-height linewidth (Avj/2) and isotherm data for an unbleached linerboard pulp beaten to various degrees.

The problem of the sign of AR/R for the divalent tin compounds was investigated by Lees and Flinn (16). In the relationship between the quadrupole splitting and chemical shift for the stannous compounds, two distinct correlations became apparent—compounds with a linear covalent bond, and compounds with a predominantly planar bond. Furthermore, there exists a linear relationship between the number of 5 p electrons and the chemical shift and hence the total 5 electron density. Using free tin ion wave functions in a self-consistent field calculation, they showed that the direct eflEect of adding 5 electrons is considerably... 

To calculate the nuclear quadrupole moment from the measured quadrupole splitting, it is necessary to know the electric field gradient, q, at the Te nucleus as well as the asymmetry parameter, rj. These can be calculated in the Townes and Dailey approximation (4) by knowing the chemical bonding in Te. 

Chemical Bonding. From the above calculations, it is clear that information on chemical bonding of Te compounds can be inferred from the associated quadrupole splitting data. We have neglected the ionic character of the Te bonds in tellurium. However, this parameter may need to be included in bonding calculations of Te compounds as is done, for example, in the Townes and Dailey approximation. 

Due to the electric quadrupole interaction, the Mi = 1/2 and Mi = 3/2 components of the 7 = 3/2 state of 57Fe split up, giving rise to the quadrupole splitting. Derived from the interaction of the nuclear quadrupole moment with the electric field gradient at the iron nuclei, AEq provides information about the asymmetry of the electron density around the iron nucleus. The electric field gradient at the iron nucleus can be calculated to obtain AEq (97). Since both 6 and AEq are related to the electron density at the nucleus, basis sets with an enlarged flexibility at the core region... 

An extended Huckel calculation of the quadrupole splitting in Fe(R2-Dtc)2Cl and [Fe(R2Dtc)2] 2 has been reported (384). The abnormally large... 

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