化学位移 Chemical shift — 公式推导、符号与局限

\[\delta = \frac{\nu - \nu_\text{ref}}{\nu_0}\times10^6\ \text{ppm} = (\sigma_\text{ref} - \sigma)\times10^6\]

含义Meaning

以 TMS 为零点、按仪器频率归一化的共振频率偏移，单位 ppm，与磁场强度无关，可在不同仪器间比较。

The resonance offset from TMS, normalised by the spectrometer frequency (ppm), so it is field-independent and comparable between instruments.

符号Symbol	含义 Meaning	单位 Unit
\(\delta\)	化学位移chemical shift	ppm
\(\sigma\)	屏蔽常数shielding constant	1
\(\nu_0\)	仪器（参比）工作频率spectrometer frequency	Hz

核实际感受的场 \(B_\text{loc} = (1 - \sigma)B_0\)，所以 \(\nu = \gamma(1-\sigma)B_0/2\pi\)。
\(B_\text{loc} = (1-\sigma)B_0\), so \(\nu = \gamma(1-\sigma)B_0/2\pi\).
频率差 \(\nu - \nu_\text{ref} \propto (\sigma_\text{ref} - \sigma)B_0\)，除以 \(\nu_0 \propto B_0\) 消去场强。
Dividing by \(\nu_0 \propto B_0\) removes the field dependence.
屏蔽来自抗磁项（电子云密度，电负性基团使其减小）与顺磁项及邻近基团磁各向异性（芳环电流、羰基、三键）。
Shielding has diamagnetic (electron density), paramagnetic and neighbouring-anisotropy (ring currents, C=O, C≡C) contributions.

δ 受溶剂、浓度、温度、氢键影响；可交换质子变化最大。
δ depends on solvent, concentration, temperature and H-bonding.
以 Hz 表示的偶合常数 J 不随场强变，所以高场下多重峰相对“变窄”、谱图更一级。
J (Hz) is field-independent, so spectra become more first-order at high field.

400 MHz 谱中某峰比 TMS 高 2908 Hz：δ = 2908/400 = 7.27 ppm（芳香 H）。

A peak 2908 Hz from TMS at 400 MHz: δ = 7.27 ppm (aromatic H).