NMR BasicNMR Basic Principle Principle

노 정 래군산대학교

2009. 7. 30

• Magnetization in the magnetic field

• Magnetization under RF pulse

• Detection of Magnetization

• Digitization of FID

• Fourier Transformation

• Experiment Setup

• Chemical shift & Spin coupling constant

Energy E = h h is Planck constant frequency

nucleus

Spin-0 Spin-1/2 Spin>1/212C, 16O, 18O 1H, 13C, 15N,

19F, 31P

2H, 14N, 17O

- Positive charge

- Magnetogyric ratio,

Magnetic moment,

- spin, I

I = 1/2

Iz = +1/2

Iz = -1/2

I = 1

Iz = +1

Iz = 0

Iz = -1/2

Z

E = - z Bo = Iz Bo

If magnetic field, Bo is applied to the direction of Z,

Magnetic moments in the magnetic field, Bo

(one-spin system)

Bo

I=1/2

E = Boh / 2

Bo

: Larmor Frequency

≡

≡

Mz = Mo

Magnetic moments in the magnetic field, Bo

Mz

Bo

Mx,y

Bo In the Magnetic field, Bo

- Magnetization, Mo

Mo = Nh2 2 Bo / 4kT

- Precession of Mo at frequency, about the axis of Bo

Bo

The behavior of magnetic moments in the magnetic field, Bo

Equilibrium

Mo

0,

0

yx

z

M

MM

Bo

= B/2 H = 2.675 108 T-1 rad s-1

(MHz) T (Tesla)

100 2.35

300 7.05

500 11.74

700 16.45

Bo

nucleus

11.74 T H / Srel Nat.Abd.(%)

1H 500MHz 2.675 1.00 1.00 99.9813C 125.72 0.673 3.977 1.76 10-4 1.1119F 470.39 2.517 1.063 0.83 10015N 50.66 -0.271 9.870 3.85 10-6 0.3731P 202.40 1.083 2.470 0.0665 100

First NMR Spectra on Water

Bloch, F.; Hansen, W. W.; Packard, M. Bloch, F.; Hansen, W. W.; Packard, M. The nuclear induction experiment.The nuclear induction experiment. Physical Review (1946), 70 474-85. Physical Review (1946), 70 474-85.

11H NMR spectra of waterH NMR spectra of water

Magnetization under RF pulse

partially correlated spins (Mx,y)

Coherence

coherence

Bo

x

y y

x

x

yy

x

Spin inversioncoherence

+RF Energy

Equilibrium Non equilibrium

Relaxation

x

y

z

Mo

rotating frame ( 회전 좌표계 )

x

y

z

Mo

BoBo

On-resonance Off-resonancex

y

z

Mo

Bo =0

x

y

z

Mo

Bo- /

2B1sin(+ )

RF wave ( 에너지 )

2B1

B1 ()

xx

B1 ()

z

x

y

2B1cos(+ )

B1

B

M

My

tp

effect of B1 at (on-resonance)

phase = x

x

y

z

Magnetization in the RF field (phase =0)

Bo = 0

On-resonance

B1 (o)

Magnetization in the RF field (phase =0)

y

eff eff

effect of B1 at

(off-resonance)

Beff

10 )( iBBkBeff

x

y

z

Mo

Bo - /

B1

Off-resonance

RF pulse description

2B1cos(+ )

p

B110 )( iBBkBeff

B1 Beff >> Bo – /

pulse

Mo

x

z

y

Mo

x

z

y

Mo

x

z

y

0,

0

yx

z

M

MM

Mo

x

z

y

0

, 0

MM

M

y

zx

0,

0

yx

z

M

MM

0

, 0

MM

M

x

zy

90x

90y

180x,y

Mox

z

y

Mo

x

z

y

Mo

x

z

y

90x 180y

1 2 3 4 5

t t

1

Mo

x

z

y

Mo

x

y

1 2

t

3

t

4

z

5

Spin-echo

Relaxation

Non equilibrium Equilibrium( Mx,y= 0, Mz = M0)

1. Longitudinal (spin-lattice) relaxation : Recovery to Mo

])0([)( 0/

01 MMeMtM ZTt

Z

2. Transverse (spin-spin) relaxation : recovery to Mx,y=0

2/0, )( Tt

yx eMtM Mx,

y

t

tMo

0

> 5 T1

Magnetization for one spin system

on-resonace)

90x

Coil (induction current)

Signal detection

PPSD

Hz

FID(free induction decay)

Hz

RF

Mo

x

z

y

90x

(Off-resonace) > o

Summary

x

y

z

Fourier Transformation (FT)

dtttsidttts

dtetsS ti

)sin()()cos()(

)()(

real imaginary

real imaginary

A() D()

Hz

Hz

Fourier Transformation (FT)

Real part

Reference frequencyOffset frequency

FT real imaginary

2/)cos( Tty etM

0

0

0

0

PPSD

2/)sin( Ttx etM

x

y

+

+

0Quadrature Detection

RF

Scan 1 Scan 2

Relaxation delay (d1)

Pulse width(pw)

Pulse power(tpwr)

Acquisition time (at)

(nt)

Spectral width (sw)

Offset frequency (tof)

Digitization of FID

PSD

ADC = Analog to Digital Converter

Digitization of FID

Nyquist frequency

주파수 f 인 주기 함수를 data point 로 나타내기 위한 최소 주파수 , 2f 따라서 한 주기 당 적어도 data point 를 적어도 2 개 이상 얻어야 한다 .

