波谱学杂志, 2023, 40(1): 30-38 doi: 10.11938/cjmr20223005

研究论文

用于指导仲氢诱导核极化状态保存的己烯分子中五自旋的单重态制备和寿命研究

慈杰, 杨雪, 辛家祥, 魏达秀,*, 姚叶锋,#

上海市磁共振重点实验室,华东师范大学 物理与电子科学学院,上海 200062

Preparation and Lifetime Studies of the Singlet State of Five Spins in Hexene Molecules Used to Guide the Preservation of the Parahydrogen-induced Nuclear Polarization State

CI Jie, YANG Xue, XIN Jiaxiang, WEI Daxiu,*, YAO Yefeng,#

Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China

通讯作者: * Tel: 021-62233281, E-mail:dxwei@phy.ecnu.edu.cn;# Tel: 021-62234328, E-mail:yfyao@phy.ecnu.edu.cn.

收稿日期: 2022-06-7  

Corresponding authors: * Tel: 021-62233281, E-mail:dxwei@phy.ecnu.edu.cn;# Tel: 021-62234328, E-mail:yfyao@phy.ecnu.edu.cn.

Received: 2022-06-7  

摘要

仲氢诱导核极化(PHIP)技术能极大地增强核磁共振(NMR)信号的灵敏度,已被应用于磁共振成像、原位化学反应监测等领域.除了不断提高不同分子极化后的灵敏度外,延长和保存高极化度状态对PHIP技术的应用也至关重要,其中将极化后的状态制备成核自旋单重态是目前被研究较多的一种方法.本文以能被PHIP技术极化的己烯分子为研究对象,通过设计优化控制脉冲,对分子中的一个五自旋体系进行操控,制备了多种核自旋单重态,结果表明:己烯分子的碳-碳双键上存在三种不同的核自旋单重态,它们的寿命均长于仲氢极化后产生的初始态的寿命,可以作为延缓极化度衰减的一种中间态;通过对比单重态的寿命与相应自旋的纵向弛豫时间发现,将极化后己烯的状态转化为纵向磁化可能也是一种保存极化度的有效方法.

关键词: 仲氢诱导核极化; 核磁共振; 核自旋单重态; 优化控制脉冲

Abstract

Parahydrogen-induced polarization (PHIP) technique can greatly enhance the sensitivity of nuclear magnetic resonance (NMR) signals, and has been applied in the fields of magnetic resonance imaging, in situ chemical reaction monitoring, etc. In addition to improving the sensitivity of different molecules in the PHIP, it is also crucial to extend and preserve the high polarization state. To achieve this, a possible approach is to transfer the polarized state into a nuclear spin singlet state. Here, we focus on the singlet states preparation in hexene molecule that can be polarized by PHIP. By designing optimal control pulses, a five-spin system in hexene molecule was manipulated, and various quantum states were prepared respectively. Our results show that three different nuclear spin singlet states could be prepared with the group CH2=CH- in hexene. The three different nuclear spin singlet states have longer lifetime than that of the initial state polarized by PHIP, and thus can be utilized as the intermediate states to delay the decay of the polarization state. By comparing the lifetime of the singlet state with the longitudinal relaxation time of the corresponding spin, it is deduced that converting the state of the polarized hexene to longitudinal magnetization may also be an effective way to preserve the polarizability.

Keywords: parahydrogen-induced polarization (PHIP); nuclear magnetic resonance (NMR); nuclear spin singlet state; optimal control pulse

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本文引用格式

慈杰, 杨雪, 辛家祥, 魏达秀, 姚叶锋. 用于指导仲氢诱导核极化状态保存的己烯分子中五自旋的单重态制备和寿命研究[J]. 波谱学杂志, 2023, 40(1): 30-38 doi:10.11938/cjmr20223005

CI Jie. Preparation and Lifetime Studies of the Singlet State of Five Spins in Hexene Molecules Used to Guide the Preservation of the Parahydrogen-induced Nuclear Polarization State[J]. Chinese Journal of Magnetic Resonance, 2023, 40(1): 30-38 doi:10.11938/cjmr20223005

引言

核磁共振(nuclear magnetic resonance,NMR)技术具有分辨率高、原位实时、非破坏性等特点,能够为了解原子核的化学环境、分子的具体构象和动力学行为提供重要信息,已成为化学、物理、生物、医学等领域不可或缺的分析工具[1-4].随着检测要求的不断提高,进一步增强信号灵敏度是NMR技术发展的重要方向.目前文献中报道了多种用于增强灵敏度的方法,包括自旋交换光泵(spin exchange optical pumping,SEOP)[5]、动态核极化(dynamic nuclear polarization,DNP)[6,7]、化学诱导动态核极化(chemically induced dynamics nuclear polarization,CIDNP)[8]等.这些极化技术能够有效地提高NMR检测灵敏度,但设备成本高、操作复杂等问题在一定程度上限制了其应用范围.

