15.11.02 · orgchem / spectroscopy-organic

1H NMR: chemical shift, coupling constants, integration, and 2D NMR

stub3 tiersLean: nonepending prereqs

Anchor (Master): Claridge — High-Resolution NMR Techniques in Organic Chemistry, 3e (2016)

Intuition Beginner

A proton NMR spectrum gives you three independent pieces of information about every group of hydrogen atoms in a molecule: where the signal appears, how big it is, and how it splits. These three readouts — chemical shift, integration, and coupling — are often enough to identify the molecule outright.

Chemical shift is the horizontal position of a signal, measured in parts per million (ppm). It reports on the electronic environment around each proton. Electronegative atoms (O, N, halogens) pull electron density away from nearby protons, leaving them less shielded from the external magnetic field. Less-shielded protons resonate further downfield (higher ppm). Protons in alkyl regions (surrounded only by C and H) appear near 0–2 ppm; protons next to oxygen appear near 3–4 ppm; aromatic protons near 7–8 ppm; aldehyde protons near 9–10 ppm.

Integration is the area under each signal, which is proportional to the number of protons producing that signal. A peak with twice the area of another corresponds to twice as many equivalent protons. The ratio of integration values across all signals matches the ratio of proton counts in each chemically distinct environment.

Coupling is the splitting of a signal into multiple lines caused by neighbouring protons. A proton next to one other proton appears as a doublet (two lines). Next to two equivalent protons, a triplet. Three equivalent neighbours, a quartet. The pattern follows the n+1 rule: $n$ equivalent neighbouring protons split the signal into $n + 1$ lines. This tells you how many protons are on the adjacent carbon.

Visual Beginner

A proton NMR spectrum is read from right (low ppm, upfield) to left (high ppm, downfield). Each signal is a peak or group of peaks rising from a baseline. The horizontal axis is chemical shift in ppm; the vertical axis is signal intensity.

Typical chemical-shift regions: alkyl protons (0–2 ppm), allylic and protons alpha to carbonyls (2–3 ppm), protons on carbons bonded to oxygen or nitrogen (3–4.5 ppm), aromatic protons (6.5–8.5 ppm), aldehyde protons (9–10 ppm), carboxylic acid protons (10–12 ppm).

Worked example Beginner

Assign the $^{1}$ H NMR spectrum of 1-bromopropane ( $C H_{3} C H_{2} C H_{2} Br$ ).

1-Bromopropane has seven protons in three chemically distinct groups:

$C H_{3}$ — the terminal methyl (3H), furthest from bromine.
$C H_{2}$ — the central methylene (2H), one carbon away from bromine.
$C H_{2} Br$ — the methylene bonded to bromine (2H), most deshielded.

Signal A: triplet at 1.0 ppm, integration 3H. The terminal methyl is in the alkyl region (1.0 ppm). It is adjacent to the central CH $_{2}$ with 2 protons, so $n = 2$ and the n+1 rule gives 3 lines (triplet).

Signal B: sextet at 1.9 ppm, integration 2H. The central CH $_{2}$ is slightly deshielded by the nearby bromine (1.9 ppm). It is adjacent to the terminal CH $_{3}$ (3H) and the CH $_{2}$ Br (2H) — five equivalent neighbouring protons — giving $n = 5$ and 6 lines (sextet).

Signal C: triplet at 3.4 ppm, integration 2H. The CH $_{2}$ Br is significantly deshielded by the electronegative bromine (3.4 ppm). It is adjacent to the central CH $_{2}$ with 2 protons, giving a triplet ( $n = 2$ , so 3 lines).

The three signals, their chemical shifts (increasing with proximity to Br), splitting patterns, and integration ratios (3:2:2) uniquely identify 1-bromopropane.

Check your understanding Beginner

Formal definition Intermediate+

The three observables of $^{1}$ H NMR — chemical shift, coupling, and integration — each arise from a distinct term in the spin Hamiltonian.

Chemical shift arises because electrons around each nucleus generate a local field that opposes the applied field $B_{0}$ . The effective field at nucleus $i$ is:

B_{eff, i} = B_{0} (1 - σ_{i})

where $σ_{i}$ is the shielding constant. The chemical shift is defined relative to tetramethylsilane (TMS):

δ_{i} = \frac{ν _{i} - ν _{TMS}}{ν _{spectrometer}} \times 1 0^{6} (ppm)

The shielding constant is a tensor, but rapid molecular tumbling in solution averages it to its isotropic value. The isotropic chemical shift has three contributions: the diamagnetic term (always shielding, proportional to electron density), the paramagnetic term (deshielding, arising from mixing of ground and excited electronic states), and the ring-current contribution (anisotropic, responsible for the downfield shift of aromatic protons and the upfield shift of protons shielded above an aromatic ring).

