NMR spectroscopy. Matti Hotokka Physical Chemistry Åbo Akademi University

Size: px

Start display at page:

Download "NMR spectroscopy. Matti Hotokka Physical Chemistry Åbo Akademi University"

Abner Porter
5 years ago
Views:

1 NMR spectroscopy Matti Hotokka Physical Chemistry Åbo Akademi University

2 Angular momentum Quantum numbers L and m (general case) The vector precesses

3 Nuclear spin The quantum numbers are I and m Quantum number I =, ½,, 3/,,... The most important nuclei Proton, H, I = ½ Carbon-3, 3 C, I = ½ Value of angular momentum, z component I m z

4 Rule of thumb Atomic number Z Atomic mass A Spin quantum number I Even Even Zero Even or odd Odd Half integer, ½, 3/, 5/,... Odd Even Integer,,, 3,...

5 Hydrogen Frequency MHz Spin I Abundance % H / H 3 H /.5-4

6 Periodic table 7 Li / 93 9 e 4. 3/ 3. 3/ C 5. /. 4 N O 3.6 5/.37 9 F 94. / Ne 7.8 3/.6 3 Na 6.5 3/ 5 Mg 6. 5/. 7 Al 6. 5/ 9 Si 9.9 / P 4.5 / 33 S 7.7 3/.8 35 Cl 9.8 3/ Ar 39 K 4.7 3/ Ca 6.7 7/.4 45 Sc 4.3 7/ 47 Ti 5.6 5/ V 6.3 7/ Cr 5.7 3/ Mn 4.7 5/ 57 Fe 3. /. 59 Co 3.7 7/ 6 Ni 8.9 3/. 63 Cu 6.5 3/ Zn 6.3 5/ Ga 4. 3/ Ge 3.5 9/ As 7. 3/ 77 Se 9. / r 5. 3/ Kr 3.8 9/.6 85 Rb 9.7 5/ 7 87 Sr 4.3 9/ Y 4.9 / 9 Zr 9.3 5/. 93 Nb 4.5 9/ 95 Mo 6.5 5/ Tc Ru 5. 5/ 7. 3 Rh 3. / 5 Pd 4.6 5/. 7 Ag 4. / 5.8 Cd. /.8 5 In.9 9/ Sn 37.3 / 8.6 Sb 3.9 5/ Te 3.6 / 7. 7 I. 5/ 9 Xe 7.7 / Cs 3. 7/ 37 a. 3/.3 38 La Hf 4. 7/ Ta. 7/ W 4. / Re.5 5/ Os 7.8 3/ Ir.9 3/ Pt.5 / Au.7 3/ 99 Hg 9.9 / Tl 57.8 / Pb.9 /.6 9 i 6. 9/ 9 Po At Rn

7 Magnetic moment For every nuclear spin angular momentum there is a related magnetic moment Its magnitude can be written in two ways I Component along the z-axis m z gn I N /

8 Constants for common nmr nuclei

9 Energy levels The Zeemann effect gives an energy in a magnetic field E The magnetic moment and thus the energy is quantitized E z m Selection rule m=± E m

10 Transition energy Proton, I=/, external field =.49 T E( ) ( J 8 HzT ) J Hz (.49T ) E( ) J E E( 6 ) E( ) J 6. MHz

11 A spin ½ particle E E -/ E E +/

12 A spin particle N.. Spin ½ particles are assumed if not otherwise stated E m=- E - E E E m= E + m=+

13 One nucleus z The x- and y-components of the magnetic moment are blotted out because the vector precesses.

14 Several nuclei

15 Populations g E N N m kt g N N e N N / x e x kt g N N N N N A N N N kt g N N N N A kt g N N N N A kt g N N N n N N A Proton,.49 T, 3 K => n/n A = -5

16 Larmor frequency A nucleus without electrons (fictious case) The nucleus feels the field Transition energy E Larmor The nucleus is actually shielded It feels a lower field

17 Chemical shift The electron cloud shields the nucleus The nucleus feels a lower field ( ) Transition energy E Obs Displacement from Larmor frequency E E Chemical shift Larmor Obs E Larmor

18 Practical scale E Ref Ref E Obs E Larmor Obs ( 6 Ref Obs) [Hz] The more electrons the better shielding and lower.

19 Practical scale N.. Fictious spectrum, no coupling Ar-H CH CH CH 3 TMS [ppm]

20 Practical scale Negative shielding No shielding Positive shielding Downfield, negative σ Paramagnetic shielding [T] Upfield, positive σ Diamagnetic shielding