近年来,仲氢诱导极化(parahydrogen induced polarization,PHIP)[9,10]作为一种操作简便、原料易得、对设备要求低的极化技术,受到了广泛关注.PHIP的主要过程是在合适的化学条件下,使氢气分子的布居数主要集中分布在某一个能级上,该能级会与其余能级存在极大的布居数差,由此产生极化度非常高的仲氢分子.当仲氢分子与特定目标分子发生加成反应时,仲氢分子的高极化度会转移到目标分子中相应的原子核上,同样也会使得相应自旋的部分能级上的布居数分布远高于其它能级,进而实现特定分子信号的灵敏度增强[11,12].这种高灵敏度的分子具有广阔的应用前景,目前已被用于理论计算、磁共振成像、痕量分析、化学指纹以及反应监控等方面[13-16].仲氢研究之初,德国的Spiess小组[13,17]在己炔加成仲氢生成极化己烯方面做了大量的工作.己炔分子由于存在不饱和的碳碳三键,并且化学性质活泼,容易与氢气分子发生反应,因而以己炔和己烯为对象研究仲氢极化的现象和机理相对简便.同时其研究结果对于理解三键变成双键的极化过程具有一定的参考意义.

仲氢加成之后产生的初始态不再是NMR中通常的热平衡态,根据所处磁场环境不同,仲氢与目标分子的加氢反应主要分为ALTADENA和PASADENA两种.ALTADENA实验是在地磁场下进行加氢反应,即弱磁场环境,被极化的两个核自旋(I1I2)的初始态为$ \rho_{\mathrm{A}}=0.5\left(I_{z}^{1}+I_{z}^{2}\right)-I_{z}^{1} I_{z}^{2}$.PASADENA实验是在NMR谱仪腔体内进行加氢反应,即强磁场环境,目标分子中两个被极化的核自旋(I1I2)的初始态为$ \rho_{\mathrm{p}}=I_{z}^{1} I_{z}^{2}$.两种情况下产生的仲氢极化状态的初始态均不同于热平衡态,这种极化态一旦产生之后会逐渐演化为其它状态,极化度逐渐衰减.为了增加极化状态的保存时间,有文献[18]提出通过将极化后的初始态转化为一种具有较长寿命的单重态能有效延缓极化度的衰减.

己烯分子是一个包含12个氢原子核的多自旋体系,自旋之间的耦合网络较为复杂,利用目前已被报道的单重态的制备方法,如M2S[19]、gM2S[20]、SLIC[21]、APSOC[22]等脉冲,难以保证较高的单重态制备和转化效率.文献[23]提出利用优化控制的数值脉冲制备N-乙酰天冬氨酸(N-acetyl aspartic acid,NAA)三自旋体系单重态的方法也不适用于己烯分子中多自旋体系的状态控制.

值得注意的是,与热平衡状态下己烯中的自旋状态相比,仲氢极化后的己烯主要区别是原子核能级上的布局数发生了变化,原子核之间的偶极耦合、J耦合,以及化学位移差都没有发生变化,由此可以推断热平衡状态下己烯分子中自旋的弛豫现象和机理应该与极化己烯类似.本文以热平衡状态下的己烯分子为研究对象,通过综合分析12个氢原子核的特点,选取了其中的一个五自旋体系作为研究对象,通过施加脉冲,制备了态$ \rho_{\mathrm{p}}^{\prime}=I_{z}^{1} I_{z}^{2}$,所用的脉冲如补充材料中图S1所示,该状态与PASADENA条件下的初始态$ \rho_{\mathrm{p}}=I_{z}^{1} I_{z}^{2}$的算符形式相似,本文认为它们的弛豫时间也应相同.另外,通过设计优化脉冲控制五自旋体系的演化,制备了三种核自旋单重态,并测量了三种单重态的寿命.通过综合分析己烯中氢核的纵向弛豫时间,以及初始态$ I_{z}^{1} I_{z}^{2}$和三种单重态的寿命,提出了多个能用于保存极化己烯分子极化度的可能方案.

