1. Hyperfine Effects in Non-Rigid Molecules with 5 Equivalent Nuclei Laurent H. Coudert Laboratoire Inter-Universitaire des Systèmes Atmosphériques Créteil, France

2. Introduction This kind of coupling is displayed by non-rigid molecules such as H 5 + and PF 5. This kind of hyperfine structure has not yet been investigated. 5 atomes are exchanged by large amplitude motions

3. Overview 2. The effective hyperfine Hamiltonian. 1. The tunneling energy levels of H 5 +. 3. The hyperfine energy levels. 4. Symmetry adapted nuclear spin functions. 5. Results.

4. The 3 large amplitude motions of H 5  H 2 Rotation Isomerisation H 3  Rotation Kraemer, Spirko, and Bludsky, J. Molec. Spectrosc. 164, 500 (1994). There are 60 equilibrium configurations. Complete scrambling of all 5 hydrogen atoms. The symmetry group is G 240  S 5  {E, E*}

5. The tunneling sublevels of H 5  23 cm  1 Kraemer, Spirko, and Bludsky, J. Molec. Spectrosc. 164, 500 (1994).

6. The effective hyperfine Hamiltonian For A-type sublevels H = C S (I 1  I 2  I 3  I 4  I 5 )·J For G-, H-, or I-type sublevels H = C S (I 1  I 2  I 3  I 4  I 5 )·J + other terms

7. The hyperfine energy levels For J  5 and C S  1 MHz Pauli principle A 2  for H 5   A 1  for D 5 

8. Symmetry adapted nuclear spin functions 1 1 Soviet Maser Research, Acad. D. V. Skobel'tsyn, 1964 2 Wolf, Williams, and Weatherly, J. Chem. Phys. 47, 5101 (1967). 3 Bhattacharjee, Muenter, and Coudert, J. Chem. Phys. 97, 8850 (1992).  i, I  They are characterized by their symmetry species  i in S 5 and by I the total nuclear spin quantum number. Available for n  2, 3, 2 and 4 3

9. Symmetry-adapted nuclear spin functions

11. Hyperfine energy levels symmetry For J  5 and C S  1 MHz

12. Hyperfine pattern J = 5, A 2   4, A 2 

13. Hyperfine pattern J = 5, G 1   4, G 1 

14. Hyperfine pattern J = 5, H 2   4, H 2 

15. Hyperfine pattern J = 5  4

16. Building the functions 1 1 Jahn and Hope, Phys. Rev. 93, 318 (1954) and Ord-Smith, Phys. Rev. 94, 1227 (1954)

17. The symmetry group of H 5  G 240  S 5  { E, E* } S5S5