📚 Proton (¹H) Nuclear Magnetic Resonance | 质子核磁共振波谱
Proton nuclear magnetic resonance (¹H NMR) spectroscopy is a core analytical technique used to unravel the structures of organic molecules. By observing the behaviour of hydrogen nuclei in a strong magnetic field, chemists can determine the number, chemical environment and connectivity of hydrogen atoms in a sample. A single spectrum therefore answers three questions at once: how many different types of hydrogen are present, how many of each type there are, and how those hydrogens are connected to their neighbours.
质子核磁共振 (¹H NMR) 波谱是解析有机分子结构的核心技术。通过观察氢原子核在强磁场中的行为，化学家能够确定样品中氢原子的数目、化学环境及其连接方式。因此，一张谱图同时回答三个问题：样品中有几种不同的氢、每种氢各有多少个、以及这些氢与其邻近氢如何相连。
This article builds the topic from first principles - nuclear spin, energy levels and the resonance condition - then develops the four pieces of information that every A-Level student must be able to extract from a spectrum: chemical shift, integration, splitting pattern and coupling constant. Worked examples and exam pitfalls are included at the end.
本文从基本原理出发 - 核自旋、能级与共振条件 - 进而展开 A-Level 学生必须掌握的四类谱图信息：化学位移、积分、裂分模式与偶合常数。文末配有实例解析与考试易错点总结。
1. Introduction to ¹H NMR Spectroscopy | ¹H NMR 波谱简介
NMR spectroscopy takes advantage of the magnetic properties of certain nuclei. In ¹H NMR, we focus on the hydrogen-1 nucleus, which behaves like a tiny magnet. Placed in an external magnetic field, these nuclei absorb radiofrequency radiation at characteristic frequencies, generating a spectrum that serves as a molecular fingerprint.
核磁共振波谱利用某些原子核的磁性。在 ¹H NMR 中，我们聚焦于氢-1 核，它如同一个微小的磁体。在外加磁场中，这些原子核吸收特征频率的射频辐射，产生如同分子指纹的谱图。
The technique is non-destructive and requires only a few milligrams of sample dissolved in a deuterated solvent. It is widely applied to identify isomers, confirm the purity of synthesised compounds and map the carbon-hydrogen framework of organic molecules.
该技术无损且仅需数毫克溶于氘代溶剂的样品。它被广泛应用于异构体鉴定、合成产物纯度确认以及描绘有机分子的碳氢骨架。
The hydrogen-1 nucleus is the most sensitive commonly available NMR-active nucleus, which is why ¹H NMR is the routine first choice in both teaching laboratories and research. Its natural abundance is about 99.98%, so almost every hydrogen atom in a molecule contributes to the signal. By contrast, ¹³C has a natural abundance of only about 1.1%, which is why carbon NMR is far less sensitive and normally requires Fourier-transform averaging.
氢-1 核是常用核中灵敏度最高的 NMR 活性核，因此 ¹H NMR 是教学实验室与科研工作中的常规首选。其天然丰度约为 99.98%，所以分子中几乎每一个氢原子都会贡献信号。相比之下，¹³C 的天然丰度仅约 1.1%，这正是碳谱灵敏度低得多、通常必须依靠傅里叶变换累加的原因。
What a ¹H NMR spectrum tells you:
¹H NMR 谱图能告诉你什么：
- Number of proton environments - from the number of distinct signals (chemical shift).
氢环境数目 - 由不同信号（化学位移）的个数得到。 - Ratio of protons in each environment - from the relative peak areas (integration).
各环境中氢的相对数目 - 由峰面积比（积分）得到。 - Number of neighbouring non-equivalent protons - from the splitting pattern (multiplicity).
邻近非等价氢的数目 - 由裂分模式（多重度）得到。 - Stereochemical and conformational detail - from coupling constants, which differ for cis and trans arrangements.
立体化学与构象信息 - 由偶合常数获得，顺式与反式排布的偶合常数不同。
2. Nuclear Spin and Magnetic Moments | 核自旋与磁矩
The ¹H nucleus has a spin quantum number I ment, making the nucleus act like a bar magnet. In the absence of an external magnetic field, the magnetic moments of a collection of protons are randomly oriented, resulting in no net magnetisation.
¹H 核的自旋量子数 I = ½。该自旋产生磁矩，使原子核如同条形磁铁。在没有外加磁场时，众多质子的磁矩随机取向，净磁化为零。
When the sample is placed in a strong magnetic field B₀, the nuclear moments may align parallel to the field (lower energy, α state) or antiparallel (higher energy, β state). Only these two orientations are allowed for I . The energy gap ΔE between the two states is directly proportional to the field strength.
当样品置于强磁场 B₀ 中时，核磁矩可平行（低能 α 态）或反平行（高能 β 态）于磁场排列。对 I = ½ 的核仅允许这两种取向。两态间的能量差 ΔE 与磁场强度成正比。
ΔE = hν₀ = (γ h B₀) ÷ (2π)
. The magnetogyric ratio γ is a constant for each nucleus; for ¹H, γ ÷ 2π ≈ 42.58 MHz T⁻¹.