1 理论部分

1.1 仲氢诱导极化产生的自旋状态

处于高磁场中的两个核自旋(I1I2)在弱耦合情况下,体系的能级对应的本征态分别为|αα>,|αβ>, |βα>,|ββ>.当两个自旋之间的化学位移差逐渐缩小,体系逐渐转为强耦合情况.体系的本征态变为: T1=|αα>、T0=(|αβ>+|βα>)2、T-1=|ββ>和S0=(|αβ>-|βα>)/2

氢气分子有两种不同的核自旋状态,分别为正氢和仲氢,常温常压下,普通氢气中的仲氢和正氢的组成比约为1:3,当降低氢气分子的温度,在活性炭或者氧化铁的催化作用下,仲氢和正氢之间能互相转化,最终能得到仲氢高度富集的氢气分子.当这种高度富集的氢气分子与其他分子中的氢原子核发生加成反应时,能将其高极化度转移到该分子中.仲氢分子能与己炔分子末端的碳碳三键发生加成反应,生成如图1中所示的己烯分子,反应之后氢气分子的高极化度被转移到氢原子核Hb、Hc上.在高磁场中,加成后产生的状态为${{\rho }_{\text{p}}}$,该初始态的矩阵形式为:

$\rho_{\mathrm{p}}=\frac{1}{2}\left(\begin{array}{cccc}0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 0\end{array}\right)=\frac{1}{4} I-I_{z}^{b} I_{z}^{c}$

图1

图1   己烯分子的结构式和在氘代丙酮溶液中的单脉冲1H NMR谱(500 MHz)

Fig. 1   The molecular structure and 1H NMR spectrum of hexene in deuterated acetone solution (500 MHz)


这里,$I \propto \frac{2 \Delta}{3}+\epsilon$,其中$\frac{2\Delta}{3}$为仲氢增强因子,为玻尔兹曼因子.由上式中的矩阵可知,仲氢加成后得到的状态是一个两自旋态,其布居数分布集中在T0态和S0态所对应的能级上.该状态可以进一步分解为如下形式:

$I_{z}^{b} I_{z}^{c}=-\left[\left(2 I_{x}^{b} I_{x}^{c}+2 I_{y}^{b} I_{y}^{c}-2 I_{z}^{b} I_{z}^{c}\right)-\left(2 I_{x}^{b} I_{x}^{c}+2 I_{y}^{b} I_{y}^{c}+2 I_{z}^{b} I_{z}^{c}\right)\right] / 4$

上式中,前半部分为前面介绍的T0态;后半部分即为S0态,也称为单重态,状态ρp产生之后会由于弛豫的作用逐渐衰减.液态体系中对T0S0态的弛豫,主要来源于临近核的偶极偶极相互作用和自身的化学位移各项异性.关于单重态的研究文献[24]指出,处于特定构型的原子核之间的单重态能避免偶极偶极弛豫的影响.但通常情况下,如不施加任何外界作用,ρp会以较快的速度弛豫.

上面的单重态S0是存在于Hb、Hc之间的状态,可以标记为S0bc,相似地,己烯分子中的其他氢原子核之间也存在其他的单重态,如Ha、Hc之间的状态S0ac,Ha、Hb之间的状态S0ab.

1.2 利用优化脉冲控制五自旋体系的演化并制备不同的单重态

己烯分子中存在12个氢原子核(如图1所示),由于仲氢加成主要发生Hb、Hc上,同时Hc与Hd、Hd'均存在耦合作用,当研究单重态S0acS0ab时,不能简单地只关注Ha、Hb、Hc三个自旋,即文献[21]中提出的针对三自旋体系中单重态的制备脉冲不适用于己烯分子.分析可知,如果只关注S0bcS0acS0ab三个单重态,则可以选择Ha、Hb、Hc、Hd、Hd'构成的五自旋体系为研究对象,在制备以上三个单重态的同时对Hd、Hd'进行同核去耦.由于这五个核自旋之间的化学位移相差不大,利用传统的NMR脉冲难以精确地控制自旋体系的演化.而优化控制的数值脉冲由于脉冲设计中可变量多,理论上能以接近100%的效率实现特定初末态的转化.

