生物核磁共振波谱学
NMR in Biological Science
2,Basics of NMR
THNMR
YAN
What is NMR?
? NMR,Nuclear Magnetic Resonance,is a phenomenon
which occurs when the nuclei of certain atoms are
immersed in a static magnetic field and exposed to a
second oscillating magnetic field,
? 核磁共振 是指核磁矩不为零的核，在外磁场的作用下，核
自旋能级发生塞曼分裂 (Zeeman splitting）,共振吸收某一
特定频率的射频（ radio frequency,RF） 辐射的物理过程。
? Ref,http://www.nmr.de
THNMR
YAN
2.1 Spin Physics
? What is spin?
Spin is a fundamental property of nature like
electrical charge or mass,
Spin comes in multiples of 1/2 and can be + or -,Protons,
electrons,and neutrons possess spin,Individual
unpaired electrons,protons,and neutrons each
possesses a spin of 1/2,
THNMR
YAN
2.1 Spin Physics
? Nuclei with spin
? 1） I = 0,当中子数、质子数均为偶数；如,12C,16O…
? 2） I = 半整数，当中子数与质子数一为奇数，一为偶数
? 如,I = 1/2,1H,13C,15N,19F,31P…
I = 3/2,23Na,35Cl,39K…
I = 5/2,17O,25Mg…
? 3） I = 整数，当中子数与质子数均为奇数，如 2H,14N…
原子核的自旋角动量与磁矩
自旋量子数 I不为零时，原子核具有自旋角动量 P
原子核磁矩与自旋角动量之间存在如下关系：
?为磁旋比 (magnetogyric ratio)或
旋磁比 (gyromagnetic ratio)
?)1(2)1( ????? IIhIIP
P???
原子核在外磁场中的运动
- in a magnetic field,both I and Iz are quantized
- the nuclear spin can only be orientated in (2 I + 1) possible ways,with
quantum number m ranging from -I to I (-I,-I+1,-I+2,… I)
- the most important nuclei in biology are the spin-1/2 isotopes 1H,13C,15N,
19F,and31P
- as spin-1/2 nuclei they can assume two states in a magnetic field,a (m = -
1/2) and b (m = + 1/2)
THNMR
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磁矩的空间量子化
? 量子力学原则：外磁场中，自旋角动量与磁矩的取向是量
子化的
? 自旋角动量在 z轴上的投影由磁量子数 m决定,m有 2I+1个
可能取值，即 - I,-I + 1,…,I -1,I
? 核磁矩在 z轴上的投影
? 磁矩和磁场的相互作用能
? 原子核相邻能级间发生跃迁所需要的能量
?mPz ?
?mP zz ?????
00 BBE z???????
00 BBmE ?? ??????
THNMR
YAN
Properties of Spin
? When placed in a magnetic field of strength
B0,a particle with a net spin can absorb a
photon,of frequency ?,The frequency ?
depends on the gyromagnetic ratio,? of the
particle,
?0 = (?/2?) ? B0
? For hydrogen,? = 42.58 MHz / T,
00 B???
Memo:
THNMR
YAN
0BEhv ?????
Nuclei with Spin
N u c le i U n p a ire d
P r o t o n s
U n p a ire d
N e u tro n s
N e t Sp in ?
(MH z /T )
1
H 1 0 1 /2 4 2, 5 8
2
H 1 1 1 6, 5 4
31
P 0 1 1 /2 1 7, 2 5
23
Na 2 1 3 /2 1 1, 2 7
14
N 1 1 1 3, 0 8
13
C 0 1 1 /2 1 0, 7 1
19
F 0 1 1 /2 4 0, 0 8
THNMR
YAN
The Larmor frequency can be understood as the
precession frequency of the spins about the axis of
the magnetic field B0
THNMR
YAN
Rotating Frame of Reference
It is convenient to define a rotating frame of reference
which rotates about the Z axis at the Larmor
frequency,We distinguish this rotating coordinate
system from the laboratory system by primes on the
X and Y axes,X'Y',
A magnetization vector rotating at the Larmor
frequency in the laboratory frame appears stationary
in a frame of reference rotating about the Z axis,
A transverse magnetization vector rotating about the
Z axis at the same velocity as the rotating frame will
appear stationary in the rotating frame.
