1
Chemical shift for a given molecule:
• Number of signals = nonequivalent nuclei
molecular symmetry
• Relative intensity = number of nuclei
• Position in the spectrum = shielding/chemical shift
electronic structure
• Multiplicity = connectivity of atoms and groups
2
Magnetic Coupling
The interaction of nuclear spins is composed of two parts:
1. Dipolar coupling
direct interaction of magnetic moments thru space
solids
oriented phases
NOE
relaxation
2. Scalar coupling
indirect interaction mediated by electrons
chemical information about the bonding
Bz ~  rAX
3(3cos2  1)
3
Dipolar Coupling
Dipolar coupling constant
DAX ~ h A X rAX
3
hetero = DAX(3cos2 1)
homo = 1.5 DAX(3cos2 1)
DAX
2DAX
4
Dipolar Coupling
Bz ~  rAX
3(3cos2  1)
5
Scalar Coupling
Analysis of the coupling patterns consists of
three parts:
• number of lines in a multiplet
• relative intensities of lines in the multiplet
• magnitude (and possibly sign) of the
coupling constants (Hz)
6
Scalar (Spin-Spin) Coupling
The simplest case:
Two magnetically active nuclei
Interacting through bonds (see each other)
Both spins I = ½
0.20.40.60.81.01.21.41.61.82.02.22.42.62.83.0
0.20.40.60.81.01.21.41.61.82.02.22.42.62.83.0
Ha
HbJ = 0
J  0
7
Scalar Coupling
A splitting of a signal = more
energy levels involved in the
transitions
Origin = The magnetic moment of
the nucleus Ha produces
polarization at Hb (and vice versa)
Spectrum of Ha
8
Two Spins I = ½
9
Homo vs. Hetero Coupling
10
Number of Lines in a Multiplet
CH3-CHCl2
3Hb
Ha
M = 2 n I + 1
11
M = 2 n I + 1
12
13
14
Scalar Coupling
M = 2 n I + 1
15
Relative Intensities of Lines
in the Multiplet
Spin, IX Polynomial, n = number of nuclei X Examples
1/2 (x + y)n 1H
1 (x2 + xy + y2)n 2H, 6Li, 14N
3/2 (x3 + x2y + xy2 + y3)n 11B, 7Li
2 (x4 + x3y + x2y2 + xy3 + y4)n -
5/2 (x5 + x4y + x3y2 + x2y3 + xy4 + y5)n 17O, 27Al
3 (x6 + x5y + x4y2 + x3y3 + x2y4 + xy5 + y6)n 10B
7/2 (x7 + x6y + x5y2 + x4y3 + x3y4 + x2y5 + xy6 + y7)n 51V, 59Co
Line intensities of the multiplet A are given by the coefficients of
polynomial expansion
AXn
16
Spin ½ Pascal’s Triangle
Pattern n Relative Peak Height (x + y)n
Singlet 0 1
Doublet 1 1 : 1
Triplet 2 1 : 2 : 1
Quartet 3 1 : 3 : 3 : 1
Quintet 4 1 : 4 : 6 : 4 : 1
Sextet 5 1 : 5 : 10 : 10 : 5 : 1
And so on ……
17
(a) 1H (400 MHz) and (b) 2H NMR (60.7 MHz) spectra (o-dichlorobenzene-d4) of the
region for encapsulated hydrogen molecule inside open-cage fullerene 1
18
Coupling with Several Spins
B
FF3C
F
F3C CF3
CF3
11B NMR
CF3 n = 9
F(2) n = 1
F(3) n = 1
CF3(too far)
K+
M = (2 ni Ii + 1)
19
11B NMR Spectrum of
K[B(CF=CF2)4]
11B NMR spectrum of K[B(CF=CF2)4] in
CD3CN: an overlapping quintet of
quintets of quintets
(2JB,F = 21.5, 3JB,F = 3.2, 3JB,F = 2.2 Hz).
Multiplet overlap
20
K[AgF4]
K[AgF4] d8 square planar
109Ag I = ½ NA = 48.2%  = - 1.2448 107 rad T-1 s-1
107Ag I = ½ NA = 51.8%  = - 1.0828 107 rad T-1 s-1
19F NMR
21
K[AgF4]
M = 2nI + 1
1J(109Ag – F) = 425.8 Hz
1J(107Ag – F) = 370.4 Hz
109Ag NMR
1J(109Ag – F) must have the same value in both 109Ag and 19F spectra
22
Signal Multiplicity
17O NMR
TcO4
- in 20.1% enriched H2
17O.
H2
17O
23
Signal Multiplicity
CCN
Pt
Tl
NCB
NCC
CAN
CCN
CCN
M = (2 ni Ii + 1)13C enriched CN-
24
2J (Tl– CC) < 1J (Tl– CB) < 2J (Tl– CA)
cis CC 0.45 kHz
trans CA 9.71 kHz
205Tl NMR
1H Scalar Coupling
25
26
Magnitude and Sign of the
Coupling Constants
