Daniel Haxton Atomic, Molecular, and Optical theory group, Lawrence Berkeley National Lab

1. 0 1 2 3 4 5 6 7 Calculation of dissociative electron attachment cross sections Daniel Haxton Atomic, Molecular, and Optical theory group, Lawrence Berkeley National Lab  Joint Workshop with IAEA on Uncertainty Assessment for Atomic and Molecular Data ITAMP, July 8 2014

2. Calculation of dissociative electron attachment cross sections D.E.A. : AB + e- A- + B Dissociative Electron Attachment (DEA) is a basic physical process that may occur in plasmas, or in everyday materials bombarded by ionizing radiation. Reactive products: ions and radicals. CF + e- C* + F- H2 + e- H + H- CHOOH + e- CHO2- + H DEA leads to damage in technological and biological systems.

3. DNA damage via double strand breaks Most energy deposited in cells by ionizing radiation is channeled into free secondary electrons with energies between 1 eV and 20 eV (B. Boudaifa et al., Science 287 (2000) 1658) Secondary electrons produced by fast ion tracks in radioactive waste There has been a resurgence of interest in low-energy DEA to biologically relevant systems - water, alchohols, organic acids, tetrahydrofuran, DNA base pairs, etc.

4. Basic Mechanism • e- + AB  AB- (attachment) • AB- A + B- (dissociation) Reverse of process 1 competes with process 2.

5. Basic Mechanism Resonant processes include DEA Nonresonant processes

6. Competition with vibrational excitation For short-lived anion states, or those trapped in a potential well, the electron is likely to detach, leading to vibrational excitation, e- + AB -> e- + AB* Dissociative Attachment VibrationalExcitation “Boomerang Model” V A + B- V A + B A + B- Attachment and detachment probability is proportional to intrinsic width Γ of state In the Born-Oppenheimer picture the resonance is a metastable state with energy A + B R R

7. Summary - Basics Dissociative electron attachment is described by TWO STEPS Big picture: calculating FIRST STEP (attachment) is relatively easy. If second step (dissociation) goes 100% (survival probability is 100%), then calculating second step is not necessary to get total cross section. Survival probability (and branching ratios) associated with second step may be VERY DIFFICULT to calculate requiring major effort, if the polyatomic nuclear dynamics is complicated. So if the molecule takes a time tdiss to dissociate, the cross section depends on the width as

8. Summary - Basics So uncertainty in dissociative electron attachment (DEA) cross section depends upon survival probability Survival probability given roughly by ratio of DEA to vibrational excitation So prior knowledge of this ratio (from experiment or theory) should affect uncertainty in DEA cross section. ( Isotope effect is also due to survival probability )

9. Different initial and final states, different uncertainty DEA to H2O occurs via three different states and leads to different final channels with VASTLY different cross sections 1500 H- Can get within 5% 200 O- Within 50% 1/100th experimental result Don’t even have a theory OH- 6

10. Angular distributions Combination of experiment and theory allows us to determine that the molecule dissociates into the three-body channel via scissoring backwards

11. Angular distributions Our interest currently is in angular distributions because they can tell us about dynamics. Combination of experiment and theory allows us to determine that the molecule dissociates into the three-body channel via scissoring backwards

12. Angular distributions Our interest currently is in angular distributions because they can tell us about dynamics. Combination of experiment and theory allows us to determine that the molecule dissociates into the three-body channel via scissoring backwards

13. Angular distributions Our interest currently is in angular distributions because they can tell us about dynamics. Combination of experiment and theory allows us to determine that the molecule dissociates into the three-body channel via scissoring backwards

14. Angular distributions Acetylene AXIAL RECOIL 30 DEGREES MORE ELABORATE TREATMENT Calculations / experiment indicate breakup at ~30 degrees H-C-C bond angle consistent with Orel and Chorou PRA 77 042709

