Spin algebra and<scp>NMR</scp>theory using numerical software

Grivet, Jean‐Philippe

doi:10.1002/cmr.a.21335

Cited by 3 publications

(3 citation statements)

References 33 publications

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“…This work does not compete with the existing spin dynamics simulation software [ 87 , 88 , 89 , 90 , 91 , 92 , 93 , 94 , 95 , 96 , 97 ] and pursues a different goal. Its raison d’etre is not how to compute, but rather how to not compute and still obtain useful insights about spin dynamics.…”

Section: Introductionmentioning

confidence: 99%

Geometrization for Energy Levels of Isotropic Hyperfine Hamiltonian Block and Related Central Spin Problems for an Arbitrarily Complex Set of Spin-1/2 Nuclei

Stass

2022

IJMS

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Description of interacting spin systems relies on understanding the spectral properties of the corresponding spin Hamiltonians. However, the eigenvalue problems arising here lead to algebraic problems too complex to be analytically tractable. This is already the case for the simplest nontrivial (Kmax−1) block for an isotropic hyperfine Hamiltonian for a radical with spin-12 nuclei, where n nuclei produce an n-th order algebraic equation with n independent parameters. Systems described by such blocks are now physically realizable, e.g., as radicals or radical pairs with polarized nuclear spins, appear as closed subensembles in more general radical settings, and have numerous counterparts in related central spin problems. We provide a simple geometrization of energy levels in this case: given n spin-12 nuclei with arbitrary positive couplings ai, take an n-dimensional hyper-ellipsoid with semiaxes ai, stretch it by a factor of n+1 along the spatial diagonal (1, 1, …, 1), read off the semiaxes of thus produced new hyper-ellipsoid qi, augment the set {qi} with q0=0, and obtain the sought n+1 energies as Ek=−12qk2+14∑iai. This procedure provides a way of seeing things that can only be solved numerically, giving a useful tool to gain insights that complement the numeric simulations usually inevitable here, and shows an intriguing connection to discrete Fourier transform and spectral properties of standard graphs.

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Section: Introductionmentioning

confidence: 99%

Geometrization for Energy Levels of Isotropic Hyperfine Hamiltonian Block and Related Central Spin Problems for an Arbitrarily Complex Set of Spin-1/2 Nuclei

Stass

2022

IJMS

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“…It is relatively easy to study molecules including nuclei with 1/2 spin such as 1H 1 , 6C 13 , and 9F 19 which are call for NMR-active nuclei (Gerald et al, 2001) and also NMR studies of these nuclei is common work (Katoh, 1994;Holzgrabe et al, 1998). Spin algebra and simulating 1D and 2D NMR experiments have also been realized (Grivet, 2015).…”

Section: Introductionmentioning

confidence: 99%

Simulation of NMR Hyperfine Structure Constant for AB2, A2B2 and A2B3 Systems

Ovalıoğlu

2021

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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The energy matrices of molecules of AB2, A2B2 and A2B3 type have been calculated for three different chemical shifts and several indirect spin-spin coupling coefficients (Jij) to obtain the Nuclear Magnetic Resonance (NMR) hyperfine structure. A computer program implemented in JACOBI method, which is a numerical iterative method for solving linear equation systems or a matrix equation on a matrix that has no zeros among its main diagonal elements, was used to calculate the eigenvalues and eigenvectors of these systems. We have developed a code to obtain the transition probabilities and transition energies. The theoretically calculated spectra has been compared with the experimental spectra and it has been observed a quite acceptable compliance between them.

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“…Nowadays, we already know few ways to simulate the dynamics of spins under the influence of magnetic field gradients, and some software and algorithms are already available [29][30][31][32][33][34][35][36][37]. Among these methods, here we will be interested in the one presented by Allard et.…”

Section: Introductionmentioning

confidence: 99%

Fast Simulation of Magnetic Field Gradients for Optimization of Pulse Sequences

Peterson,

Katiyar,

Laflamme

2020

Preprint

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We study how to simulate, efficiently, pulse field gradients (PFG) used in nuclear magnetic resonance (NMR). An efficient simulation requires discretization in time and space. We study both discretizations and provide a guideline to choose best discretization values depending on the precision required experimentally. We provide a theoretical study and simulation showing the minimum number of divisions we need in space for simulating, with high precision, a sequence composed of several unitary evolution and PFG. We show that the fast simulation of PFG allow us to optimize sequences composed of PFG, radio-frequency pulses and free evolution, to implement non-unitary evolution (quantum channels). As an evidence of the success of our work, we performed two types of experiments. First, we implement two quantum channels and compare the results with their theoretical predictions. In the second experiment, we used the fast simulation of PFG to optimize and implement a sequence to prepare pseudo pure state with better signal to noise ratio than any known procedure till now.

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Spin algebra andNMRtheory using numerical software

Cited by 3 publications

References 33 publications

Geometrization for Energy Levels of Isotropic Hyperfine Hamiltonian Block and Related Central Spin Problems for an Arbitrarily Complex Set of Spin-1/2 Nuclei

Geometrization for Energy Levels of Isotropic Hyperfine Hamiltonian Block and Related Central Spin Problems for an Arbitrarily Complex Set of Spin-1/2 Nuclei

Simulation of NMR Hyperfine Structure Constant for AB2, A2B2 and A2B3 Systems

Fast Simulation of Magnetic Field Gradients for Optimization of Pulse Sequences

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