其中 ν₀ 为拉莫尔频率，在常用波谱仪磁场下位于射频区。磁旋比 γ 对每种核是常数；对 ¹H，γ ÷ 2π ≈ 42.58 MHz T⁻¹。
mperature. The Boltzmann distribution gives the population ratio N(β) ÷ N(α) = exp(−ΔE ÷ kBT r) is about 0.99994 - an excess of only roughly 1 proton in 10⁵ in the lower energy state.
由于 ΔE 极小，室温下两个自旋态的占据数几乎相等。玻尔兹曼分布给出占据比 N(β) ÷ N(α) = exp(−ΔE ÷ kBT)，在 298 K、9.4 T（即 400 MHz 波谱仪）下约为 0.99994 - 低能态仅多出约十万分之一的质子。
Worked magnitude: ⁸ s⁻¹ ≈ 2.65 × 10⁻²⁵ J per nucleus, about 0.16 J mol⁻¹. Compare this with thermal energy kBT y why NMR is an intrinsically insensitive technique and why signal averaging is essential.
数值演算：当 ν₀ = 400 MHz 时，ΔE = hν₀ = 6.626 × 10⁻³⁴ J s × 4.00 × 10⁸ s⁻¹ ≈ 2.65 × 10⁻²⁵ J 每核，约合 0.16 J mol⁻¹。与之相比，300 K 时热运动能量 kBT ≈ 4.14 × 10⁻²¹ J：NMR 跃迁比热运动弱数百万倍，这正是 NMR 本质上灵敏度低、必须进行信号累加的根本原因。
3. Energy Levels and the Resonance Condition | 能级与共振条件
Resonance occurs when the energy of the applied radiofrequency radiation exactly matches the energy gap between the α and β states. At that point the nuclei flip between spin states and energy is absorbed, giving a signal in the spectrum.
当外加射频辐射的能量恰好等于 α 态与 β 态之间的能隙时，即发生共振。此时核在两自旋态间翻转并吸收能量，在谱图中给出信号。
hν = ΔE = hν₀, therefore ν = ν₀ = γ B₀ ÷ (2π)
The Larmor frequency ν₀ increases linearly with the applied field B₀. A 400 MHz spectrometer therefore operates with a superconducting magnet of about 9.4 T, while a 600 MHz instrument needs about 14.1 T.
拉莫尔频率 ν₀ 随外加磁场 B₀ 线性增加。因此 400 MHz 波谱仪使用约 9.4 T 的超导磁体，而 600 MHz 仪器则需要约 14.1 T。
Every proton in a molecule would resonate at exactly the same frequency if all protons experienced the same magnetic field. Fortunately they do not: the electrons surrounding each nucleus circulate in the applied field and generate a small opposing local field, so the nucleus experiences an effective field Beff slightly smaller than B₀. This is the origin of chemical shift and of the whole diagnostic power of the technique.
若分子中所有质子感受到完全相同的磁场，它们将在同一频率共振。所幸事实并非如此：每个核周围的电子在外加磁场中环流，产生微小的反向局部磁场，因此核实际感受到的有效磁场 Beff 略小于 B₀。这正是化学位移的来源，也是该技术具有结构诊断能力的根本所在。
Relaxation. After absorbing energy, a nucleus must return to the lower state by relaxation (spin-lattice T₁ and spin-spin T₂ processes). Relaxation rates govern peak widths: slow relaxation gives sharp peaks, while rapid exchange of a proton (as in OH or NH) gives broad signals.
弛豫。吸收能量后，原子核必须通过弛豫（自旋-晶格 T₁ 与自旋-自旋 T₂ 过程）返回低能态。弛豫速率决定谱峰宽度：弛豫慢则峰尖锐，而质子交换快（如 OH 或 NH）则给出宽峰。
4. Chemical Shift and Shielding | 化学位移与屏蔽效应
The chemical shift of a proton depends on how much its surrounding electron density shields it from the applied field. Electron-withdrawing groups reduce the electron density, deshield the proton, and move its signal downfield to a higher δ value.
质子的化学位移取决于其周围电子云对磁场的屏蔽程度。吸电子基团降低电子密度，使质子去屏蔽，其信号向低场（更高 δ 值）移动。
Alkyl groups are electron-donating and therefore shield; protons on carbon next to oxygen, nitrogen or a halogen are deshielded. Ring current effects add a further twist: the delocalised π electrons of a benzene ring generate an induced field that strongly deshields aromatic protons (δ 6.5-8.0), whereas the protons sitting above the plane of a porphyrin ring can be strongly shielded.
