Quadrupole coupling constant theory

Schwerdtfeger, P., Pernpointner, M. and Nazarewicz, W. (2004) Calculation of Nuclear Quadrupole Coupling Constants, in Calculation ofNMR and EPR Parameters Theory and Applications, (eds M. Kaupp M. Biihl and V.G. Malkin), Wiley-VCH Verlag GmbH, Weinheim, pp. 279-291. 

R. Ludwig, T. C. Farrar, and F. Weinhold. Quantum cluster equilibrium theory of liquids temperature dependent chemical shifts, quadrupole coupling constants, and vibrational frequencies of liquid ammonia. Ber. Bunsenges. Phys. Chem. 102, 205-12 (1998). 

A simple semiempirical theory for the interpretation of nuclear quadrupole coupling constants in terms of chemical bonding was developed by Townes and Dailey 2 24). This theory is treated in many summary papers on NQR, e.g. 39 4S 94.i43.is9) An extension of the Townes-Dailey treatment was given by Cotton and Harris 113-123>. Besides these simple model theories, a variety of more elaborate calculations have been done on the influence of intramolecular bonding on NQR spectra (see the discussion in 143- S9)). 

The temperature dependence of the quadrupole coupling constant is usually interpreted in terms of the Bayer theory 18>, modified and completed by Kushida 19 Kushida, Benedek and Bloembergen 2°), and by Gutowsky and Williams21). 

As in the case of 2H quadrupole coupling constants discussed above, this relationship is supported by the bond polarisation theory. Furthermore, a linear relationship between SH and the 2H quadrupole coupling constant was reported [70] ... 

E. A. C. Lucken, Nuclear Quadrupole Coupling Constants , Academic Press, London, 1969, A good summary of NQR theory and applications to different bonding situations, with selectedNQR data. 

Response properties have central roles in the theories describing intermolec-ular forces and the behaviour of molecules in external fields. It was recently demon8trated(l) that one such property which can be calculated ab initio is also accessible from the measured nuclear quadrupole coupling constants... 

The paper is divided into sections as follows. First, ab initio calculations on Br2 and then some approximate supermolecule calculations on H3N Br2 are reported. Then the Townes-Dailey model for nuclear quadrupole coupling constants and its connection with response theory are briefly reprised. Finally the model is applied to the complex H3N" -Br2, and empirical and ab initio results are compared. 

Often the Townes-Dailey approximation is used rather successfully. This approximation assumes that contributions to the EFG from nonsphericity of core electron and from lattice charge distributions offset each other. Then the EFG results from imbalances in valence electron populations. The calculations also show that the errors introduced by the approximations of the T ownes - Dailey theory do not exceed 5%. Thus Townes-Dailey calculations generally do well in showing trends m quadrupole coupling constants or NQR frequencies. 

The 2 2-component of the EFG operator q is now to be determined by electronic structure theory either from relativistic or nonrelativis-tic wave functions. The expression e Qqzz in eq- (17) is the nuclear quadrupole coupling constant (NQCC) and can be obtained by experiment leading to the sought quadrupole moment eQ. Due to its dependence the EFG operator especially stresses the core region of the electronic wave function and relativity can be expected to play a major role. For the adequate treatment of heavy atoms and molecules containing heavy elements relativity is therefore indispensable and we will mention nonrelativistic results only for comparative purposes. Before we treat the subject of relativistic qzz calculations in detail a few common experimental techniques for accurate NQCC measurements are briefly discussed and the underlying physical principles mentioned. 

De Luca G, Russo N, Koster AM, Calaminici P, Jug K (1999) Density functional theory calculations of nuclear quadrupole coupling constants with calibrated 0-17 quadrupole moments. Mol Phys 97 347... 

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