15. Complex Kohn Method for Electron-Molecule Scattering Complex Kohn Electron-Molecule Scattering Code: Developed 1987-1995 T. N. Rescigno, A. E. Orel, B. Lengsfield, C.W. McCurdy Lawrence Livermore National Lab, Lawrence Berkeley National Lab Continuum Functions The “Kohn Suite” consists of scattering codes coupled to MESA, a flexible electronic structure code from Los Alamos written in the 1980s and no longer maintained. Quantum Chemistry Complex Kohn Variational Method: Stationary principle for the T-Matrix (scattering amplitude), Walter Kohn

16. Complex Kohn Method for Electron-Molecule Scattering 3 parts of wave function for Kohn method in usual implementation. Similar capabilities as UK R-matrix. Only in particular situations are there significant differences in Kohn or R-matrix capabilities.

17. Complex Kohn Method for Electron-Molecule Scattering Limitations of Present Capabilities • Small size of Systems – Small Polyatomics 6-10 atoms maximum but only limited target response for more than ≈5 atoms • Highly Correlated Target States only for smaller systems – strongly target states ≈ 5,000- 10,000 configurations • Energies < ≈ 50 eV and low asymptotic angular momentumsetfor inner region of continuum functions • Poor Computational efficiency – Recently removed the limit of 160 orbitals, but serial calculations with legacy code require weeks of computation – No parallel versions of either structure or scattering codes. • NEW IMPLEMENTATION HAS BEEN PLANNED (Rescigno, McCurdy, Lucchese)

18. Complex Kohn Method for Electron-Molecule Scattering But the future looks promising for calculating total widths (lifetimes). Advancements in Kohn suite – McCurdy RescignoLucchese Electronic structure methods for metastable states (SciDAC project) It’s the survival probability that’s the problem.

19. Dissociative Attachment to CO2 • e- - CO2 DEA and vibrational excitation have been studied since the 1970s • 4 eV2Πu shape resonance produces O- and vib excitation • 8.2 eV2Πg Feshbach resonance produces O- • 13 eVFeshbach resonance produces O- • Schulz measured O2- from an 11.2 eV resonance in 1970s • Three DEA peaks identified by Sanche in CO2 films at 8.2 eV 11.2 eV and 15 eV in 2004 Chantry (1972) and Fayard (1976)

20. Dissociative Attachment to CO2 DEA is minor channel; mostly vibrational excitation. 1.5 x 10-16cm2vibrational excitation 1.5 x 10-15cm2 total cross section McCurdy Isaacs Meyer Rescigno PRA 67, 042708 (2003) DEA cross section: 1.5 x 10-19 cm2

21. Dissociative Attachment to CO2 Width of (one component of the) resonance is very large when molecule is bent. STRONG effect of lifetime on final breakup channel. McCurdy Isaacs Meyer Rescigno PRA 67, 042708 (2003)

22. Dissociative Attachment to CO2 Feshbach resonance conical intersection CO2- shape resonance 3 components of O-2P make a 2Π resonance and a 2Σ virtual state CO2 ground state (CAS + single and doubles CI on both neutral and anion states) Dashed = neutral, solid colored = anion

23. Proposed Mechanism: Bend to stay on lower cone and dissociate to ground state products 2Πu→ 2A’+ 2A”states upon bending and stretching dissociation on 2A’ θOCO = 180o θOCO = 140o Moradmand et al. Phys. Rev. A 88, 032703 (2013)

25. NO2

26. Dissociative Recombination ofNO2+ + e- Calculation done blind, no experiment now or then Step 1: Identify candidate states! Attachment at zero electron energy. NO2+ ground neutral NO2 excited states Work done with Chris Greene at JILA, University of Colorado Boulder

27. Dissociative Recombination ofNO2+ + e- Candidates for direct DR

28. Dissociative Recombination ofNO2+ + e- Simple estimate of cross section as function of energy

29. Dissociative Recombination ofNO2+ + e-

30. Dissociative Recombination ofNO2+ + e- Put the pieces together

31. Dissociative Recombination ofNO2+ + e- The result Highly sensitive to position of resonant states in this case.

32. Dissociative Attachment to H2O 2B1 H- production 2A1 O- production 2B2 2A1 2B1 3 resonance states, with multiple products from each H2O + e- H2O- (2B1, 2A1, 2B2) { H- + OH (2) H- + OH (2) H + H + O- H2 + O- C. E. Melton, J. Chem. Phys., 57, 4218 (1972)

