¹³C NMR (overview); DEPT — Chemistry notes

WHY does ¹³C NMR even work?

WHY is this a problem? Sensitivity. Combining the low abundance (1.1%) with a small magnetic moment (gyromagnetic ratio $\gamma_C \approx \tfrac14\,\gamma_H$ ), the ¹³C signal is roughly ~5700× weaker than ¹H per nucleus. So we need:

Many scans (signal averaging) — signal grows as $N$ , noise as $\sqrt N$ , so S/N $\propto \sqrt N$ .
Fourier-transform (pulsed) NMR.

WHAT a ¹³C spectrum looks like

Rough chemical-shift map (ppm)

Carbon type	δ (ppm)
Alkyl C–H ( $sp^3$ )	5–50
C–N, C–O ( $sp^3$ , next to electronegative)	40–80
Alkyne ( $sp$ )	65–90
Alkene / aromatic ( $sp^2$ )	100–150
C=O ester/acid/amide	160–185
C=O ketone/aldehyde	190–220

DEPT — sorting carbons by attached H

HOW it works (conceptually): Magnetization is transferred from H → C, then evolves for a time tuned to $1/J_{CH}$ . The final-pulse angle $\theta$ controls the sign of each multiplicity:

Formula DEPT signal sign vs

$\theta$ The intensity of a carbon bearing $n$ protons follows roughly $I_{CH_n} \propto \sin\theta\,\cos^{\,n-1}\theta$ Quaternary carbons (n=0) receive no polarization transfer ⇒ always absent in DEPT.

Evaluate at the three standard angles:

	$\theta=45°$	$\theta=90°$	$\theta=135°$
CH ( $n=1$ ): $\sin\theta$	+	+	+
CH₂ ( $n=2$ ): $\sin\theta\cos\theta$	+	0	−
CH₃ ( $n=3$ ): $\sin\theta\cos^2\theta$	+	0	+

Reading it (the 80/20 rule): Most people just run DEPT-135:

Up (positive): CH and CH₃
Down (negative): CH₂
Absent: quaternary C (and C=O, etc.)

Combine with the normal ¹³C (which shows all carbons): any peak present in ¹³C but missing in DEPT is quaternary.

Worked example 1 — Ethanol, CH₃CH₂OH

Step 1 — Count unique carbons. Two: the CH₃ and the CH₂. Why? No symmetry makes them equivalent. ⇒ 2 peaks in ¹³C.

Step 2 — Assign shifts. CH₂ is bonded to O (electronegative) ⇒ more deshielded, ~58 ppm. CH₃ ~18 ppm. Why? Oxygen withdraws electron density from the adjacent carbon.

Step 3 — DEPT-135. CH₃ → up; CH₂ → down. Why? From $\sin\theta\cos^{n-1}\theta$ at 135°: $n=3$ gives +, $n=2$ gives −. (The OH carries no carbon, so no peak.)

Worked example 2 — Acetone, (CH₃)₂C=O

Step 1 — Count unique carbons. The two CH₃ groups are equivalent by symmetry ⇒ they give one peak. The C=O is another. ⇒ 2 peaks. Why this step? Symmetry-equivalent atoms are indistinguishable to NMR.

Step 2 — Shifts. Carbonyl C ~206 ppm (very deshielded ketone). CH₃ ~30 ppm.

Step 3 — DEPT-135. CH₃ → up. The C=O is quaternary (n=0) → absent. Why? No attached H ⇒ no polarization transfer.

Conclusion: A peak near 206 ppm that disappears in DEPT confirms a ketone carbonyl.

Worked example 3 — Para-xylene (1,4-dimethylbenzene)

Step 1 — Find the symmetry, then count environments carefully. Para-xylene has a $C_2$ axis (and mirror planes) that make the two CH₃ groups equivalent and the two ring-substituted (ipso) carbons equivalent. But the four un-substituted aromatic CH carbons are NOT all equivalent: the symmetry maps them into two pairs.

The two CH₃ groups → 1 environment.
The two ipso carbons (ring C bearing CH₃, quaternary) → 1 environment.
The four aromatic C–H carbons split into two equivalent pairs → 2 environments.

⇒ 4 ¹³C signals, not 3. Why this step? Equivalence requires a symmetry operation to map one carbon exactly onto the other; not every aromatic CH in para-xylene is related by such an operation, so they fall into two distinct sets.

Step 2 — Shifts. CH₃ ~21 ppm; the two aromatic CH environments ~126–129 ppm (close together); ipso quaternary ~134 ppm.

Step 3 — DEPT-135. CH₃ → up (~21); both aromatic CH environments → up (~126–129); ipso carbon absent (quaternary). Why? DEPT instantly flags the one carbon (ipso) that bears the substituent because it carries no H.