Spin-spin couplings between two nuclei will be dependent
upon several factors:
• the nuclei involved – magnetogyric ratio
• the distance between the two nuclei
• the angle of interaction between the two nuclei
• the nuclear spin of the nuclei
Indirect nuclear spin–spin coupling constants
•through-bond
•through-space
•through hydrogen bonds
27
Scalar Coupling
Isotropic part of J
Four (Ramsey) contributions:
• Fermi-contact (FC)
• Spin-dipolar (SD)
• Paramagnetic orbital (PARA)
• Diamagnetic orbital (DIA)
28
Scalar Coupling
The most important contribution to scalar coupling arises
from the FERMI-CONTACT INTERACTION
which can be described in the Dirac-vector model:
B0 A B
The nuclear spin polarization of nucleus A in a magnetic field
polarizes the spins of a bonding electron pair, which in turn
transfer this polarization to nuclear spin B.
Scalar Coupling
29
30
Scalar Coupling
FERMI-CONTACT INTERACTION is mediated only by selectrons
(p, d, f electrons have no contact with the nucleus)
s-electron has definite probability at nucleus
e-spin and nuclear spin can interact only when they occupy
same space
An approximate expression for the scalar coupling constant J
was given by Mc CONNELL:
JAB ~ A B sA
2(0) sB
2(0) (E)1 AB
2
s2(0) = s-electron density at the nucleus
AB
2 = s-character in the A-B bond
31
Conventions on the Notation
of Scalar Coupling Constants
Spin-spin couplings are generally expressed in terms of
the COUPLING CONSTANT nJ
where n denotes the number of bonds between coupled nuclei
Dimension [ J ] = s1 [Hz]
The magnitude of J depends on the gyromagnetic ratios A, B
of the coupled nuclei. For comparison of coupling constants
involving different isotopes use
the REDUCED COUPLING CONSTANT K
KAB = (42/h) (A B )1 JAB
Dimension [ K ] = 1019 N A2 m–3
32
Scalar Coupling Constants
To compare substituent influences on coupling for different
nuclei, use
the EFECTIVE REDUCED COUPLING CONSTANT K’
K’AB = KAB [sA
2(0) sB
2(0)]1
Dimension [K’ ] = 1042 N A–2 m3
33
Signs of Scalar Coupling Constants
Signs of scalar coupling may be both POSITIVE or NEGATIVE.
The sign of a coupling constant is defined as follows:
KAB < 0 if PARALLEL alignment of the spins I(A) and I(B) is
energetically favored
KAB < 0
A B
KAB > 0
A B
KAB > 0 if ANTIPARALLEL alignment of the spins I(A) and
I(B) is energetically favored
34
Signs of Scalar Coupling Constants
> 0 if A, B have same sign
< 0 if A, B have different sign
KAB
JAB
NMR spectroscopic measurements in liquids yield generally only
information on RELATIVE SIGNS of two couplings,
i.e. KAB / KAC > 0 or KAB /KAC < 0.
Determination of absolute signs for KAB or KAC requires other
experiments (e.g. molecular beam experiments, observation of
dipolar interactions in the solid state)
35
Signs of Scalar Coupling Constants
The sign of 1KEH is generally positive.
(E = any first to fourth row atom)
If the relative sign of a coupling constant nKXY can be
determined from nKXY / 1KEH , it can be translated into an
absolute sign.
Methods for sign determination:
analysis of higher order spectra
homo- or heteronuclear 2D-Experiments
selective irradiation experiment
Coupling signs may provide useful structural information on:
the number of bonds connecting two nuclei
the oxidation state of elements
the stereochemical details (conformation and configuration analysis)
36
Visualization of Spin–Spin Coupling
     EEKJ ABBAAB
2
1
2