烷基是给电子基团，因而起屏蔽作用；与氧、氮或卤素相连碳上的质子则被去屏蔽。环电流效应还带来额外变化：苯环离域 π 电子产生的诱导磁场强烈去屏蔽芳环质子（δ 6.5-8.0），而位于卟啉环平面正上方的质子则可能被强烈屏蔽。
| Proton environment | Typical δ / ppm | 质子环境 |
| TMS reference, (CH₃)₄Si | 0 | TMS 参比，(CH₃)₄Si |
| R-CH₃ (alkane) | 0.7-1.2 | R-CH₃（烷烃） |
| R-CH₂-R | 1.2-1.6 | R-CH₂-R |
| R-CO-CH₃ (ketone) | 2.1-2.6 | R-CO-CH₃（酮） |
| R-O-CH₃, R-O-CH₂ | 3.3-4.0 | R-O-CH₃、R-O-CH₂ |
| Alkene C=C-H | 4.6-6.0 | 烯烃 C=C-H |
| Aromatic Ar-H | 6.5-8.0 | 芳环 Ar-H |
| Aldehyde R-CHO | 9.0-10.0 | 醛 R-CHO |
| Carboxylic acid R-COOH | 10-13 | 羧酸 R-COOH |
| Alcohol R-OH, amine R-NH₂ | 1-5 (variable, often broad) | 醇 R-OH、胺 R-NH₂ |
Notice that δ is a ratio of frequencies and is therefore field-independent: an aldehyde proton appears near δ 9.8 on every spectrometer. Peak separations measured in Hz, however, do depend on the field, which is why higher-field instruments give better dispersion and simpler spectra.
请注意，δ 是频率之比，因此与磁场无关：醛基质子在任意波谱仪上都在 δ 9.8 附近出现。但以 Hz 表示的峰间距却依赖磁场，这正是高场仪器色散更好、谱图更简单的原因。
5. TMS, the δ Scale and Reference Standards | TMS、δ 标度与参比标准
Chemical shifts are quoted relative to tetramethylsilane, Si(CH₃)₄, universally abbreviated TMS. TMS is ideal as a reference because all twelve of its protons are equivalent, giving a single sharp peak; it is chemically inert, volatile, soluble in organic solvents, and it resonates at a position more shielded than almost every other proton.
化学位移以四甲基硅烷 Si(CH₃)₄（简称 TMS）为基准。TMS 作为参比的理想之处在于：它的十二个质子全部等价，只给出一个尖峰；它化学惰性、易挥发、可溶于有机溶剂，且其共振位置比几乎所有其他质子都更受屏蔽。
δ = (ν_sample − ν_TMS) ÷ ν_spectrometer × 10⁶ (ppm)
ument used. By convention TMS is assigned δ = 0; most protons appear at positive δ, i.e. downfield of TMS.
由于分子除以波谱仪工作频率，δ 以百万分率 (ppm) 表示，且与所用仪器无关。按约定 TMS 的 δ = 0；大多数质子出现在正 δ 值处，即位于 TMS 的低场侧。
In aqueous or highly polar media, sodium 3-(trimethylsilyl)propanoate-2,2,3,3-d₄ (TSP) is used instead of TMS, because TMS is not water-soluble. Some modern instruments use the residual solvent peak as an internal reference, but this requires accurate knowledge of the solvent shift.
在水溶液或强极性介质中，由于 TMS 难溶于水，通常改用 3-(三甲基硅基)丙酸钠-2,2,3,3-d₄ (TSP)。部分现代仪器使用残余溶剂峰作为内标，但这要求准确掌握该溶剂的化学位移。
6. Integration: Counting Protons | 积分：氢原子计数
The area under each signal is directly proportional to the number of protons giving rise to that signal. Integration therefore gives the ratio of proton numbers, not the absolute number of protons in the molecule.
每个信号下方的面积与该信号所对应的质子数目成正比。因此积分给出的是质子数目之比，而不是分子中质子的绝对个数。
In printed spectra the integrals are usually recorded as a stepped curve with numbers beside each step. If a molecule contains 6 protons distributed as 1 : 2 : 3, the integrals might read 1.0 : 2.0 : 3.0, or 10 : 20 : 30, or 0.5 : 1.0 : 1.5 depending on the scale chosen.
在打印谱图中，积分通常以阶梯曲线表示，每一阶旁标注数字。若分子共 6 个质子，分布为 1 : 2 : 3，则积分可能显示为 1.0 : 2.0 : 3.0，也可能为 10 : 20 : 30，或 0.5 : 1.0 : 1.5，取决于所选的标度。
Rules of thumb:
经验法则：
- Divide every integral by the smallest one to obtain the simplest whole-number ratio.
将每个积分除以最小积分值，即可得到最简整数比。 - Total the ratio and compare it with the number of hydrogens indicated by the molecular formula.
把比值加和，并与分子式所示的氢原子总数比较。 - Treat OH and NH integrals with caution: exchange with traces of water makes them unreliable and sometimes absent.
对 OH 与 NH 的积分要谨慎：与痕量水交换会使其不可靠，有时甚至完全消失。
Integration is the only routine measurement that gives quantitative information directly from an NMR spectrum without calibration against a standard of known concentration, which is why NMR is also used for purity assays and reaction monitoring.
积分是唯一一种无需对照已知浓度标准品、即可直接从 NMR 谱图获得定量信息的常规测量，这也是 NMR 可用于纯度测定与反应监测的原因。
7. Spin-Spin Splitting and the n+1 Rule | 自旋-自旋裂分与 n+1 规则
A proton signal is split by the magnetic effect of neighbouring non-equivalent protons. The general rule for first-order spectra is the n+1 rule: a proton with n equivalent protons on adjacent atoms appears as n+
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