Electron-Driven Chemistry

1. Electron-Driven Chemistry C. William McCurdy, Lawrence Berkeley National Lab and The University of California Collaborators:D. Haxton, D. Horner (UCB), W. Vanroose, Z. Zhang, T. Rescigno (LBNL),H-D. Meyer (U. of Heidelberg) M. Baertschy (U. of Colorado, Denver) and F. Martin (U. Autonoma de Madrid)

2. Electron-Driven Chemistry Plays a Crucial Role in a Multitude of Applications High Intensity Plasma Arc Lamp (OSRAM-Sylvania) Plasma Flat Panel Display (Fujitsu) Plasma vapor deposition and plasma etching – no chemistry without electrons.

3. Electron-Driven Chemistry Associated with Ionizing Radiation Secondary electron cascades in mixed radioactive/ chemical waste drive much of the chemistry that determines how those materials age, change, and interact with the natural environment. Cascades of secondary electrons from ionizing radiation Low energy electrons with energies significantly below the ionization energies of DNA molecules can initiate single and double strand-breaks by attaching to components of DNA molecules or the water around them and driving bond dissociation. Most energy deposited in cells by ionizing radiation is channeled into secondary electrons between 1eV and 20eV (Research group of L. Sanche)

4. A Landmark Experiment H- production Double Strand Breaks Single Strand Breaks

5. Secondary electrons play a pivotal role in radiation damage • Dissociative attachment and resonant processes occur primarily for electron energies below 20 eV • The energy distribution of secondary electrons emphasizes those processes Figure from Thom Orlando, Ga Tech

6. Electron-Molecule Interactions Electron-driven chemistry hinges on the mechanisms by which electronic energy is transferred into nuclear motion to produce reactive species by excitation and/or fragmentation • No optical selection rules • Below ~ 25 eV excitation of triplets and singlets is about equally probable Electron-Molecule collisions fall into two broad categories • Short-lived collisions – Electronic excitation • me/M~10-4 => disparate collisional time scales => impulsive electronic excitation followed by nuclear fragmentation – electron dynamics and nuclear dynamics decouple • Resonant collisions – Formation of a temporary negative ion • Incident electron either “falls into an empty MO” (shape resonance) or “excites an electronic state and attaches to it” (Feshbach resonance) • Electron collision times commensurate with molecular vibrational period (~10s of femtoseconds) • Multidimensional nuclear dynamics in polyatomics lead to new effects

7. Topics for Today Molecular Dynamics of Electron-Driven Chemistry • Dissociative Attachment of electrons to water • With an overview of how we can now approach these problems • Selective vibrational excitation of carbon dioxide • Some results showing some of surprising effects in Electron-Driven Chemistry • Electron-impact Ionization and Coulomb Break-up • One electron in, two or more electrons out – just a sketch of the hardest problem of all in Electron-Driven Chemistry

8. A Primer on the Electron-Driven Chemistry of Water • The ground state configuration of water is • 1a122a121b223a121b12 1A1 • Electron-driven chemistry through both dissociative excitation and dissociative attachment Electron impact dissociation Dissociative Attachment

9. Electronic Structure of Water and Ice 4a1 is strongly antibonding In the band gap, it has localized (excitonic) character 3a1and 1b1 largely describe the lone pairs Some dissociative electronic excitations of water and their principal products H+ H, O H- 4a1 1b1 3a1 1b2 Sieger et al. Phys. Rev. B 1997

10. Simple molecular orbital picture of the dissociation processes • Dissociative excitation proceeds by excitation of low-lying dissociative electronic states, e.g, those observed in EELS spectra: • 1a122a121b223a121b114a111,3 B1 • 1a122a121b223a111b124a11 1,3A1 • 1a122a121b213a121b124a11 1,3B2 • Dissociative attachment of H2O proceeds through “Feshbach resonances”. • 1a122a121b223a121b114a122B1 (~ 6.5 eV) • 1a122a121b223a111b124a12 2A1 (~ 9 eV) • 1a122a121b213a121b124a12 2B2 (~ 12 eV)

11. H- production is primarily through the 2B1 Resonance C. E. Melton, Journal of Chemical Physics, 57, pp.4218-25, (1972). From H- + H2O -> OH- + H !

