Erratum: Relaxation and dynamics of coupled spin systems subjected to continuous radio frequency fields [J. Chem. Phys. 9 5, 3092 (1991)]

Spin Relaxation and Chemical Exchange in NMR Simulations

“…(This is evident because the trace of represents a linear dependency in the elements of the density matrix.) Ravikumar et al (24) have presented an elegant way out of this difficulty. They reduce the dimensionality of the matrix (R Ϫ i⍀) by one by subtracting the trace relation times the first element of each row of the matrix from that row.…”

“…Whereas the equations for describing relaxation during an RF pulse are complicated (21)(22)(23)(24)(25)(26), the alteration of those equations that is necessary to account for exchange is simple. In the presence of an RF field, the steady state that is attained at infinite time (in the frame rotating at the RF frequency) differs from equilibrium.…”

“…Then we reduce the dimensionality of the problem by eliminating the first row and the first column corresponding to each exchange site. This results in an Nn 2 Ϫ N dimensional nonsingular matrix which is inverted, and the rest of the computation proceeds as in the exchange-free situation (21)(22)(23)(24)(25).…”

“…It is the determination of that steady-state density matrix that is crucial. The important equation is the Liouville equation in the rotating frame (22,24), which can be written as Ѩ Ѩt ͑t͒ ϭ ͑R Ϫ i⍀͒͑t͒ Ϫ R eq , [20] where the matrix ⍀ is defined as ⍀ ␣␣Ј␤␤Ј ϭ ␣␣Ј ␦ ␣␤ ␦ ␣Ј␤Ј . At infinite time, the time derivative of the density matrix must vanish, and the density matrix becomes the steady-state limit ss .…”

Pulsed Field Gradients in Simulations of One- and Two-Dimensional NMR Spectra

“…We begin by writing the Redfield equation which describes the relaxation of the density matrix in the appropriate interaction representation (designated byˆ) (21,24,28,38):…”