Real + imaginary data points at simultaneous time (Varian)

sw

npnptat dw 2

np: 총 data point sw: spectral width

In Quadrature detection

npswnp 2

Real part (COS)

Imaginary part (SIN)

160s

Nyquist Theorem 에 위배

Sampling rate & alias(folding)

주파수가 1600Hz 인 cos 함수

주파수가 400Hz 인 cos 함수 (alias 함수 )

Nyquist 주파수 :1000Hz

Folding

(aliased)

Window function

FT

S/N

61.8

72.0

30.6

122.0

Window Functions

probe

Experiment Setup

Locking - 시간에 따른 자장의 변화를 보정 - NMR 용매로 사용하는 deuterium 핵을 이용 - acetone-d6, methanol-d4, chloroform-d, DMSO

- NMR 시료에 균일한 자장을 만드는 작업- x,y 방향은 spin, z 방향은 shim coil 의 전류량으로 조절- shim 은 NMR 시료 높이에 따라 의존

1. FID 를 이용 한 spin 핵에 대한 FID 이 지수함수로 감소되도록 shim 값을

변화2. Lock level 를 이용 lock level 이 최대가 되도록 shim 값을 변화3. Field gradient 를 이용 (Gradient shimming) field map 에 회귀분석적으로 shim 값 조정

스펙트럼에서 최상의 해상도와 감도를 위해서는 shim 조절이 필수

Shimming

Shimming method

정상 Z2 감소 후 Z1 재 조정 Z4 감소 후 Z1,Z2 재 조정Z3 감소 후 Z1,Z2 재 조정

Z5 감소 후 Z1,Z2 재 조정

Z3 증가Z4 감소 후 Z1,Z2 재 조정

X, Y, XZ, YZ XY, X2-Y2

1. Spin2. Temperature setting3. Probe tune (dependence on solvent and temperature)4. Lock & shim5. Adjust reference frequency to the singlet line6. Array pulse width tp

Observer 90o pulse calibration

X

1H ( 13C )

(1H )

90X 180X

X

BB BB

S (13C)

I (1H)

1/2J 1/2J

Decoupler 90o pulse calibration with IS spin system(e.g. CH)

1. Decoupler 1H 90o calibration

DEPT, Hetcor, INADEQUATE, etc

13C {1H}J

90X 180X

X

I (1H)

S (13C)

1/2J 1/2J

2. Decoupler 13C 90o calibration

HMQC, HMBC, etc

1H {13C}J

1H-12C

1H-13C

1H-13C

1H-12C

1H-13C

1H spectrum of 13CH3I

Observer decoupler on-resonance settingTemperature settingTunning -minimize

15N-benzamide

151 Hz

90Hz

Decoupler field strength(B2) calibration

90X

low-power CW mode

S (13C)

I (1H)

90X

low-power CW mode

I (1H)

S (13C)

B2

B2

JCH

Jr

rJ

JB

CH

2

r 2

13C

1H

Chemical Shift

1H 1H

Shielding (Screening) factor,

aa

a

b

<

bbfrequency >

600 500 400 300 200 100 MHz

10 9 8 7 6 5 4 3 2 1 0 ppm

HOCH2CH3

CH3CH2

OH

220 200 180 160 140 120 100 80 60 40 20 0

CDCl3

125

CH2CH3

Chemical shift & spin coupling constants

1H

12 11 10 9 8 7 6 5 4 3 2 1 0

C CH

HC O

HC OHO

CH3O

CH3N

CHCH2

CH3

CH3C

1H and 13C Chemical shifts

(1.15~1.16)

(~0.75)

(1.5~1.6)

13C

220 200 180 160 140 120 100 80 60 40 20 0

C O C

CH3O

CH

CCH3N

CH3

CH2

CH

C OO, N

(13~23)

(22~35)(30~42)

TMS

TMS

ppm

ppm

alkane

some featured some featured 1313C chemical shiftsC chemical shifts

= -2.3 + 9.1n + 9.4n -2.5 n

CH4 H3C CH3 H2CCH3

CH3HC

CH3

CH3

CH3

-2.3 6.5

16.116.3 24.6

23.3

H2C CH2

alkyne

H2C CH

CH3

H2C CCH3

CH3123.5

115.9

133.4

19.9

111.3

141.8

24.2

HC CH71.9

alkene

arene

128.5 133.3

127.7

125.6

N O

136.0

123.5

149.9143.6

110.4

C C C

H

HH

H

212.6

73.5

CC

CO

OH

170.4

127.2

CH3

CH3

16.5

24.1

H2C

CH2

CH2

CH2

34.128.2

-gauche effect

Symmetry and Topicity

■ Homotopicity - indistinguishable atoms or groups by symmetry

■ Enantiotopicity - atoms or groups having the mirror image in a molecule

■ Diastereotopicity - atoms or groups not producing the mirror image

H2N COOH

HH

H2 H1

NH2

HHOOC

H1

H2

NH2

HHOOC

H

H1

NH2

HHOOC

CH3

H3C CH3

H

H

HCH3

CH3

CH3HO OH

O O

H H

CH3H3C

HO OH

O O

H3C H

CH3

CH3

H

Spin-spin coupling(scalar coupling, J-coupling)

