Chapter 9 — NMR Spectroscopy: The Most Powerful Tool for Determining Molecular Structure

"NMR is to molecules what cartography is to continents. One map is worth a thousand descriptions." — paraphrase of chemistry adage

If IR tells you what functional groups a molecule contains, and mass spectrometry tells you what molecular weight, then nuclear magnetic resonance (NMR) tells you how the atoms are connected. NMR is the most powerful single-instrument structure-determination technique in all of organic chemistry. Virtually every published synthesis paper reports NMR data; every graduate student learns to interpret NMR spectra fluently. It is the daily language of working chemists.

This chapter is an introduction. By the end you should be able to:

• Interpret a basic $^1H$ NMR spectrum: identify the number of distinct proton environments, use integration to count protons at each environment, use splitting patterns to identify neighbors.
• Understand chemical shift ($\delta$, ppm) and recognize typical values for common functional groups.
• Apply the n+1 rule to predict splitting.
• Interpret simple $^{13}C$ NMR spectra.
• Use coupling constants to assign cis/trans alkenes and other geometric features.
• Combine NMR with IR and MS to solve unknowns.
• Recognize the strengths of 2D NMR (COSY, HSQC, NOESY) for harder structures.

9.1 What NMR measures

Certain atomic nuclei (those with non-zero spin) behave like tiny magnets. The most important for organic chemistry:

• $^1H$ (proton): spin = 1/2, natural abundance > 99.98%. Most frequently used NMR nucleus.
• $^{13}C$: spin = 1/2, natural abundance 1.1%. Distinguishes carbons in a molecule.
• $^{19}F$, $^{31}P$: spin = 1/2, 100% abundance. Useful for fluorinated and phosphorus compounds.
• $^{15}N$: spin = 1/2, low abundance. Used for proteins (after isotopic enrichment).

When placed in a strong external magnetic field, these nuclei align either with or against the field (two allowed orientations for spin-1/2 nuclei). The energy gap between the two orientations is tiny (radio-frequency range) but measurable.

Irradiating the sample with radio waves of the right frequency causes the nuclei to flip from the lower to higher energy state — a "resonance." The frequency at which resonance occurs depends on the local chemical environment of the nucleus: nuclei in different chemical environments (different bonding, different neighbors) resonate at slightly different frequencies.

The chemical shift ($\delta$, in parts per million, ppm) measures how much a nucleus's resonance frequency differs from a reference standard (TMS, tetramethylsilane, by convention). Different environments → different chemical shifts.

Larmor frequency and field strength

The fundamental NMR equation: $$\omega = \gamma B_0$$

where $\omega$ = resonance frequency, $\gamma$ = gyromagnetic ratio (a nuclear constant), and $B_0$ = magnetic field strength.

For $^1H$ at 11.7 Tesla (a 500 MHz spectrometer): resonance frequency = 500 MHz. For $^{13}C$ at the same field: resonance frequency ≈ 125 MHz (because the gyromagnetic ratio of $^{13}C$ is ~25% that of $^1H$).

Modern NMR instrumentation

Modern NMR spectrometers use superconducting magnets at 11-21 Tesla (500-900 MHz). Higher field = higher resolution + sensitivity but also more expensive (a 900 MHz spectrometer costs ~$8 million). Most academic and pharmaceutical research is at 400-700 MHz; the highest-field instruments are reserved for protein NMR and other specialized work.

Typical sample requirements: - 1-10 mg of compound dissolved in 0.5-0.7 mL deuterated solvent. - Common solvents: CDCl₃ (most common), D₂O, DMSO-d₆, CD₃CN, methanol-d₄. - Acquisition time: 1 minute (¹H) to several hours (¹³C, dilute samples, 2D).

9.2 The $^1H$ NMR spectrum

A $^1H$ NMR spectrum is a plot of signal intensity vs. chemical shift. Peaks appear at positions corresponding to protons in different chemical environments.