21 Practical scale The scale is δ [ppm] for all nuclei C 6 H 6 CHCl 3 H C H 4 OC(CH 3 ) C H 6 TMS ML 5 H to -3 3 C CS OC(Me)OH C 6 H 6 CHCl 3 OC(CH 3 ) TMS N NO - CH 3 NO RSCN RNC NH

22 Classical theory Definitions r

23 Classical theory oth the nuclei and the electrons precess under an external field. Precession frequency of electrons in their orbit e mec Electrons moving in their orbit create a current I e e 4m c e

24 Classical theory Current gives rise to a magnetic field This field has the mgnitude ' I sin cr e sin m rc It lies opposite to the external field The total field felt by the nucleus is the external field minus the field generated by the electrons. ' e

25 Classical theory The total field is obtained by integrating Assume a spherical charge distribution (r) ) ( 3 4 ) ( )sin (cos 3 ' r rdr m c e r rdr d m c e e e ) ( 3 4 dr r r m c e e

26 Ramsey s theory Consider a free molecule in space No field, Hamiltonian H The unperturbed Shrödinger equation H k E k where k = is ground state, k > electronically excited state k

27 Ramsey s theory Perturbation is the magnetic field The perturbed Hamiltonian z z y y x x M M M H H Pert xyz xyz z z y y x x H chemistry! polarization diamagnetic frequency Larmor induced dipole gives dipole permanent Pert H M

28 Ramsey s theory Solve using perturbation theory Zeroth order First order Second order E E E E E Pert H E E E E E m m Pert m m Pert E E H H E

29 Ramsey s theory Chemical shift asic equation Interaction energy Diamagnetic and paramagnetic term E E E p d E E

30 Ramsey s theory In a detailed treatment σ is a tensor Explicit expression for perturbation gives for nucleus A 3 8 N el i ia ia i ia i e d r r r r r m e m m m N i i N i ia ia m m N i ia ia m m N i i e p E E L r L E E r L L m e el el el el

31 Chemical shifts Example: benzene Current I Induced Paramagnetic Diamagnetic

32 Coupling Consider the field felt by nucleus X Extra electrons A Extra electrons X

33 Coupling E Energy levels of nucleus X Nucleus A is Nucleus A is Nucleus A is Nucleus A is Without field With field With coupling

34 Coupling scheme Chemical shift Coupling TMS J [ppm] The coupling constant J is given in Hz

35 Coupling patterns Two spin ½ nuclei, e.g., protons J

36 Coupling patterns Two spin nuclei, e.g., deuterium J J J J -,- -, -,+ +, +,+,-,,+ +,-

37 Satellites Different elements do not interact. However Deuterium of heavy water solvent may contaminate the sample, e.g., acetone J(HD)=.4 Hz H 3 C-C(O)-CH 3 D HC-C(O)-CD 3 (oth H spectra!)

38 Spin vectors A quantum mechanical description of the nuclear spin

39 Angular momentum operator The operator for a general angular momentum Pauli spinors Ŝ z y x S i i S S

40 Square of S i i S S S S z y x

41 Eigenvalues z z S S S S

42 Two particles Wavefunction Note the order 3 4 () () () () () () () ()

43 Hamiltonian The Hamilton operator for high-resolution nmr is Note: the nuclear angular momentum is denoted by I, H H I I J I g H N i j j i j i ij N i zi i N i

44 Matrix elements Two spin ½ nuclei zero. are The rest I I I I I I I I I I I I

45 How to calculate () () () () 4 3 k ij i k ij i k j i i i k j i i i I I I I () () () () () () () () z z z z I I I I

46 Hamilton matrix J J J J J J L L L L

47 Solutions L L L J C J E C J E C J E J E ' i i i i i c c c c 4 3 c Q Q Q c Q Q Q c c J Q L C

48 Intensities The intensity is ' ' i j i j I P ) /( ) ( ) /( ) ( ) /( ) ( ) /( ) ( Q Q P Q Q P Q Q P Q Q P

49 Example 4 J AX 3 J 4 C J Midpoint 3 A J C ε Midpoint ε

50 Classification of spectra AX AM A δ δ δ

51 Classification of spectra A A spectrum schematically A J J J

52 Classification of spectra A A spectrum schematically A J J J ββα βαβ αββ βαα βββ αβα ααβ ααα

53 Klassificering av spektra Ett AMX spektrum schematiskt X M A J AX J AM J AX J MX J MX J MX J MX J AM J AM

54 Relaxation Excess of α spins Macroscopic magnetic moment Relaxation M n Ng N kt Equilibrium excess is n magnetic moment M Excess in a disturbed system n and M N Ng N N kt N N dn dt n n dm dt M M