Spin-spin coupling (J-coupling) arises through the bonding electrons. The Hamiltonian for two coupled spins is:

\hat{H} = - ν_{A} \hat{I}_{z, A} - ν_{B} \hat{I}_{z, B} + J_{A B} \hat{I}_{A} \cdot \hat{I}_{B}

where $J_{A B}$ is the scalar coupling constant in Hz. The coupling is independent of the external field strength (unlike chemical shift in Hz, which scales linearly with $B_{0}$ ). This field-independence is diagnostically useful: the coupling pattern in Hz remains the same regardless of spectrometer frequency, while the chemical-shift separation in Hz grows with field.

Coupling constants are labelled by the number of bonds: $^{1} J$ (one-bond, rarely observed in $^{1}$ H NMR because directly bonded H's are geminal only on the same carbon), $^{2} J$ (geminal, two bonds, typically $- 10$ to $- 15$ Hz for CH $_{2}$ groups), $^{3} J$ (vicinal, three bonds, 0–18 Hz, the most diagnostically useful), and $^{4} J$ (long-range, 0–3 Hz, observed in rigid or conjugated systems).

The Karplus relationship connects the vicinal coupling constant $^{3} J_{H H}$ to the dihedral angle $ϕ$ :

^{3} J_{H H} = A + B cos ϕ + C cos 2 ϕ

For an ethane fragment with typical substituents, $^{3} J$ is large for $ϕ = 0^{\circ}$ (cis, $\sim$ 12 Hz) and $ϕ = 18 0^{\circ}$ (trans, $\sim$ 8 Hz), and small for $ϕ = 9 0^{\circ}$ ( $\sim$ 2 Hz). This relationship is a direct structural probe of conformation from NMR data.

Integration relies on the proportionality between the area under an NMR signal and the number of nuclei contributing to it. In the linear-response regime (small flip angle or full relaxation between scans), the integrated intensity is:

A_{i} \propto N_{i} \cdot (1 - e^{- T_{R} / T_{1, i}}) \cdot sin α

where $N_{i}$ is the number of equivalent protons, $T_{R}$ is the repetition time, $T_{1, i}$ is the longitudinal relaxation time, and $α$ is the flip angle. For quantitative integration, $T_{R} \geq 5 T_{1}$ ensures that all protons are fully relaxed and the integrated area is proportional to $N_{i}$ alone.

First-order vs second-order spectra. The n+1 rule applies only in the weak-coupling limit where $∣Δ ν ∣ ≫ ∣ J ∣$ (the chemical-shift difference in Hz is much larger than the coupling constant). The ratio $Δ ν / J$ quantifies this: values above 10 give clean first-order spectra; below 10, second-order effects (roofing, extra lines, non-binomial intensities) appear. Higher magnetic fields increase $Δ ν$ (in Hz) without changing $J$ , pushing more spin systems into the first-order regime — one of the principal motivations for high-field magnets.

FT-NMR basics. Modern NMR spectrometers do not sweep frequency. Instead, a short radio-frequency pulse excites all nuclei simultaneously. The resulting free induction decay (FID) — a sum of decaying sinusoids at the Larmor frequencies of all nuclei — is digitised and Fourier-transformed to produce the frequency-domain spectrum. The signal-to-noise ratio improves as the square root of the number of transients (scans), so that $n$ scans give $n$ improvement. This $n$ sensitivity gain is the Ernst sensitivity theorem.

Counterexamples to common slips

The n+1 rule counts only equivalent neighbouring protons. If a proton is adjacent to two protons that are not equivalent (different chemical shifts), the splitting is $(n_{1} + 1) (n_{2} + 1)$ , not $(n_{1} + n_{2}) + 1$ . A proton flanked by one proton at 3.5 ppm and another at 4.0 ppm appears as a doublet of doublets, not a triplet.
Integration gives ratios, not absolute counts. An integration ratio of 1:2:3 could mean 1H:2H:3H or 2H:4H:6H. The molecular formula is required to resolve the ambiguity.
Chemical shift is dimensionless. Although reported in ppm, the shift is not a concentration. The ppm scale normalises for spectrometer frequency: a shift of 1.0 ppm corresponds to 400 Hz on a 400 MHz spectrometer and 500 Hz on a 500 MHz spectrometer. The coupling constant $J$ , by contrast, is in Hz and does not change with field strength.
Coupling does not occur through space. J-coupling is transmitted through the bonding electrons (Fermi contact mechanism), not through space. Protons that are spatially close but not connected by bonds do not show J-coupling — their through-space interaction is the nuclear Overhauser effect, which is a relaxation phenomenon, not a coupling.