THNMR
YAN
Pulsed Magnetic Fields
An alternating current will produce a magnetic
field which alternates in direction,
THNMR
YAN
In a frame of reference rotating about the Z
axis at a frequency equal to that of the
alternating current,the magnetic field along the
X' axis will be constant,When the alternating
current through the coil is turned on and off,it
creates a pulsed B1 magnetic field along the X'
axis,
The spins respond to this pulse in such a way
as to cause the net magnetization vector to
rotate about the direction of the applied B1 field,
Pulsed Magnetic Fields
THNMR
YAN
The rotation angle depends on the length of
time the field is on,?,and its magnitude B1,
? = 2 ??? B1,
The proton possesses a
property called spin which,
1 can be thought of as a small
magnetic field,and
2 will cause the nucleus to
produce an NMR signal.
THNMR
YAN
THNMR
YAN
Boltzmann Statistics
? When a group of spins is placed in a magnetic field,each spin
aligns in one of the two possible orientations,
? At room temperature,the number of spins in the lower energy
level,N+,slightly outnumbers the number in the upper level,N-,
Boltzmann statistics tells us that
? N-/N+ = e-?E/kT,
? ?E is the energy difference between the spin states; k is
Boltzmann's constant,1.3805·10-23 J/Kelvin; and T is the
temperature in Kelvin,
? For 11.7 T (= 100 MHz) and 300 K one gets for 1H a population
difference N?-N+ of ca,77·10-6 —— NMR is insensitiveTHNMR
YAN
核磁共振的产生
在外磁场中，具有磁矩的核存在着不同的能级。
如果用某一频率的电磁波来照射样品，并使得
电磁波满足核跃迁所需要的能量，就会产生核
磁共振现象。
跃迁所需要满足的选律为
即 ?=?Bo/2?
或 ?=2??=?Bo
0Bh ????
Memo:
THNMR
YAN
Nuclei with Spin
THNMR
YAN
THNMR
YAN
2.2 弛豫过程
? 发生核磁共振现象时，样品吸收电磁波量子（能量等于能级差），从低
能级跃迁到高能级。同时，高能级的粒子也能跃迁到低能级。这两种过
程发生的几率相同。
? 由于波尔兹曼分布，低能级粒子多于高能级粒子。
? 因此，发生核磁共振现象时，将观察到净吸收信号。
? 高能态粒子可以通过自发辐射回到低能级，但在 NMR中，由于能级之间
的能量非常小，自发辐射的几率非常小
? 当高、低能级的布居数相等时，将无法观察到 NMR现象，这种现象叫做
饱和（ saturation）
? 因此，必须有某种过程存在，使高能级的粒子能够回到低能级，这个过
程就是弛豫过程（ relaxation）
? 了解：纵向弛豫和横向弛豫
THNMR
YAN
T1 Processes
THNMR
YAN
Mz = Mo ( 1 - e-t/T1 )
1
0
T
MM
dt
dM zz ??
THNMR
YAN
T2 Processes
MXY =MXYo e-t/T2
THNMR
YAN
2
0
T
M
dt
dM xyxy ??
Time Domain NMR Signal —— >
NMR Spectrum
THNMR
YAN
2.3 Fourier Transforms
? A Fourier transform is
an operation which
converts functions from
time to frequency
domains,An inverse
Fourier transform ( IFT )
converts from the
frequency domain to
the time domain.
THNMR
YAN
Fourier Transformation
All periodic functions (e.g.,of time t) can be described as a sum
of sine and cosine functions:
f(t) = a0 / 2 + a1cos(t) + a2cos(2t) + a3cos(3t) +,..
+ b1sin(t) + b2sin(2t) + b3sin(3t) +,..
The coefficients an and bn can be calculated by FOURIER
transformation:
with exp{i?t} = cos(?t) + i sin(?t)
THNMR
YAN
THNMR
YAN
- the two functions of a FOURIER transform pair can be converted into
each other by FT oder inverse FT (same algorithm,just sign flip from
iwt to -iwt),
- FT and iFT are linear operations,i.e.:
A f(t) ? ? A F(?) (A = complex constant)
f(t) + g(t) ? ? F(?) + G(?)
- broadening in one dimension leads to narrowing in the FT dimension:
f(A t) ? ? 1/A F(?/A)
- a time shift of the FID leads to a phase twist j of the spectrum:
f(t - ?) ? ? F(?) exp (-ijt)
- convolution theorem
- ……
Important properties of FOURIER transformation
THNMR
YAN
THNMR
YAN
MX (Real)
MY (Imaginary)
Phase Correction
MX (Real)
MY (Imaginary)
NMR in Biological Science
2,Basics of NMR
THNMR
YAN
What is NMR?
