weak
ˆ
ˆ ˆ
ˆ ˆ
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HJ = IzSAz + IzSBz
The strong coupling regime includes the full isotropic coupling
Hamiltonian written in terms of ladder operators, whereas in weak
coupling, typically defined to be when |Dw| ꢀ 2pJ, only the z
components are retained.
The eigenvalues Xp and normalized eigenvectors xp of the
Hamiltonian were determined using the linear algebra routines
of the Scipy library.32 The spectral peak frequencies correspond to
the frequencies of the coherences between the eigenvalues, given
by:
Xpq = -Xp+ Xq
while the peak amplitudes correspond to the square of the matrix
elements of the transition moment:
14 H. R. G. Bender, M. Nieger and E. Niecke, Z. Naturforsch. Tiel B.
T
+
2
Chem Sci., 1993, 48, 1742.
ˆ
apq = |xp · I · xq|
with the raising operator being constructed in the same basis as:
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Borrmann and H. G. V. Schnering, Z. Anorg. Allg. Chem., 1996, 622,
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+
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
16 M. Kopan and G. M. Reisner, Acta Crystallogr., Sect. C: Cryst. Struct.
I = (Ix + SAx + SBx) + i(Iy + SAy + SBy)
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The NMR spectra were then synthesized by placing
Lorentzian lines of width w and intensities apq at positions
Xpq.
Acknowledgements
We thank the Royal Society and University of Sussex for financial
support. IRC gratefully acknowledges the award of a Royal Society
University Research Fellowship.
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284 | Dalton Trans., 2012, 41, 278–284
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