Key theorem with proof Intermediate+

Proposition (First-order splitting). Let nucleus A be coupled to $n$ equivalent spin-1/2 nuclei B with coupling constant $J_{A B}$ , and let the chemical-shift difference $∣ δ_{A} - δ_{B} ∣$ satisfy $∣Δ ν ∣ ≫ J_{A B}$ . Then the signal for A consists of $n + 1$ equally-spaced lines separated by $J_{A B}$ Hz, with relative intensities given by the binomial coefficients $(0 n), (1 n), \dots, (n n)$ .

Proof. Each of the $n$ equivalent B spins can be in state $α$ ( $m = + 1/2$ ) or $β$ ( $m = - 1/2$ ). The total magnetic quantum number of the B spins is $m_{B} = m_{1} + m_{2} + \dots + m_{n}$ . The number of B-spin configurations giving a particular value of $M$ (the number of $α$ spins) is $(M n)$ . Each value of $m_{B}$ shifts the A resonance by $J_{A B} \cdot m_{B}$ Hz. The distinct values of $m_{B}$ are $- n /2, - n /2 + 1, \dots, + n /2$ , giving $n + 1$ equally-spaced lines separated by $J_{A B}$ Hz. The intensity of each line is proportional to the number of B-spin configurations producing it, which is $(M n)$ for $M = 0, 1, \dots, n$ . The weak-coupling condition ensures that the A and B transitions do not mix, so each line remains independent. $■$

Bridge. The first-order splitting theorem is the direct continuation of the Zeeman-splitting and spin-Hamiltonian framework in 15.11.01. The same spin Hamiltonian, when the chemical-shift difference is large, factorises into independent subspaces that produce the binomial intensity pattern. When the shift difference is small (second-order regime), the Hamiltonian does not factorise and the full matrix must be diagonalised — this is the entry point for the product-operator formalism used in the Master tier to design and analyse 2D experiments.

Exercises Intermediate+

Exercise 5 (medium, short-answer).

Predict the $^{1}$ H NMR splitting pattern for the vinyl protons in vinyl acetate ( $C H_{2} = CHOCOC H_{3}$ ). The three vinyl protons are not chemically equivalent.

Hint

The three protons on the double bond have different chemical shifts (cis, trans, and geminal relative to the acetoxy group). Each proton is coupled to the other two with different coupling constants ( $^{3} J_{trans} \approx 17$ Hz, $^{3} J_{cis} \approx 10$ Hz, $^{2} J_{gem} \approx 2$ Hz).

Answer

Each of the three vinyl protons is coupled to the other two with different coupling constants (nonequivalent neighbours). Therefore each proton appears as a doublet of doublets rather than a simple triplet. The proton trans to the acetoxy group shows splitting of approximately 17 Hz (trans coupling) and 2 Hz (geminal coupling). The proton cis to the acetoxy group shows splitting of approximately 10 Hz (cis coupling) and 2 Hz (geminal coupling). Because the neighbours are not equivalent, the n+1 rule does not apply and the pattern is $(n_{1} + 1) (n_{2} + 1) = 2 \times 2 = 4$ lines per proton.

Exercise 6 (hard, short-answer).

Predict the $^{1}$ H NMR spectrum of 1,1,2-trichloroethane ( $C l_{2} CHC H_{2} Cl$ ) at 400 MHz. How many signals, what splitting patterns, and what integration? If the same compound were recorded at 60 MHz, would the spectrum change qualitatively?

Hint

The CH proton and the CH $_{2}$ protons are not equivalent. Apply the n+1 rule, then consider whether $Δ ν / J$ is large enough for first-order analysis at both fields.

Answer

Two distinct proton environments: CH (1H) and CH $_{2}$ (2H). At 400 MHz, the shift difference in Hz is large relative to $J$ , giving a first-order spectrum: the CH appears as a triplet ( $n = 2$ from CH $_{2}$ ) and the CH $_{2}$ appears as a doublet ( $n = 1$ from CH). Integration 1:2.