NMR技术中,核自旋状态的演化由体系密度算符的刘维方程描述,体系的哈密顿量主要包括主磁场、射频脉冲及自旋之间的相互作用三个成分,三者皆对应相应的幺正变换形式,传统NMR脉冲序列通常由射频脉冲和延时组成,不同的脉冲方向、角度及延时长短则对应不同的幺正变换,通过变化射频脉冲的形式和延时时间的长短,能控制自旋体系的演化,实现热平衡态到目标末态的转化.与传统NMR脉冲不同的是,优化脉冲中射频脉冲和自旋耦合同时进行,其主要思路是:将整个脉冲序列分成若干个小脉冲片段,每个小脉冲的幅度和相位各不相同,小脉冲施加期间自旋之间的耦合同时影响体系状态的演化.能实现特定初态到末态转化的优化脉冲形状可以利用数值算法得到.文献中报道的优化脉冲的实现主要基于GRAPE数值算法[25],优化过程中通过逐渐变化脉冲的幅度,使最终得到的脉冲能以极大的效率实现初末态的转化.本文的脉冲优化在SIMPSON模拟[26]平台实现,关键步骤包括自旋体系耦合参数的输入、脉冲对应的初末态的确认及脉冲宽度等参数的优化等.表1列出了己烯分子的NMR参数.优化过程以Ha、Hb、Hc、Hd、Hd'构成的五自旋体系为研究对象,图1展示了己烯分子的结构及其氘代丙酮溶液的一维1H NMR谱图.其中,Ha、Hb、Hc、Hd/Hd'的化学位移分别为δH 5.00、4.92、5.82、2.08.

表1   J耦合和化学位移差值

Table 1  J coupling and chemical shift differences

Ha-HbHc-HaHc-HbHc-HdHc-Hd'Hd-Hd'
J耦合/Hz1.5817.1610.216.736.73-7.5
化学位移差/Hz-40-410-450-1870-1870-

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己烯分子的三个氢原子核的单重态可以表示为:$S_{0}^{\mathrm{bc}}=-2\left(I_{x}^{\mathrm{b}} I_{x}^{\mathrm{c}}+I_{y}^{\mathrm{b}} I_{y}^{\mathrm{c}}+I_{z}^{\mathrm{b}} I_{z}^{\mathrm{c}}\right)$$S_{0}^{\mathrm{ac}}=-2\left(I_{x}^{\mathrm{a}} I_{x}^{\mathrm{c}}+I_{y}^{\mathrm{a}} I_{y}^{\mathrm{c}}+I_{z}^{\mathrm{a}} I_{z}^{\mathrm{c}}\right)$$S_{0}^{\mathrm{ab}}=-2\left(I_{x}^{\mathrm{a}} I_{x}^{\mathrm{b}}+I_{y}^{\mathrm{a}} I_{y}^{\mathrm{b}}+I_{z}^{\mathrm{a}} I_{z}^{\mathrm{b}}\right)$ ,这里的IxIyIz为积算符,字母a、b、c分别代表Ha、Hb、Hc.值得注意的是,这里我们研究的己烯分子的初始态为热平衡态,并不是极化时的初始态${{\rho }_{\text{p}}}(I_{z}^{\text{b}}I_{z}^{\text{c}})$,虽然${{\rho }_{\text{p}}}$里面包含单重态成分,但得到单重态的方法有很多种.这里,我们采用的方法是通过对热平衡态施加如下的幺正变换得到不同的单重态:${{U}_{\text{bc}}}={{\text{e}}^{\text{i}\pi (I_{y}^{\text{b}}-I_{y}^{\text{b}}I_{x}^{\text{c}})}}$${{U}_{\text{ac}}}={{\text{e}}^{\text{i}\pi (I_{y}^{\text{a}}-I_{y}^{\text{a}}I_{x}^{\text{c}})}}$${{U}_{\text{ab}}}={{\text{e}}^{\text{i}\pi (I_{y}^{\text{a}}-I_{y}^{\text{a}}I_{x}^{\text{b}})}}$.单重态制备完成之后,对核自旋施加去耦脉冲消除化学位移对单重态的弛豫影响,此时单重态能够被保存一定的时间.当需要观测单重态的衰减情况时,可以通过施加合适的脉冲将单重态转化为可观测态后采集信号.以幺正变换${{U}_{\text{bc}}}$为例,热平衡态在其作用后将演化为:

$I_{z}^{\text{a}}+I_{z}^{\operatorname{b}}+I_{z}^{\text{c}}+I_{z}^{{\text{{d}'}}}+I_{z}^{\text{d}}\xrightarrow{{{U}_{\text{bc}}}}I_{z}^{\text{a}}+2I_{x}^{\text{b}}I_{x}^{\text{c}}+2I_{y}^{\text{b}}I_{y}^{\text{c}}+I_{z}^{{\text{{d}'}}}+I_{z}^{\text{d}}$

