The University of Southampton
University of Southampton Institutional Repository

Grid-free powder averages: on the applications of the Fokker–Planck equation to solid state NMR

Grid-free powder averages: on the applications of the Fokker–Planck equation to solid state NMR
Grid-free powder averages: on the applications of the Fokker–Planck equation to solid state NMR
We demonstrate that Fokker–Planck equations in which spatial coordinates are treated on the same conceptual level as spin coordinates yield a convenient formalism for treating magic angle spinning NMR experiments. In particular, time dependence disappears from the background Hamiltonian (sample spinning is treated as an interaction), spherical quadrature grids are avoided completely (coordinate distributions are a part of the formalism) and relaxation theory with any linear diffusion operator is easily adopted from the Stochastic Liouville Equation theory. The proposed formalism contains Floquet theory as a special case. The elimination of the spherical averaging grid comes at the cost of increased matrix dimensions, but we show that this can be mitigated by the use of state space restriction and tensor train techniques. It is also demonstrated that low correlation order basis sets apparently give accurate answers in powder-averaged MAS simulations, meaning that polynomially scaling simulation algorithms do exist for a large class of solid state NMR experiments.
121-129
Edwards, Luke J.
fc858f09-2669-4a26-9b25-6a00364954cd
Savostyanov, D.V.
e96cbd06-e7b0-4712-8cb6-d786e34bf796
Nevzorov, A.A.
05bfe07e-ef81-43ea-97c9-c14944641a28
Concistrè, M.
43a2d4ed-9d98-41fd-a999-38f197a1a55e
Pileio, G.
13f78e66-0707-4438-b9c9-6dbd3eb7d4e8
Kuprov, Ilya
bb07f28a-5038-4524-8146-e3fc8344c065
Edwards, Luke J.
fc858f09-2669-4a26-9b25-6a00364954cd
Savostyanov, D.V.
e96cbd06-e7b0-4712-8cb6-d786e34bf796
Nevzorov, A.A.
05bfe07e-ef81-43ea-97c9-c14944641a28
Concistrè, M.
43a2d4ed-9d98-41fd-a999-38f197a1a55e
Pileio, G.
13f78e66-0707-4438-b9c9-6dbd3eb7d4e8
Kuprov, Ilya
bb07f28a-5038-4524-8146-e3fc8344c065

Edwards, Luke J., Savostyanov, D.V., Nevzorov, A.A., Concistrè, M., Pileio, G. and Kuprov, Ilya (2013) Grid-free powder averages: on the applications of the Fokker–Planck equation to solid state NMR Journal of Magnetic Resonance, 235, pp. 121-129. (doi:10.1016/j.jmr.2013.07.011).

Record type: Article

Abstract

We demonstrate that Fokker–Planck equations in which spatial coordinates are treated on the same conceptual level as spin coordinates yield a convenient formalism for treating magic angle spinning NMR experiments. In particular, time dependence disappears from the background Hamiltonian (sample spinning is treated as an interaction), spherical quadrature grids are avoided completely (coordinate distributions are a part of the formalism) and relaxation theory with any linear diffusion operator is easily adopted from the Stochastic Liouville Equation theory. The proposed formalism contains Floquet theory as a special case. The elimination of the spherical averaging grid comes at the cost of increased matrix dimensions, but we show that this can be mitigated by the use of state space restriction and tensor train techniques. It is also demonstrated that low correlation order basis sets apparently give accurate answers in powder-averaged MAS simulations, meaning that polynomially scaling simulation algorithms do exist for a large class of solid state NMR experiments.

Full text not available from this repository.

More information

Published date: October 2013
Organisations: Computational Systems Chemistry

Identifiers

Local EPrints ID: 369174
URI: http://eprints.soton.ac.uk/id/eprint/369174
PURE UUID: 2467f4af-39ab-42ed-a491-3da2ecbc460e
ORCID for G. Pileio: ORCID iD orcid.org/0000-0001-9223-3896

Catalogue record

Date deposited: 29 Sep 2014 10:59
Last modified: 18 Jul 2017 01:39

Export record

Altmetrics

Contributors

Author: Luke J. Edwards
Author: D.V. Savostyanov
Author: A.A. Nevzorov
Author: M. Concistrè
Author: G. Pileio ORCID iD
Author: Ilya Kuprov

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×