Chemical bond (electron colud)

1H 19F 1H 19F

state state

1H

J/2 J/2

J

- Hybridization of the atoms- Bond lengths- Bond angles and dihedral angles- Substituent effects- The presence of neighboring -bonds

JHH [Hz] sign JCH [Hz] sign JCC [Hz] sign

1J 125-250 + 30-80 +

2J 0-30 -* -10~20 +/- <20 +/-

3J 0-18 + 1-10 + 0-5 +

3+nJ 0-7 +/- <1 +/- <1 +/-

* Usually negative, but sometimes positive

Factors influencing scalar coupling

The order of magnitude and sign of scalar couplings

Direct coupling ( Direct coupling ( 11J J ))

1JCH= 500 sH3C-CH3 H2C=CH2 C6H6 HC≡CH

1JCH [Hz] 124.9 156.4 158.4 249.0

Hybridization sp3 sp2 sp2 sp

S-fraction 0.25 0.33 0.33 0.5

C C

H

H

F

F

H

C

H

H

H

1JCH= 160.3Hz

Electronegative substituents at the position increase J value

1JCH= 202.2 Hz

Two-Bond coupling ( Two-Bond coupling ( 22J J ))

The greater the bond angle, more positive is coupling constant

H

H

H

H

H

H

-12.4 Hz

109o120o 120o

-4.5 Hz +2.5 Hz

C

H

C HC

H

H

- 4.5 Hz

109o

120o

120o

- 2.4 Hz +1.1 Hz

C H

+49.6 Hz

2JHH

180o

2JCH

H

H(C)

H

C CH(C)

0o 90o 180o

5

10

3J (Hz)

1H, 1H coupling3JHH = 7- cos + 3.83 cos 2

1H, 13C coupling3JCH = 3.81 - 0.9 cos + 3.83 cos 2

Karplus relation

Three-Bond coupling ( Three-Bond coupling ( 33J J ))

3JCH ≈ 0.6 3JHH

H1a

H2a

H2e

3Jaa ≈ 7 - 9 Hz

3Jac ≈ 3Jac ≈ 2 - 5 Hz

HH

H

H

3Jcis ≈ 6 - 14 (10Hz)

3Jtrans ≈ 14-20 (16 Hz)

H3C

H

HC

H

7.5Hz

12.4Hz

7.6Hz

3JCH3JHH

HH

H H

Long-range coupling (Long-range coupling ( 2+n 2+nJ J ))

allylic coupling

W configuration

H H

H

H

H

Hhomoallylic coupling

+1.1 Hz

-0.3 ~ -3.0 Hz

+0.4 Hz

11 1

1 2 11 3 3 1

1 4 6 4 1

11stst order spectrum order spectrum

>> J

J(H-Ha) = J(H-Hb) = J(H-Hc)

Pascal Triangle

CH2

J(H-Ha)

J(H-Hb)

J(H-Hc)

O

HH

Hc

Hb

Ha

J(H-Hb)

J(H-Hc) J(H-Hc)

H

HC CH

CH2

A

MR

X

JAR=5Hz,

JAX=6Hz

JAM=8Hz

8 Hz

5 Hz

6 Hz

5 Hz A

5 Hz

The general two cases below will most likely have 2nd order patterns▪ Aromatic protons chemical shift difference, = 0.1 ~0.5 ppm coupling constant 3JHH = 9.0 Hz, 4JHH = 3.0 Hz, 5JHH = 0.5 Hz

▪ Protons in the restricted environment

22ndnd order spectrum order spectrum

≈ J

1 2 3 4A BZA B

>> J

= 0

A B

A

≈ J

HA OH

HB

HA

Cl HB

Br

S

HA HB

ClBr

H3C CH3

H3C O

H

H

H

H

H

4-isopropylacetophenone

10 9 8 7 6 5 4 3 2 1 0

a

b

c

e

a

bcd

e

d

220 200 180 160 140 120 100 80 60 40 20 0

C

CC

C

CC

CH3C CH3

CH3C O

H

H

H

H

Ha

b

c

de

fg

h

a

b

c

d

e

f

h

g

CDCl3

1H and 13C spectra for a sample

1H

13C

220 200 180 160 140 120 100 80 60 40 20 0

a

bc

def

g

h

CDCl3

C

CC

C

CC

CH3C CH3

CH3C O

H

H

H

H

H

a

b

c

d

e

f

h

gProton Decoupling