1. Physical Methods in Inorganic Chemistry Magnetic Resonance
Lecture Course Outline
Lecture 1: A quick reminder
A few trends in Inorganic NMR
A little more on Chemical Exchange
Essential NMR Methods
Spin Decoupling
Spin Relaxation Measurements (again and more)
Lecture 2: NMR Methods continued – 2D and others
Correlated Spectroscopy (COSY)
Nuclear Overhauser (NOE)
Magic Angle Spinning (MAS)
Lecture 3: Electron Paramagnetic Resonance
The why and when of EPR in Inorganic Chemistry
EPR methods (ENDOR, DEER)
Physical Methods – Magnetic Resonance

2. Physical Methods in Inorganic Chemistry Magnetic Resonance
Literature
H. Friebolin One and Two Dimensional NMR Spectroscopy
H. Günther NMR Spectroscopy
P. J. Hore Nuclear Magnetic Resonance (primer)
A. K. Brisdon Inorganic Spectroscopic Methods (primer)
C. P. Slichter Principles of Magnetic Resonance
R. Freeman Spin Choreography
Physical Methods – Magnetic Resonance
Website and

3. Magnetic
Resonance

4. Selected NMR properties of some elements
Gyromagnetic ratio
(107 rad T-1s-1)
26.75
8.58
6.72
1.93
-2.71
29.18
6.98
-5.31
10.84
7.05
6.35
5.12
-0.85
-1.25
-10.02
6.43
-8.50
1.12
0.50
5.80
4.82
Physical Methods – Magnetic Resonance

5. Trends in Chemical Shifts
Remember: The diamagnetic shielding generally becomes smaller as the electron density at the nucleus decreases.
Thus electronegative substituents, positive charge or increase in oxidation state usually result in decreased shielding and increased shift.
Physical Methods – Magnetic Resonance
Opposite effects may be observed for transition metals (ligand effects).

6. Effect of Charge, Substituents
and Oxidation State
Physical Methods – Magnetic Resonance

7. The effect of coordination on the chemical shift of a transition metal
Remember
The paramagnetic shielding contribution sp ~ 1/DE
2. paramagnetic currents AUGMENT the magnetic field (sp is negative, hence a DESHIELDING parameter!) DE
|sp|* d
 / ppm
E / cm-1
Co(PF3)3-
-4200 -
Co(CN)63-
26300
Co(NH3)63+
6940
23210
Co(en)33+
7010
21400
Co(NO2)63-
7350
20670
Co(acac)3
12300
16900
Physical Methods – Magnetic Resonance
Typically, shifts follow the spectrochemical series: strong field ligands give small or negative chemical shifts whilst halogens give larger chemical shifts.

8. Chemical Exchange Examples of Fluxional inorganic systems.
Remember:
Physical Methods – Magnetic Resonance
Examples of Fluxional inorganic systems.
Axial-equatorial exchange in trigonal bipyramidal systems
(PF5, SF4, PF4NMe2 , Fe(CO)5)
Bridging/axial exchange in carbonyls.
Bridging terminal exchange in boranes (B2H6 etc.);borohydrides (Al(BH4)3)
Ring-whizzing in 1-cyclopentadienides (Cu(PMe3)( 1-C5H5)
Interchange of ring bonding modes in compounds with mixed heptacity
( e.g. (1-C5H5)2(5C5H5)2Ti: (4-C6H6)(6-C5H5)Os

9. 17O spectrum of Co4(CO)12
Physical Methods – Magnetic Resonance

10. The 31P spectrum of PF4N(Me)2
All 19F equivalent at high Temperature P Fa Fe
N(Me)2
Physical Methods – Magnetic Resonance
I(31P) = (19F) = 1/2
19Fe and 19Fea not equivalent at low Temperature

11. 13C{H} spectrum of [(CH3)3C 6Li]4
Recall: multiplets 2nI + 1
I(6Li) = 1
n = 4
Jav = (5.4 Hz x 3 + 0)/4
= 4.1 Hz
Physical Methods – Magnetic Resonance
J(13C-6Li) = 5.4 Hz
n = 3