Four pieces of information from each peak:

1. Chemical shift (position on the x-axis): tells you the electronic environment of that proton.
2. Integration (peak area): tells you how many protons are at that environment. (Relative areas, normalized.)
3. Multiplicity (splitting pattern): singlet, doublet, triplet, multiplet. Tells you how many NEIGHBORING protons there are.
4. Coupling constant ($J$, in Hz): distance between adjacent peaks within a multiplet. Tells you details about the geometry.

Figure 9.1 — Schematic $^1H$ NMR spectrum. Three environments, three multiplets. Integration (written as numbers) gives the relative proton count. Chemical shifts are on the x-axis in ppm. The TMS reference is at 0 ppm.

Chemical shift (δ)

Typical $^1H$ chemical shifts by environment:

Why these shifts? Shielding and deshielding

The chemical shift reflects the electron density around the proton: - Higher electron density → more shielding → lower δ (upfield). - Lower electron density → less shielding → higher δ (downfield).

Electronegative atoms (O, N, halogens) withdraw electron density from neighboring C-H, deshielding the H, shifting it downfield. This is why -CH₂-Cl is at 3.5 ppm, while -CH₂- in alkane is at 1.3 ppm.

Anisotropy (ring current): aromatic rings produce a ring current in the magnetic field that deshields protons in the plane of the ring (the aromatic protons themselves) but shields protons above/below the ring (e.g., axial cyclohexane protons in some conformations).

Hydrogen bonding can shift -OH or -NH protons; varies with concentration and temperature.

Integration

The total area under a peak is proportional to the number of protons causing that peak. Modern NMR spectrometers report relative integrations (e.g., "3:2:2:3" meaning four peaks in ratio 3:2:2:3).

For ethanol ($CH_3CH_2OH$): - The $CH_3$ has 3 protons. - The $CH_2$ has 2 protons. - The $OH$ has 1 proton. - Integration: 3:2:1 (after normalization).

Multiplicity — the n+1 rule

A proton's peak is split by neighboring non-equivalent protons. The number of peaks in the multiplet is $(n+1)$, where $n$ = number of neighbors.

• Singlet (s): 0 neighbors.
• Doublet (d): 1 neighbor.
• Triplet (t): 2 neighbors (on the same atom or adjacent atoms with equivalent coupling).
• Quartet (q): 3 neighbors.
• Quintet (quint) or pentet: 4 neighbors.
• Sextet (sext): 5 neighbors.
• Septet (sept): 6 neighbors (e.g., -CH(CH₃)₂ central H is split by 6 methyl H's).

For ethanol: - $CH_3$: has 2 neighboring protons (the $CH_2$). So triplet. - $CH_2$: has 3 neighbors (the $CH_3$). So quartet. (The -OH could couple too but is often exchanging.) - $OH$: often a broad singlet or not seen.

The pattern "3H triplet + 2H quartet" is nearly diagnostic for an ethyl group.

Pascal's triangle and intensities

Within a multiplet, the relative intensities follow Pascal's triangle: - Singlet: 1 - Doublet: 1:1 - Triplet: 1:2:1 - Quartet: 1:3:3:1 - Quintet: 1:4:6:4:1 - Septet: 1:6:15:20:15:6:1

For -CH(CH₃)₂ central H split by 6 equivalent CH₃ protons: intensities 1:6:15:20:15:6:1.

Coupling constants — what they tell you

The spacing between peaks in a multiplet is called the coupling constant, $J$, in Hz. Common values:

• $^3J$ (three-bond coupling, vicinal): typically 6-10 Hz for sp³-sp³.
• $^2J$ (two-bond, same carbon, geminal): 12-15 Hz for sp³ CH₂ (usually only seen in specific geometries where the two H's are diastereotopic).
• $^4J$ (four-bond, long range): 0-3 Hz for W-shaped paths; otherwise often unresolvable.

Coupling constants for alkenes are very diagnostic: - cis alkene H-H ($^3J$): 6-12 Hz (usually 7-10). - trans alkene H-H ($^3J$): 12-18 Hz (usually 15-18). - gem (same C) sp² H-H ($^2J$): 0-3 Hz.

