The document discusses the n+1 rule in NMR spectroscopy, detailing its application to tree diagrams for splitting patterns in aliphatic chains and rings. It highlights the conditions under which the n+1 rule is valid, primarily focusing on equal coupling constants and free rotation among hydrogens. Examples such as 2-phenylpropanal and vinyl acetate further illustrate how unequal j values affect splitting patterns and NMR analysis.

1. UNEQUAL COUPLING
TREE DIAGRAMS
SPLITTING DIAGRAMS
aka “TREE” DIAGRAMS

2. WHERE DOES THE N+1 RULE WORK ?
The n+1 rule works only for protons in aliphatic chains
and rings, and then under special conditions.
1) All 3J values must be the same all along the chain.
There are two requirements for the n+1 rule to work:
2) There must be free rotation or inversion (rings) to
make all of the hydrogens on a single carbon be
nearly equivalent.

3. C
H
H
C
H
H
C
H
H
3Ja = 3Jb
Hydrogens can
interchange their
positions by
rotations about
the C-C bonds.
All the couplings
along the chain
have the same J value.
THE TYPICAL SITUATION WHERE THE n+1 RULE APPLIES
This makes all the
hydrogens on each
of the carbon atoms
equivalent.

4. WHAT HAPPENS WHEN THE J VALUES ARE NOT EQUAL ?
C
H
H
C
H
H
C
H
H
3Ja
3Jb
3Ja = 3Jb
In this situation each coupling must be considered
independently of the other.
A “splitting tree” is constructed

5. C
H
H
C
H
H
C
H
H
7 Hz 3 Hz
USE THESE VALUES

6. C
H
H
C
H
H
C
H
H
3Ja = 7
-CH2-CH2-CH2-
CONSTRUCTING A TREE DIAGRAM
The largest J value
is usually used first.
SPLITTING FROM
HYDROGENS TO THE LEFT
The next splittings will
be added to each leg of
the first splitting.
LEVEL ONE
Two neighbors gives
a triplet.
Each level of the
splitting uses the
n+1 rule.

7. C
H
H
C
H
H
C
H
H
3Ja = 7
-CH2-CH2-CH2-
CONSTRUCTING A TREE DIAGRAM
C
H
H
C
H
H
C
H
H
3Jb = 3
triplet of triplets
ADD SPLITTING FROM
HYDROGENS TO THE RIGHT
The smaller splitting
is used second.
FIRST LEVEL
SECOND LEVEL LEVEL TWO
It is also a triplet.
EACH LEG OF LEVEL ONE IS SPLIT

8. WHEN BOTH 3J VALUES ARE THE SAME
-CH2-CH2-CH2-
….. because of overlapping legs.
You get the quintet predicted by
the n+1 rule.
The n+1 rule is followed …..
n+1 = (4 + 1) = 5
Splitting from
hydrogens on
the left
Splitting from
hydrogens on
the right
Splittings
overlap
1:2:1
1:2:1
1:2:1
1:2:1
1:4:6:4:1
INTENSITIES
+
LEVEL ONE
LEVEL TWO
WHEN THE n+1 RULE APPLIES WE CAN JUMP TO THE FINAL RESULT - NO TREE NEEDED

9. 2-PHENYLPROPANAL
A case where there are unequal J values.

10. Spectrum of 2-Phenylpropanal
J = 2 Hz
J = 7 Hz
a
b
c
d
CH
CH3
CHO
a b d
c TMS

11. CH
CH3
CHO
3J1 = 7 Hz
7 Hz 2 Hz
3J2 = 2 Hz
the methine hydrogen
is split by two different
3J values.
Rather than the expected
quintet …..
ANALYSIS
OF METHINE
HYDROGEN’S
SPLITTING
quartet
by -CH3
doublet
by -CHO
quartet of doublets

12. PURE ETHANOL

13. ETHANOL
Old sample
Rapid exchange catalyzed
by impurities
quartet
triplet
broad
singlet
HO-CH2-CH3
hydrogen on OH
is decoupled
400 MHz

14. ETHANOL
Ultrapure sample (new)
Slow or no exchange
triplet
doublet of
quartets
triplet
400 MHz
expansion expansion

15. quartet of doublets
J = 7
J = 5
triplet triplet
J = 7
J = 5

16. VINYL ACETATE
ALKENE HYDROGENS

17. • 3J-cis = 8-10 Hz
• 3J-trans = 16-18 Hz
• protons on the same carbon
2J-geminal = 0-2 Hz
H
H
H
H
H
H
PROTONS ON C=C DOUBLE BONDS
COUPLING CONSTANTS
For protons on saturated aliphatic chains 3J ~ 8 Hz

18. NMR Spectrum of Vinyl Acetate
CH3 C
O
O CH CH2
60 MHz

19. Analysis of Vinyl Acetate
HC HB HA
CH3 C
O
O
C
HC
C
HA
HB
3JBC
3JAC
3JAC
3JBC
2JAB
2JAB
trans trans
cis
cis
gem gem
3J-trans > 3J-cis > 2J-gem

20. 2,4-DINITROANISOLE
BENZENE HYDROGENS

21. 2,4-DINITROANISOLE
400 MHz
9.0 8.0 7.0

22. 2,4-DINITROANISOLE
8.72 ppm 8.43 ppm 7.25 ppm

23. END