? NMR,Nuclear Magnetic Resonance,is a phenomenon
which occurs when the nuclei of certain atoms are
immersed in a static magnetic field and exposed to a
second oscillating magnetic field,
? 核磁共振 是指核磁矩不为零的核，在外磁场的作用下，核
自旋能级发生塞曼分裂 (Zeeman splitting）,共振吸收某一
特定频率的射频（ radio frequency,RF） 辐射的物理过程。
? Ref,http://www.nmr.de
THNMR
YAN
2.1 Spin Physics
? What is spin?
Spin is a fundamental property of nature like
electrical charge or mass,
Spin comes in multiples of 1/2 and can be + or -,Protons,
electrons,and neutrons possess spin,Individual
unpaired electrons,protons,and neutrons each
possesses a spin of 1/2,
THNMR
YAN
2.1 Spin Physics
? Nuclei with spin
? 1） I = 0,当中子数、质子数均为偶数；如,12C,16O…
? 2） I = 半整数，当中子数与质子数一为奇数，一为偶数
? 如,I = 1/2,1H,13C,15N,19F,31P…
I = 3/2,23Na,35Cl,39K…
I = 5/2,17O,25Mg…
? 3） I = 整数，当中子数与质子数均为奇数，如 2H,14N…
原子核的自旋角动量与磁矩
自旋量子数 I不为零时，原子核具有自旋角动量 P
原子核磁矩与自旋角动量之间存在如下关系：
?为磁旋比 (magnetogyric ratio)或
旋磁比 (gyromagnetic ratio)
?)1(2)1( ????? IIhIIP
P???
原子核在外磁场中的运动
- in a magnetic field,both I and Iz are quantized
- the nuclear spin can only be orientated in (2 I + 1) possible ways,with
quantum number m ranging from -I to I (-I,-I+1,-I+2,… I)
- the most important nuclei in biology are the spin-1/2 isotopes 1H,13C,15N,
19F,and31P
- as spin-1/2 nuclei they can assume two states in a magnetic field,a (m = -
1/2) and b (m = + 1/2)
THNMR
YAN
磁矩的空间量子化
? 量子力学原则：外磁场中，自旋角动量与磁矩的取向是量
子化的
? 自旋角动量在 z轴上的投影由磁量子数 m决定,m有 2I+1个
可能取值，即 - I,-I + 1,…,I -1,I
? 核磁矩在 z轴上的投影
? 磁矩和磁场的相互作用能
? 原子核相邻能级间发生跃迁所需要的能量
?mPz ?
?mP zz ?????
00 BBE z???????
00 BBmE ?? ??????
THNMR
YAN
Properties of Spin
? When placed in a magnetic field of strength
B0,a particle with a net spin can absorb a
photon,of frequency ?,The frequency ?
depends on the gyromagnetic ratio,? of the
particle,
?0 = (?/2?) ? B0
? For hydrogen,? = 42.58 MHz / T,
00 B???
Memo:
THNMR
YAN
0BEhv ?????
Nuclei with Spin
N u c le i U n p a ire d
P r o t o n s
U n p a ire d
N e u tro n s
N e t Sp in ?
(MH z /T )
1
H 1 0 1 /2 4 2, 5 8
2
H 1 1 1 6, 5 4
31
P 0 1 1 /2 1 7, 2 5
23
Na 2 1 3 /2 1 1, 2 7
14
N 1 1 1 3, 0 8
13
C 0 1 1 /2 1 0, 7 1
19
F 0 1 1 /2 4 0, 0 8
THNMR
YAN
The Larmor frequency can be understood as the
precession frequency of the spins about the axis of
the magnetic field B0
THNMR
YAN
Rotating Frame of Reference
It is convenient to define a rotating frame of reference
which rotates about the Z axis at the Larmor
frequency,We distinguish this rotating coordinate
system from the laboratory system by primes on the
X and Y axes,X'Y',
A magnetization vector rotating at the Larmor
frequency in the laboratory frame appears stationary
in a frame of reference rotating about the Z axis,
A transverse magnetization vector rotating about the
Z axis at the same velocity as the rotating frame will
appear stationary in the rotating frame.