55 Perturbations Longitudinal The magnetization M z is affected Alters the ratio of α and β nuclei Energy is absorbed Transversal The magnetizations Mx and My are affected The number of α and β nuclei unchanged Precession phase is affected Energy is not absorbed

56 Relaxation times After longitudinal perturbation Longitudinal or spin-lattice relaxation time τ After a transversal perturbation Transversal or phase coherence relaxation time τ The relaxation times are seconds or even minutes The relaxation times are additive m m i i i i

57 Longitudinal perturbation

58 Transversal perturbation

59 Relaxation mechanisms A few of the factors that cause relaxation Inhomogeneties in the field rownian motion Dipol-dipol interactions The electric quadrupole moment Spin-rotation interactions Anisotropy of the coupling tensor J

60 rownian motions Local inhomogeneties in magnetic field There is a characteristic correlation time τ C All local oscillation frequencies from to / τ C are present The perturbing fieldstrength is K( C ) Here ν C is the frequency of the perturbation Time τ C is typically - s From Debye s theory C C C 4a 3k C 3 T

61 Dipole-dipole interaction Affects both τ and τ C C C C DD r K C C C C C DD r K

62 Electric quadrupole interaction I 3 Q d V C I dz Q Q I

63 loch s equations asis for all relaxation treatments Macroscopic magnetic moment Total external field 3 M i i cos( t)î sin( t)ĵ k Here is the intense static field and is the radio frequency at ν

64 loch s equations Relaxation after a perturbation dm z dt dm x dt dmy dt M M M z x y M

65 loch s equations Equation of motion dm dt M î M x cos( t) ĵ M y sin( t) k M z

66 loch s equations loch s equations From these M x, M y and M z can be solved ) sin( ) sin( ) cos( ) sin( M t M M dt dm t M M M dt dm t M t M M M dt dm x z y y z y x x y x z z

67 loch s equations Magnetic susceptibility χ Value in the xy plane depends on the radio signal Value in z direction, χ, is uninteresting because the field is static Susceptibility defined via M

68 loch s equations Consider only susceptibility in xy plane The x and y are usually given as a complex number Assuming a non-saturated system ' " i L L L ) "( ) '(

69 Absorption Susceptibility Χ gives dispersion Χ gives absorption χ τ Δν χ

70 Absorption Assuming a radio field in x direction, x Absorbed energy sin( t) Absorbed effect P E M x x de dt ( ) At resonance χ may be much larger than χ " L

71 Macroscopic sample Only an extremely small net magnetisation M z is observed. The radio pulse affects all nuclei and therefore the macroscopic magnetisation M z will also behave in the same way. Only the macroscopic magnetisation can be observed.

72 Pulse types

73 Normal FT-NMR spectrum Accumulate Accumulate Accumulate

74 ATP pulse sequence Attached Proton Test Run 3 C FT-NMR spectrum H decoupling Decoupling off 3 C

75 ATP pulse sequence Up: Normal proton decoupled spectrum. Middle: = /J, only signals from the quaternary carbons will show. Down: = /J, even/odd separation. Lines pointing up refer to CH carbons, lines pointing down refer to CH and CH 3 groups Jokisaari, Lecture notes, Oulu

76 INEPT Insensitive Nuclei Enhanced by Polarization Transfer Transfer intensity from the strong absorbers (e.g., H) to unsensitive nuclei (e.g., 3 C, 4 N, 9 Si).

77 INEPT (9 o ) x 8 o (9 o ) y H: X 3 C: A Prepare transfer

78 Spin-echo experiment Pulse sequence 9 8 Wait time t Wait time t Read the spin echo

79 Spin-echo experiment y y b a x a x Sväng. Alla spinn precesserar koherent i xy planet. b Vänta. Kärnorna förlorar koherens. Sväng 8. Kärnorna återförs till koherens.

80 Spinnekoexperiment

-"l" also contributes ENERGY. Higher values for "l" mean the electron has higher energy.

-l also contributes ENERGY. Higher values for l mean the electron has higher energy. 175 - Giving the four parameters will uniquely identify an electron around an atom. No two electrons in the same atom can share all four. These parameters are called QUANTUM NUMBERS. PRINCIPAL QUANTUM