Chapter 3: Coupling Constants

Transcription

Coupling Constants (J)
•
•
Coupling constants are a very important and useful feature of an NMR
spectrum
Importantly, coupling constants identifies pairs of nuclei that are chemically
bonded to each other
1
H
1
H
•
Multiplicity identifies the number of protons (or other nuclei) that are chemical
bonded to the other nuclei
•
The magnitude of the coupling constants identifies the coupling partner, and
provides information on dihedral angles, hydrogen bonds, the number of
intervening bonds, and the type of coupled nuclei (1H, 13C, 15N, 19F, etc.)
- spin-spin coupling, scalar coupling or J-coupling
Random tumbling of molecules averages
through-space effect of nuclear magnets
to zero
Bo
b
b
ab2
ab1
Bo
a
a
random tumbling leads to no interaction between the
spin-states despite the small magnetic fields
- spin-spin coupling, scalar coupling or J-coupling
Instead, nuclear spin state is communicated through bonding electrons
Energy of electron spin states are
degenerate in absence of nuclear spin
With a nuclear spin, the electron spin
opposite to nuclear spin is lower energy
Number of possible energy states of nuclearelectron spin pairs increases with the number
of nuclear spins
Spin state is “sensed” through bonds resulting in higher or lower energy
- aligned or anti-aligned with magnetic field
Coupling Constants
Energy level of a nuclei are affected by covalently-bonded neighbors spin-states
Mixing of Spin
Systems One and Two
bb
b
ab
ab
b
ab
ba
a
a
aa
Spin System One
Spin System Two
Coupling Constants
Mixing of energy levels results in additional transitions – peaks are split
+J/4
I
-J/4
bb
S
ab
J (Hz)
J (Hz)
I
S
ba
S
+J/4
I
aa
Spin-States of covalently-bonded nuclei want to be aligned
The magnitude of the separation is called coupling constant (J) and has units of Hz
Coupling Constants
•
Through-bond interaction that results in the splitting of a single peak into
multiple peaks of various intensities

Spacing in hertz (hz) between the peaks is a constant

Independent of magnetic field strength
Multiple coupling interactions may exist

Increase complexity of splitting pattern
Coupling can range from one-bond to five-bond

One, two and three bond coupling are most common

Longer range coupling usually occur through aromatic systems
Coupling can be between heteronuclear and homonuclear spin pairs

Both nuclei need to be NMR active i.e. 12C does not cause splitting
•
•
•
1
1
H
13
1
H
1
H
H
three-bond
C
four-bond
one-bond
1
1
H
five-bond
H
Coupling Constants
•
Splitting pattern depends on the number of equivalent atoms bonded to
the nuclei


Determines the number of possible spin-pair combinations and energy levels
Each peak intensity in the splitting pattern is determined by the number of spin
pairs of equivalent energy
Coupling Constants
•
Splitting pattern follows Pascal’s triangle

Number of peaks and relative peak intensity determined by the number of
attached nuclei

Peak separation determined by coupling constant (J)

Negative coupling  reverse relative energy levels
1
1 1
1 2 1
1 3 3 1
1 4 6 41
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
Pascal’s triangle
3
3
3 attached nuclei
1
J
J
J
Quartet
1
Relative
Intensity
Coupling Constants
Common NMR Splitting Patterns
singlet doublet triplet quartet
1:1
1:2:1 1:3:3:1
pentet
1:4:6:4:1
Coupling Rules:
1.
2.
3.
4.
5.
6.
7.
equivalent nuclei do not interact
coupling constants decreases with separation ( typically # 3 bonds)
multiplicity given by number of attached equivalent protons (n+1)
multiple spin systems  multiplicity  (na+1)(nb+1)
Relative peak heights/area follows Pascal’s triangle
Coupling constant are independent of applied field strength
Coupling constants can be negative
IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei.
Coupling Constants
Common NMR Splitting Patterns
Coupling Constants
•
Coupling only occurs between non-equivalent nuclei

