1. A tour of the vibrational motion of some unusual molecules Acteylene/vinylidiene H 3 O + Acknowledgements: Shengli Zou, Stuart Carter, Xinchuan Huang, Jaime Rheineker, Alex Brown, Department of Energy and Office of Naval Research

2. Experiments In search of the vinylidene needle in the acetylene haystack

4. Ervin, Ho and Lineberger (1989) H 2 C 2 - + hv  “vinylidene”+ e -

5. Active Normal modes of Vinylidene 6 - rocking 6 - scissors

6. J. Levin, H. Feldman, et al. Phys. Rev. Lett. 81, 3347 (1998). H 2 C 2 - + hv  “vinylidene”+ e - Study of Unimolecular Reactions by Coulomb Explosion Imaging: The Nondecaying Vinylidene “The data analysis given here shows unambiguously that a large part (,50%) of the molecules measured 3.5 ms after their production as vinylidene isomers retains the vinylidene geometry. This is inconsistent with the generally accepted concept of the vinylidene being a short-lived isomer which decays into the linear isomer within a few picoseconds.”

7. Theory and Calculations

8. Tunneling Picture -unimolecular decay 16058 cm -1 900 cm -1 “Isomerization coordinate”

9. “Barrier recrossing in the vinylidene–acetylene isomerization reaction: A five-dimensional ab initio quantum dynamical investigation” Rainer Schork and Horst Koeppel (2001) 5 dof wavepacket calculations of vinylidene with an absorbing potential just beyond TS - new ab initio calculations

10. Summary of calculations 2001 Direct dynamics (classical) C 2 D 2 - much re-crossing of the isomerization barrier RD Time-dependent wavepacket, with absorbing potential - long-lived states. (“Good” agreement with exp photodetachment spectrum with artificial broadening.) Better characterization of energetics and saddle point What would an exact quantum calculation tell us? Is such a calcualation feasible?

11. Acetylene Exact Hamiltonian      H H C C r CH 1 r CH 2 r CC M. Bramley and N. C. Handy, J. Chem. Phys. 98, 1378 (1993)

12. Acetylene Exact Hamiltonian

13. Acetylene/ Vinylidene Coordinates

14. Acetylene/ Vinylidene Isomerization C’ C H H r HH H H C’ C 22 R r cc H H C’ C r cc r HH r cc 1. Isomerization “easy” to describe 2. Permutational symmetry easy to incorporate 3. Hamiltonian is relatively simple

15. Acetylene/ Vinylidene Energetics 16058 900 “Isomerization coordinate”

16. Energetics of the Potential Surface

17. Exact Hamiltonian (J=0)

18. Diagonalization of H Let H op be the Hamiltonian operator and Let {  } be a complete orthonormal basis Always use a finite size basis, say N. Then the H-matrix is N x N. For a 2-variable problem, the direct-product space is of order N 1 xN 2 and the order of H is N 1 xN 2. Thus if we used 10 functions per mode for a six degree-of freedom problem the order would be 10 6.

19. Challenges Guo and co-workers (2002) Used force-field (no vinylidene), eigenvalues (only) Direct-product grid (DVR),H-matrix of order 44 x 10 6 Reduced to 11 x 10 6 using symmetry. Lanczos method Used to get eigenvalues only up up to 13000 cm -1. CPU time: 90 hours on a DEC alpha EV6 workstation Large-amplitude dofs: three angular, R, r HH Density of states at 20000 cm -1 : ~10 per cm -1

20. Our Diagonalization Strategy Don’t aim for spectroscopic accuracy Succesive diagonalization method Matrix diagonalizations of order 10 4 Check robustness of results Investigate the nature of molecular eigenstates above the threshold for isomerization to vinylidene

21. The 3 dof Hamiltonian J = 0 The angular basis Make linear combinations that are eigenfunctions of parity and then use the symmetry in CC-HH V 3D is from the full potential with R fixed at R cut and minimized with respect to r HH and r CC

22. Four dof Hamiltonian Combine 3D angular eigs with sine basis in R and diagonalize H 4D Two dof Hamiltonian Use a 1d cut for CC and generally no potential for HH, use sine basis instead.

23. Final Step Combine 4D eigs of H 4D with 2D eigs of H 2D Need ca 100 2D x 300 4D = 30 000. Diagonalize in the middle of the 4D basis

24. Test of the new code Low-lying states of acetylene

25. Results I. r HH 6.28 acetylene 3.54 vinlyidene R 0 acetylene 2.25 vinlyidene

26. Results II. r HH 6.28 acetylene 3.54 vinlyidene R 0 acetylene 2.25 vinlyidene

27. Wavefunction Plots (R,r HH )

28. Wavefunction Plots (R,  2 ) -0.50.00.51.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 cos (  2 ) R (bohr) E = 21680 cm - 1 -0.50.00.51.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 cos (  2 ) R (bohr ) E = 21709 cm -1

29. Simulated Photodetachment Spectra Stanton-Carter potential has incorrect vinylidene CC-stretch so we did a new potential surface, just submitted to CPL

30. All calculations on S-C potential have been re-done on new potential Energy (cm -1 ) Length (bohr)

31. Some conclusions Acetylene/vinylidene isomerization is a symmetric double well Molecular eigenstates with vinylidene character exist Doublet structure exists (ground state splitting is a few cm -1 ) QM study of highly excited states of tetratomics is possible in full dimensionality Some open questions How extensive is the vinylidene “spectrum”? What are signatures of vinylidene states? Is the double well and all the symmetry responsible for the ‘divided’ spectrum

32. Proton transfer in water the ‘Zundl’ ion H 5 O 2 + H 3 O + + H 2 O -> H 2 O + H 3 O +

33. The hydronium ion H 3 O + Inversion doublets” in the spectrum observed and calculated By our group for the first time in full dimensionality (2002)

34. MULTIMODE Based on “Watson Hamiltonian” - normal coordinates and the following crucial representation of the potential Vibration self-consistent field “Virtual” state CI Check convergence wrt above representation “No limits” Needs a reference geometry Usually a minimum, but saddle points ok

35. New Potential

36. An ab initio potential energy surface and vibrational energies of H 3 O + and its isotopomers Huang, Carter, Bowman