This distinction lets you assign (E) vs (Z) alkenes by NMR.

The Karplus equation

The vicinal coupling $^3J$ depends on the dihedral angle between the two C-H bonds:

$$^3J = A\cos^2\theta + B\cos\theta + C$$

(Karplus, 1959). $A$, $B$, $C$ are constants. The result: - 0° (eclipsed) → $J$ ≈ 8-10 Hz - 60° (gauche) → $J$ ≈ 1-3 Hz - 90° → $J$ ≈ 0 Hz (lowest) - 120° → $J$ ≈ 4-7 Hz - 180° (anti) → $J$ ≈ 8-12 Hz (highest for normal sp³-sp³)

So: large $J$ = either anti or eclipsed (rare); small $J$ = gauche or perpendicular. NMR coupling tells you about conformations and stereochemistry directly.

For sp²-sp²: maximum $J$ at 0° or 180° (cis or trans alkene); much smaller (1-3 Hz) at 90° (rare in alkenes but seen in cyclic systems).

9.3 $^{13}C$ NMR

$^{13}C$ NMR is complementary to $^1H$ NMR. It shows signals for each carbon environment. Key differences:

• Chemical shift range: 0-220 ppm (vs. 0-13 for protons). Much wider, less crowding.
• No splitting (usually) due to the typical use of broadband decoupling — each carbon is a single line.
• Lower sensitivity: $^{13}C$ is only 1.1% abundant; spectra typically take 1-12 hours to acquire (vs minutes for $^1H$).

$^{13}C$ chemical shift ranges:

$^{13}C$ NMR counts carbons and classifies them. A molecule with three distinct carbon environments shows three peaks.

DEPT experiments

DEPT (Distortionless Enhancement by Polarization Transfer) experiments further classify $^{13}C$ by the number of directly attached hydrogens:

• DEPT 90: only CH peaks visible (CH₂, CH₃, and quaternary C are absent).
• DEPT 135: CH and CH₃ peaks point UP, CH₂ points DOWN, quaternary C is invisible.
• Comparison with regular ¹³C: quaternary C appears in regular ¹³C but not in DEPT.

A complete DEPT analysis lets you classify every carbon as CH₃, CH₂, CH, or quaternary.

Sample DEPT interpretation

A molecule's regular ¹³C shows 5 peaks. The DEPT 135 shows: - 1 up, 1 down, 1 up, no peak (i.e., quaternary), 1 up.

So the carbons are: CH₃ (or CH), CH₂, CH₃ (or CH), quaternary, CH₃ (or CH). DEPT 90 distinguishes CH from CH₃: only CH peaks appear.

9.4 2D NMR — bringing it together

For more complex molecules, 2D NMR experiments give correlations between nuclei. Common ones:

COSY (Correlation Spectroscopy)

$^1H$-$^1H$ correlations. Shows which protons are coupled (J-coupled, i.e., neighbors). Fastest 2D experiment; used for assigning connectivity.

HSQC (Heteronuclear Single Quantum Coherence)

$^1H$-$^{13}C$ one-bond correlations. Shows which proton is attached to which carbon. Reveals a "carbon environment for each proton."

HMBC (Heteronuclear Multiple Bond Correlation)

$^1H$-$^{13}C$ multi-bond correlations (typically 2-4 bonds). Shows which carbons are near a given proton, even if not directly attached. Useful for assigning quaternary carbons.

NOESY (Nuclear Overhauser Effect Spectroscopy)

$^1H$-$^1H$ through-space correlations. Shows protons close in space (≤5 Å), independent of bond connectivity. Useful for stereochemistry: cis substituents on a ring give NOE; trans don't.

ROESY (rotating-frame NOE)

Similar to NOESY but better for medium-sized molecules.

TOCSY (Total Correlation Spectroscopy)

Shows all protons in a J-coupled spin system. Useful for sugars and proteins.

1D NOE (selective)

Saturate one resonance; observe enhancement at others (within ~5 Å). Used to assign cis/trans on rings or to distinguish closely-related stereoisomers.