Recall Feynman: explain it to a 12-year-old

Imagine your molecule is a tinker-toy made of carbon balls connected by sticks. ¹³C NMR is a special camera that lights up each different carbon ball so you can count them. The catch: only about 1 in 100 carbon balls is the "glowing" kind, so the camera must take thousands of photos and add them up to get a clear picture. Then DEPT is a clever filter: it counts how many little hydrogen beads stick onto each carbon ball, and paints them in code — balls with 2 hydrogens point down, balls with 1 or 3 hydrogens point up, and bald balls with no hydrogens don't show up at all.

Flashcards

Why is ¹²C invisible in NMR but ¹³C is active?

¹²C has nuclear spin

I=0

(no magnetic moment); ¹³C has

I=\tfrac12

What is the natural abundance of ¹³C, and why does it matter?

1.1% — makes ¹³C NMR insensitive (needs many scans) but also makes ¹³C–¹³C coupling negligible.

Approximate chemical-shift range of ¹³C NMR?

~0–220 ppm (vs ~0–12 ppm for ¹H).

Why does each carbon appear as a singlet in routine ¹³C spectra?

Broadband proton decoupling removes C–H coupling (and NOE boosts intensity).

Are routine ¹³C peak heights quantitative?

No — they depend on

T_1

relaxation and uneven NOE; quaternary carbons are often weak.

What does DEPT stand for?

Distortionless Enhancement by Polarization Transfer.

In DEPT-135, which carbons point up, down, and are absent?

Up: CH & CH₃; Down: CH₂; Absent: quaternary C.

Why are quaternary carbons absent in all DEPT spectra?

They have no attached H, so no H→C polarization transfer occurs.

How do you distinguish CH from CH₃ using DEPT?

Run DEPT-90: only CH survives; CH₃ (and CH₂) vanish at

\theta=90°

Formula for DEPT signal intensity of a

CH_n

carbon vs pulse angle θ?

I \propto \sin\theta\,\cos^{n-1}\theta

A peak in normal ¹³C but missing in DEPT-135 is what kind of carbon?

Quaternary (no attached hydrogen), e.g. carbonyl or ipso aromatic C.

Number of ¹³C signals for acetone and why?

2 — the two CH₃ are equivalent by symmetry; plus the C=O.

How many ¹³C signals does para-xylene give and why?

4 — CH₃, ipso quaternary, and TWO non-equivalent aromatic CH environments (the four ring CH's split into two pairs).

Connections

¹H NMR (overview) — complementary hydrogen skeleton, integration is quantitative there.
Chemical Shift & Shielding — same deshielding logic, larger range for ¹³C.
Spin–Spin Coupling (J) — what decoupling removes.
Nuclear Overhauser Effect (NOE) — intensity enhancement & polarization transfer.
IR Spectroscopy — pairs with ¹³C to confirm C=O.
Mass Spectrometry — gives molecular formula / degrees of unsaturation to support carbon count.
Symmetry & Equivalent Nuclei — why peak counts < total carbons.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, ¹³C NMR ka matlab hai ki ab hum molecule ke carbon skeleton ko directly dekh rahe hain, na ki hydrogens ko. Problem ye hai ki carbon ka sirf ¹³C isotope NMR-active hai (spin ½), aur ye nature me sirf 1.1% hota hai — baaki ¹²C totally invisible. Isliye signal bahut weak aata hai aur machine ko hazaaron scans add karne padte hain taaki clear picture mile. Plus point: itna kam abundance hone ki wajah se do ¹³C ek dusre ke paas hone ka chance almost zero hai, isliye C–C coupling nahi dikhta — spectrum simple rehta hai.

Ek normal ¹³C spectrum me hum proton decoupling karte hain, jisse har carbon ek single sharp peak (singlet) ban jaata hai. Range bahut badi hoti hai, 0 se 220 ppm tak, isliye peaks aapas me overlap nahi karte. Yaad rakho: ¹³C me peak ki height quantitative nahi hoti (¹H jaisa integration kaam nahi karta), kyunki relaxation aur NOE alag-alag hote hain — quaternary carbons (jaise C=O) chhote ya weak dikhte hain. Bas peaks count karo, lekin symmetry carefully lagao — para-xylene me bhi char alag environments hote hain (do aromatic CH alag-alag), teen nahi!

Ab DEPT asli magic hai. Ye batata hai ki har carbon pe kitne hydrogen lage hain. Sabse common DEPT-135 chalaate hain: CH aur CH₃ upar (positive), CH₂ neeche (negative), aur quaternary carbon gayab (kyunki uspe hydrogen hi nahi, to polarization transfer nahi hota). Trick: jo peak normal ¹³C me hai par DEPT me nahi → wo quaternary hai (jaise carbonyl). CH aur CH₃ dono upar hote hain, to confuse mat ho — DEPT-90 chala lo, usme sirf CH bachta hai. Mantra simple: "Even down, odd up, none gone."

Test yourself — Spectroscopy & Analysis (Intro)

Connections