上式中的多量子成分可以写成如下的形式:

$2I_{x}^{\text{b}}I_{x}^{\text{c}}+2I_{y}^{\text{b}}I_{y}^{\text{c}}=\left[ (2I_{x}^{\text{b}}I_{x}^{\text{c}}+2I_{y}^{\text{b}}I_{y}^{\text{c }}-2I_{z}^{\text{b}}I_{z}^{\text{c}})+(2I_{x}^{\text{b}}I_{x}^{\text{c}}+2I_{y}^{\text{b}}I_{y}^{\text{c}}+2I_{z}^{\text{b}}I_{z}^{\text{c}}) \right]/2$

当以此态作为基础,对体系施加去耦脉冲时,上式中前半部分的量子态在去耦脉冲施加期间会因为弛豫的影响迅速衰减,后半部分即为单重态,在去耦脉冲实施期间,单重态由于弛豫慢而被保留下来.最后,为了观测单重态的信号,可以再次施加幺正变化${{U}_{\text{bc}}}$和90˚脉冲,实现如下的转换:

$I_{x}^{\text{b}}I_{x}^{\text{c}}+I_{y}^{\text{b}}I_{y}^{\text{c}}+I_{z}^{\text{b}}I_{z}^{\text{c}}\xrightarrow{{{U}_{\text{bc}}}}(I_{z}^{\text{b}}+I_{z}^{\text{c}})/2+I_{z}^{\text{b}}I_{z}^{\text{c}}\xrightarrow{90_{-y}^{\circ }}(I_{x}^{\text{b}}+I_{x}^{\text{c}})/2+I_{x}^{\text{b}}I_{x}^{\text{c}}$

这里,将单重态转化为可观测态的整个脉冲可以集成为一个优化脉冲,其对应的幺正变换为${{{U}'}_{\text{bc}}}={{\text{e}}^{-0.5\text{i}\pi (I_{y}^{\text{b}}+I_{y}^{\text{c}})}}*{{U}_{\text{bc}}}$.相应地,当需要观测单重态$S_{0}^{\text{ac}}$$S_{0}^{\text{ab}}$的信号,也可以分别通过施加${{{U}'}_{\text{ac}}}={{\text{e}}^{-0.5\text{i}\pi (I_{y}^{\text{a}}+I_{y}^{\text{c}})}}*{{U}_{\text{ac}}}$${{{U}'}_{\text{ab}}}={{\text{e}}^{-0.5\text{i}\pi (I_{y}^{\text{a}}+I_{y}^{\text{b}})}}*{{U}_{\text{ab}}}$而实现.需要注意的是,(5)式中虽然只写出了Ha、Hb、Hc的积算符形式,但整个优化脉冲的计算过程考虑的是五自旋体系中的耦合网络.

利用优化控制方法计算脉冲的过程主要包括三步:第一步是编写SIMPSON优化程序,将自旋体系的参数输入到程序中;第二步是确定实现自旋状态转化所需的幺正变换的形式,并估算实现该转化的优化脉冲所需的时间;第三步是调整脉冲的时间和最大功率限制,反复运行SIMSPON程序,得到效率达到预期值的优化脉冲.根据己烯分子中氢原子核的耦合特点,本文计算优化脉冲时,考虑了Ha、Hb、Hc、Hd、Hd'五个自旋之间的耦合,以确保单重态的转化率接近100%.

图2分别列出了制备单重态的优化脉冲的波形图,所有脉冲的最大功率限制为400 Hz,相位变化范围为-π到π之间. 图2(a1)、2(a2)分别对应幺正变换${{U}_{\text{bc}}}$的幅度和相位,图2(b1)、2(b2)分别对应幺正变换${{{U}'}_{\text{bc}}}$的幅度和相位,脉冲包含500个小脉冲,总时间为55 ms;图2(c1)、2(c2)分别对应幺正变换${{U}_{\text{ac}}}$的幅度和相位,图2(d1)、2(d2)分别对应幺正变换${{{U}'}_{\text{ac}}}$的幅度和相位,脉冲包含500个小脉冲,总时间为35 ms;图2(e1)、2(e2)分别对应幺正变换${{U}_{\text{ab}}}$的幅度和相位,图2(f1)、2(f2)分别对应幺正变换${{{U}'}_{\text{ab}}}$的幅度和相位,脉冲包含 1 000个小脉冲,总时间为100 ms.优化控制脉冲是根据核自旋间的J耦合和化学位移差设计的,是一种无规的数值脉冲,每个小脉冲的幅度均小于或等于最大功率400 Hz. 图2(g)为实验所用的脉冲序列,其中OC I表示单重态的制备脉冲,对应的幺正变换为${{U}_{\text{bc}}}$${{U}_{\text{ac}}}$${{U}_{\text{ab}}}$(计算不同优化脉冲的代码脚本请见附件材料A1),OC II表示将单重态转化为可观测信号的脉冲,对应的幺正变换为${{{U}'}_{\text{bc}}}$${{{U}'}_{\text{ac}}}$${{{U}'}_{\text{ab}}}$,以上所有脉冲的理论效率均>99%.