the energy splitting between states with parallel
and antiparallel nuclear spins
AB(r) = the coupling energy density (CED)
integral of CED over all space = KAB
CED is a real-space function, can be visualized in 3D
contains all the information about the propagation of the
nuclear spin–spin interaction throughout a molecule
        
dVrdVrrKJ ABBAABBAAB 


 22
1
2

37
Visualization of Spin–Spin Coupling
        
dVrdVrrKJ ABBAABBAAB 


 22
1
2

3JHH
through-bond
Benzene
through-space
H2P-CH2-CH2-PH2
3JPP
38
Visualization of Spin–Spin Coupling
     
21


rr
rAB



The coupling electron deformation
density (CDD), the integration of
CDD over space = 0
CDDCED
3JHH
39
Types of Coupling
Coupling between two nuclei can be categorized as follows:
Homonuclear Coupling
- coupling between nuclei of the same type
1H-C-C-1H, 195Pt-195Pt, 31P-C-31P, 199Hg-C-C-199Hg
Heteronuclear Coupling
- coupling between nuclei of different types
1H-13C, 1H-31P, 205Tl-195Pt, 14N-51V
40
Distance Dependence
The absolute value of the coupling constant decreases as the number of
interceding bonds between coupled nuclei increases.
The order of the strength of coupling is as follows: 1J > 2J > 3J > 4J > nJ
1J one-bond or direct
2J two-bond or geminal
3J three-bond or vicinal nJ long-range
41
Distance Dependence
P
3JPCCC = 14 Hz
2JPCC = 12 Hz
1JPC = 55 Hz
1J > 3J > 2J
42
Largest Heteronuclear J
CN
PtNC CN
CN
CN
Tl
NC
CN
PtNC CN
CN
CN
Tl
CN
PtNC CN
CN
CN
Tl
NC
CN
2 CN
PtNC CN
CN
CN
Tl
NC
CN
3
NC
1J(205Tl-195Pt), kHz !!!!
71 57 47 38
43
Largest Homonuclear J
1J(199Hg-199Hg) =
220 300 Hz
1J(199Hg-199Hg) =
263 200 Hz in CD2Cl2
284 100 Hz in MeOH
44
Dependence of J
on Magnetogyric Ratio
1H spectrum of natural abundance NH4Cl (1.5 M) in 1M HCl/H2O
• coupling to 14N (I = 1) – a triplet (1:1:1)
• coupling to 15N – a weak doublet
The 14N coupling constant is smaller than that of 15N WHY??
1H
45
Dependence on Magnetogyric Ratio
For the same elements, different nuclides
JAB ~ A B sA
2(0) sB
2(0) (E)1 AB
2
BH4

1J(11B – H) = 80 Hz (11B) = 8.57 107 rad T1s1
1J(10B – H) = 28 Hz (10B) = 2.87 107 rad T1s1
46
Dependence on Magnetogyric Ratio
*
*
*)(
)(
*)(
)(
B
B
BA
BA
BAJ
BAJ
FBAJ
FBAJ