9.5 NMR and stereochemistry

NMR's connection to Chapter 7 stereochemistry:

cis/trans and E/Z by coupling constants

• (Z)-2-butene: methyl-vinyl coupling $J \approx 11$ Hz (cis).
• (E)-2-butene: methyl-vinyl coupling $J \approx 17$ Hz (trans).

Just by looking at coupling constants in the alkene region, you can usually distinguish (E) from (Z).

NOE and 3D structure

NOESY tells you which protons are within ~5 Å in space, regardless of bonds. For a cyclohexane with two substituents: - If both axial (or both equatorial): they are cis (close in space). - If one axial, one equatorial: they may be trans (far apart) or cis (closer if both equatorial alternately).

Diastereotopic protons

A -CH₂- next to a stereocenter has two diastereotopic protons. They show up as two separate NMR signals (not equivalent), often as an "AB pattern" or "ABX pattern." This is how you can detect a chiral center even without optical rotation.

Chiral shift reagents

Adding a chiral lanthanide complex (Eu(hfc)₃, etc.) to a chiral molecule shifts the two enantiomers' signals to different positions. Lets you measure ee directly by NMR (without chiral HPLC).

9.6 Combining information: solving an unknown

Every modern NMR-based structure determination uses all four pieces of information (chemical shift, integration, multiplicity, coupling). Plus two or more of: DEPT, COSY, HSQC, HMBC, NOESY, and other 2D methods in harder cases.

Basic workflow:

1. Count distinct proton environments (from peak count).
2. Determine proton counts (from integration).
3. Identify each environment (from chemical shift).
4. Identify neighbors (from multiplicity).
5. Assemble the structure by fitting environments together.
6. (For complex cases) Use 2D NMR to verify connectivity.

Worked Problem 9.1 — Ethanol

A $^1H$ NMR spectrum shows: - Triplet at δ 1.18, integration 3H, $J = 7$ Hz - Quartet at δ 3.65, integration 2H, $J = 7$ Hz - Broad singlet at δ 2.5 (variable, integration 1H)

Interpretation: - 3H triplet at 1.18: a CH₃ group, with 2 neighbors (so adjacent to CH₂). Chemical shift is alkyl. - 2H quartet at 3.65: a CH₂ group, with 3 neighbors (so adjacent to CH₃). Chemical shift is α to O. - 1H broad singlet at 2.5: an OH proton (variable, exchangeable).

Structure: $CH_3CH_2OH$ (ethanol).

Worked Problem 9.2 — Identifying an isomer of C₄H₁₀O

An unknown $C_4H_{10}O$ has: - 6H doublet at δ 1.16, $J = 6$ Hz - 1H multiplet (septet) at δ 4.0 - 1H broad singlet at δ 2.5 (variable, OH)

Interpretation: - 6H doublet: two equivalent CH₃ groups, each with 1 neighbor. Implies an iPr group. - 1H septet at 4.0: a CH adjacent to 6 equivalent CH₃ H's. The 4.0 ppm shift suggests α to O. - 1H broad: -OH.

Structure: $(CH_3)_2CH-OH$ = isopropanol (2-propanol).

Worked Problem 9.3 — Combined IR + NMR

Compound $C_3H_6O$: - IR: strong C=O at 1715 cm⁻¹; no broad O-H. - ¹H NMR: 6H singlet at δ 2.15.

Interpretation: - C=O present but no -OH → ketone or aldehyde. - 6H singlet at 2.15 ppm: 6 equivalent H's, no neighbors. Two equivalent CH₃ groups, each isolated. - Chemical shift of 2.15 is characteristic of CH₃ adjacent to C=O (acetyl).

Structure: $CH_3-C(=O)-CH_3$ = acetone (propan-2-one).

Spectroscopy Clue 9.1 — How to see a chiral center in NMR

A chiral center near a -CH₂- group makes the two H's of that CH₂ diastereotopic — they show up as an AB or ABX pattern (two coupled doublets), not a single peak. This is a sign of nearby chirality.

