forbidden transitions in epr professor p. t. manoharan dept. of chemistry and rsic i i t- madras...
TRANSCRIPT
![Page 1: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/1.jpg)
FORBIDDEN TRANSITIONS IN EPR
Professor P. T. ManoharanDept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India
![Page 2: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/2.jpg)
Zeeman Hamiltonian (Hydrogen atom as an example)
The electron and the nucleus both interact with the steady magnetic field
H0 = g B Sz – gn n B Iz
Isotropic Hyperfine Coupling is introduced into the Hamiltonian to take care of the interaction between the magnetic moments of electrons and the nucleus.
H1 = a I. S = a (Ix Sx + Iy Sy + Iz Sz)
where a = 8/3 g gn n | (r) |2
Anisotropic (dipolar) part of hfcc averages out to zero since the unpaired electron is present in an s-orbital
So H = g B Sz - gn n B Iz + a S. I = g B Sz - gn n B Iz + a Sz Iz + a [Sx Ix + Sy Iy]
Basis functions
e n 2 = | e n 3 = | e n 4 = | e n
![Page 3: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/3.jpg)
Transition probability for an EPR transition is
Pmn = /ħ2 | < n |V| m> |2 g()
For an EPR transition V(t) = (g B1 Sx) cos t = 2v cos t
Pmn = 2/ħ2 g2 2 B12 | < n | Sx| m > |2 g()
where Sx = ½ (S+ + S-)
Typical matrix elements would be< en | Sx | en > = < e | ½ [S+ + S-] e > < e | n> = ½ < e | S+ | e > = ½
i.e mS = ± 1 mI = 0
Transition Probability P = /2ħ2 g22B2g() .
![Page 4: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/4.jpg)
![Page 5: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/5.jpg)
Consider now
Second-order EPR levels of H-atom, inclusive of a(SxIx+ SyIy) term in the Hamiltonian Second-order ESR Spectrum/ Forbidden ESR transition
Note that en en
e n en Strictly forbidden due to the fact mI = 1
This transition now weakly allowed,if the oscillating field is polarized parallel to B0 (not perpendicular as in allowed transition) due to 2nd – order improved wave-functions.
Mixing coefficient, = a/2(gB + gn nB) i.e., V = 2g B1Sz i.e., 2|Sz|3 = (e n + e n) |Sz| (en - e n) = en | Sz | en - = -
i.e., P = 2 2g22B12g()
will be small at high field 2 negligible
![Page 6: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/6.jpg)
![Page 7: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/7.jpg)
Triplet States, S = 1
It is now possible to observe ms = 2 transitions(in addition to the normal ms = 1 transitions)
Under Cubic field (or isotropic samples) ms = 2 cannot be observed by a microwave field of any polarisation and is strictly forbidden
Axial crystal field
H = B. g. S + D [Sz2 – 1/3 S(S + 1)]
B0 || z “Diagonal Hamiltonian” gives D term Behaviour Similar to
Cubic field.
![Page 8: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/8.jpg)
But B0 || from z-axis, states gets mixed; forbidden (ms = 2 ) transitions occur.Similarly Bo || x, we get the electron spin states
|+ = a+ { | 1 + | -1} + b+ | 0 |0 = 1/2 { |1 - | -1}|- = a- { | 1 + | -1} – b-| 0
a/b depend on relative magnitudes of g B and D (of course, a function of )When B1
B0 0 + and - 0 allowed.
B1 || B0 - + allowed since
< - | Sx | + > = 2 [ a- b+ - a+ b- ]
In strong field, g B0 >> D, a+ = a- and b- = b+,
Forbidden transition intensity is zero
![Page 9: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/9.jpg)
![Page 10: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/10.jpg)
Note this is effectively the forbidden transition m = ± 2 and the axis of quantization is determined by the applied field.
Rhombic Field
The term E (Sx2 – Sy
2) E (S+2 + S-
2) is now added to the spin Hamiltonian,
which mixes the states | -1> and | +1> irrespective of the direction of B0.
Since | + > = cos | 1> + sin |-1> | 0 > = | 0 > tan 2 = E / gB0
| - > = sin | 1> - cos |-1>
Here, even when B1' || B0, the transition | - > | + > is allowed. Generally
i.e Ms = ± 1 allowed when B’ B0
Ms = ± 2 may be allowed when B1’ || B0
If basic states are sufficiently mixed.
![Page 11: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/11.jpg)
General form of transition probability
(e.g) S = 3/2 in an axial or rhombic symmetry. B0 at an arbitrary angle to the crystall axis
General form of the eigen states
| n > = an | 3/2 > + bn | ½ > + cn | ½ > + dn | -3/2>
With n = 1, 2, 3, or 4.
It is possible to have more than one “Forbidden Transitions” in terms of “Ms = 2” within the rigours of normal quantum numbers [described by the major component of an, bn, cn, dn at a moderate external field.
![Page 12: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/12.jpg)
![Page 13: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/13.jpg)
![Page 14: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/14.jpg)
2D
D
Synder & Zager, JCP (1964) 41 1763
Triphenyl Benzene dianion(Frozen soltion)
![Page 15: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/15.jpg)
free radical
gyy
C10D8
gzz
gxx
![Page 16: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/16.jpg)
![Page 17: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/17.jpg)
![Page 18: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/18.jpg)
Cu- Cu
ms ±2
ms= ±2
Ag - Ag
![Page 19: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/19.jpg)
2D
![Page 20: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/20.jpg)
![Page 21: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/21.jpg)
IT (h/kT) 1/[1+exp(-(D+h)/kT) + exp(-2h/kT) + exp(-(2J+1/3D+h/kT)] x (DT/h)2
Ddip(cm-1) = 0.433gz2/r3
System Range of T studied 2J (cm-1)
Cu(II)/Zn(II)
Ag(II)/Zn(II)
150 – 300K
180 – 300K
+40.2
+62.5
![Page 22: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/22.jpg)
‘Forbidden’ Transitions in Nuclear Hyperfine Structure.
![Page 23: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/23.jpg)
I 1
![Page 24: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/24.jpg)
Pure | ms, mI states
g
3A
![Page 25: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/25.jpg)
Complete Hamiltonian
With S = ½, I = 3/2 (eg 63, 65 Cu 2+),
the eigen spinstates are |M,mWhere M = 1/2 , m = 3/2, ½
A sample function would be like i|M,m = ai|M, 3/2 + bi|M, 1/2 + ci|M, -1/2 + di|M, -3/2 with M = 1/2
I mixes by raising or lowering the m to m 1 causing a “Forbidden Nuclear Hyperfine Line” with mI= 1 as against the EPR allowed mI= 0.
Similarly the quadrupolar operators I2 mix the functions to cause “Forbidden transition with” mI= 2
![Page 26: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/26.jpg)
![Page 27: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/27.jpg)
![Page 28: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/28.jpg)
H = . g. S + S. A. I + I. P. I – n B. gn . I. The quadrupole part of the Hamiltonian can then be expressed
as
H EQ =[ e2q Q/ 4I (2I –1)] [3Iz2 – I (I + 1) + ½ (I+
2 + I-2)]
where eq is the electric field gradient at the nucleus
eQ is the nuclear quadrupole moment is the asymmetry parameter
= (Vxx – Vyy)/Vzz
If the electric field gradient has axial symmetry, then = 0,
Since Vxx = Vyy, and HEQ
Becomes.
HEQ = e2qQ/4I(2I – 1) [3Iz2 - I(I + 1)]
![Page 29: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/29.jpg)
![Page 30: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/30.jpg)
![Page 31: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/31.jpg)
![Page 32: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/32.jpg)
![Page 33: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/33.jpg)
![Page 34: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/34.jpg)
![Page 35: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/35.jpg)
![Page 36: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/36.jpg)
Complex Q’ value (in 10-4cm-1)
Co(NH4)2(SO4)26H2O -0.2 0.05Na4CoPTS -0.2 0.1
Tutton Salt(theoretical estimation)
Co(BPT)
0.8
+1.60 0.05
Q’ = 3e2qQ/84 and Q’’ = (e2qQ/84) (/2) = (Q’/3) (/2)
From Q’ = 1.6 x 10-4cm-1 and Q’’ = 0.1 x 10-4cm-1, Hence asymmetry parameter, = 0.375
The field gradient at the nucleus can be separated into valence and lattice contributions as
eq = e(1 – R) qval + e(1-) qlig
where (1 – R) and (1 - ) are the Sternheimer antishielding factors.
Qval = nj 3 cos2j - 13d rj-3 3d
![Page 37: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/37.jpg)
Qlig = nLi 3cos2Li – 1/rLi3 + ZL3cos2 - 1/rL
3
Q’ = (3e2 Q/84) (1 – R) nj 3cos2j - 13d rj-33d
![Page 38: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/38.jpg)
![Page 39: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/39.jpg)
Double Quantum Transition and Regular Half-field Transition
Involves ms = 2 but it arise from the rapid consecutive absorption of two single Quanta i.e final state is reached via transition to an intermediate state.
Requirement: Energy separations between the adjacent levels be equal Occurs at magnetic fields comparable to those for g = 2
However, half-field transitions (since they occur at a half field of the main ms = 1 transition)Occur (in S = 1) systems when D/h < ¾Usually, Bmin = 2.0023/gmin [B2
0/4 –(D’)2 / 3 – (E’)2]12
BDq = 2.0023/gav [(B02 – (D’)2 / 3 – (E’)2]1/2
If D/h increases, the resonances may be off the available magnetic field, it is necessary to work at higher fields
![Page 40: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/40.jpg)
(eg) Ni (S = 1)
Total transition probability for a DQ transition in a 3 level system = Pik = Pij x Pjk
If D/h increases, the resonances may be off the available magnetic field, it is necessary to work at higher fields
![Page 41: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/41.jpg)
![Page 42: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/42.jpg)
Spin Flip Transitions
Any nucleus in the environment of a unpaired spin will feel a magnectic field Be
coming from the isotropic and dipolar fields. Depending on the orientation of the
electron, the fields felt by the nucleus can be termed Be+ and Be
- which in turn will
orient with respect to the applied field. The resulting field will be along, say Bx and
By, at an angle .
The angle will be almost close to zero in the case of very weakly interacting
nucleus, i.e B > Be and will be large in strongly interacting system ie. Be > B.
![Page 43: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/43.jpg)
![Page 44: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/44.jpg)
![Page 45: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/45.jpg)
It produces spin flip transition with simultaneous flip of electron and nuclear spins.
s = 1, I = 1,
As increases, mixing of the spin states increases resulting in hyperfine (allowed) lines
H = g SZ – gnnBIz + AIz. Sz
E = gms – g. B mI + ams mI
In otherwords, the second term is overtaken by the third term.
The spin flip lines occur on either side of the EPR lines with an energy separation of gn n B
hence Better resolution at higher frequencies(say Q - band)
But Higher Intensitiesat lower fields. (say s - band)
Medium freq i,.e X-band most appropriate
![Page 46: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/46.jpg)
Larger the gn better the resolution
Hence only nuclei like,1H (gn = 5.585)P9F (gn = 5.26)7Li (gn = 2.17)
(eg) 2D(gn = 0.857) gn n B ~ 2.9G at X band and with in the linewidth and its spin – flips cannot be observed
Systems with S>1/2 and I>1/2 give rise to zero field splitting due to electrons and quadrupole coupling constants due to interaction between the electric field gradient and quadrupole moment of the nucleus.
Satellite lines occur ath = g B + D (2Sz –1) gn n B + ½ (Azz 2P) (2Iz – 1) ½ Azz (2Sz – 1)
Main lines occur at h = g B + D (2Sz –1) + AzzIz
Depending on the number of interacting neighbours, complexities increase.
![Page 47: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/47.jpg)
Intensities of spin-flip Satellites
n
Isat / Imain = 9/8 g2 2 cos2i sin2i / ri6 B2
i = 1
for n different nuclei
For an effective single proton in a randomly oriented system
Isat / Imain = 3/20 g2 2 / B2 reff6 ; ri = n1/6 reff
sat = satellite line main= main line
in the case of n nearby nuclei
![Page 48: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/48.jpg)
r can be calculated by two different methods
From Intensity Isat
Imain
n= 9/8 g22 sin2i cos2 i/B2ri
i = 1From spacings
(E)2 = (gnnB)2 + (3/4 ggn n/r3E)2
E is the average distance to all of the nearest matrix nuclei interaction with the electron spins.
Possibility of Errors
(i) At x-band, the limit of weak mixing and high Field approximation assumed in this equation does not hold good and may introduce an error.
(ii) Insufficient resolution at x-band frequency
(iii) Contribution to the satallite intensity from the hyperfine coupling.
![Page 49: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/49.jpg)
![Page 50: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/50.jpg)
![Page 51: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/51.jpg)
![Page 52: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/52.jpg)
![Page 53: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/53.jpg)
![Page 54: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/54.jpg)
![Page 55: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/55.jpg)
![Page 56: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/56.jpg)
![Page 57: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/57.jpg)
![Page 58: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/58.jpg)
![Page 59: FORBIDDEN TRANSITIONS IN EPR Professor P. T. Manoharan Dept. of Chemistry and RSIC I I T- Madras Chennai- 600 036 India](https://reader036.vdocuments.mx/reader036/viewer/2022062408/56649f325503460f94c4e716/html5/thumbnails/59.jpg)
Thank You