1. Molecules in highly excited rotational states J  100

2. H 2 Te Rigid Rotor Energy Levels [E(J Ka,Kc )-E(J J,0 )] J J,0 J J,1 J J-1,1 J J-1,2 J J-2,2 J J-2,3 J J-3,3 J J-3,4 J J-4,4 J J,0 J J,1 J J-1,1 J J-1,2 J A e =6.26, B e =6.11, C e =3.09 cm -1

3. Actual H 2 Te Energy Levels [E(J Ka,Kc )-E(J J,0 )] J J J,0 J J,1 J J-1,1 J J-1,2 J J,0 J J,1 J J-1,1 J J-1,2 J J-2,2 J J-2,3 J J-3,3 J J-3,4 J J-4,4

4. 1R 1L 2L 2R 1 2 1 1 1 2 2 2 J J,0 J J,1 J J-1,1 J J-1,2 in C 2v (M)

5. Are there similar effects for XH 3 molecules – say PH 3 ?

6. Morse oscillators Two-dimensional isotropic harmonic oscillators for doubly degenerate bending vibrations Numerov-Cooley solution of inversion Schrödinger equation for Rigid rotor eigenfunctions [1] H. Lin et al., J. Chem. Phys. 117, 11265 (2002) [2] S.N. Yurchenko et al., Mol. Phys. 103, 359 (2005) and references given there. We investigate by variational rotation-vibration calculations Basis functions: Hougen-Bunker-Johns theory: Eckart & Sayvetz conditions  T nuc = expansion in the  i 

7. Vibrational basis set: J ≤ 80 cc-pwCVTZ [1] refined by fitting to experimental vibrational term values [2] [1] D. Wang, Q. Shi, and Q.-S. Zhu, J. Chem. Phys., 112, 9624 (2000) [2] S. N. Yurchenko et al., Chem. Phys. 290, 59 (2003) Variational rotation-vibration calculations for PH 3 Potential energy surface:

8. Yes, there are six-fold clusters! A1/A2A1/A2 A2/A1A2/A1 E E  Cluster = A 1  A 2  2E in C 3v (M) Character table for C 3v (M) E (123),(132) (12)*,(13)*,(23)* A 1 1 1 1 A 2 1 1 -1 E 2 -1 0 E J,K  E max /cm  1 J

9.  1 PCS  = E  1 PCS   3 PCS  = (132)  1 PCS   4 PCS  = (23)*  1 PCS   2 PCS  = (123)  1 PCS   5 PCS  = (12)*  1 PCS   6 PCS  = (13)*  1 PCS   Cluster = A 1  A 2  2E in C 3v (M)

10. Watson-type Hamiltonian for PH 3 L. Fusina, G. Di Lonardo, J. Mol. Struct. 517-518, 67 (2000) J E J,K  E max /cm  1

11. Rotational coordinates xyz is molecule-fixed; XYZ is space-fixed x y z x y z X Y Z Z ( , ,  ) define orientation of molecule (xyz) relative to laboratory (XYZ). ( ,  ) define orientation of Z axis relative to molecule (xyz).      N N

12. For states with m = J (and J large), is the probability distribution for the orientation of the angular momentum relative to the molecule Integration over all vibronic coordinates and For a rovibronic eigenstate  is the probability distribution for the orientation of the Z axis relative to the molecule. Z J J

13. x y z “Top cluster states” for J = m = 40, vibrational ground state of PH 3 zz zz z y y y y y x x x x x

14. Then invert the unitary transformation to obtain = Primitive cluster states  j PCS  First symmetrize, e.g. = with similar expressions for the E functions....  

15.  1 PCS  J=20  = 94º z y x

16.  1 PCS  J=40  = 98º z y x

17.  1 PCS  J=60  = 108º z y x

18.  1 PCS  J=80  = 113º z y x  eq = 123º

19. Thanks & Acknowledgments The principal doer: Sergei N. Yurchenko, Wuppertal, Ottawa, Mülheim Other doers: Miguel Carvajal, Huelva Hai Lin, Minneapolis Serguei Patchkovskii, Ottawa A fellow ponderer: Walter Thiel, Mülheim Thanks for support from the European Commission, the German Research Council (DFG), and the Foundation of the German Chemical Industry (Fonds der Chemie).

20. Simulations of absorption spectra of NH 3 : MF09 in 1153 Smith Hall at 4:01 p.m. i.e., in 34 minutes if we‘re on schedule.......