Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator. Karabanov, A., Kwiatkowski, G., & Köckenberger, W. Molecular Physics, 112(14):1838–1854, July, 2014. ![Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex Relaxation plays a crucial role in the spin dynamics of dynamic nuclear polarisation. We review here two different strategies that have recently been used to incorporate relaxation in models to predict the spin dynamics of solid effect dynamic nuclear polarisation. A detailed explanation is provided on how the Lindblad–Kossakowski form of the master equation can be used to describe relaxation in a spin system. Fluctuations of the spin interactions with the environment as a cause of relaxation are discussed and it is demonstrated how the relaxation superoperator acting in Liouville space on the density operator can be derived in the Lindblad–Kossakowski form by averaging out non-secular terms in an appropriate interaction frame. Furthermore we provide a formalism for the derivation of the relaxation superoperator starting with a choice of a basis set in Hilbert space. We show that the differences in the prediction of the nuclear polarisation dynamics that are found for certain parameter choices arise from the use of different interaction frames in the two different strategies. In addition, we provide a summary of different relaxation mechanisms that need to be considered to obtain more realistic spin dynamic simulations of solid effect dynamic nuclear polarisation. 1. Introduction Dynamic nuclear polarisation (DNP) can be used to substantially enhance the nuclear spin polarisation. There is currently an increased interest in the use of DNP by the magnetic resonance community since with the availability of robust hardware this strategy may help to overcome the sensitivity limitations of a wide range of applica-tions including magic angle spinning nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging [1–3]. Several DNP pathways in solid state have been described in the literature. Depending on the number of electrons that interact with the same nuclei and the linewidth of the electron resonance spectrum, solid effect DNP (SE DNP), cross effect DNP and DNP by thermal mixing have been distinguished [4,5]. SE DNP relies on (1) a spin system with negligible interactions between electrons, so it is sufficient to consider only one electron interacting with an ensemble of nuclear spins. Nuclear spins are coupled to the electron through the hyperfine in-teraction and form a coupled network through their dipolar interactions between each other. (2) The electron linewidth is smaller than the Zeeman splitting of the nuclear spins and hence spectral diffusion effects across the electron resonance line can be neglected. (3) The saturation of either the zero-or double-quantum transition frequency in the electron resonance spectrum. An important feature of DNP is relaxation processes that form the response of the spin
@article{Karabanov2014a,
title = {Spin dynamic simulations of solid effect {DNP}: the role of the relaxation superoperator},
volume = {112},
issn = {0026-8976},
url = {http://dx.doi.org/10.1080/00268976.2014.884287},
doi = {10.1080/00268976.2014.884287},
abstract = {Relaxation plays a crucial role in the spin dynamics of dynamic nuclear polarisation. We review here two different strategies that have recently been used to incorporate relaxation in models to predict the spin dynamics of solid effect dynamic nuclear polarisation. A detailed explanation is provided on how the Lindblad–Kossakowski form of the master equation can be used to describe relaxation in a spin system. Fluctuations of the spin interactions with the environment as a cause of relaxation are discussed and it is demonstrated how the relaxation superoperator acting in Liouville space on the density operator can be derived in the Lindblad–Kossakowski form by averaging out non-secular terms in an appropriate interaction frame. Furthermore we provide a formalism for the derivation of the relaxation superoperator starting with a choice of a basis set in Hilbert space. We show that the differences in the prediction of the nuclear polarisation dynamics that are found for certain parameter choices arise from the use of different interaction frames in the two different strategies. In addition, we provide a summary of different relaxation mechanisms that need to be considered to obtain more realistic spin dynamic simulations of solid effect dynamic nuclear polarisation. 1. Introduction Dynamic nuclear polarisation (DNP) can be used to substantially enhance the nuclear spin polarisation. There is currently an increased interest in the use of DNP by the magnetic resonance community since with the availability of robust hardware this strategy may help to overcome the sensitivity limitations of a wide range of applica-tions including magic angle spinning nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging [1–3]. Several DNP pathways in solid state have been described in the literature. Depending on the number of electrons that interact with the same nuclei and the linewidth of the electron resonance spectrum, solid effect DNP (SE DNP), cross effect DNP and DNP by thermal mixing have been distinguished [4,5]. SE DNP relies on (1) a spin system with negligible interactions between electrons, so it is sufficient to consider only one electron interacting with an ensemble of nuclear spins. Nuclear spins are coupled to the electron through the hyperfine in-teraction and form a coupled network through their dipolar interactions between each other. (2) The electron linewidth is smaller than the Zeeman splitting of the nuclear spins and hence spectral diffusion effects across the electron resonance line can be neglected. (3) The saturation of either the zero-or double-quantum transition frequency in the electron resonance spectrum. An important feature of DNP is relaxation processes that form the response of the spin},
number = {14},
journal = {Molecular Physics},
author = {Karabanov, Alexander and Kwiatkowski, Grzegorz and Köckenberger, Walter},
month = jul,
year = {2014},
keywords = {Lindblad–Kossakowski master equation, Liouville space, relaxation superoperator, solid effect dynamic nuclear polarisation, spin dynamics},
pages = {1838--1854},
}
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Fluctuations of the spin interactions with the environment as a cause of relaxation are discussed and it is demonstrated how the relaxation superoperator acting in Liouville space on the density operator can be derived in the Lindblad–Kossakowski form by averaging out non-secular terms in an appropriate interaction frame. Furthermore we provide a formalism for the derivation of the relaxation superoperator starting with a choice of a basis set in Hilbert space. We show that the differences in the prediction of the nuclear polarisation dynamics that are found for certain parameter choices arise from the use of different interaction frames in the two different strategies. In addition, we provide a summary of different relaxation mechanisms that need to be considered to obtain more realistic spin dynamic simulations of solid effect dynamic nuclear polarisation. 1. Introduction Dynamic nuclear polarisation (DNP) can be used to substantially enhance the nuclear spin polarisation. There is currently an increased interest in the use of DNP by the magnetic resonance community since with the availability of robust hardware this strategy may help to overcome the sensitivity limitations of a wide range of applica-tions including magic angle spinning nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging [1–3]. Several DNP pathways in solid state have been described in the literature. Depending on the number of electrons that interact with the same nuclei and the linewidth of the electron resonance spectrum, solid effect DNP (SE DNP), cross effect DNP and DNP by thermal mixing have been distinguished [4,5]. SE DNP relies on (1) a spin system with negligible interactions between electrons, so it is sufficient to consider only one electron interacting with an ensemble of nuclear spins. Nuclear spins are coupled to the electron through the hyperfine in-teraction and form a coupled network through their dipolar interactions between each other. (2) The electron linewidth is smaller than the Zeeman splitting of the nuclear spins and hence spectral diffusion effects across the electron resonance line can be neglected. (3) The saturation of either the zero-or double-quantum transition frequency in the electron resonance spectrum. 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