图2

图2   制备和检测单重态所用的优化脉冲的幅度,相位及对应的脉冲序列.(a1)、(c1)、(e1)分别为幺正变换${{U}_{\text{bc}}}$${{U}_{\text{ac}}}$${{U}_{\text{ab}}}$对应脉冲的幅度;(a2)、(c2)、(e2)分别为幺正变换${{U}_{\text{bc}}}$${{U}_{\text{ac}}}$${{U}_{\text{ab}}}$对应脉冲的相位;(b1)、(d1)、(f1)分别为幺正变换${{{U}'}_{\text{bc}}}$${{{U}'}_{\text{ac}}}$${{{U}'}_{\text{ab}}}$对应脉冲的幅度;(b2)、(d2)、(f2)分别为幺正变换${{{U}'}_{\text{bc}}}$${{{U}'}_{\text{ac}}}$${{{U}'}_{\text{ab}}}$对应脉冲的相位;(g)为实验所用的优化脉冲序列

Fig. 2   The amplitudes and phases of different optimal control pulses, and the pulse sequence for the experiments. (a1), (c1), (e1) are the amplitudes of unitary transformation ${{U}_{\text{bc}}}$,${{U}_{\text{ac}}}$,${{U}_{\text{ab}}}$, respectively. (a2), (c2), (e2) are the phases of unitary transformation${{U}_{\text{bc}}}$,${{U}_{\text{ac}}}$,${{U}_{\text{ab}}}$, respectively. (b1), (d1), (f1) are the amplitudes of unitary transformation${{{U}'}_{\text{bc}}}$,${{{U}'}_{\text{ac}}}$,${{{U}'}_{\text{ab}}}$, respectively. (b2), (d2), (f2) are the phases of unitary transformation${{{U}'}_{\text{bc}}}$,${{{U}'}_{\text{ac}}}$,${{{U}'}_{\text{ab}}}$, respectively. (g) The experimental pulse sequence


2 实验部分

2.1 仪器与试剂

仪器:Bruker Avance III 500型NMR谱仪(5 mm液体BBO探头).

试剂:己烯(Sigma,AR)、氘代丙酮(CIL,99.9%氘代),未经进一步纯化,直接使用.

2.2 NMR实验

样品准备:将20 μL己烯溶解于500 μL氘代丙酮,将混合溶液装于5 mm NMR样品管中.单重态制备NMR实验参数设置:1H NMR工作频率为500.17 MHz;采样谱宽(SW)为8 000 Hz;射频中心O1为5.82 ppm;循环等待时间(d1)为2 s;梯度脉冲g1和g2时间为1 200 μs,功率分别为200 mT/m和100 mT/m;采样时间为1.5 s;累加次数(NS)为1.将SIMPSON计算得到的优化脉冲转化为Bruker形状脉冲的格式,根据图2(g)中的脉冲方框图编辑脉冲序列,在合适的位置调用形状脉冲.

3 结果与讨论

3.1 三种单重态的NMR实验实现

我们首先在NMR谱仪上验证了图2(g)所示的脉冲序列,分别选择${{U}_{\text{bc}}}$${{U}_{\text{ac}}}$${{U}_{\text{ab}}}$所对应的优化脉冲形状,实现Ha、Hb、Hc中三个核自旋单重态的制备和观测(图3).图3(a)为施加单脉冲得到的谱图,图3(b)~(d)分别代表制备$S_{0}^{bc}$$S_{0}^{ac}$$S_{0}^{ab}$所对应的实验谱图.通过与单脉冲图谱对比可知:制备和观测$S_{0}^{bc}$时,最后采集的谱图中只保留了Hb与Hc的信号,Ha的信号得到了很好的压制;制备和观测$S_{0}^{ac}$时,谱图中只保留了Ha与Hc的信号,Hb的信号得到了很好的压制;即使Ha与Hb的化学位移只相差40 Hz,通过制备单重态也能较明显地对Ha或Hb的信号进行选择性观测.

