Long‐lived States in Multiple‐Spin Systems

Puneet Ahuja,Riddhiman Sarkar,Paul R Vasos,Geoffrey Bodenhausen

doi:10.1002/cphc.200900335

Abstract

Long-lived spin states are excited in molecules featuring more than two isolated coupled spins, including amino acids. The figure shows the exponential recovery with the longest time-constant in aspartic acid, T1max=5.842±0.004 s, and of the decay of the long-lived state, TLLS=10.9±0.2 s). An improvement in spin memory by a factor 2 compared to longitudinal spin-lattice relaxation time constants is obtained for most systems.

Highlights

Slow dynamic processes, such as folding or unfolding of proteins, can be witnessed by nuclear spins, provided that nonequilibrium populations of the energy levels can be sustained over time intervals that are on the order of the inverse of the rate constants of the dynamic processes
A more elegant approach is based on ‘longlived states’ (LLS), which in isolated two-spin systems are immune to relaxation mechanisms that are symmetric with respect to spin-exchange.[11,12]
The populations of these states have relaxation time constants TLLS that can be much longer than T1

Summary

IySy þ

Ð1Þ where the negative sign indicates that this operator corresponds to the difference between the populations of singlet and triplet states. In the case of acrylic acid (Figure 1), the rotational correlation time tc ~ 22 ps at 298 K could be inferred from the initial spin–lattice recovery rates of the protons T1(HI) ~ T1(HR) = 5.7 s and T1(HS) = 22.5 s (Figure 1) Considering this correlation time, the molecular structure, and the continuous-wave rf field with amplitude gB1x/(2p) = 2.5 kHz used to sustain the LLS, with the carrier set at the mean frequency of spins I and R, n0 = (nI + nR)/2 (Figure 1), the coefficients were found to be, for the quadratic state QISR of Equation (2): lIS 1⁄4 À0:23, lIR 1⁄4 0:93, and lSR 1⁄4 0:28, ð7Þ and for the cubic state CISR of Equation (3): m0 1⁄4 0:51, mIS 1⁄4 À0:19, mIR 1⁄4 0:80, and mSR 1⁄4 0:24: ð8Þ.

Acrylic Acid Aspartic Acid Asparagine Serine Cysteine Histidine

Experimental Section