Interpreting electron–nuclear–magnetic field interactions from a hamiltonian expressed in tensorial notation

Golding, R.M.

doi:10.1016/j.jmr.2007.04.001

Cited by 2 publications

(6 citation statements)

References 8 publications

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“…This is an option for example in the international programme EPR-NMR [10,11] on the grounds that the Cartesian and Stevens' forms are most familiar to would-be users-but, is the SH thus framed valid when high-spin terms of the type described above are present? This is a particular question raised in [9]. We shall address this question later in the paper.…”

Section: Introductionmentioning

confidence: 92%

“…(J 1 , J 2 ) are Koster and Statz [14] normalized spherical tensor operators where, herein, one of k 1 , k 2 , k 3 will always be assumed zero so Single-vector decomposition products of TSTO SHs in the form of equations (9). Refer to section 2.4 for implicit relationships for other high-spin forms.…”

Section: Tesseral Spherical Tensor Operators (Tstos)-definitionsmentioning

confidence: 99%

“…Table 3. Cartesian tensor elements as defined in equations (11) as linear functions of tesseral spherical tensor parameters as defined in equations (9).…”

Section: Sh Term Generic Equationmentioning

confidence: 99%

“…The spectra were analysed with international programme EPR-NMR [10] where equation ( 5) is used to describe second rank 'tensor' quantities, Stevens' operators to describe ZFS terms of dimension I 4 (actually EPR-NMR allows ZFS terms to be expressed optionally in TSTO form) and TSTOs to describe higher-spin terms, B I n , S I n (n = 3, 5). It has been suggested [9] that such a mixed SH is invalid when the higher-order terms are present and could, depending on relative magnitudes of derived parameters, lead to false values of, for example, g and A principal values.…”

Section: A Consideration Of Shs Containing Mixed Tsto Cartesian and S...mentioning

confidence: 99%

“…Firstly, our 'gold standard' MRSH produces, in principle, an exact mathematical way of framing the SH and, combined with very precise measurements, can produce SH parameters that lead to principal directions of 'tensors' comparable in precision to bond-angle determination in x-ray diffractometry (see for example [7,8]); but, what is the significance of the parameters produced in terms of electron-nuclear interactions? Secondly, as addressed in a recent paper [9], is it valid to frame a SH in, for example, a combination of Cartesian (for g, A, D, P and g n ), Stevens' (for ZFS terms J 2(J = S, I )) and TSTO forms? This is an option for example in the international programme EPR-NMR [10,11] on the grounds that the Cartesian and Stevens' forms are most familiar to would-be users-but, is the SH thus framed valid when high-spin terms of the type described above are present?…”

Section: Introductionmentioning

confidence: 99%

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Higher-order Zeeman and spin terms in the electron paramagnetic resonance spin Hamiltonian; their description in irreducible form using Cartesian, tesseral spherical tensor and Stevens’ operator expressions

McGavin¹,

Tennant²

2009

J. Phys.: Condens. Matter

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In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS(3) and BS(5). Starting from the well-known decomposition of the general Cartesian tensor of second rank to three irreducible tensors of ranks 0, 1 and 2, the decomposition of Cartesian tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, [Formula: see text] Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.

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Section: Introductionmentioning

confidence: 92%

Section: Tesseral Spherical Tensor Operators (Tstos)-definitionsmentioning

confidence: 99%

“…Table 3. Cartesian tensor elements as defined in equations (11) as linear functions of tesseral spherical tensor parameters as defined in equations (9).…”

Section: Sh Term Generic Equationmentioning

confidence: 99%

Section: A Consideration Of Shs Containing Mixed Tsto Cartesian and S...mentioning

confidence: 99%