The nuclide with larger  has larger coupling constant
J(A-B)~ A B sA
2(0) sB
2(0) (E)1 AB
2
47
Dependence on Magnetogyric Ratio
compound (X)
107 rad T1s1
1J(117Sn – X)
Hz
1J(119Sn – X)
Hz
nBu3Sn – H 26.7510 1505 1575
nBu3Sn – D 4.1064 231 242
nBu3Sn – T 28.5335 1610 1685
JAB ~ A B sA
2(0) sB
2(0) (E)1 AB
2
48
Effects of Electronegative
Substituents
1. Changes in hybridization: Bent’s rule, more electronegative
substituents prefer orbitals with more p-character. Remaining
orbitals have more s-character - AB
2, hence the J increases
2. Removal of electron density increases effective nuclear
charge, contraction of e-cloud, s-density increases - sA
2(0),
hence the J increases
JAB ~ A B sA
2(0) sB
2(0) (E)1 AB
2
49
Effects of Electronegativity
PAEt3
Pt
Cl
PBEt3Me
PAEt3
Pt
Cl
PBEt3
PAEt3
Pt PBEt3Me
Me
More p-character
More s-character
Cl
1J(195Pt - PA) = 4179 Hz
1J(195Pt - PB) = 1719 Hz
JAB ~ A B sA
2(0) sB
2(0) (E)1 AB
2
50
Effects of Electronegativity
J increases with increasing sum of substituent electronegativity
CO
WOC
CO
PX3
OC
CO
51
Effects of Coordination Number
Et3P Pt
Cl
Cl
PEt3
Cl
Cl
Et3P Pt
Cl
Cl
PEt3
1J(195Pt - P) = 1455 Hz 1J(195Pt - P) = 2397 Hz
Et3P Pt
PEt3
PEt3
PEt3 PhMe2P Pt
PMe2Ph
PMe2Ph
PMe2Ph
2+
1J(195Pt - P) = 3740 Hz 1J(195Pt - P) = 2342 Hz
Increasing coordination number results in decreasing J
52
Effects of Coordination Number
[Cp2WH2] [Cp2WH3]+
1J(183W - H) = 73.2 Hz 47.8 Hz
Increasing coordination number results in decreasing J
53
Effects of s-Character
B
XPs
XsPs
AXPJ 


)(1
)()%(%
)( 2
1
s2 (P-X) = overlap integral in the P-X bond
1J(P - X) decreases with increasing coordination
number and oxidation state
54
Effects of s-Character
Group hybridization 1J(183W – 13C), Hz
alkyl sp3 80
alkylidene sp2 120
alkylidyne sp 210
W
PMe3H2
C
CH
C
PMe3
t-Bu
t-Bu
t-Bu
W oxidation state
Point group
Coupling C-H, P-C
55
Effects of s-Character
F
P
F
F
F
F
P
F
F
F
F
P
F
F
F
1J(31P - C) = 189.2 Hz 261.1 Hz 476.0 Hz
C
H
C
H H
C
1J(13C- H) = 120 Hz 160 Hz 250 Hz
56
Effects of s-Character
1J(P-Faxial) = 777 Hz
1J(P-Fequat) = 966 Hz
F
P
F
F
CF3
F
CF3
P
CF3
NMe2
Cl
F3C
2J(P-Faxial) = 53 Hz
2J(P-Fequat) = 130 Hz
57
Effects of s-Character
H
H
H
H 123
130
134
161
1J (C-H), Hz
Increasing J
Intraring angle decreases
More p-character in C-C
More s-character in C-H
58
Effects of s-Character
H2
P
B B
PH2
PH2
PH2
H2P
H2P
PH2
1J(P-11B) = 56.9 Hz
1J(P-11B) = 26.3 Hz
Explain the difference
59
Effects of s-Character
1J(P-11B) = 56.9 Hz
1J(P-11B) = 26.3 Hz
Lone pair = substituent with zero
electronegativity
Resides in orbital with large s-character
P
B
B
P
H2P
H2P
PH2
H
HH
H
60
Effects of Coordination Number
F
P
F
F
F
F
F
P
F
F
FF
F
P
F
F
F
H
P
F
F
F
1J(31P - F) negative
1400 Hz 1109 Hz 1080 Hz 706 Hz
Increasing coordination number results in decreasing J
Dilution of s-character into more bonds
61
Effects of Oxidation State
Cl Pt
Cl
Cl
PBu3
P(OPh)3
Cl
Cl Pt
Cl
P(OPh)3
PBu3Bu3P Pt
Cl
Cl
PBu3
Bu3P
Pt
PBu3
PBu3
PBu3
1J (195Pt - 31P)
3740 Hz 2411 Hz Bu 3159 1921
OPh 6304 4060
Increasing oxidation state results in decreasing J
Decreasing electron density
62
Information from signs of KAB
PIII PV PV
lp
changes
sign
1J(P - C) 14 56 68
SnII SnIV SnIV
1J(Sn - C) 155 380 339
P
Me
Me
Me
P
Me
Me
Me
Me
P
Me
Me
Me
O
Sn
Me
Me
Me
Me Sn
Me
Me
Sn
Me
Me
Me
Me
63
Angle Dependence
Two types of coupling are most affected by bond angles:
• geminal coupling (two-bond coupling or 2J)
• vicinal coupling (three-bond coupling or 3J)
64
Geminal Coupling
Geminal coupling or 2J coupling is dependent upon the
bond angle between the nuclei.
The smaller the angle the bigger the coupling constant.
65
Geminal Coupling
The smaller the angle the bigger the coupling constant.
2J (1H – 1H)
66
Trans/Cis Coupling
H
H
H H
H
H
gem 0 – 3
vic cis 6 – 12
vic trans 12 – 18
nJ (1H – 1H), Hz
67
Trans/Cis Coupling
Ph2
P
Pd
PPh2H
H PPh2H
(OC)4Mn
2J (31P – Pd – 31P)
cis 0 Hz
trans 213 Hz
68
Trans/Cis Coupling
2J (31P – M – 31P) cis < trans
Complex Coord. 2J PP cis, Hz 2J PP trans, Hz
PdCl2(PMe3)2 SPl 8 610
PtBr2(PMe3)2 SPl 16 514
Cr(CO)4(PF3)2 Oh 36 28
Mo(CO)4(PF3)2 Oh 55 312
Mo(CO)4[P(NMe2)3]2 Oh 12 101
W(CO)4(PF3)2 Oh 38 315
mer-RhCl3(PMe3)3 Oh 29 567
69
Vicinal Coupling
Vicinal coupling or 3J coupling is dependent upon the dihedral angle
between the nuclei.
The more eclipsed or antiperiplanar the nuclei the greater the coupling
constant.
The relationship between dihedral angle and coupling constant is known
as the Karplus curve.
C
C
H
H
C
C
H
H C
C
H
H