Chemical shift equivalence

Magnetic equivalence

For no coupling to occur, nuclei has to be BOTH chemical shift and magnetic
equivalent
The CH3 protons (H1, H2, H3) are in
identical environments, are equivalent,
and are not coupled to one another
The Ha and Hb protons are in different
environments (proximity to Cl), are
not equivalent, and are coupled
Coupling Constants
Rules for Chemical Shift Equivalence:
•
Nuclei are interchangeable by symmetry operation
i.
Rotation about symmetric axis (Cn)
ii.
Inversion at a center of symmetry (i)
iii. reflection at a plane of symmetry (s)
iv. Higher orders of rotation about an axis followed by reflection in a
plane normal to this axis (Sn)
v.
Symmetry element (axis, center or plane) must be symmetry
element for entire molecule
Examples of Chemical Shift Equivalent Nuclei
Ha
Hb
Ha
C
C
Ha
Ha
Ha
180o
C
Ha
Ha
Ha
Hb Ha
Ha
Ha
Ha
Symmetry planes
Coupling Constants
Rules for Chemical Shift Equivalence:
•
Nuclei are interchangeable by a rapid process
i.
ii.
> once in about 10-3 seconds
Rotation about a bond, interconversion of ring pucker, etc.
Examples of Chemical Shift Equivalent Nuclei
Ha
Rapid
Ha
Ha
exchange
Ha
Rapid
exchange
Coupling Constants
Magnetic Equivalence:
•
Nuclei must first be chemical shift equivalent
•
Must couple equally to each nucleus in every other set of chemically equivalent nuclei
i.
need to examine geometrical relationships
ii.
the bond distance and angles from each nucleus to another chemical set must be
identical
iii. Nuclei can be interchanged through a reflection plane passing through the nuclei
from the other chemical set and a perpendicular to a line joining the chemical shift
equivalent nuclei
Examples of Non-magnetically equivalent nuclei
Ha
Fa
Ha
C
Hb
Chemical shift
equivalent, but not
magnetic equivalent
Cl
Fa'
Ha'
Fa
Fa'
C
Hb'
C
C
Ha
Cl
Ha'
Ha'
Fa
Ha'
ab ≠
a’b
3J
3
ab’ ≠ Ja’b’
3J
3J
C
Ha
HaHc
Fa'
≠ 3JHa’Fa
3J
3
HaFa’ ≠ JHa’Fa’
3J
HaFa
≠ 3JHaHc’
3J
3
HbHc ≠ JHbHc’
3J
3
HaHc ≠ JHbHc
3J
3
HaHc’ ≠ JHbHc’
3J
C
Coupling Constants
Magnetic Equivalence:
•
Non-magnetically equivalent nuclei may lead to second order effects and very complex
splitting patterns
•
Second order effects will be discussed later
i.
Due to small chemical shift differences between coupled nuclei (Dn ~ J)
http://www.chem.wisc.edu/areas/reich/chem605/index.htm
Coupling Constants
Multiple Spin Systems
multiplicity  (na+1)(nb+1)
Cl
What is the splitting
pattern for CH2?
H
3J
Hb
Hb
C
C
C
Ha
3J
Ha
Cl
H
3J
1
11
121
1331
14641
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
Ha
= 6 Hz
= 7 Hz
Ha
Hb
= 6 Hz
Coupling to Hb splits the
CH2 resonance into a
doublet separated by 6 Hz
Down-field resonance
split into quartet
up-field resonance
split into quartet
Coupling to Ha splits each
doublet into a quartet
separated by 7 Hz
Coupling Constants
What Happens to Splitting Pattern if J changes?
5.5
5.0
4.5
3J
Hb
= 7 Hz
4.0
3.5
Looks like a pentet!
3.0
3J
Ha = 7 Hz
2.5
2.0
1.5
Intensities don’t follow
Pascal’s triangle (1 4 6 4 1)
1.0
0.5
0.0
3J
Hb
2.00
= 6 Hz
3.5
3J
Ha = 3 Hz
3.0
2.5
2.0
1.5
Looks like a sextet!
1.0
Intensities don’t follow Pascal’s
triangle (1 5 10 10 5 1)
0.5
0.0
2.00
Occurs because of overlap of peaks within the splitting pattern
Coupling Constants
Coupling Constants Provide Connectivity Information
– chemical shifts identify what functional groups are present
Cl
Hb
H
Ha
C
C
C
Cl
H
Ha
Ha
NMR Peaks for coupled nuclei share
the same coupling constants
CH3
CH
CH2
7 Hz
6 Hz
6 Hz
7 Hz
Integral:
1
6 Hz
6 Hz
2
7 Hz
7 Hz
3
Coupling Constants
Deconvoluting a spin system
– determining the J-values
– determining the multiplicities present
J coupling analysis:
i. Is the pattern symmetric about the center?
ii. Assign integral intensity to each line, outer lines assigned
to 1
iii. Are the intensities symmetric about the center?
iv. Add up the assigned intensities
– Sum must be 2n, n = number of nuclei
– Ex: sum = 16, n = 4
v. Separation of outer most lines is a coupling constant
– Relative intensity determines the number of coupled
nuclei
– Ex: intensity ratio: 1:2, 2 coupled nuclei
– 1st splitting pattern is a triplet (1:2:1)
vi. Draw the first coupling pattern
vii. Account for all the peaks in the spin pattern by repeatedly
matching the 1st splitting pattern
viii. Smallest coupling constant has been assigned
Coupling Constants
Deconvoluting a spin system
– determining the J-values
– determining the multiplicities present
J coupling analysis:
ix. Coupling pattern is reduced to the center lines of the 1st
splitting pattern.
x.
Repeat process
–
Ex: sum = 8, n = 3
–
Ex: intensity ratio: 1:1, 1 coupled nuclei
–
2nd splitting pattern is a doublet (1:1)
xi. Repeat until singlet is generated
Coupling Constants
Demo ACD C+H NMR Viewer software
– first order coupling constants
Coupling Constants
Description of Spin System
– each unique set of spins is assigned a letter from the alphabet

