Abstract
The problem investigated within this thesis is the theoretical evaluation of: (i) the nuclear magnetic shielding in paramagnetic molecules; and (ii) the hyperfine interaction tensor components in paramagnetic molecular systems. In each case attention is restricted to only that part which arises from the so-called 'pseudo-contact' part of the hyperfine interaction between an electron centred on one nucleus, say A, and another nucleus with a non-zero magnetic moment, say B. The position of nucleus A with respect to B is given by a vector R, and the results given here are applicable for all distances R and all orientations of the vector R.
The foundations upon which the nuclear magnetic shielding and tensor component calculations rest are two-centre integrals of the form <φ’A| OB |φA> where OB represents the hyperfine interaction on nucleus B. A method of analytically evaluating these integrals which is valid for all R is achieved using a non-multipole expansion method, and results are given for 2p and 3d Slater-type orbitals. A master formula is given for the 3d-orbital dipolar integrals, and this may be used to evaluate any such integrals that are not given in this thesis.
Theoretical expressions are given for the pseudo-contact contribution to the NMR shift for: (a) d1 systems in the following strong crystal field environments: (i) octahedral; (ii) tetragonal; (iii) trigonal; and (iv) octahedral, incorporating bonding effects; (b) a d1 system in a crystal field of octahedral symmetry, where the condition of strong field coupling has been removed; and (c) a d2 system in a strong crystal (iii) field of octahedral symmetry. lsoshielding diagrams (i.e. contour maps where the contours are lines of equal chemical shift) are used to illustrate some of the results. Tables are given comparing the present results to those that would be gained using the point-dipole approximation or the multipole expansion method.
A d1 system in a strong crystal field of octahedral symmetry results in a 2T2 groundstate, which is split into three doubly spin degenerate levels by the spin-orbit coupling interaction and a crystal field component of lower symmetry. The hyperfine interaction tensor A is theoretically evaluated for each level, and in general A is asymmetric. For octahedral symmetry the 2T2 level is split into two - the 2T2E” and 2T2U’ levels. For the 2T2U’ level higher order terms must be added to the spin Hamiltonian, and theoretical expressions are given for the higher order terms for this level.
The major conclusion to be drawn from the results of this thesis is that a method is now available of theoretically evaluating the NMR shifts and hyperfine interaction tensor components which overcomes the inaccuracies that may result if the multipole expansion method or, a fortiori, the point-dipole approximation is used. The former method gives good agreement with the exact calculations for R > 0.2nm, the latter for R > 0.3nm. The results of this thesis overcome the approximations inherent in these two methods, as the results here are valid for all R.
The foundations upon which the nuclear magnetic shielding and tensor component calculations rest are two-centre integrals of the form <φ’A| OB |φA> where OB represents the hyperfine interaction on nucleus B. A method of analytically evaluating these integrals which is valid for all R is achieved using a non-multipole expansion method, and results are given for 2p and 3d Slater-type orbitals. A master formula is given for the 3d-orbital dipolar integrals, and this may be used to evaluate any such integrals that are not given in this thesis.
Theoretical expressions are given for the pseudo-contact contribution to the NMR shift for: (a) d1 systems in the following strong crystal field environments: (i) octahedral; (ii) tetragonal; (iii) trigonal; and (iv) octahedral, incorporating bonding effects; (b) a d1 system in a crystal field of octahedral symmetry, where the condition of strong field coupling has been removed; and (c) a d2 system in a strong crystal (iii) field of octahedral symmetry. lsoshielding diagrams (i.e. contour maps where the contours are lines of equal chemical shift) are used to illustrate some of the results. Tables are given comparing the present results to those that would be gained using the point-dipole approximation or the multipole expansion method.
A d1 system in a strong crystal field of octahedral symmetry results in a 2T2 groundstate, which is split into three doubly spin degenerate levels by the spin-orbit coupling interaction and a crystal field component of lower symmetry. The hyperfine interaction tensor A is theoretically evaluated for each level, and in general A is asymmetric. For octahedral symmetry the 2T2 level is split into two - the 2T2E” and 2T2U’ levels. For the 2T2U’ level higher order terms must be added to the spin Hamiltonian, and theoretical expressions are given for the higher order terms for this level.
The major conclusion to be drawn from the results of this thesis is that a method is now available of theoretically evaluating the NMR shifts and hyperfine interaction tensor components which overcomes the inaccuracies that may result if the multipole expansion method or, a fortiori, the point-dipole approximation is used. The former method gives good agreement with the exact calculations for R > 0.2nm, the latter for R > 0.3nm. The results of this thesis overcome the approximations inherent in these two methods, as the results here are valid for all R.
| Original language | English |
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| Qualification | Doctor of Philosophy |
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| Thesis sponsors | |
| Award date | 15 May 1980 |
| Publication status | Unpublished - Aug 1978 |
| Externally published | Yes |