12. NMR Acronyms Nuclear Overhauser Spectroscopy
Electron Nuclear Double Resonance
Magic Angle Spinning
Correlated Spectroscopy
Physical Methods – Magnetic Resonance

13. Methods
Continuous wave E hn
Physical Methods – Magnetic Resonance B B

14. Spin Lattice Relaxation and The Inversion-Recovery Experiment
Physical Methods – Magnetic Resonance
p/2
p/2
p/2
p/2

15. Inversion Recovery Method
p/2 t3 t4 z z z z y y y y x x x x
NMR Signal
I(t)
Physical Methods – Magnetic Resonance

16. Spin Spin Relaxation and the Spin Echo Experimenty p t
echo z x y z x y = x y
Physical Methods – Magnetic Resonance f m s t z x y = x y x y s m f

17. What is the effect of relaxation on the echo amplitude?
Spin spin
Relaxation
random magnetic fields destroy phase coherence and are not refocused by p pulse
Physical Methods – Magnetic Resonance
NMR Echo of each signal:

18. Echo Trains
Physical Methods – Magnetic Resonance

19. The Method of Spin Decoupling
FACT: Spin–Spin Coupling yields important information but NMR data interpretation complicated by line splittings.
A SOLUTION: simplify spectra by removing some (chosen) splittings and learn about which nuclei couple to which.
HOW: apply a second Radiofrequency source (S2) with strength B2 in addition to transmitter S1 used for detection of spectrum (a so-called double resonance experiment). S2 is positioned at the resonance of a particular nucleus.
Physical Methods – Magnetic Resonance
RESULT: decoupled spectra are less crowded and have much higher sensitivity as all available NMR intensity concentrated into single line (and Nuclear Overhauser).

20. The Origin of the Spin Decoupling Effect
I(X) = I(A) = 1/2
A X J
Irradiation of X at its resonance frequency induces rapid transitions from X( ) to X( ) and vice versa. A “sees” a single, averaged field.
irrad at nX nA nX
X( ) X( )
A( ) A( )
Physical Methods – Magnetic Resonance
B2 of same order as 2pJAX
nX should be sufficiently far away from nA
Notation: A{X} nA

21. The Method of Spin Decoupling
i) irrad
Fluorine Spectrum I(19F) = 1/2 A Fa Fe X
ii) irrad i)
Fe{Fa}
Physical Methods – Magnetic Resonance
ii)
Fa{Fe}
I(A) = I(X) = 0

22. 31P(CH3CH2O)3 irrad 31P(CH3CH2O)3 31P(CH3CH2O)3
I(31P)=1/2
irrad
Physical Methods – Magnetic Resonance
31P(CH3CH2O)3

23. Recall: Exercise B = 1.41T Electron:
Can we transfer this polarisation?
Physical Methods – Magnetic Resonance
1H:

24. The Nuclear Overhauser Effect
1) Enhancement of Sensitivity
ie, the heteronuclear (13C – H) Nuclear Overhauser Effect
g(1H) = rad T-1 s-1
g(13C) = rad T-1 s-1
Physical Methods – Magnetic Resonance
2) Information about proximity of two nuclei (ie, protons)
3) Dependent on Cross Relaxation between different spins. Prerequisite for this cross relaxation experiment is that the spin lattice relaxation of the nuclei is dominated by dipole-dipole interaction with the other nuclear spins.

25. The origin of the Nuclear Overhauser Effect
Result: saturated proton transitions, 13C population difference increased 3-fold
Irradiate proton resonances 2 1
13C H
sat 1 3 4 1 4 2 H
sat
13C
Physical Methods – Magnetic Resonance 5 3 4
Boltzmann
Protons saturated
Cross Relaxation
Takes spins from top to bottom level, competition with 13C relaxation (restoring Boltzmann in 13C population)

26. The maximum attainable enhancement (the fractional increase in intensity)
hmax = 1/2 gI/gS
where I is the saturated spin and S is the observed spin.
Physical Methods – Magnetic Resonance
Maximum effect occurs when there is no “leakage” as a result of relaxation mechanisms other than the dipole-dipole interaction (a through space interaction!).
For homonuclear systems, maximum enhancement is 50%.
Remember that 15N and 29Si have negative g.

