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A GROUP THEORETICAL ANALYSIS OF ESR SPECTRUM OF tert-BUTYL RADICAL AT LOW TEMPERATURES S. Kubota, T. Momose and T. Shida H3CH3C CH 3 C.

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Presentation on theme: "A GROUP THEORETICAL ANALYSIS OF ESR SPECTRUM OF tert-BUTYL RADICAL AT LOW TEMPERATURES S. Kubota, T. Momose and T. Shida H3CH3C CH 3 C."— Presentation transcript:

1 A GROUP THEORETICAL ANALYSIS OF ESR SPECTRUM OF tert-BUTYL RADICAL AT LOW TEMPERATURES S. Kubota, T. Momose and T. Shida H3CH3C CH 3 C

2 1) Three equivalent methyl groups 2) Non-planar carbon skeleton according to an MO calculation. 3) Large amplitude motion If non-planar, an umbrella motion of the skeleton is conceivable. Three features of tert-butyl radical

3 Structure predicted by an MO calc.  : out-of -plane angle : H : C   = 8.2 degrees

4 C(CH 3 ) 3 Cl + e - (  -rays) ・ C(CH 3 ) 3  Cl - 6.6K S = a n = 9 2nS + 1 = 10 B / Gauss 75K

5 Previous analysis A planar carbon skeleton (no umbrella motion). Internal rotations of the methyl groups only. Analysis in terms of a proton permutation groups. Thus, each state was labeled as, e.g., AAA, AAEa …. S.Kubota et al. Bull. Chem. Soc. Jpn. 68 (1995) 140.

6 Present work G 27 G 324 324= 3 3 x (3! x 2) 3! x 2= 12 operations including skeletal inversion 3 3 = 27 methyl proton permutations Purpose: Search for the possible involvement of the umbrella motion.

7 H.C.Longuet-Higgins, Mol. Phys. 6 (1963) 445. G 324 character table

8 Correlation diagram between G 27 and G 324 AAAA 1, A 2, A 3, A 4, E 1, E 2 AAEI 3, I 4 AEE(AEaEa)I 1, I 2 AEE(AEaEb)I 7, I 8 EEE(EaEaEa)E 3, E 4, G EEE(EaEaEb)I 5, I 6

9 Hamiltonian proper to G 324 H=(umbrella  ) (methyl rotation  ) (nuclear spin) = H H H 

10 Quantum states  total =  elec  vib  overall rot  internal rot  nuc spin A 2 or A 4 A2A2 A1A1 A 1 or A 3

11 Hamiltonian matrix proper to G 324 Off-diagonal elements in G 27 are assumed to be zero (e.g. AAA - AAE) A 1 (ns)A 1 (hr) I 3 (ns)I 3 (hr) I 1 (ns)I 1 (hr) E 3 (ns)E 3 (hr) I 5 (ns)I 5 (hr) 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 I 7 (ns)I 7 (hr) 000 0 0 0 0 0 AAA(G 27 )... AAE(G 27 )... AEE(G 27 )... EEE(G 27 )...

12 Example of leveling splitting after the diagonalization ( In the case of I 1 and I 7 Symmetries) Zeeman Hyperfine coupling m s =  1/2 m s = 1/2 m I = 1/2 m I =  1/2

13 G 27 G 324  = 8.2

14 Conclusions E-lines of ESR spectrum of tert-butyl radical were studied with the permutation-inversion group G 324. The agreement of the theoretical spectrum with experimental is improved by changing the group from G 27 to G 324.

15 Assumptions for Simplification NH 3 tert-butyl Low enough potential to permit the neglect of tunneling effect

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