At 60 MHz, $Δ ν$ in Hz shrinks by a factor of 400/60 $\approx$ 6.7. If the coupling constant is comparable to the reduced $Δ ν$ , the ratio $Δ ν / J$ may fall below 10, producing second-order effects: the clean triplet and doublet distort into an ABX pattern with roofing, extra lines, and non-binomial intensities. The spectrum would change qualitatively from first-order to second-order.

2D NMR and advanced structure elucidation Master

One-dimensional $^{1}$ H NMR provides chemical shift, coupling, and integration for each proton environment. For simple molecules this is sufficient. For complex molecules — natural products, pharmaceuticals, peptides — the 1D spectrum is congested and ambiguous: overlapping multiplets, unresolved couplings, and the inability to trace connectivity across quaternary centres or heteroatoms. Multidimensional NMR resolves these problems by spreading the information across two frequency axes.

The principle of all 2D experiments is the same: a pulse sequence creates coherence on one set of spins, transfers it to another set during a mixing period, and detects the result. A 2D Fourier transform maps the data onto a plane with two independent frequency axes. Cross-peaks (off-diagonal signals) connect nuclei that are related by the specific interaction probed by the experiment. The concept was proposed by Jeener in 1971 and developed by Ernst and coworkers into the family of experiments described below.

COSY — Correlation Spectroscopy

COSY detects through-bond proton-proton coupling. A cross-peak at coordinates ( $δ_{A}$ , $δ_{B}$ ) indicates that protons A and B are J-coupled, typically through two or three bonds. The diagonal of a COSY spectrum reproduces the 1D spectrum; the useful information is in the off-diagonal cross-peaks.

For a molecule with several coupled spin systems, COSY traces out the proton connectivity network. In ethyl acetate, a single COSY cross-peak connects the OCH $_{2}$ quartet (4.1 ppm) and the CH $_{3}$ triplet (1.3 ppm), confirming that these two groups are adjacent. The acetyl methyl (2.0 ppm) has no cross-peaks — it is isolated from the ethyl protons by the carbonyl, confirming the structure.

Phase-sensitive COSY (the modern standard) uses States-TPPI or Echo-Antiecho detection to preserve the sign of cross-peak phase, allowing discrimination of active coupling (the coupling responsible for the cross-peak, appearing in anti-phase) from passive couplings (additional splittings within the cross-peak, appearing in-phase). This phase information resolves ambiguities in crowded spectra where cross-peaks overlap.

Double-quantum filtered COSY (DQF-COSY) suppresses singlet peaks on the diagonal (which carry no correlation information and can obscure nearby cross-peaks) by selecting only double-quantum coherence during the mixing period. DQF-COSY is the default COSY experiment in modern organic-chemistry practice because the clean diagonal suppression reveals cross-peaks between protons with similar chemical shifts that would be hidden under the diagonal in a standard COSY.

HSQC and HMQC — Heteronuclear Single/Multiple Quantum Coherence

HSQC correlates each proton with the carbon it is directly bonded to via the one-bond coupling $^{1} J_{C H}$ (125–170 Hz). Each proton signal appears as a cross-peak connecting its $^{1}$ H chemical shift (F2 axis) to its parent carbon's $^{13}$ C chemical shift (F1 axis). HSQC is the most commonly used 2D experiment for organic structure determination because it provides unambiguous C-H pair assignments.

The $^{13}$ C dimension of HSQC has much larger chemical-shift dispersion ( $\sim$ 200 ppm) than the $^{1}$ H dimension ( $\sim$ 12 ppm), resolving overlapping proton signals that are inseparable in 1D $^{1}$ H NMR. Two protons at 3.50 and 3.55 ppm that overlap in the 1D spectrum are readily separated if their carbons resonate at 55 and 72 ppm in the HSQC.

HMQC (Heteronuclear Multiple Quantum Coherence) provides the same one-bond correlation as HSQC but via a different coherence-transfer pathway. HMQC has $^{1}$ H- $^{1}$ H coupling active during the evolution period, producing cross-peaks that are broadened along the indirect ( $^{13}$ C) dimension. HSQC gives higher $^{13}$ C resolution and is generally preferred, but HMQC uses fewer pulses and can be more robust on older spectrometers.