27. Selective Nuclear Overhauser enhancements
irrad a b g d
Difference Spectrum
Physical Methods – Magnetic Resonance
Integration d g a b

28. 29SiH(Ph)3 gSi = - 5.31 107 rad T-1s-1 Magnitude: 1+hmax = 1+1/2 gI/gS
~ -1.5
gH = rad T-1s-1
29Si{1H}
Proton Decoupled
Physical Methods – Magnetic Resonance
Coupled

29. Principles of 2-Dimensional NMR
Father of 2D NMR: Jeener, Belgium
Main Developers: RR Ernst (Switzerland),
R Freeman (UK, Oxford)
Physical Methods – Magnetic Resonance

30. What we know from FT NMR
p/2 FT
Physical Methods – Magnetic Resonance

31. 2D NMR is a domain of FT and pulsed spectroscopy
Physical Methods – Magnetic Resonance

32. Principles of 2-Dimensional NMR
The time-intervals of 2D NMR
Physical Methods – Magnetic Resonance

33. A 2-Dimensional Experiment
evolution
Series of one-dimensional NMR spectra must be recorded t1
evolution
Physical Methods – Magnetic Resonance t1
evolution t1

34. Amplitude Modulation Phase Modulation t1 t1
Physical Methods – Magnetic Resonance

35. Fourier transformation of FID signal, S(t1, t2)
must be performed to obtain 2D spectrum
as function of two frequency variables S(F1, F2)
Physical Methods – Magnetic Resonance
Spin-spin coupling was active during t1, hence F1 contains coupling constant
Larmor precession active during t2, hence F2 contains chemical shift

36. What happens during the pulse sequences?
p/2x
p/2x t1 t2
Pulse Sequence z x y z x y z x y ?

37. What happens during the second p/2x Pulse?
Pulse does not affect x-component! z x y z x y

38. ? = Pulse Sequence: t1 t2 t2 p/2x z x y z x y x y x y
Physical Methods – Magnetic Resonance = x y x y t2

39. A Simple 2D NMR Spectrum resultsF2 F1 W
Physical Methods – Magnetic Resonance W

40. Correlated Spectroscopy (COSY)
Pulse Sequence
p/2x
p/2x
Aim : To discover spin-spin couplings in a molecule.
Answer: Which resonance belongs to which nucleus? t1 t2
Physical Methods – Magnetic Resonance
Schematic COSY spectrum of an AX system

41. Physical Methods – Magnetic Resonance

42. Use of COSY to assign 11B NMR of B10H14.
(no couplings via H-bridges) 2 2 4 2
3=4
1=2
5=6=7=8
9=10 a d b c
a: 2B coupled to all kinds of B
= 3,4
Physical Methods – Magnetic Resonance
b: 4B coupled to 2 kinds of B
= 5,6,7,8
c: 2B coupled to 1 kind of B
= 9,10
d: 2B coupled to 2 kinds of B
= 1,2

43. 2D-Nuclear Overhauser Spectroscopy
p/2x
p/2x
p/2x
p/2x t1 tm t2 D
I S t1 t2 tm WI WS

44. And the resulting spectrum
I S WI WS
Physical Methods – Magnetic Resonance
Cross Peaks tell us about interacting spins.

45. 2D NOESY vs 1D NMR Physical Methods – Magnetic Resonance
69 amino acids, M = 7688
Physical Methods – Magnetic Resonance

46. 2 D NOESY – Why? Advantages wrt 1D 1H{1H} NOE:
Simplification of crowded spectra
No need for selective excitation of individual resonances
Higher efficiency
Physical Methods – Magnetic Resonance

47. NMR in Solids Problems:
Through Space dipolar coupling not averaged out (broadened spectra)
Hence, long spin lattice relaxation times T1 (lack of modulation of dipolar coupling) and therefore restriction of pulse repetition rate, consequently, poor S/N
Fast spin-spin relaxation times T2 (line broadening)
Chemical Shift anisotropy not averaged out (line broadening)
Distance dependent – information on spin separations!
Physical Methods – Magnetic Resonance
Often broad, structureless resonance

48. Temperature dependence of line width
Proton resonance line
Physical Methods – Magnetic Resonance
Solid complex adduct

49. The Dipolar Coupling-Through Space Coupling
repulsion
attraction
Every nucleus with non-zero I, has a magnetic dipole m=gI x y z
Bmz
Bmx
Physical Methods – Magnetic Resonance r q m
Anisotropic quantity

50. In a single crystal, this is simple:
Recall: D
A X
Physical Methods – Magnetic Resonance
KAX: splitting in spectrum of X caused by dipolar coupling to A

51. Magic Angle Spinning = 0 for q = 54.7o
Physical Methods – Magnetic Resonance
At this angle all dipolar interactions disappear!
Recall here that the resonance frequency of a given nucleus X coupled to a nucleus A is determined by the total field it experiences in z-direction, ie, B0 ± BAmz where BAmz is the dipolar field generated by A on X.

52. But what about a powder?
Every molecule AX has a unique q but different molecules
have different q. We need a trick.
54.7o
54.7o
Physical Methods – Magnetic Resonance
A powder sample is mounted for magic angle spinning and gives the internuclear vectors an average orientation at the spinning angle.
Also removes chemical shift anisotropy (also follows the (3cos2q-1) law).

53. How fast can you spin? - Or the relevance of the spinning speed.
Assume:
Static line width of resonance to be studied (ie, undesired interaction) is f Hz then spinning speed must exceed f Hz if all broadening interaction are to be nullified.
Spinning speeds of up to 35 kHz possible.
Physical Methods – Magnetic Resonance

54. (Ph)331PO
sper
spar
Typical spectrum of a system with axial chemical shift anisotropy.
static
1.9kHz
At low spinning rates, observation of side bands (info about principal components of shielding tensor).
3.8kHz
Physical Methods – Magnetic Resonance
At high spinning rate we see a single resonance at isotropic chemical shift.
siso

55. CP-MAS 15N spectrum of (NH4)NO3 CPMAS
Physical Methods – Magnetic Resonance
The CP(Cross polarisation)-MAS (Magic Angle Spinning) 15N spectrum of NH4NO3 shows two interesting effects:
1) the bigger chemical shift anisotropy for NO3- as compared with NH4+
2) the greater intensity for NH4+ due to magnetisation transfer from 1H.

56. 2Ca(CH3CO2)2.H2O
Physical Methods – Magnetic Resonance

57. Electron Paramagnetic Resonance (EPR) = Electron Spin Resonance (ESR)
Physical Methods – Magnetic Resonance

58. EPR is developing fast… …because its APPLICATIONS
Physical Methods – Magnetic Resonance
ENDOR at 275 GHz
(Schmidt et al 2005).
The HIPER project
“Bringing the NMR
paradigm to ESR”
Graham Smith et al.
Möbius & coworkers 360GHz
EPR is developing fast…
…because its APPLICATIONS
so demand

59. E R samples P Paramagnetic
Most substances do not contain paramagnetic species and are hence EPR silent
Advantage
Easier to interpret
Introduction of “Spin Spies”
Disadvantage
Fewer accessible systems a) b) O N O
H2N OH
Physical Methods – Magnetic Resonance S S N O O
+ Protein-SH S S
Protein N O

60. Applications of EPR Study of Electron Transfer Processes
Physical Methods – Magnetic Resonance

61. Applications of EPR Study of N@C60 (and others) Quantum Computing
Phase transition temp: 260K
4S3/2
(14N) = 1
FT-EPR
Physical Methods – Magnetic Resonance
K.P. Dinse

62. Local Structure ENDOR/ESEEM in proteins
Physical Methods – Magnetic Resonance

63. Applications of EPR Long range structure Use of Spin Labels Light Harvesting complexes
Physical Methods – Magnetic Resonance

64. Energy Splittings and Selection Rule
ES= +mSgemBB0
DmS=±1
-geh = gemB
cf.
EI = - mIghB0
(nucleus)
200
400
1H – frequency/MHz
mS = -1/2
mS = +1/2
B0/T 10 20
Physical Methods – Magnetic Resonance
100
300
ESR frequency/GHz X Q W

65. The g-value E = mSgemBB0 E = mSgmBB0 ge = 2.00232
The g-value is a unique property of the molecule as a whole and independent of any electron – nuclear hyperfine interactions.
E = mSgemBB0
E = mSgmBB0
SO coupling (SO constant l) leads to derivation of g from that of free electron
ge =
In case the electron is the only source of magnetism in the sample
Physical Methods – Magnetic Resonance
When unpaired electron couples to
1) Empty orbital (e.g., d1), g<ge
2) Occupied orbital (e.g., d9), g>ge

66. For most organic radicals, g ≈ ge
For transition metals, large deviations from ge possible
g can be measure to high accuracy (±0.0001)
g is the “chemical shift” of NMR
Physical Methods – Magnetic Resonance
g depends on structure of radical, excitation energies, strengths of spin-orbit couplings
Note: later, we will discuss that g is anisotropic and not actually a scalar but a tensor.

67. Isotropic Coupling between an electron and a nuclear spin 1/2
S in field S I
I in field
Hyperfine Coupling
aiso/4 wI wS wS
Physical Methods – Magnetic Resonance
|aiso| wS

68. More than one nucleus aSaI bSaI bSbb aSbb bSaI1aI2aI3 aSaI1aI2aI3
1 spin ½ nucleus
bSaI1aI2aI3
aSaI1aI2aI3
bSaI1aI2bI3
aSaI1aI2bI3
bSaI1bI2aI3
aSaI1bI2aI3
bSbI1aI2aI3
aSbI1aI2aI3
bSbI1bI2aI3
aSbI1bI2aI3
bSbI1aI2bI3
aSbI1aI2bI3
bSaI1bI2bI3
aSaI1bI2bI3
bSbI1bI2bI3
aSbI1bI2bI3
3 spin ½ nuclei
bSaI1aI2
aSaI1aI2
2 spin ½ nuclei
bSbI1aI2
aSbI1aI2
bSaI1bI2
bSbI1bI2
Physical Methods – Magnetic Resonance

69. Allowed Transitions for N nuclei with spins Ik
N nuclei couple to S
Total Number of states:
Total number of allowed transitions
Physical Methods – Magnetic Resonance
Frequencies of allowed transitions

70. The EPR signal is typically in the first derivative form
Employ modulation technique
Physical Methods – Magnetic Resonance

71. EPR of a Simple Isotropic C-centred radical
1mT e
Physical Methods – Magnetic Resonance

72. Another isotropic system in solution: BH3-.
EPR spectrum of [BH3●]— in solution. The stick diagram marks the resonances for the 11B(I=3/2) and the three protons. The remaining weak resonances are due to the radicals containing 10B(I=3).
Physical Methods – Magnetic Resonance

73. Oxidation of a Chromium (III) porphyrine derivative
Oxidation of a Chromium (III) porphyrine derivative* (still, isotropic in solution)
S(Cr5+) = 1/2
I(14N) = 1
I(53Cr) = 3/2 (9.6% abundant) *
Physical Methods – Magnetic Resonance

74. But nothing is ever that simple…
Anisotropic Interactions (of significance in solids, frozen solutions, membranes etc.)
with the applied field
with surrounding magnetic nuclei
between electron spins (if more than one, obviously)
Physical Methods – Magnetic Resonance
Recall:
Description of physical quantities
Isotropic: scalars
Directional: vectors
Interactions between vectorial quantities: tensors

75. g is anisotropic and varies with direction
Diagonalise
Principal values
where
Physical Methods – Magnetic Resonance
Isotropic g:
Anisotropy:
Asymmetry:

76. For an arbitrary orientation of a crystal in a magnetic field
In spherical coordinates:
Physical Methods – Magnetic Resonance

77. And the resulting powder spectrum for a rhombic g-tensor
Low spin Fe3+ in cytochrome P450
Powder
spectrum
1st derivative
Physical Methods – Magnetic Resonance

78. Often the g tensor has axial symmetry
Then: ║ ┴
And: ║ ┴
Physical Methods – Magnetic Resonance

79. ESR spectrum of a simple d1 system║ ┴
Physical Methods – Magnetic Resonance

80. But things are not that easy…
The hyperfine couplings can also be anisotropic (and often are!)
Recall:
Fermi contact Interaction
(discussion of J)
Density of unpaired electron at nucleus (s-orbital character in SOMO)
ISOTROPIC
Recall:
Dipolar Interaction, D
p,d,f orbital character in SOMO
Averages out in solution
ANISOTROPIC
Physical Methods – Magnetic Resonance

81. A Model Cu2+ system Axial symmetry I(65Cu) = 3/2 d9, S=1/2 ║ ┴
Physical Methods – Magnetic Resonance

82. Li+(13CO2─) 12C I(13C) = ½, I(7Li) = 3/2
Physical Methods – Magnetic Resonance
A(13C)>>A(7Li): Spin density mainly on 13C

83. Transition Metal EPR
Complicated by the fact that transition metal systems might have several unpaired electrons and several approximately degenerate orbitals
3d elements important as only moderate spin-orbit coupling
Ability to distinguish between high spin and low spin complexes (in ligand fields): coordination number and geometry accessible via EPR
Difficult to observe EPR on systems with integer S
Physical Methods – Magnetic Resonance
Systems:
Ti3+(d1)S=1/2
Fe3+(d5) S=5/2 (high spin) often high anisotropy, S=1/2 (low spin)
Cu2+(d9) S=1/2 I=3/2 for 63Cu and 65Cu
Co2+(d7) S= 3/2 (high spin) S=1/2 (low spin)

84. Multiple Resonance Techniques
EPR spectrum of the phenalenyl radical
Physical Methods – Magnetic Resonance

85. Physical Methods – Magnetic Resonance
“The problems of resolving the hyperfine lines may be linked to that of a man with several telephones on his desk all of which ring at the same time. If he tries to answer them all, he hears a jumble of conversations as all callers speak to him at once. Of course his callers have no problem – they only hear one voice.

86. This is analogous to recognising
…that each nucleus experiences the hyperfine field of only one electron.
Each (spin-1/2) nucleus then gives rise to two resonance conditions depending on whether the electron hyperfine field opposes or augments the applied field.
Physical Methods – Magnetic Resonance
How?
A strong radiofrequency (NMR) field induces NMR transitions which are observed as a change in the intensity of an electron resonance condition.
Electron Nuclear Double Resonance (ENDOR)

87. Electron Nuclear Double Resonance
Physical Methods – Magnetic Resonance

88. Isotropic Coupling between an electron and a nuclear spin 1/2
Recall: S I
aiso/4 wI wS S wS
Physical Methods – Magnetic Resonance

89. The ENDOR experiment (simplified)
NMR transition(3-4) at
Recall:
Thermal
Equil.
EPR 1-3
saturated.
sat 4 3
Physical Methods – Magnetic Resonance 2 1

90. Previous overhead
Relative populations are given by Boltzmann at thermal equilibrium (wI<<wS, hence populations of 1 & 2, 3 & 4 assumed identical)
Irradiate 1-3 transition (saturate at high power) – same populations in 1&3 now
Irradiate system with RF (NMR) and sweep frequency whilst continually saturating EPR transition; observe the intensity of its absorption
When RF frequency matches |wI-a/2|, transition 3-4 will be induced, restoring some population difference between levels 1&3
More EPR absorption now possible – this is an ENDOR signal
Equally, when RF frequency matches |wI + a/2| (1-4 transition), this time a pumping from 1-4 occurs (as 4 has the higher population) and a population difference between 1&3 is again achieved and EPR transition enhance – the second ENDOR signal
In practice, need to consider spin lattice relaxation processes
Physical Methods – Magnetic Resonance

91. Tetracene cations in sulphuric acid
EPR spectrum
Physical Methods – Magnetic Resonance
ENDOR

92. Orientation Selection
EPR
Hyperfine
couplings not resolved
1H ENDOR
Toluene Solvent
Physical Methods – Magnetic Resonance
Two wide doublets which give the hyperfine couplings to protons in the C8H8 and C5H5 rings directly. Repeat for parallel components and find spin densities.