THNMR
YAN
Pulsed Magnetic Fields
An alternating current will produce a magnetic
field which alternates in direction,
THNMR
YAN
In a frame of reference rotating about the Z
axis at a frequency equal to that of the
alternating current,the magnetic field along the
X' axis will be constant,When the alternating
current through the coil is turned on and off,it
creates a pulsed B1 magnetic field along the X'
axis,
The spins respond to this pulse in such a way
as to cause the net magnetization vector to
rotate about the direction of the applied B1 field,
Pulsed Magnetic Fields
THNMR
YAN
The rotation angle depends on the length of
time the field is on,?,and its magnitude B1,
? = 2 ??? B1,
The proton possesses a
property called spin which,
1 can be thought of as a small
magnetic field,and
2 will cause the nucleus to
produce an NMR signal.
THNMR
YAN
THNMR
YAN
Boltzmann Statistics
? When a group of spins is placed in a magnetic field,each spin
aligns in one of the two possible orientations,
? At room temperature,the number of spins in the lower energy
level,N+,slightly outnumbers the number in the upper level,N-,
Boltzmann statistics tells us that
? N-/N+ = e-?E/kT,
? ?E is the energy difference between the spin states; k is
Boltzmann's constant,1.3805·10-23 J/Kelvin; and T is the
temperature in Kelvin,
? For 11.7 T (= 100 MHz) and 300 K one gets for 1H a population
difference N?-N+ of ca,77·10-6 —— NMR is insensitiveTHNMR
YAN
核磁共振的产生
在外磁场中，具有磁矩的核存在着不同的能级。
如果用某一频率的电磁波来照射样品，并使得
电磁波满足核跃迁所需要的能量，就会产生核
磁共振现象。
跃迁所需要满足的选律为
即 ?=?Bo/2?
或 ?=2??=?Bo
0Bh ????
Memo:
THNMR
YAN
Nuclei with Spin
THNMR
YAN
THNMR
YAN
2.2 弛豫过程
? 发生核磁共振现象时，样品吸收电磁波量子（能量等于能级差），从低
能级跃迁到高能级。同时，高能级的粒子也能跃迁到低能级。这两种过
程发生的几率相同。
? 由于波尔兹曼分布，低能级粒子多于高能级粒子。
? 因此，发生核磁共振现象时，将观察到净吸收信号。
? 高能态粒子可以通过自发辐射回到低能级，但在 NMR中，由于能级之间
的能量非常小，自发辐射的几率非常小
? 当高、低能级的布居数相等时，将无法观察到 NMR现象，这种现象叫做
饱和（ saturation）
? 因此，必须有某种过程存在，使高能级的粒子能够回到低能级，这个过
程就是弛豫过程（ relaxation）
? 了解：纵向弛豫和横向弛豫
THNMR
YAN
T1 Processes
THNMR
YAN
Mz = Mo ( 1 - e-t/T1 )
1
0
T
MM
dt
dM zz ??
THNMR
YAN
T2 Processes
MXY =MXYo e-t/T2
THNMR
YAN
2
0
T
M
dt
dM xyxy ??
Time Domain NMR Signal —— >
NMR Spectrum
THNMR
YAN
2.3 Fourier Transforms
? A Fourier transform is
an operation which
converts functions from
time to frequency
domains,An inverse
Fourier transform ( IFT )
converts from the
frequency domain to
the time domain.
THNMR
YAN
Fourier Transformation
All periodic functions (e.g.,of time t) can be described as a sum
of sine and cosine functions:
f(t) = a0 / 2 + a1cos(t) + a2cos(2t) + a3cos(3t) +,..
+ b1sin(t) + b2sin(2t) + b3sin(3t) +,..
The coefficients an and bn can be calculated by FOURIER
transformation:
with exp{i?t} = cos(?t) + i sin(?t)
THNMR
YAN
THNMR
YAN
- the two functions of a FOURIER transform pair can be converted into
each other by FT oder inverse FT (same algorithm,just sign flip from
iwt to -iwt),
- FT and iFT are linear operations,i.e.:
A f(t) ? ? A F(?) (A = complex constant)
f(t) + g(t) ? ? F(?) + G(?)
- broadening in one dimension leads to narrowing in the FT dimension:
f(A t) ? ? 1/A F(?/A)
- a time shift of the FID leads to a phase twist j of the spectrum:
f(t - ?) ? ? F(?) exp (-ijt)
- convolution theorem
- ……
Important properties of FOURIER transformation
THNMR
YAN
THNMR
YAN
MX (Real)
MY (Imaginary)
Phase Correction
MX (Real)
MY (Imaginary)
