Geometrization for Energy Levels of Isotropic Hyperfine Hamiltonian Block and Related Central Spin Problems for an Arbitrarily Complex Set of Spin-1/2 Nuclei.
Int J Mol Sci
; 23(23)2022 Dec 02.
Article
em En
| MEDLINE
| ID: mdl-36499535
ABSTRACT
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.
Palavras-chave
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Assunto principal:
Espectroscopia de Ressonância de Spin Eletrônica
Idioma:
En
Revista:
Int J Mol Sci
Ano de publicação:
2022
Tipo de documento:
Article
País de afiliação:
Federação Russa