minimum
 23
coscos CBAJ 
70
Vicinal Coupling
 23
coscos CBAJ 
the Karplus equation
71
The Karplus Equation
72
Population Analysis
Z
H
H
X
H
Y
H
H
Z
X
H
Y
H
ZH
X
H
Y
p1 p2
p3
)180(
)60(
1321
3212
3211


t
g
gtg
tgg
J
J
ppp
pJpJpJJ
pJpJpJJ





from independent
measurements
3 inequivalent protons
2 time-averaged vicinal J
(1 geminal J)
pi = population of rotamers
g = gauche, t = trans
experiment
73
Population Analysis
KOH
OH
HX
HX
HA
HB
HA
HB
Axial Equatorial
p 1 - p
)exp(
1
)1(
)1(
0
RT
G
p
p
K
JppJJ
JppJJ
Equ
BX
Axial
BXBX
Equ
AX
Axial
AXAX






74
Decoupling
Heteronuclear broadband decoupling
Selective homonuclear decoupling
75
15N–15N Coupling Across an NHN
Hydrogen Bond
CD2Cl2/[d6]DMSO (5:1)
a) 233 K b) 233 K
c) 193 K d) 193 K
2J(15N–15N) = 16.5 Hz
76
6Li–15N Coupling
6Li I = 1 NA = 7.42 %
15N I = 1/2 NA = 0.37 %
77
6Li–15N Coupling
6Li NMR:
•two triplets 1:1
 = 2.15 ppm (JLiN = 3.7 Hz)
 = 2.32 ppm (JLiN = 6.1 Hz)
•triplet  = 1.63 ppm (JLiN = 4.5 Hz)
78
6Li–15N Coupling6Li NMR:
•two triplets 1:1  = 2.15 ppm
(JLiN= 3.7 Hz) a  = 2.32 ppm (JLiN=
6.1 Hz)
•triplet  = 1.63 ppm (JLiN= 4.5 Hz)