12. DA products are vibrationally (and rotationally) excited • Up to v = 7 is observed for OH stretch in the H- production channel • Rotational excitation: J=7 most populated for ground state OH, j=4 or 5 for v =4 OH stretch D. S. Belic, M. Landau and R. I. Hall, Journal of Physics B 14, pp.175-90 (1981) Vibrational excitation cross sections H- energy distribution for various electron energies

13. The problem: From first principles, solve the scattering problem including the nuclear dynamics, predict the cross sections and show how they display the polyatomic dynamics of the collision. • Breaking up the problem into two parts: • Electron scattering for fixed nuclei: Calculate the position and lifetime of the Feshbach resonances • Nuclear dynamics during the resonant collision: Calculate the quantum molecular dynamics leading to dissociative attachment Complex Energies of States with Finite Lifetimes

14. O r R H H A Complete ab initio Treatment of Polyatomic Dissociative Attachment: 2B1 Resonance • Electron scattering: Calculate the energy and width of the resonance for fixed nuclei • Complex Kohn calculation of fixed-nuclei electron scattering cross sections (7 state close coupling)– produce • CI calculations -- produce • Fitting of complete resonance potential surface including the electronically bound (product) regions • Nuclear dynamics in the local complex potential model on the anion surface • Multiconfiguration Time-Dependent Hartree (MCTDH) • Flux correlation function calculation of DA cross sections

15. A D B C Complex Kohn Variational Method Variational Functional for the T-Matrix (scattering amplitude) Trial wave function for the N+1 electron system [Fixed Nuclei] target continuum exchange Correlation and Polarization Continuum functions are further expanded in combined basis of Gaussians and continuum (Bessel) functions Electron dynamics and electronic structure are NOT separable

16. ER and G are determined from the eigenphase sums in the Complex Kohn calculation near the resonance Another example from a different Complex Kohn calculation E.g. at equilibrium geometry G = 0.005819eV The essential coupling of nuclear to electronic motion arises because the energy and lifetime (width) change with geometry

17. Real part of resonance energy, ER(r,R,g), nearly parallels the “parent” 3B1 state When the resonance becomes bound, the CI calculation of ER(r,R,g) must dissociate properly Dominant configuration is 1a122a121b223a121b114a12 A robust basis set is necessary: au-cc-pvTZ (augmented, correlation consistent, polarization and valence triple zeta) CI (898,075 configurations): Singles and doubles excitation from the CAS reference space (1b2, 3a1, 1b1, 4a1, 5a1, 2b2)7 4a1 is the “resonance” orbital, 5a1 and 2b2are important for correct dissociation and correlation Configuration Interaction calculation for real part of the 2B1 (2A’’) resonance surface

18. r1 O r2 H H Entire 2B1 (2A’’) potential surface is fit with combination analytic fit and 3-D spline. OH +H- Break up OH +H-

19. r1 O r2 H H Q = 00 O-+ H2 150 350 OH +H- 700 104.50 1250 OH +H- 1500 1800 q

20. O H H A view of the O- channel H2 +O-

21. Width of 2B1 (2A’’) resonance q = 104.5 Contours every 0.0005 eV r2 = 1.81 C2v symmetry At equilibrium geometry G = 0.005819eV

22. O r R H H A Complete ab initio Treatment of Polyatomic Dissociative Attachment: 2B1 Resonance • Electron scattering: Calculate the energy and width of the resonance for fixed nuclei • Complex Kohn calculation of fixed-nuclei electron scattering cross sections – produce • CI calculations -- produce • Fitting of complete resonance potential surface including the electronically bound (product) regions • Nuclear dynamics in the local complex potential model on the anion surface • Multiconfiguration Time-Dependent Hartree (MCTDH) • Flux correlation function calculation of DA cross sections

23. Local Complex Potential Model W(R) = ER(r,R,g)-i G(r,R,g) Time propagation on complex resonance potential surface Solution, z(R), is Fourier Transform Cross section from the asymptotic behavior of z(R)

24. Local complex potential wave packet starting from ground state H2O(Integrated over angle g)

25. H- production from the ground state of H2O

26. H- from single excitation of bend

27. H- from single excitation of asymmetric stretch

28. H- from single excitation of symmetric stretch

29. Cross Sections for OH vibrational states compared with experiment Total 0 1 2 3 4 5 6 7 D. S. Belic, M. Landau and R. I. Hall, Journal of Physics B 14, pp.175-90 (1981)

30. Cross Sections compared with experiment – experiment shifted +0.34eV to match peak of total cross section 0 1 2 3 4 5 6 7

31. O-+H2 channel Experimental peak at about 6.5 eV is

32. It is now possible to treat dissociative attachment to a triatomic in full dimensionality from first principles. Dynamics of the 2B1 (2A’’) resonance leads almost exclusively to H - +OH An ab initio treatment reproduces the cross sections for producing OH in excited vibrational states Interesting energy dependence is predicted for cross sections from H2O excited in symmetric stretch The dynamics of the other two resonances (2A1 and2B2) remains unknown. This calculation does not account for all of the observed O – production. Is the surface not accurate enough or is there production of O - from Renner-Teller or other nonadiabatic coupling between resonances? What will this dynamics look like for clusters and are they a model for condensed phases? Conclusions and Open Questions About Dissociative Attachment to Water

