Quasi-equilibria in reduced Liouville spaces

Meghan E. Halse, Jean-Nicolas Dumez, Lyndon Emsley

Research output: Contribution to journalArticlepeer-review


The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.
Original languageEnglish
Article number224511
Number of pages14
JournalJournal of Chemical Physics
Issue number22
Publication statusPublished - 14 Jun 2012

Cite this