the total number of nuclei in the set are indicated as a subscript
– the relative chemical shift difference is represented by separation in the alphabet
sequence

Large chemical shift differences are represented by AX or AMX (nAX >> JAX)

Small chemical shift differences are represented by AB (nAB < 5JAB)

Can also have mixed systems: ABX
magnetically in-equivalent nuclei are differentiated by a single quote: AA’XX’ or
brackets [AX]2

Ha
Hx
Cl
Hx'
CH2ClCHCl2
CH3CH2R
CH3CH2F
A2X system
A3X2 system
A2M2X system
Cl
Ha'
[AX]2 or AA’XX’
system
AB system
A
M
A
A
J(AM)
J(AX)
J(AX)
J(AM)
M X
TMS
M
X
J(MX)
J(MX)
J(AM)
X
J(AX)
J(AM) = 4 Hz
J(AX)
J(AX) = 2.5 Hz
J(MX) = 6 Hz
Observed splitting is a result of this electron-nucleus hyperfine interaction
•
Coupling is measured in hertz (Hz)


reversed
reversed
reversed
Range from 0.05 Hz to thousands of Hz
Can be positive or negative
1J
o
C-H and many other one-bond coupling are positive
1J
o
A-X is negative if g are opposite sign
2J
3
o
H-H in sp CH2 groups are commonly negative
3J
o
H-H is always positive
For an AX system, JAX is negative if the
energy of the A state is lower when X has the
same spin as A (aa or bb)
The spin states and transitions are swapped
Measure the Relative Sign of Coupling Constants
•
Multiple experimental approaches (different NMR pulse sequences) or
simulations
E. COSY – two-dimensional
NMR experiment
cross peaks identify which
chemical shifts are coupled
Measure the Relative Sign of Coupling Constants
•
The cross-peak patterns identifies the coupling constant sign and
magnitude
Based on the slopes of the diagonal
line drawn through coupling pattern
3J
and 3JBX have the same sign
3J
opposite sign of 3JAX and 3JBX
AX
AB
Yellow-highlighted
regions are expanded
•
Magnitude of the splitting is dependent on:

Number of bonds
3J
9.4 Hz
4J
AC 1.1 Hz
5J
AB 0.9 Hz
AB

Bond order (single, double triple)
3J
HH
8
Hz

3J
HH
11.6 & 19.1 Hz
3J
HH
9.1 Hz
Angles between bonds
trans 3JHH ~ 17 Hz
cis 3JHH ~10 Hz
geminal 2JHH ~2.5 Hz
•

dihedral angle
−
Fixed or average conformation
•
Cyclohexanes dihedral angles

−
3J
3J
9-12 Hz
ee or
ea 3-4 Hz
3J
aa
3J
aa >>
3J
ee,
3J
ea
Dual Karplus curves for
the axial and equatorial
protons
•

Cyclohexanes dihedral angles
−
examples
•

Cyclopentanes dihedral angles
−
•



Comparison between Cyclohexanes and Cyclopentanes
In chair cyclohexane, only one
In cyclopentane, two or three vicinal
vicinal coupling can be large (>7 Hz)
coupling can be large (>7 Hz)
Because of range of cyclopentane conformations, vicinal couplings are
variable: Jcis > Jtrans and Jcis > Jtrans
Only in rigid cyclopentanes can a stereochemistry be defined: Jcis > Jtrans
•

Cyclobutanes are flatter than cyclopentanes, so: Jcis > Jtrans
−

unless structure features induce strong puckering of the ring or electronegative
substituents are present
Cyclopropanes are rigidly fixed, so Jcis > Jtrans is always true
•

Orientation
−
unless structure features induce strong puckering of the ring or
electronegative substituents are present
Since methyl groups can freely rotate,
the observed coupling is the average of
the three individual coupling constants
−
Internal hydrogen bonds may lead to constrained conformations and
distinct different coupling constants

3J
3J
Electronegativity of Substituents
coupling constant decreases
as electronegativity increases
H-H
decreases even more with
two electronegative substituents
H-H

3J
Electronegativity of Substituents
coupling constant decreases as
electronegativity of substituents
increases for cycloalkenes
H-H
3J
coupling constant decreases as
electronegativity of substituents
increases for alkenes
H-H

Ring Size
−
Coupling constants decrease as ring size gets smaller
−
Coupling constants also decrease as ring is formed and gets smaller

Bond order
−
Coupling constant decreases as bond order decreases
3J
H-H

= 8.65 x (n bond order) + 1.66
Heterocycles
–
Heterocycles have smaller coupling constants compared to hydrocarbons
systems
•

Proportional to gagb
1J
C-H
125 Hz
2J
F-H
1J
N-H

95 Hz
s character of bonding orbital
–
Increases with increasing s-character in C-H bond
48.2 Hz
•

Attenuated as the number of bonds increase
–
Usually requires conjugated systems (aromatic, allylic, propargylic,
allenic) or favorable geometric alignment (W-coupling)
–
Not usually seen over more than 4 to 5 bonds (acetylenes and allenes)

Geminal protons (H-C-H) fall into two major groups
–
Unstrained sp3 CH2 protons: 2JH-H -12 Hz
–
Vinyl sp2 CH protons: 2JH-H 2 Hz

Geminal protons coupling constants are effected by the electronic effects of
substituents
–
Note:
opposite
trend
Based on the interaction between the filled and empty orbitals of the CH2
fragment
Magnitude of the splitting is dependent on electronic effects:


In acyclic and unstrained ring systems: 2JH-H ~ -10 to -13 Hz
When CH2 is substituted with a p-acceptor, like carbonyl or cyano coupling
becomes more negative: 2JH-H ~ -16 to -25 Hz
−

Reliable and can help with structure assignments
Conjugated aryl, alkene and alkyne substituents also makes coupling
becomes more negative




In unsaturated carbons: 2JH-H ~ 2.5 Hz
Electronegative substituents (F,O) behave as p-acceptors with a negative
effect with 2JH-H close to zero
Electropositive substituents (Si, Li) behave as p-donors with a negative
effect with 2JH-H
Oxygen substituents can behave as a strong s-acceptor and strong p-donor
(lone pair), both positive effects leading to a large 2JH-H or as a strong pacceptor leading to large negative coupling

Summary of effects, s and p acceptors have opposite effects on coupling, as
do s and p donors
Coupling Constants
Weak coupling or first-order approximation
•
Up to now, we have assumed the frequency difference (chemical shift) between the
coupled nuclei is large
i.
•
Dn >> J
Second order effects come into play when this assumption is no longer valid
i.
Dn < 5J
•
Second order effects lead to very complex splitting patterns that are difficult, if not
impossible to interpret manually and leads to incorrect chemical shifts and coupling
constants
•
Interpreting NMR spectra with second-order effects usually requires software
Second-Order Effects (Strong Coupling)
– occurs when chemical shift differences is similar in magnitude to coupling
constants (Dn/J < 5)

chemical shifts and coupling constants have similar energy and intermingle

results from mixing of the equivalent ab and ba spin states

none of the transitions are purely one nuclei

described by quantum mechanical wave functions
AB spin system

perturbs peak intensity and position
AB spin system
as chemical shift differences decrease, intensity of outer lines become
weaker and internal lines become stronger

the multiplet leans towards each other (“roof” effect) which increases as
chemical shift difference decreases


becomes easier to interpret at higher magnetic field strengths
Higher field increases Dn/J
– hierarchy of coupling constants with increasing second-order effects
1. AX and all other first order systems (AX2, AMX, A3X2, etc.)
2. AB
i.
Line intensities start to lean
ii.
J can be measured, d can be calculated
3. AB2
i.
Extra lines
ii.
Both J and d have to be calculated
4. ABX, ABX2, ABX3
i.
JAB can be measured, everything else requires calculation
5. ABC
i.
Both J and d have to be determined from computer simulation
6. AA’XX’
i.
Do not become first order even at high magnetic fields
ii.
Both J and d have to be determined from computer simulation
7. AA’BB’
8. AA’BB’X
9. Etc.
– general effect of strong couplings on NMR spectra
1. Line intensities are no longer integral ratios, no longer follow Pascal’s
triangle
2. Line positions are no longer symmetrically related to chemical shift position
i.
Multiplet center may no longer be chemical shift (AB and higher)
3. Some or all coupling constants can no longer be obtained from the line
separations (ABX and higher)
4. The signs of coupling constants affect the line positions and intensities
(ABX and higher)
5. Additional lines over the number predicted by simple coupling rules appear
i.
Peaks with intensities of 2 or more are split into individual components
More lines then the
expected triplet for
the boxed CH2 pair
– general effect of strong couplings on NMR spectra
6. Coupling between equivalent nuclei (JAA’ or JXX’) affects line count and
position
i.
Second order effects appear even if Dn/J is large for groups of magnetically
non-equivalent protons with identical chemical shifts which are coupled
i.
Do not get simpler at higher fields
7. Computer analysis becomes mandatory to extract accurate J and d values
(ABC and higher)
8. Ultimately spectra become so complex that the only useful information is
integration, chemical shift and general appearance.
Second-Order Effects
– as the chemical shifts coalesce

intensity of outer lines decrease
inner peaks eventually collapse to
singlet

nuclei become chemically and
magnetically equivalent

Weaker outer lines may
be overlooked and
interpreted as a doublet
May be misinterpreted
as a quartet
AB spin system
Second-Order Effects (AB)
– analysis of second-order splitting patterns

remember: resonance positions are also perturbed

separation between outer lines and inner lines (a-b, c-d) yields coupling constant


JAB = (na-nb) = (nc-nd)
true chemical shift is not the doublet centers

ncenter = ½(nb+nc)

DnAB = √ (na-nd) (nb-nc)

nA = ncenter + ½ DnAB

nB = ncenter - ½ DnAB
dA
dB
Second-Order Effects (AB2)
– as the chemical shifts coalesce

line intensities no longer follow simple rules
arithmetic average of the line positions no
longer give true chemical shifts

