M. Goldman. Quantum description of high‐resolution NMR in liquids. Oxford University Press, 1988. £35.00

We present an algebraic foundation for the state space restriction approximation in spin dynamics simulations and derive applicability criteria as well as minimal basis set requirements for practically encountered simulation tasks. The results are illustrated with NMR, ESR, DNP and Spin Chemistry simulations. It is demonstrated that state space restriction yields accurate results in systems where the time scale of spin relaxation processes approximately matches the time scale of the experiment. Rigorous error bounds and basis set requirements are derived.

Section: Numerical Examplessupporting

confidence: 76%

On the accuracy of the state space restriction approximation for spin dynamics simulations

Karabanov

Kuprov

Charnock

et al. 2011

“…These integrals used to be evaluated by diagonalizing 0 H and computing the Fourier transform analytically 1,3,11,12 as shown in Equation (2). Diagonalization has cubic cost and eigenvector arrays of sparse spin Hamiltonians are full -this has limited the applicability of BRW theory to systems with fewer than about six spins.…”

Section: Spin Relaxation Theoriesmentioning

confidence: 99%

“…Their common feature is the complexity of evaluation: expensive matrix factorizations * are usually required 3,11,12 . This makes the application of the associated theories difficult when matrix dimension exceeds 10 3 , i.e.…”

Section: Introductionmentioning

confidence: 99%

Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories

Goodwin

2015

Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.3

“…20 Thus, the dynamics of a spin 5/2 with axial symmetry can be evaluated as a 3ϫ3 matrix. The thermal equilibrium reduced density matrix can be written as…”

Section: Appendix: Density Matrix Approach For the Evaluation Of Spinmentioning

confidence: 99%

Two-dimensional nuclear magnetic resonance correlation spectroscopy at zero field

Liao

Harbison

1999

Three methods for two-dimensional correlation nuclear magnetic resonance spectroscopy at zero field are discussed. All three involve coherence transfer via longitudinal polarization, double quantum coherence, or both in parallel. The double quantum pulse sequences exploit the spinor property of spin states. These sequences have been applied to connected ⌬mϭ1 transitions, as well as for the indirect detection of forbidden or nearly forbidden ⌬mϾ1 transitions. © 1999 American Institute of Physics. ͓S0021-9606͑99͒00331-1͔ INTRODUCTIONDespite their success in high-field nuclear magnetic resonance ͑NMR͒, extension of multidimensional Fourier transform methods to zero-field NMR has been limited. There are several legitimate reasons for this; principally, high-field spectra are often complex, with literally thousands of resonance signals; in such systems, two-dimensional methods are necessary both to increase the resolution and provide spectral assignments. In contrast, zero-field spectra are often very simple, both because of the paucity of chemically distinct species in the material, and because there is usually only a single significant term in the spin Hamiltonian, resulting in a lack of spectral multiplicity.Nonetheless, there are occasions when multidimensional techniques can be usefully applied at zero field. The first such applications [1][2][3] were directed at extracting the asymmetry parameter, ordinarily unavailable for spin 3/2 nuclei at zero field. For spins 5/2 and higher, can be obtained from the ratios of two or more spectral frequencies observable for each species. However, in samples with several distinct quadrupolar species, such as partially deuterated amine and amino acid hydrohalides, 4 connected transitions must be correctly assigned to extract this information. This was the purpose of our original nuclear quadrupolar correlation experiment. 5 Since then, we have also applied the experiment to inhomogeneously broadened systems, since in such systems the quadrupolar frequencies are strongly correlated. The resulting removal of this broadening has allowed us to estimate the hexadecapolar interaction for 127 I In cadmium iodide with high accuracy. 6 Figure 1 correlates the energy levels and transitions for a spin 5/2 nucleus at zero field with the high-field energy levels. At zero field, the high-field eigenstates, labeled by the quantum number m associated with the z component of the angular momentum, become twofold degenerate, with the Ϯm states having the same energy. There are two connected single-quantum transitions at frequencies 1 and 2 and one double-quantum transition at dq ϭ 2 ϩ 1 . For an axially symmetric electric field gradient 2 ϭ2 1 , and the eigenstates are identical to the high-field eigenstates. If the electric field gradient is not axially symmetric, the ratio between the two single-quantum frequencies decreases until it reaches a value of 1 for an asymmetry parameter ϭ(ٌE yy ϪٌE xx )/ٌE zz ϭ1, and concomitantly there is some mixing of the high-field eigenstates, the mϭϮ5/2 state...