HMBC — Heteronuclear Multiple Bond Correlation

HMBC detects protons coupled to carbons two or three bonds away via long-range couplings $^{2} J_{C H}$ and $^{3} J_{C H}$ (0–10 Hz). The experiment is optimised for a small coupling constant (typically set to 8 Hz), which selects against the large one-bond coupling that HSQC detects. HMBC cross-peaks therefore connect protons to non-adjacent carbons.

The critical utility of HMBC is bridging across quaternary centres and functional groups where no directly bonded C-H pair exists. A proton on one side of a carbonyl shows an HMBC cross-peak to the carbonyl carbon, identifying the carbonyl's position in the skeleton. Aromatic substitution patterns are assigned by HMBC: a proton ortho to a substituent shows a three-bond cross-peak to the ipso carbon of the substituent.

HMBC is always recorded alongside HSQC. The HSQC identifies which carbons bear protons; HMBC connects those protons to the remaining carbons (quaternary carbons, carbonyls, substituted aromatics). Together, they map the complete carbon framework.

NOESY and ROESY — Through-space correlation

NOESY (Nuclear Overhauser Effect Spectroscopy) detects through-space proximity, not through-bond coupling. The NOE intensity depends on $r^{- 6}$ (internuclear distance to the minus sixth power), making it effective for proton-proton distances under approximately 5 Angstroms. A NOESY cross-peak indicates that two protons are spatially close, regardless of how many bonds separate them.

The principal application of NOESY is assigning relative stereochemistry. Two protons that are cis on a ring or a double bond are spatially close and show a strong NOESY cross-peak; the trans arrangement places them further apart and gives a weak or absent cross-peak. For acyclic systems, the NOESY pattern constrains the rotameric population and identifies the dominant conformation.

ROESY (Rotating-frame Overhauser Spectroscopy) is a variant that gives positive NOEs for all molecular sizes. The conventional NOE changes sign for molecules with molecular weights near 1000–2000 Da (where $ω τ_{c} \approx 1$ ), passing through zero at the crossover — a problem for mid-sized organic molecules. ROESY avoids this sign change. For synthetic organic chemistry (MW 200–2000), ROESY is often preferred.

TOCSY — Total Correlation Spectroscopy

TOCSY extends COSY by transferring magnetisation across an entire J-coupled spin system through isotropic mixing. All protons within a continuous J-coupled network appear as cross-peaks, even those not directly coupled to each other. In a peptide, TOCSY identifies all protons belonging to a single amino acid residue because the J-coupled network of each residue is isolated from its neighbours by the amide bond.

The standard structure-elucidation workflow

For a molecule of unknown structure, the standard protocol combines all of the above experiments:

Obtain the molecular formula by high-resolution mass spectrometry.
Record 1D $^{1}$ H and $^{13}$ C spectra. Count signals, note chemical-shift ranges, measure integration ratios.
Assign C-H pairs by HSQC. Each cross-peak identifies a carbon that bears at least one proton.
Trace proton connectivity by COSY. Cross-peaks map adjacent proton pairs.
Bridge across quaternary centres and functional groups by HMBC. Long-range C-H correlations complete the carbon skeleton.
Assign stereochemistry by NOESY/ROESY and coupling-constant analysis (Karplus relationship).

This protocol determines the full structure, including relative stereochemistry, for most organic molecules up to MW $\sim$ 1000. For larger molecules (peptides, natural products), isotopic labelling ( $^{15}$ N, $^{13}$ C) and triple-resonance experiments extend the same logic.

Product-operator formalism

All of the 2D experiments above are described compactly by the product-operator formalism, which represents the density matrix as a linear combination of Cartesian spin operators ( $\hat{I}_{x}, \hat{I}_{y}, \hat{I}_{z}$ ) and their products. Chemical-shift evolution rotates operators in the $x y$ -plane; J-coupling evolution creates anti-phase terms (e.g., $2 \hat{I}_{x} \hat{S}_{z}$ ); radio-frequency pulses rotate operators about specified axes. Each step of a pulse sequence is a deterministic transformation of the operator basis. The observed signal is read off from the coefficient of $\hat{I}_{x}$ or $\hat{I}_{y}$ at the start of acquisition.