33. O C O C O O CO2 – Multiple resonances couple to produce selective vibrational excitation There is a well-known resonance at ~3.8eV through which vibrational excitation occurs. The electron attaches in the lowest unoccupied molecular orbital(pu ) to make a 2Pu metastable state of CO2- New experiments reveal structure in the vibrational excitation cross sections that probes the polyatomic nature of the collision (1) Electron scattering for fixed nuclei -- 2Pu symmetry, => 2A1 and 2B1 upon bending (2) Nuclear dynamics during the resonant collision: non-adiabatic coupling of electronic and nuclear motion pux puy

34. Experiments of Michael Allen -- 2002

35. Vibrational states of CO2 -- Near degeneracy of nstretch ~2nbend (0,0,0) Fermi dyad {coupled (1,00,0)/(0,20,0) (bend) (stretch) Fermi triad {coupled (2,00,0)/(1,20,0)/(0,40,0)

36. Local Complex Potential (or “Boomerang”) Approach One Dimensional Case (diatomics) Time-dependent formulation Experiment of Josic et al. 2001

37. Multiple Coupled Resonance “Boomerang” Dynamics 2A1 2B1

38. Multiple Resonances and Renner-Teller Coupling • Upon bending the 2Pu state splits into two resonances, 2A1 and 2B1 • The Born Oppenheimer approximation breaks down and these two states are coupled by an effect first characterized by Renner and Teller in 1934. • Nuclear angular momentum and electronic orbital angular momentum are coupled JzLz/r2 • Coupled Boomerang Equations- Wave Packets on Both Surfaces Degenerate bending modes can combine to give an angular momentum around the figure axis Normal Coordinates for CO2 R = CO bond length Q= bend angle of CO from linear s = 2R cos(Q) -Symmetric Stretch r = R2sin2(Q)/(1+mC/(2mO))2 - bend

39. Coupled Wave Packet Dynamics Starting on 2A1 2B1 survives

40. Cross Sections for Excitation of Fermi Dyad Overall shape from decaying packet on 2A1 But subpeaks from rebounding packet on 2B1 Selectivity from overlap of packets with different shapes of final dyad states

41. Cross Sections for Excitation of Fermi triad

42. Some Things We Learned • The resonance structure is an intrinsically polyatomic effect -- 1D models cannot account for it. The physical vibrational states of CO2 are Fermi polyads that mix the bending and symmetric stretching modes • Renner-Teller coupling of 2A1 and 2B1 resonance states is necessary to describe the nuclear dynamics during resonant collisions. • The separate signatures of the two resonances are written on the cross sections But what about the spectacular selectivity for one member of the dyad and each polyad at threshold?

43. Two orders of Magnitude Selectivity at Low Energies Associated with the way in which CO2- becomes bound -- an intrinsically polyatomic effect – (Phys Rev. Letters, 2004).

44. e- e- e- Fundamental Challenges in Electron Driven Chemistry Electron impact ionization (of hydrogen) was the only two-electron problem not completely “solved” by the 1990s Finally solved by a combination of a new theoretical paradigm, “Exterior Complex Scaling” and supercomputers in 1999 Cross Section (10-18 cm2/eV) q1

45. Double Photoionization of Helium Exp: Brauning et al, J. Phys. B 31 5149 (1998). Black line: kskp, kpkd and kdkf Unequal energy sharing and q1 = 30o

46. Experiments at the Advanced Light Source Double photoionization of oriented D2 D2 + hn ---> D+ + D+ + e- + e- Angular Distributions with one electron coming towards you Thorsten Weber, Ph.D thesis Varying Internuclear Distance

47. The Themes • Electron-Driven Chemical Processes – • Opening the door to understanding the fundamental processes • Finding ways to treat them in condensed phases • Coulomb Breakup by Electron and Photon Impact • First complete theory for atoms, and first treatments of molecules • Elegant Experiments at the Advanced Light Source Progress Is Made By A Combination Of • New formulations and methods • Large-scale computation

48. Credits “For excellence, the presence of others is required.” Hannah Arendt, 1906-1975

49. Supplementary Slides

50. r R g H H Hamiltonian for Nuclear Motion O • For J = 0 the wave function is a function of only internal coordinates • For arbitrary J: