Dynamic NMR Spectroscopy

- 8 Dynamic NMR Spectroscopy

NMR spectroscopy is not only a spectroscopic method of determining the chemical structure of the unknown compounds; at the same time, it is also a powerful tool for observing the dynamic processes that may be occurring within or between molecules: bond rotation about bond axes, ring inversion, and tautomerism (intramolecular and intermolecular exchange of nuclei between functional groups). All of these dynamic processes result in changes of the chemical environment. These changes appear in NMR spectra as changes in chemical shifts and coupling constants. The most obvious way of altering the rate of these dynamic processes is to alter the temperature. With variable temperature probes as standard accessories to modem NMR spectrometers, such experiments are easily performed. With these experiments very important physical parameters can be determined, such as the rate of the dynamic processes, and the activation parameters (E^,, AH^, A5'*, and AG*) of equilibrating systems. The appearance of the NMR spectra of an equilibrating system is a function of the rate of interconversion of the molecule. To determine the existence of a dynamic process between the two molecules A and B, the NMR spectra of this system are recorded at different temperatures. Then the observed changes in the spectra are the subject of interpretation.

AF^B

By lowering the temperature, the internal dynamic processes are slowed down, and by increasing the temperature they are accelerated. Let us assume that the activation energy of an interconverting system (A ^ B) is 25 kcal/mol. Components A and B can be separately observed by NMR spectroscopy at room temperature. On raising the temperature the activation barrier is overcome, and if the rate of the interconverting becomes sufficiently rapid, compounds A and B can no longer be distinguished by NMR spectroscopy. Only one signal is then observed in the spectrum. There are some dynamic processes in which the activation barriers are much lower. For example, the activation barriers for the rotation about the C - C single bond of the substituted ethanes are between 5 and 15 kcal/mol. This kind of 'fast process' can be observed directly on cooling the system. Most spectrometers allow the NMR spectra to be measured in a range of + 200 to - 1 5 0 ° C . 213

214

8.

8.1

DYNAMIC NMR SPECTROSCOPY

BASIC THEORIES [73]

Let us assume a system (A ^ B) that is relatively fast on the NMR time scale. This process can be an electrocycHc reaction: a cycloheptatriene-norcaradiene system (56/57) or the ring inversion of cyclohexanes (131/132). Another example is keto-enol tautomerism (133/134), which involves intramolecular proton transfer from one atom to another.

56

57

131

132 ^

equatorial

axial

G O II II HsC"^ CH^ ^CH3

.

133

? ',? I II HgC^ CH ^CHg 134

In an NMR experiment, the systems shown above have two separate signals if interconversion between these systems is slow. In a fast reaction, in which we have a fast dynamic equilibrium, we describe two rate constants k and J^ for the forward and reverse reactions. Of course, the concentrations of A and B will be different (although they may be equal accidentally). The concentrations of A and B are described with the mole fractions n^ and n^.

where n^ ^nd n^ are the mole fractions of A and B, respectively. This equilibrium can be shifted to the left as well as to the right. The position of the equilibrium is determined by AG, the free energy of the process. ^

= e"^^/^^

(40)

The rate constant of the interconversion is determined by the well-known Eyring equation. )fc=^e-^^/«^ Nh

(41)

8.1 BASIC THEORIES

215

where AG^ is the free activation energy, N is the Loschmidt number, and h is the Planck constant. We have to consider two different cases: Slow exchange: As we have discussed above, if the rate of the interconversion of A and B is slow on the NMR time scale, then we will observe separate signals for A and B. The measurement of the relative intensities of the signals will directly give the mole fractions rip, and n^ and, therefore, AG. Fast exchange: If the rate of interconversion is fast, we will observe an average NMR spectrum in which the position of the signal will be determined by the mole fractions n^ and ^B • The chemical shift of the signal is given by the following equation: ^obs

=

«A^A +

(42)

WB^

Since ^A + «B = 1

we have ^obs = ^A^A + (1

- « A ) ^

With the aid of this equation, the mole fractions of the interconverting system can be determined easily provided that we know the exact chemical shifts of A and B, which can be determined by freezing the system. Figure 109 shows the temperature-dependent NMR spectra of an interconverting system. We assume that the components A and B resonate as singlets. In the range of

2>

fast exchange

Q.

E

0

slow exchange

^A

VB

Figure 109 Variable temperature ^H-NMR spectra of an equilibrating system A t=; B.

216

8. DYNAMIC NMR SPECTROSCOPY

slow exchange we can separately observe the individual compounds A and B resonating as singlets. However, by raising the temperature, the NMR spectrum will change. When the barrier of this equilibrium is overcome, and the rate of interconverting accelerates, the signals start to broaden in the intermediate temperature range, finally collapsing into a single line. The temperature at which the individual resonance lines merge into a broad resonance line is referred to as the coalescence temperature. For this coalescence temperature TQ the rate constant of this interconverting system is given by the following equation: TT

'r.-^(A.)

TT (^A -

(43)

^ )

Here Ai' is the difference in hertz between the two signals in the absence of exchange. This equation shows that the rate constant at the coalescence temperature depends only on the chemical shift difference ^v. Since this difference varies with the strength of

84 °C

65 °C

HaC^

/CH3

O'

'CH3

Coalesence Temperature •

^

61 °C

4-

57 °C

4-

38 °C

^W 1 4

1

Oppm

Figure 110 60 MHz ^H-NMR spectra of dimethyl acetamide, recorded at different temperatures. (Reprinted with permission of John Wiley & Sons, Inc. from R.J. Abraham and P. Loftus, Proton and Carbon-13 NMR Spectroscopy: An Integrated Approach, 1978.)

8.2 EXERCISES 61-101

217

the magnetic field, it is expected that the coalescence temperature for a given system will vary with the strength of the magnetic field. By replacing k in the Eyring equation (eq. 41) we obtain the following equation:

^ ( , - , , =

^ e - ' -

(44,

and

^(f = RTc\n J^^"^

^

(45)

Measurement of TQ and the resonance frequencies in hertz can then provide the free activation energy AG*:

AG* = 19 X 10~^Tc(9.91 + log Tc - logiv^ " ^ ) )

(46)

The temperature-dependent ^H-NMR spectra of dimethylformamide 135 are given in Figure 110. The C-N bond between the carbonyl group and the nitrogen atom has a significant double bond character. Rotation of the dimethylamino group is restricted at room temperature. The protons of the two methyl groups are in different chemical environments and therefore resonate at different frequencies. When the temperature is raised, the high energy barrier of rotation is overcome, and then two methyl groups exchange position (cis and trans to carbonyl group) so fast that they cannot be distinguished by NMR spectroscopy. At first, the signals broaden and finally, at temperatures above 85 °C, coalesce to a single line. It is interesting to observe that the acetyl methyl resonance remains sharp during the line broadening of the amide methyl resonances. At the coalescence temperature, the rate constant of this dynamic process can easily be determined by using Eq. (43).

8.2

EXERCISES 61-101

Determine the structure of the compounds whose NMR spectra and molecular formulae are given below. All the spectra (61-101) given in this section are reprinted with permission of Aldrich Chemical Co., Inc. from C.J. Pouchert and J. Behnke, The Aldrich Library oflSC and IH FT-NMR Spectra, 1992.

218

8. DYNAMIC NMR SPECTROSCOPY 61.

1 200

10

10

1<0

120

100

(0

40

«

20

0

1!

C7H17NO

1 1

\

"—

• .4 J ^

1

\'\

_«

-•eL-rr-r-:--10

•

1

lao

lao

J '

'1 "

:::i„ •—K\ 4

3

ioo

so

ao

70.76 68.93 39.78 33.68 31.85 19.39 13.94

'\\\\\

A-

1

13CNMR

mM

1

v^

a»

0

62. [200

140

',^

120

U Li,

i 1

40

^

i 1

i

! • . A

1

C7H12O

k:,,,,,,

»'

1

,

L

. ^ ,

|k,

a

i

4

1

120

100

BO

flO

T

nfnqS .uVi L i

1

40

pt

194.62 150.50 133.70 29.95 27.52 22.39 13.82

=4 1^

113C NMR

.. }

63. T

'

'^W

IfO

140

i

0

C7H14O2

1

1

'

IfIj n i

1

,, 1 , , 1

10

•

,_^

. _ « - « — • ^

1 ''''

—4

1

p3CNMR

,,, 1 i

1111 f "'""i—

jJULWl

176.64 60.02 41.13 26.85 16.63 14.30 11.60

8.2

EXERCISES 61-101

219

64. 200

1 !S

!^iSj

1i

ISfi

ifi

1CS

ii

B

1

11.

13C NMR

s

L

. _

C9H-14O4

IT

l\

1 1 i . 1i^ I r

_ ^

1

171.69 61.03 22.35 15.26 14.18

65. 1 200

180

100

140

IS•0

80

100

60

40

20

0

Ml 1

i 1

13C NMR C7H14O2

k.. ~

174.47 70.41 27.77 27.64 19.09 9.21

1

1

r

lao

140

>

10

JL.

1

i

/

LL 1

t

1

)

66. [MO

'00

120

ao

100

Ml

M

jfl

0

1

i

. '

1

iU.

1

1 j

1'

l_l p

10

t

1

,J

T

e

jl ,,, M

•

•

•

"

•

'

1

f

'

L 4

r*

3

1\

;

13CNMR C9H-14O4 165.34 163.89 144.54 129.80 61.14 15.47 14.13

220

8. DYNAMIC NMR SPECTROSCOPY

67. r?S

180

1<0

140

1

120

ao

100

u

60

I

40

20

13CNMR j

0

1)

1J

C7H12O3 166.37 130.71 128.41 64.42 62.03 29.03 25.10

r*

11

•'

-

^

-

1

•

i

1

,

•,.

,

1

n1

H

^^—^^

1 tt [k ^ /'I

n I

ri(

; • { ; ;

1

ll

1

3

4

68. M2 !K Onwt40ppm. '

!S2

^

1

2i2 i

IS i

1

:

!fiS

SS 1

J 1

a_

!

_22_

iI

,

1

J

1

1

1

i

J.i ,

i fi

I__ . J

10

t

1

Ti 1 I I ' 1 ' • 1

. J\

%...

1

3

201.67 171.25 168.32 61.77 60.95 54.62 32.36 29.93 14.11 14.02

/

f

13C N M R C10H16O5

<>

69. »2

Ua

!9S

Ufi

!2

!S2

92

'

9S

'

fS

.

I

iS

I

I 1

1

Lr^"

J

\^Jr

[ 1

a JU —w>

A-

2__^

,

13C N M R C5H802Br2

M

167.36 62.51 41.21 29.72 13.89

8.2

EXERCISES 61-101

221

70. 1 200

180

160

140

120

100

tO

ao

M

20

0

13c NMR 1

_ 1

C4H6O2 1 • • • 1

h i : rr\ii hir

ii i n 1 n!tei n 1 10

1

1

180

160

168.20 68.03 44.30 20.60

hn ilU i;

4

2

1

40

20

1

71. [MO

'

U 10

120

'

100

8(

'

1

\ 1

60

jiSCNMR "

0

[., II.

C6H12O3

^^-^

109.38 76.28 65.83 63.05 26.72 25.30

., _ ^ /

10

1

L rl -rrr^ IML

A

, .,HJt~*

1

r

i

i

4

3

140

!2S

igg

gs

gs

!

>

72. W

112

1M

40

2&

2

1 ,

-L- - 1

1^

,,, /,

_^r' r - ^

10

uL=j

^

13c NMR C11H17N

H

144.02

132.86

Tl

129.03 115.11 35.04

,1 /j

31.49 22.58

14.06

I

Jkd

1

i i Liuv.• I J l 1

}

222

8.

DYNAMIC NMR SPECTROSCOPY

74. fw

'

180

1^

140

120

i

1

\

\i

100

ao

aO

20

40

13C NMR

0

1

1

!

JL

C12H8

•

139.53 129.23 128.15 127.99 127.54 127.08 124.02

r 1 1 I 10*

i

S:

A^^i^

...,,.t., 7

i''''''' '

1

' '"' ' ' ' >' '

4

75. [200

180

' ~ MO

140

120

100

n

mf

, ,

4f

20

11 1f^

if /

••

1

J1

1 lo"^'""^' '

1

-nrd'l

1

7

4

1 jli 1 2

M3CNMR

0

1

1

J C9H8CI2 134.50 128.75 128.19 127.48 60.70 35.39 25.62

8.2

EXERCISES 61-101

223

76, [200

11 0

14p

11 0

120

100

80

BO

40

20

13CNMR

(

C6H4BrCI 1

n '

133.18 132.71 130.13 120.22

\\

1 ,Q

,wl/ ^l,

t

7

1

1

.

1

.

^

1

"'"'

77.

un

_»

ISfP „

140

'

100

•0

M

4^

20

0

L_,

C6H4BrCI 135.10 131.42 130.68 129.70 127.26 122.73

-+-,-

1

13CNMR

] i1

\\\ -H

1 10

i

11

'

1 jiy 7

«

.

4

.

a0

60

,

1

4

78. |200

in

1

160

r>o

140

1

.100

40

20

0

ll

L___L__i__

Jj

C6H4BrCI 1

^

I

1

.

•

i

. 1 1 .

. . I l l

134.69 133.99 130.63 128.60 128.06 122.73

/| 1J

n1

1V

H 1 '"

1

JAI^1^

(t

7

13CNMR

t

I

, •

1

1

224

8. DYNAMIC NMR SPECTROSCOPY

79. Izoo

too

110

140

t21

100

1 1 >

1 1

'

an

m

i.

40

»

^

0

li M

—

, J 1 CioHiaBr

r

141.70 131.17 130.09 119.18 35.02 33.43 22.23 13.89

rA

,: ./I I

ii

::'; 1 1 , 1 10

' ' '"

8

1

i

4

3

a

!SI

J\

J1

f

n i^.j^^*

M3CNMR

--

^

80. 5

!S S

1B

Jifl

_L

M rr

''""

*8

i

I

S!

1

CsHjBr

J

Irf

1 H 1A

139.60 135.42 130.56 129.92 129.05 124.79 122.67 115.27

1 1

1H

13C NMR

Hdbi-rJL^

il

.•,,L,>M

81. iao

'

1n

lae

i 10

lao

100

10

fo

40

ao

0

C12H11CI

i

1 lllll

:i=d

/ / ,/ .i L l l

to

—^1JUJL

i

•

1

•

,

1

..-r ' 4

M3CNMR

L... i

1

<

135.32 132.48 131.61 129.90 129.11 128.90 128.56 126.76 125.03 122.88 39.82 19.56

8.2

225

EXERCISES 61-101 82. [200

180

160

140

120

100

80

J

60

40

20

0

13C N M R

J ^1

C9H10O2 158.38

,

129.43 121.13 114.54 68.61 50.10 44.64

A

["^ —Iv.

)

|_10

K.

I

7

'n

1iO

t

(

120

100

1

*

. JLJff. 1L

3

4

J1

t

.

1

)

20

0

83. [2 »

1

»

.

J

»

L

1

fl0

40

M3CNMR C9H10O2

1

137.80 129.10 128.26 126.35 103.65 65.22

/ r

1 10

LJVu

•

V

•

7

1(n

1 10

»

s

12'9

1Q0

~

,.. J'711

I 3

i

a(9

40

1

0

•

84. 10

1

80

20

0

C11H-14O2

il 1

,^

147.31

1

145.27 145.02 117.76 107.57 106.32 100.66 34.59 31.57

-——~

/

1 01

lil 9

8

7

6

S

^3CNMR

4

3

\

^ w -

2

0

226

8.

DYNAMIC NMR SPECTROSCOPY

85. n

i(

19

140

120

M

too

M

40

20

1

L_ ,1.-1

_^__

0

_

1 13C NMR

I -J CsHsCINOa

J_ 1

151.37 138.30 133.72 131.56 126.73 124.37 43.85 14.45

"' / /.i

10

1

4ii

T

1

U 10

1.n

1

S

j

2

60 .

40

4

1

0

»

)

1

86. 1200

"

11«

It»

L

11»

W

N.

1

i

C11H12O2

1

197.04 163.44 146.88 129.53 126.25 112.98 112.52 55.37 38.87 30.14 23.36

f

-/ 10

>

r

ii

8

i

1

i

M3CNMR !

I

L

K1 i

4

3

S

a0

! !i

i2

1

0

87. 20Q

11

S2

l iS

IS

BL_

na

1

1

is

r

1

J

:^ ._

U' ^1

[__lii

A [u

13C N M R C13H20N2O2

1

1

s

T

166.60 150.92 131.56 119.73 113.69 62.84 51.23 47.82 12.14

8.2

227

EXERCISES 61-101

88. r»pp

~0

1»

18

t20

BO

too

00

fi

Li

:>L Ll_ 1 10

S

a

1 90

1»

r

6

S

4

1»

1Q0

80

>

20

1 1ii 1

J

-uJI

40

3

13CNMR

j

CioHioBrCIO 197.74 135.35 131.88 129.45 128.30 44.52 35.21 26.59

/

-^

n

2

1

0

89.

rs

»

1 10

L

8p

4p

a

h

II

1 1

0

C13H18O2

V

1

1 10

9

~JI

1

»

1

173.45 143.19 128.40 127.23 126.58 69.08 38.99 36.19 18.42 18.05 13.61

/

/ H 4

I

k

1

3

2

81D

*D

13CNMR

f[ ) i. Jt A

0

90. XK)

It10

1n

140

1»

1C10

8(3

JJ

21»

0

C14H12O2

1

1

165.25 148.66 135.40 133.40 130.07 129.92 129.64 128.45 121.30 20.87

/ / .... J

1 '0

t

L/ n ^—^

1M

B

13C NMR

6

S

4

i

t

1

3

1

228

8. DYNAMIC NMR SPECTROSCOPY

91, w

Sp

vn

u

p

S1

!J

!S2

t

4g

22

J

13C NMR C10H9NO5

1 1

164.31 150.62 134.97 130.84 123.54 66.44 49.18 44.65

w k

—/I

L JL1

1

1 >

LA

J

__,

=iss=

92. f?oo

r»

1 50

1410

ta1

1C10

m.

0

20

40

,1 1

>

(

1

CsHiiBrOa]

y

71.87 71.22 70.42 59.03 30.13

A

'/ /

K„l 11 10

93.

5

B

7

6

5

4

13c NMR

3

2

i

5

8.2

229

EXERCISES 61-101

94. |200

11 0

1 0

1 0

120

It P

,

to

60

40

20

Ji

CeHgO

^

1

1

J

157.78 140.62 110.02 103.77 21.34 12.18

ii

J

Jr /

Jr n MO

a

-

13CNMR i

I

T

N

6

i

4

3

t20

1»

80

90

A

.A 1

0

20

)

2

95. 200

i(HJ

t{n

140

410

J

1 ..L

CsHioOa

J

151.32 142.83 110.24 109.52 70.54 64.98 50.67 44.22

r

/"• • •

r' •

..,,,,, ._.^-.—— o"

^

96. ru0

•

1»

1«10

_____

L_ L

T

120

1 (0

1i

j1

___ ^

a

X JL

S

J I. Ixk 4

3

2

100

80

60

40

1 1 11,[

1

i\

0

«

2

)

/._ .. HJc

174.13 136.12 126.84 122.08 120.80 118.10 113.31 111.23 34.54 20.26

0«»« 23ppm.

u "

9

L-J.if i.„

a

7

e

5~

!

4

1

luL

3~"

13C NMR C11H11NO2

,

^ .^-^

•

1

13c NMR

^. 2

1 ~

0

8.

230

DYNAMIC NMR SPECTROSCOPY

97. no

180

160

140

120

80

100

— U LUI

a_J.

60

40

20

M3CNMR

S

C10H9ON

J

1

150.06 147.94 144.08 129.95 128.96 128.18 126.15 123.70 121.74 18.52

:MJ1

— ^ < IJ o

1^

1ULiL 1

7

6

140

1»

4

3

2

1

0

98. 0

1. 1

MO

80

J

1 .

80

40

»

L

J

13CNMR

g

C11H10O3 162.17 161.06 155.85 143.36 128.70 112.84 112.38 101.32. 64.16 14.55

::::;;:;;/ •

\\j\ i .-•" "

h

——

i

i

U»

1 90

==4 JL ? J L•

"-/ \i 41:. :::

i

Li:;LiJ

ILU

;

3

1

1

)

e0

40

20

0

99. 200

1»

1 40

L. ^

1 1 11

1»

80

L

JL

13c NMR CiiHeOa 160.01 155.52 151.35 147.75 144.84 124.40 120.51 115.21 113.94 106.59 99.17

'•

/

1 1 01

«

«

7

•

5

4

3

2

1

0 ^

i

8.2

231

EXERCISES 61-101 100.

1 200 _ _

0~i

1 5

10

laO

1

100

80

«0

M-/:;:

113C N M F T ] C12H8O4

: : : i r ! :::

;;:;;;[,;;

MIMMjk : M M J ~

0

^^ilW i i i i i-r*: :

\\\\\m

-

20

JL

1 1 11 m ^

1J

40

. . ^ --^ : 5 - -

J

niMiM mnln

5

5

J

5

:-;«::;:

2

;

5

'

159.93 157.60 151.94 149.26 145.67 139.27 112.14 112.14 112.08 105.52 105.41 92.92 60.08

101, 1 200

1iK)

1BO

U 10

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