图3

图3   单脉冲和单重态对应的1H NMR谱图.其中(a)为单脉冲谱图,(b)、(c)、(d)分别为单重态$S_{0}^{bc}$$S_{0}^{ac}$$S_{0}^{ab}$对应的谱图

Fig. 3   The 1H NMR spectra. (a) The spectrum after applying a 90 degree single pulse; (b), (c), (d) corresponding to the singlet states

$S_{0}^{bc}$,$S_{0}^{ac}$,$S_{0}^{ab}$, respectively


3.2 核自旋单重态的寿命

根据图2(g)中的脉冲序列可知,在施加连续波(CW)脉冲去耦期间,处于单重态的自旋由化学位移各项异性引起的弛豫被去耦脉冲压制,此时主要发生的是自旋之间由偶极耦合引起的弛豫.而不同自旋之间的单重态的弛豫受偶极耦合的影响不同.实验中,通过不断改变CW施加的时间长短,能够监测单重态衰减的快慢.图4中给出了三种不同核自旋单重态随时间的衰减曲线,通过拟合得到单重态的寿命T1S.表2中列出了实验测得的态$S_{0}^{bc}$$S_{0}^{ac}$$S_{0}^{ab}$${{{\rho }'}_{\text{p}}}(I_{z}^{b}I_{z}^{c})$的寿命,以及三个自旋对应的纵向弛豫时间,其中$S_{0}^{bc}$$S_{0}^{ac}$$S_{0}^{ab}$的寿命分别为8.61 s、11.02 s、5.93 s,态${{{\rho }'}_{\text{p}}}(I_{z}^{b}I_{z}^{c})$的寿命为2.52 s(图S1),纵向弛豫弛豫时间$T_{1}^{{{H}^{a}}}$$T_{1}^{{{H}^{b}}}$$T_{1}^{{{H}^{c}}}$分别为11.54 s、11.52 s、14.22 s(使用反转恢复法观测,图S2~图S4).对比发现,三种单重态的寿命各有长短,其中Ha与Hc之间形成的单重态的寿命最长,Hb与Hc之间形成的单重态的寿命较短,Ha与Hb之间形成的单重态的寿命最短,它们均比态${{{\rho }'}_{\text{p}}}(I_{z}^{b}I_{z}^{c})$的寿命长;三个氢原子核的纵向弛豫时间则比单重态和${{{\rho }'}_{\text{p}}}(I_{z}^{b}I_{z}^{c})$的时间更长.文献[27]中顺式异构的两个自旋之间的单重态的寿命比纵向弛豫时间短,而处于反式异构的两个自旋之间的单重态的寿命则比纵向弛豫时间长很多.己烯分子中核Hb与核Hc之间为顺式异构,核Ha与核Hc之间为反式异构,不同的分子构型使得单重态的寿命不同.在孤立的两自旋体系中,单重态能避免偶极耦合弛豫的影响,但在多自旋体系中,制备成单重态的两个自旋仍然受到其它自旋的偶极耦合的影响,因而其单重态的寿命会受影响,可能会出现单重态的寿命比纵向弛豫弛豫时间短的情况.根据以上结果可以判断:高磁场下,对加成反应得到的己烯分子中的极化状态施加合适的射频脉冲,去掉化学位移各项异性弛豫的影响,则该极化状态的衰减会变慢;如果施加脉冲将其中的单态成分转化为$S_{0}^{ac}$,则极化状态能保存更长的时间.己烯分子中这三种单重态的寿命并未长于自旋的纵向弛豫时间,该现象可能暗示将初始态${{\rho }_{\text{p}}}$转化为纵向磁化可能会更有效地延长极化度的保存时间.