This formalism makes pulse-sequence design into a constructive algebraic exercise. The COSY transfer pathway is $- \hat{I}_{y} J 2 \hat{I}_{x} \hat{S}_{z} π / 2_{x} - 2 \hat{I}_{x} \hat{S}_{y}$ , where the final anti-phase term on S generates cross-peaks. The HSQC pathway is $- \hat{I}_{y}^{1} J_{C H} 2 \hat{I}_{x} \hat{S}_{z} t_{1} 2 \hat{I}_{x} \hat{S}_{z} cos (Ω_{S} t_{1})^{1} J_{C H} - \hat{I}_{y} cos (Ω_{S} t_{1})$ , encoding the $^{13}$ C chemical shift $Ω_{S}$ in the $t_{1}$ dimension while returning observable magnetisation to $^{1}$ H for detection. Every 2D experiment follows the same pattern: preparation, evolution (encoding the indirect dimension), mixing (transferring coherence), and detection.

Variable-temperature and dynamic NMR

Many organic molecules undergo conformational or chemical exchange processes that are slow on the NMR timescale at room temperature, giving separate signals for each exchanging species. Variable-temperature (VT) NMR records spectra at multiple temperatures to observe the transition from slow to fast exchange.

At low temperature (slow exchange), the two sites give separate peaks. As temperature increases, the peaks broaden, coalesce into a single broad peak at the coalescence temperature ( $k_{ex} = π Δ ν / 2$ ), and finally sharpen into a single peak at the population-weighted average shift (fast exchange). The coalescence temperature yields the activation free energy via the Eyring equation.

Dynamic NMR (DNMR) extends VT-NMR by fitting the full lineshape at each temperature to the Bloch-McConnell equations, extracting exchange rates at intermediate temperatures and providing activation parameters from an Eyring plot. The ring-flip of cyclohexane ( $Δ G^{‡} \approx 42$ kJ/mol) and the rotation about partial double bonds in amides are classic applications.

Synthesis. The 2D experiments form a coherent toolkit because they all exploit the same spin Hamiltonian, selecting different terms through pulse-sequence design. COSY selects the $^{1}$ H- $^{1}$ H J-coupling term. HSQC selects the one-bond $^{1}$ H- $^{13}$ C term. HMBC selects the long-range $^{1}$ H- $^{13}$ C term. NOESY selects the dipolar cross-relaxation term. Each experiment is a different "filter" on the same underlying spin physics, and the product-operator formalism provides the unified language for designing and understanding all of them.

Connections Master

Carbon-13 NMR and DEPT 15.11.03 pending. Proton NMR provides half of the structure-elucidation toolkit; $^{13}$ C NMR and DEPT complete it. HSQC directly correlates the $^{1}$ H and $^{13}$ C dimensions, making the two techniques inseparable in practice. The $^{13}$ C chemical-shift range ( $\sim$ 200 ppm) is far larger than the $^{1}$ H range ( $\sim$ 12 ppm), providing the dispersion needed to resolve overlapping proton signals in the 2D experiments described here.
NMR spectroscopy fundamentals 15.11.01. This unit deepens the three observables introduced in 15.11.01: chemical shift, coupling, and integration. The first-order splitting theorem, the Karplus relationship, and the second-order regime are the intermediate-tier content that was deferred from the introductory unit. The 2D experiments are the master-tier extension of the same spin Hamiltonian.
Stereoisomerism 15.01.03. Diastereotopic protons — the two protons of a CH $_{2}$ group adjacent to a stereocentre — have different chemical shifts and give an AB subspectrum. NOESY cross-peaks assign relative stereochemistry (cis vs trans on a ring). The Karplus relationship constrains dihedral angles from coupling constants. NMR is the primary experimental tool for assigning stereochemistry in solution.
Retrosynthetic analysis 15.10.01. Structure elucidation by NMR is the analytical counterpart to retrosynthesis. The retrosynthetic planner proposes a target structure; NMR confirms or refutes it. The HMBC and COSY connectivities directly verify the disconnections and synthons of the retrosynthetic plan.
Amino acids and protein chemistry 15.12.01. Protein NMR uses the same pulse-sequence logic (HSQC, NOESY, TOCSY) with isotopic labelling and triple-resonance experiments. The small-molecule 2D techniques developed here are the direct prerequisites for understanding protein NMR.
Symmetry and group theory 16.02.01. The number of distinct $^{1}$ H NMR signals equals the number of proton environments not related by any symmetry operation. Symmetry analysis predicts the signal count; the experimental spectrum tests the proposed symmetry.

Historical notes Master

The development of proton NMR from a physics curiosity to the most powerful structural tool in organic chemistry proceeded through several key advances.

