13.3 Chemical Shifts

NMR Spectroscopy and Chemical Shifts

Measurement of Chemical Shifts

Chemical shifts are measured in parts per million (ppm) relative to a reference compound. Using ppm instead of absolute frequency gives you a standardized scale that works the same regardless of which spectrometer you use.

• Tetramethylsilane (TMS) is the standard reference for both $^1\text{H}$ and $^{13}\text{C}$ NMR, assigned a chemical shift of 0 ppm. TMS works well because its protons are highly shielded, so almost all organic signals appear downfield from it.
• The chemical shift ($\delta$) is calculated as:

$\delta = \frac{\nu - \nu_{\text{ref}}}{\nu_{\text{ref}}} \times 10^6$

where $\nu$ is the resonance frequency of your sample signal and $\nu_{\text{ref}}$ is the resonance frequency of the reference compound.

The chemical shift scale increases from right to left:

• Upfield (shielded) signals appear at lower ppm values (right side of the spectrum). Examples: TMS, alkane protons.
• Downfield (deshielded) signals appear at higher ppm values (left side of the spectrum). Examples: aldehyde protons (~9–10 ppm), aromatic protons (~6.5–8 ppm).

Chemical Shifts and Molecular Structure

Several factors determine where a signal appears on the chemical shift scale. They all come back to one idea: how much electron density surrounds the nucleus.

Electron density (shielding vs. deshielding)

More electron density around a nucleus shields it from the external magnetic field, pushing the signal upfield (lower ppm). Less electron density means less shielding, so the signal moves downfield (higher ppm).

• Alkane $\text{C–H}$ protons are well-shielded and appear around 0.5–1.5 ppm.
• Aromatic protons are deshielded and appear around 6.5–8 ppm.

Electronegativity of neighboring atoms

Electronegative atoms (O, N, F, Cl) withdraw electron density from nearby protons through inductive effects, shifting those signals downfield. The closer the electronegative atom, the stronger the effect.

• $\text{CH}_3\text{F}$ (~4.3 ppm) is much further downfield than $\text{CH}_4$ (~0.2 ppm) because fluorine pulls electron density away from the protons.
• Protons on a carbon bearing an $\text{–OH}$ group typically appear around 3.2–3.8 ppm, well downfield of simple alkane protons.

Hybridization

The hybridization of the carbon a proton is attached to affects its chemical shift. $sp^2$ carbons hold electrons in orbitals with more s-character, which changes the electron distribution around nearby protons.

• $sp^3$ C–H (alkanes): ~0.5–1.5 ppm
• $sp^2$ C–H (alkenes): ~4.5–6.5 ppm
• $sp^2$ C–H (aromatic): ~6.5–8 ppm
• $sp$ C–H (alkynes): ~1.7–3.1 ppm

Notice that alkyne protons appear upfield of alkene protons despite having more s-character. This is because of magnetic anisotropy (see below), which shields the alkyne proton.

Magnetic anisotropy

Pi systems (aromatic rings, double bonds, triple bonds) generate local magnetic fields when placed in the external field. These local fields either reinforce or oppose the external field depending on geometry.

• Aromatic ring protons sit in a region where the ring current reinforces the external field, causing strong deshielding (~6.5–8 ppm).
• Protons directly above or below an aromatic ring plane experience the opposite effect and are shielded (shifted upfield). This is less common but shows up in molecules with stacked or bridged ring systems.
• Alkyne protons sit along the axis of the triple bond's cylindrical electron cloud, where the induced field opposes the external field, causing unexpected shielding.

Hydrogen bonding

Protons involved in hydrogen bonding ($\text{O–H}$, $\text{N–H}$) lose electron density to the hydrogen bond acceptor, shifting them downfield. These signals are also often broad and can appear over a wide ppm range depending on concentration, solvent, and temperature.

• Alcohol $\text{O–H}$: ~1–5 ppm (variable)
• Carboxylic acid $\text{O–H}$: ~10–12 ppm (strongly hydrogen-bonded)

Calculation of Chemical Shift Values

A key advantage of the ppm scale is that chemical shifts are independent of spectrometer frequency. A signal at 2.1 ppm on a 300 MHz instrument is still at 2.1 ppm on a 600 MHz instrument.

However, the absolute frequency difference from TMS (in Hz) does change with spectrometer strength. To convert between ppm and Hz:

$\Delta\nu \text{ (Hz)} = \delta \text{ (ppm)} \times \nu_0 \text{ (MHz)}$

where $\nu_0$ is the operating frequency of the spectrometer.

For example, a signal at 5.0 ppm on a 500 MHz spectrometer is offset from TMS by:

$5.0 \times 500 = 2500 \text{ Hz}$

On a 600 MHz spectrometer, that same signal (still at 5.0 ppm) is offset by:

$5.0 \times 600 = 3000 \text{ Hz}$

The ppm value stays the same; only the Hz separation changes. This is exactly why we report chemical shifts in ppm rather than Hz.

The spectrometer's operating frequency is determined by the magnetic field strength:

$\nu_0 = \frac{\gamma B_0}{2\pi}$

where $\gamma$ is the gyromagnetic ratio of the nucleus ($42.58 \text{ MHz/T}$ for $^1\text{H}$) and $B_0$ is the external magnetic field strength. A stronger magnet means a higher operating frequency, which gives better spectral resolution.

Additional Factors Affecting Chemical Shifts

• Solvent effects: Interactions between solvent molecules and the analyte can shift signals slightly. Deuterated chloroform ($\text{CDCl}_3$) is the most common NMR solvent, but switching to something like $\text{DMSO-d}_6$ can noticeably change $\text{O–H}$ and $\text{N–H}$ chemical shifts.
• Concentration and temperature: These particularly affect protons involved in hydrogen bonding or exchange processes, causing shifts and broadening.
• Nuclear spin requirements: Only nuclei with non-zero nuclear spin are NMR-active. Both $^1\text{H}$ and $^{13}\text{C}$ have a spin of $\frac{1}{2}$, making them the two most commonly observed nuclei in organic chemistry NMR. $^{12}\text{C}$ and $^{16}\text{O}$ have zero spin and are NMR-silent.