JAB can still be measured directly from
spectrum


none of the line separation correspond to JAB

additional lines appear
AB2 spin system
Note:
splitting of
intense lines
– four A lines n1 – n4 and four B lines n5 – n8 and the very weak combination line n9
– calculation of nA, nB, and JAB is simple:
– how to report an AB2 spin system in a journal manuscript:
report the two chemical shifts as an AB2 multiplete (m):

2.63, 2.69 (AB2m, 3H, JAB = 12.2 Hz)
– unique features of second-order splitting pattern for AB2 system

Spectrum depends only on the ratio Dn/J

lines 1 to 4 correspond to the one proton part (A)

lines 5 to 8 correspond to the two-proton part (B2)

line 5 (n5) is the most intense line

lines 5 and 6 often do not split up

when Dn/J << 1, the spectrum appears nearly symmetrical


lines 1,2, 8 (n1, n2 ,n8) become very weak

looks like a distorted triplet with 1:10:1 area ratio
JAB and JBB do not affect the spectrum
Second-Order Effects (ABX)
– most complex spin-system that can still be manually analyzed
– ABX has a common appearance

AB – unsymmetrical 8-line pattern that integrates to 2 protons

AB – 4 doublets with the same separation JAB with strong leaning

X – symmetric 6-line pattern that integrates to 1 proton

X – 5th and 6th lines are small and not often seen, apparent doublet of doublet

JAB and nX are directly measurable from spectrum
nX - center
AB

JAX, JBX, nA and nB need to be calculated
X
of peaks
– Many ABX patterns are sufficiently close to AMX (nAB >> JAB)

first-order solution has an excellent chance of being correct
A & B doublet of doublet
separation is JAX & JBX
Center doublets
and get AB pattern
– First, identify the distorted doublet of doublets for both A and B
– Remove the splitting (identify the center of each doublet), which leaves an AB pattern
– Solve AB pattern as before to get JAB, nA, and nB

large errors when JAX and JBX are very different or nAB small compared to JAB
– Correct analysis of ABX patterns

Reverse the order of extracting coupling constants to approximate solution
Identify the two AB quartets
Jab+ = Jab-
– First, identify the two AB quartets

separation between the four pairs of lines are identical

tall inner line associated with shorter outer line (leaning)
– Correct choice of ab quartet
– Incorrect choice of ab quartet
– Solve the two ab quartets

Treat as normal AB patterns and obtain four chemical shifts (na+,nb+,na-,nb-)

Don’t know which half is a and which is b - two possible solutions
– Solution 1 and Solution 2 – depends on the relative sign of JAX and JBX

Solution 1: JAX and JBX same sign

Solution 2: JAX and JBX different sign
Swap the a & b labels
– Which solution is the correct one?
– Several criteria can be used:
1. Magnitude of the couplings – one solution may give dubious (very large or very
small) couplings
2. Signs of coupling constants – the signs can sometimes be predicted and rule
out a solution

all vicinal 3J couplings are positive,

geminal 2J couplings at sp3 carbons are usually negative

CHXCHAHB – JAX and JBX have the same sign

CHACHBHX – JAX and JBX have different signs
3. Analysis of the X-part – the intensities of the lines in the X-part are always
different – most reliable way to identify the correct solution
Two different X patterns
depending on relative sign of
JAX and JBX
– Effective of relative sign of JAX and JBX on AB pattern
Solution 1
JAX and JBX same sign
Solution 2
JAX and JBX different sign
– AB pattern from ABX spin
system as a function of
changing nAB
– AB pattern from ABX spin
system as a function of
the relative sign and
Magnitude of JAX and JBX
JAX and JBX same sign
JAX and JBX different sign
Demo ACD C+H NMR Viewer software
– second order coupling constants

Chapter 3: Coupling Constants

Transcription

Similar documents

Fernco Flexible Coupling Installation - Fernco

GEISLINGER COUPLING

Chpt 8

Pedestrian Operated Tug | Malaysia Electric Tug Solutions

Fernco Flexible Coupling Installation - Fernco

GEISLINGER SAE