The first high-resolution $^{1}$ H NMR spectra, recorded in the early 1950s by Arnold, Dharmatti, and Packard at Varian, showed three distinct peaks for ethanol (CH $_{3}$ , CH $_{2}$ , OH) and demonstrated that the chemical shift contained structural information. The discovery of spin-spin splitting by Gutowsky, McCall, and Slichter (1951) and independently by Hahn and Maxwell (1951) added the second dimension of structural information — connectivity between neighbouring protons. The n+1 rule emerged from the weak-coupling analysis of these spectra and was formalised through the spin-Hamiltonian treatment.

The Karplus relationship, derived by Martin Karplus in 1959 from valence-bond theory, connected the vicinal coupling constant to the dihedral angle and transformed J-coupling from a qualitative pattern-recognition tool into a quantitative conformational probe. The relationship was initially controversial because the original valence-bond treatment gave only approximate agreement with experiment, but empirical parametrisation by Bothner-By and others in the 1960s demonstrated its accuracy for a wide range of organic fragments.

Fourier-transform NMR, introduced by Ernst and Anderson in 1966, replaced the slow continuous-wave sweep with a broadband pulse and Fourier transformation. This increased sensitivity by orders of magnitude and made the signal-averaging needed for $^{13}$ C NMR practical. Ernst received the 1991 Nobel Prize for this work and its extension to two dimensions.

Two-dimensional NMR was proposed by Jeener in 1971 (an unpublished lecture at the Ampere Summer School) and developed into practical experiments by Ernst, Bodenhausen, and Wokaun through the 1970s and 1980s. The COSY experiment was the first 2D NMR method to see routine use in organic chemistry. HSQC and HMBC, developed in the 1980s by Bodenhausen, Ruben, and Bax, became standard with the advent of gradient-selected pulse sequences in the 1990s, which reduced artefacts and shortened experiment times. Ad Bax and his coworkers at the NIH developed many of the heteronuclear 2D experiments now in routine use, including the sensitivity-enhanced HSQC and the gradient-selected HMBC.

Kurt Wuthrich received the 2002 Nobel Prize in Chemistry for developing NMR methods for determining three-dimensional protein structures in solution, extending the 2D techniques described here to biological macromolecules through triple-resonance experiments on isotopically labelled proteins.

Bibliography Master

@book{McMurry2019,
  author = {McMurry, J.},
  title = {Organic Chemistry},
  edition = {10th},
  publisher = {Cengage},
  address = {Boston},
  year = {2019},
}

@book{Pavia2015,
  author = {Pavia, D. L. and Lampman, G. M. and Kriz, G. S. and Vyvyan, J. R.},
  title = {Introduction to Spectroscopy},
  edition = {5th},
  publisher = {Cengage},
  address = {Stamford},
  year = {2015},
}

@book{Claridge2016,
  author = {Claridge, T. D. W.},
  title = {High-Resolution {NMR} Techniques in Organic Chemistry},
  edition = {3rd},
  publisher = {Elsevier},
  address = {Amsterdam},
  year = {2016},
}

@article{Karplus1959,
  author = {Karplus, M.},
  title = {Contact Electron-Spin Coupling of Nuclear Magnetic Moments},
  journal = {J. Chem. Phys.},
  volume = {30},
  pages = {11--15},
  year = {1959},
}

@article{Jeener1971,
  author = {Jeener, J.},
  title = {Pulse Pair Techniques in High Resolution {NMR}},
  journal = {Ampere International Summer School},
  note = {Unpublished lecture},
  year = {1971},
}

@article{ErnstAnderson1966,
  author = {Ernst, R. R. and Anderson, W. A.},
  title = {Application of {F}ourier {T}ransform Spectroscopy to Magnetic Resonance},
  journal = {Rev. Sci. Instrum.},
  volume = {37},
  pages = {93--102},
  year = {1966},
}

@book{Keeler2010,
  author = {Keeler, J.},
  title = {Understanding {NMR} Spectroscopy},
  edition = {2nd},
  publisher = {Wiley},
  address = {Chichester},
  year = {2010},
}

@book{Ernst1987,
  author = {Ernst, R. R. and Bodenhausen, G. and Wokaun, A.},
  title = {Principles of Nuclear Magnetic Resonance in One and Two Dimensions},
  publisher = {Oxford University Press},
  address = {Oxford},
  year = {1987},
}