Theoretical description of pulse induced resonances in the homonuclear PIRATE experiment

IF 1.8 3区 化学 Q4 CHEMISTRY, PHYSICAL
Orr Simon Lusky , Matthias Ernst , Amir Goldbourt
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Abstract

Rotor-synchronous π pulses applied to protons (S) enhance homonuclear polarisation transfer between two spins (I) such as 13C or 15N as long as at least a single I–S heteronuclear dipolar-coupling interaction exists. The enhancement is maximum when the chemical-shift difference Δν between two spins equals an integer multiple, n, of the pulse-modulation frequency, which is half the rotor frequency νr. This condition, applied in the Pulse Induced Resonance with Angular dependent Total Enhancement (PIRATE) experiment, can be generalised for any spacing of the pulses kr such that Δν=nνr2k . We show, using average Hamiltonian theory (AHT) and Floquet theory, that the resonance conditions promote a second-order recoupling consisting of a cross-term between the homonuclear and heteronuclear dipolar interactions in a three-spin system. The minimum requirement is a coupling between the two I spins and a coupling of one of the I spins to the S spin. The effective Hamiltonian at the resonance conditions contains three-spin operators of the form 2I1±I2Sz with a non-zero effective dipolar coupling. Theoretical analysis shows that the effective strength of the resonance conditions decreases with increasing values of k and n. The theory is backed by numerical simulations, and experimental results on fully labelled 13C-glycine demonstrating the efficiency of the different resonance condition for k=1,2 at various spinning frequencies.

Abstract Image

同核PIRATE实验中脉冲诱导共振的理论描述
施加在质子(S)上的转子同步π脉冲增强了两个自旋(I)(如13C或15N)之间的同核极化转移,只要至少存在单个I–S异核偶极耦合相互作用。当两个自旋之间的化学位移差ΔΓ等于脉冲调制频率的整数倍n时,增强最大,脉冲调制频率是转子频率Γr的一半。这一条件应用于具有角度相关总增强的脉冲诱导共振(PIRATE)实验,可以推广到脉冲k/μr的任何间隔,使得Δμ=nμr2k。使用平均哈密顿理论(AHT)和Floquet理论,我们证明了共振条件促进了由三自旋系统中同核和异核偶极相互作用之间的交叉项组成的二阶重新耦合。最低要求是两个I自旋之间的耦合以及其中一个I自旋与S自旋的耦合。共振条件下的有效哈密顿量包含三个形式为2I1±I2∓Sz的自旋算符,具有非零有效偶极耦合。理论分析表明,共振条件的有效强度随着k和n值的增加而降低。该理论得到了数值模拟的支持,并且在完全标记的13C-甘氨酸上的实验结果表明,在不同的自旋频率下,k=1,2的不同共振条件的效率。
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来源期刊
CiteScore
5.30
自引率
9.40%
发文量
42
审稿时长
72 days
期刊介绍: The journal Solid State Nuclear Magnetic Resonance publishes original manuscripts of high scientific quality dealing with all experimental and theoretical aspects of solid state NMR. This includes advances in instrumentation, development of new experimental techniques and methodology, new theoretical insights, new data processing and simulation methods, and original applications of established or novel methods to scientific problems.
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