NMR Spectroscopy

NMR Spectroscopy — Foundations

Part 1 of 7 — $^1\text{H}$ NMR Basics

Nuclear magnetic resonance (NMR) is the single most powerful tool the organic chemist has for determining molecular structure. Where a melting point or a combustion analysis tells you what atoms are present, NMR tells you how those atoms are connected — which carbons bear how many hydrogens, which groups sit next to which, and how the whole skeleton is assembled.

The physics behind it: certain nuclei, including $^1\text{H}$ (a single proton) and $^{13}\text{C}$, possess a property called nuclear spin ($I = \tfrac{1}{2}$). A spinning charged nucleus behaves like a tiny bar magnet. In the absence of an external field these nuclear magnets point in random directions and all have the same energy. But when the sample is placed inside a strong, uniform magnetic field $B_0$, each nuclear magnet can adopt one of two orientations:

• aligned with $B_0$ — the lower-energy ($\alpha$) state
• aligned against $B_0$ — the higher-energy ($$) state

The energy gap between these two states, $\Delta E$, is directly proportional to the field strength: $\Delta E = \gamma\, h\, B_0 / 2\pi$, where $\gamma$ is the gyromagnetic ratio of the nucleus. Irradiate the sample with a radiofrequency (RF) pulse whose photon energy exactly matches , and nuclei in the state absorb that energy and flip to the state. That absorption — the nucleus coming into — is what the spectrometer detects.

Why a stronger magnet is "higher resolution": because $\Delta E \propto B_0$, a bigger field spreads the absorptions farther apart in frequency, so signals that overlap on a weak instrument separate cleanly on a strong one. A "300 MHz" or "500 MHz" instrument is named for the RF frequency at which $^1\text{H}$ resonates in its field.

Why Different Protons Absorb at Different Frequencies

If every proton in a molecule resonated at exactly the same frequency, NMR would be useless — it would give one peak for every organic compound. The reason NMR is informative is that each proton feels a slightly different magnetic field than the bare $B_0$ applied by the magnet.

Every proton is surrounded by electrons. When the sample sits in $B_0$, those electrons circulate and generate their own small induced magnetic field that, near the nucleus, opposes $$. The proton therefore experiences a slightly weaker :

Checkpoint — The Resonance Phenomenon

Equivalent Protons Give One Signal

Here is the rule that lets you predict how many peaks a molecule produces: chemically equivalent protons resonate at the same frequency and produce a single signal. Two protons are chemically equivalent if they are in identical electronic environments — most reliably, if a symmetry operation of the molecule (a rotation, a mirror plane, or the molecule's own rapid bond rotation) interchanges them.

The number of signals in a $^1\text{H}$ NMR spectrum therefore equals the number of distinct proton environments, not the number of hydrogen atoms. Counting environments is a skill built on recognizing symmetry.

Worked example — count the signals:

• Methane, $\text{CH}_4$: all four H's are equivalent by tetrahedral symmetry

Equivalence, More Carefully: Homotopic and Enantiotopic vs. Diastereotopic

For everyday structure problems, "related by symmetry $\rightarrow$ equivalent" is enough. But a rigorous course distinguishes how two protons are related, because one case quietly breaks the rule.

• Homotopic protons are interchanged by a rotation of the molecule (a $C_n$ axis). They are equivalent in every environment. Example: the three H's of a freely rotating $\text{CH}_3$.

Checkpoint — Counting Signals

Chemical Shift ($\delta$): A Field-Independent Address

Each signal needs an address on the horizontal axis. We could report the raw resonance frequency in hertz — but that number depends on the magnet, so a peak at one frequency on a 300 MHz instrument lands at a different frequency on a 500 MHz instrument. To make spectra comparable, chemists report position as a dimensionless chemical shift, $\delta$, in parts per million ($\text{ppm}$):

$\delta = \dfrac{\nu_{\text{sample}} - \nu_{\text{reference}}}{\nu_{\text{spectrometer}}} \times 10^6$

Exit Ticket — Part 1 Synthesis

Chemical Shift in Depth

Part 2 of 7 — Chemical Shift ($\delta$)

In Part 1 we established that $\delta$ is a field-independent address measured in $\text{ppm}$ relative to TMS at $\delta = 0$, and that electron density around a proton sets its position: shielded (electron-rich) protons sit upfield at small $\delta$, deshielded (electron-poor) protons sit downfield at large . This part turns that qualitative idea into a working chemical-shift table and explains the three structural factors — electronegativity, hybridization, and magnetic anisotropy — that move a proton along the scale.

Integration and Spin–Spin Splitting

Part 3 of 7 — Integration & Splitting

Chemical shift (Parts 1–2) tells you what kind of proton each signal represents. This part adds the two pieces of information that make $^1\text{H}$ NMR genuinely structure-determining:

• Integration — the area under each signal, which is proportional to the number of protons giving rise to it. This counts H's in each environment.
• Spin–spin splitting (coupling) — the way a signal is split into multiple lines by neighboring protons, which reveals how many protons sit next door and therefore what is bonded to what.

Together with shift, these turn a spectrum into a connectivity map. We will build the $n+1$ rule, read , define the , and draw the for the two patterns you must recognize on sight: the ethyl group and the isopropyl group.

Carbon-13 NMR

Part 4 of 7 — $^{13}\text{C}$ NMR

So far we have watched protons. But the carbon skeleton itself can be observed directly with $^{13}\text{C}$ NMR, and it is wonderfully complementary to $^1\text{H}$: it counts environments, spreads them over a much wider scale, and is often easier to read because the spectra are usually a clean set of single lines.

Putting It Together: Structure Determination

Part 5 of 7 — Structure Determination

Individually, a chemical shift or a multiplicity is a clue. The power of spectroscopy comes from combining them in a disciplined order so that each piece of data constrains the next. This part lays out the systematic workflow that turns a molecular formula plus a few spectra into a unique structure, and walks one unknown all the way through.

The four-step routine:

1. Molecular formula $\rightarrow$ degrees of unsaturation. Establish how many rings and $\pi$ bonds the molecule must contain.
2. IR $\rightarrow$ functional groups. Identify the major functional groups (C=O, O–H, N–H, C≡N, aromatic).
3. $^1\text{H}$ NMR environments, counts, neighbors. Count signals, read integration, and decode splitting to find fragments.

Problem-Solving Workshop

Part 6 of 7 — Problem-Solving Workshop

This part is all application. We take the systematic pipeline from Part 5 and run it on a series of unknowns of increasing subtlety — predicting spectra from structures, deducing structures from data, and combining IR, mass spectrometry, and NMR. Work each example with paper in front of you: write the fragments down as you read each signal, keep a running proton tally, and only commit to a structure when every datum is explained.

A reliable mental checklist for any unknown:

1. DoU from the formula — how many rings/$\pi$ bonds?
2. IR — which functional groups (C=O? O–H? N–H? C≡N? aromatic)?
3. $^1\text{H}$: for each signal note shift (what kind), integration (how many), multiplicity (how many neighbors) $\rightarrow$ a fragment.

Synthesis and Review

Part 7 of 7 — Synthesis & Review

NMR is the most powerful structural tool in the organic chemist's kit because a single pair of experiments ($^1\text{H}$ and $^{13}\text{C}$) reports on almost every atom in a molecule at once. This closing part consolidates the whole suite into one coherent picture: the four kinds of information a $^1\text{H}$ spectrum delivers, how each maps onto structure, and the decision flow that ties shift, integration, splitting, and the carbon spectrum into a single answer.