表2   单重态寿命和自旋纵向弛豫时间

Table 2  The lifetime values of singlet states and the longitudinal relaxation time values

$T{{{\rho }'}_{\text{p}}}$$T_{1\text{S}}^{ab}$$T_{1\text{S}}^{ac}$$T_{1\text{S}}^{bc}$$T_{1}^{{{H}^{a}}}$$T_{1}^{{{H}^{b}}}$$T_{1}^{{{H}^{c}}}$
时间/s2.52±0.035.93±0.0811.02±0.188.61±0.0711.54±0.4211.52±0.3114.22±0.41

新窗口打开| 下载CSV


图4

图4   三种单重态$S_{0}^{bc}$$S_{0}^{ac}$$S_{0}^{ab}$的弛豫衰减曲线

Fig. 4   The relaxation decay curves of the single states $S_{0}^{bc}$,$S_{0}^{ac}$,$S_{0}^{ab}$


4 结论

本文利用优化控制和数值计算方法设计脉冲,对己烯分子中的五自旋体系进行了精确的控制,分别在碳碳双键相连的氢原子核中制备了三种核自旋单重态,测量了三个单重态的寿命.通过综合分析己烯中氢核的纵向弛豫时间,以及初始态$I_{z}^{1}I_{z}^{2}$和三种单重态的寿命,发现将仲氢极化的初始态$I_{z}^{b}I_{z}^{c}$转化为氢核Ha和Hc之间的单重态$S_{0}^{ac}$或者转化为纵向磁化,是一种延长极化度保存时间的可选方案.本文的结果从实验上反映了己烯分子中不同单重态具有不同的寿命,今后的研究中我们将会进一步揭示单重态的寿命与分子构型的关系,并进一步比较极化状态与热平衡状态所对应的单重态寿命.

利益冲突

附件材料

图S1 制备态${{{\rho }'}_{\text{p}}}(I_{z}^{b}I_{z}^{c})$的脉冲及测量其弛豫衰减曲线.

图S2 Ha的纵向弛豫衰减曲线.

图S3 Hb的纵向弛豫衰减曲线.

图S4 Hc的纵向弛豫衰减曲线.

A1 计算不同优化脉冲的代码脚本.

可在论文网页版获取.

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胡凯瑞, 杨雪, 黄志明, .

三自旋体系核自旋单重态的制备与单重态二维谱的实现

[J]. 波谱学杂志, 2022, 39(1): 96-107.

[本文引用: 1]

CARRAVETTA M, LEVITT M H.

Theory of long-lived nuclear spin states in solution nuclear magnetic resonance. I. Singlet states in low magnetic field

[J]. J Chem Phys, 2005, 122(21): 214505.

DOI:10.1063/1.1893983      URL     [本文引用: 1]

KHANEJA N, REISS T, KEHLET C, et al.

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

[J]. J Magn Reson, 2005, 172(2): 296-305.

PMID:15649756      [本文引用: 1]

In this paper, we introduce optimal control algorithm for the design of pulse sequences in NMR spectroscopy. This methodology is used for designing pulse sequences that maximize the coherence transfer between coupled spins in a given specified time, minimize the relaxation effects in a given coherence transfer step or minimize the time required to produce a given unitary propagator, as desired. The application of these pulse engineering methods to design pulse sequences that are robust to experimentally important parameter variations, such as chemical shift dispersion or radiofrequency (rf) variations due to imperfections such as rf inhomogeneity is also explained.

TOSNER Z, VOSEGAARD T, KEHLET C, et al.

Optimal control in NMR spectroscopy: numerical implementation in SIMPSON

[J]. J Magn Reson, 2009, 197(2): 120-134.

DOI:10.1016/j.jmr.2008.11.020      PMID:19119034      [本文引用: 1]

We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.

STEVANATO G, ROY S S, HILL-COUSINS J, et al.

Long-lived nuclear spin states far from magnetic equivalence

[J]. Phys Chem Chem Phys, 2015, 17(8): 5913-5922.

DOI:10.1039/c4cp05704j      PMID:25633837      [本文引用: 1]

Clusters of coupled nuclear spins may form long-lived nuclear spin states, which interact weakly with the environment, compared to ordinary nuclear magnetization. All experimental demonstrations of long-lived states have so far involved spin systems which are close to the condition of magnetic equivalence, in which the network of spin-spin couplings is conserved under all pair exchanges of symmetry-related nuclei. We show that the four-spin system of trans-[2,3-(13)C2]-but-2-enedioate exhibits a long-lived nuclear spin state, even though this spin system is very far from magnetic equivalence. The 4-spin long-lived state is accessed by slightly asymmetric chemical substitutions of the centrosymmetric molecular core. The long-lived state is a consequence of the locally centrosymmetric molecular geometry for the trans isomer, and is absent for the cis isomer. A general group theoretical description of long-lived states is presented. It is shown that the symmetries of coherent and incoherent interactions are both important for the existence of long-lived states.

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