9.7 Practical NMR — what you'll see in the lab

In a typical organic chemistry lab class: - Sample: 1-10 mg of compound dissolved in 0.5-0.7 mL of CDCl₃. - Acquire ¹H NMR (1-5 minutes). - Acquire ¹³C NMR (10-60 minutes for adequate signal/noise). - Acquire DEPT 135 (5-15 minutes).

For research: - Acquire 2D experiments (COSY, HSQC, HMBC) — typically 1-4 hours each. - For chiral compounds: acquire NMR with chiral shift reagent. - For unknowns: use all 1D + 2D + IR + MS together.

Chemical exchange and dynamic NMR

Some molecules undergo chemical exchange (e.g., amine N-H exchange with water; tautomerization; ring flips). NMR signals can be: - Sharp if exchange is fast on the NMR timescale. - Broad if exchange is on the NMR timescale. - Two separate signals if exchange is slow on the NMR timescale.

Dynamic NMR can extract barrier heights (ring flip barriers, tautomerization rates) from temperature-dependence of NMR.

Solvent residual peaks

Each NMR solvent has small residual signals (the deuterated solvent has tiny ¹H impurity): - CDCl₃: residual CHCl₃ at δ 7.26. - DMSO-d₆: residual CHD₂SOCD₃ at δ 2.50. - D₂O: residual HOD at δ 4.79.

Plus solvent ¹³C peaks (CDCl₃ at 77 ppm; DMSO at 39 ppm).

9.8 Connections to other chapters

• Chapter 4: functional groups have characteristic ¹H and ¹³C chemical shifts.
• Chapter 6: IR and MS work alongside NMR for structure determination.
• Chapter 7: stereoisomers have distinct NMR (cis/trans alkenes; chiral centers via diastereotopic protons).
• Chapter 8: stereochemistry of products is verified by NMR.
• Every reaction chapter from Ch 10 onward: NMR is the workhorse for product characterization.
• Chapter 33: protein NMR (with $^{15}N$ labeling) determines 3D protein structures.

9.9 Summary

1. NMR measures magnetic nuclei's resonance in a magnetic field. Different environments → different chemical shifts.

2. $^1H$ NMR: four pieces of info per peak: chemical shift, integration, multiplicity, coupling constants.

3. Chemical shift table: alkyl 0.7-1.5, α to carbonyl 2.0-2.5, α to O 3.3-4.0, vinyl 4.5-6.5, aromatic 6.5-8.5, aldehyde 9-10, carboxylic acid 10-13.

4. n+1 rule: a proton with $n$ non-equivalent neighbors shows $n+1$ peaks. Pascal's triangle gives intensities.

5. Coupling constants: $^3J$ for sp³ ≈ 6-10 Hz; cis alkene $^3J$ ≈ 7-10 Hz; trans alkene $^3J$ ≈ 15-18 Hz. Diagnostic for E/Z.

6. Karplus equation: $^3J$ depends on dihedral angle. Maximum at 0° and 180°; minimum at 90°.

7. $^{13}C$ NMR: complementary to $^1H$ NMR; broader chemical shift range (0-220 ppm); single line per carbon (with broadband decoupling).

8. DEPT distinguishes CH₃, CH₂, CH, and quaternary carbons.

9. 2D NMR: COSY (¹H-¹H), HSQC (¹H-¹³C one-bond), HMBC (¹H-¹³C multi-bond), NOESY (through-space). Essential for complex structures.

10. Stereochemistry by NMR: cis/trans by coupling constants; chiral center by diastereotopic protons; 3D by NOESY.

11. Modern instrumentation: 400-900 MHz superconducting magnets; samples in deuterated solvents.

You now have the three major spectroscopic tools: IR (Chapter 6), MS (Chapter 6), NMR (Chapter 9). Every compound you meet in the rest of the book can be identified with these tools (in combination with your functional-group vocabulary from Chapter 4).

Part II ends here. Part III — Substitution and Elimination — starts with Chapter 10 and the first mechanism chapters.