33. Dissociative Attachment to H2O Calculations have Revealed Different Dynamics of the Resonances in H2O H- is produced from the 2B1 resonance directly O- production from 2B2 resonance comes from passage through conical intersection to 2A1 surface. O- production from 2A1 comes from three body breakup O- + H + H .

34. Dissociative Attachment to H2O A Complete ab initio Treatment of Polyatomic Dissociative Attachment • Electron scattering: Calculate the energy and width of the resonance for fixed nuclei • Complex Kohn calculations produce • CI calculations with ~ 900,000 configurations produce • Fitting of complete resonance potential surface to dissociation • Nuclear dynamics in the local complex potential model on the anion surface • Multiconfiguration Time-Dependent Hartree (MCTDH) • Flux correlation function (energy resolved projected flux) calculation of DA cross sections

35. Dissociative Attachment to H2O Complex Potential Energy Surfaces V(r1, r2, ) = ER - i/2 • = h/  is lifetime r1 r2 

36. Dissociative Attachment to H2O Local complex potential model Dynamics on complex potential energy surface. In general this theory is sufficient for DEA. Derivation: given L2 approximation to resonant state, φ, define effective Hamiltonian for that state. Feshbach partitioning:

37. Dissociative Attachment to H2O Local complex potential model: HOWEVER are many systems requiring more elaborate (nonlocal) treatment of effective operator – Horacek, Houfek, Domcke, others, e.g. Electron scattering in HCl: An improved nonlocal resonance model Phys. Rev. A 81, 042702 (2010) J. Fedor, C. Winstead, V. McKoy, M. Čížek, K. Houfek, P. Kolorenč, and J. Horáček

38. r1 O r2 H H Complete 2B1 (2A’’) Potential Surface q = 00 150 350 O-+ H2 700 104.50 1250 OH +H- OH +H- 1500 1800 q

39. Dissociative Attachment to H2O Triatomicrovibrational dynamics calculated withMulticonfiguration Time-Dependent Hartree Method Adaptive method capable of handling multidimensional vibrational dynamics E.g. malonaldehyde 24 atoms H.D. Meyer et al, University of Heidelberg Cross section from energy resolved projected flux. Significant but manageable expense involved in computing a double Fourier transform.

40. 0 1 2 3 4 5 6 7 Cross Sections for OH vibrational states compared with experiment 5.99 vs 6.5 10-18 cm2 D. S. Belic, M. Landau and R. I. Hall, Journal of Physics B 14, pp.175-90 (1981) Calc. Shifted by in incident energy by +0.34 eV

41. Dissociative Attachment to H2O

42. Dissociative Attachment to H2O 2B1 2A1 H- from 2A1 (middle peak) ~1 x 10-18 cm2 but overlaps 2B1 ~5 x 10-19 cm2

43. Dissociative Attachment to H2O Total O- production all states We got lucky with 2B2 Very happy with this level of agreement for 2A1 Very little O- from 2B1. . . even with Renner-Teller coupling to 2A1. . . subtleties of PES?

44. Conclusion IF we assume that DEA is driven by the direct, resonant process THEN the source of major uncertainty is the survival probability i.e. uncertainty in DEA is a function of ratio ofvibrationalexcitation to DEA, and i.e. uncertainty in DEA is function of isotope effect, so as long as these are known a priori, from experiment or theory, even with low accuracy, the model should give higher uncertainty in the theoretical result. Equivalently if the width is known to be large. Or if the width is known to be large in certain geometries and there is a decent chance of sampling those geometries. ALSO the precise energetics MAY give additional sensitivity to error Atomic, molecular, and optical theory group at LBNL CW McCurdy TN Rescigno CY Lin J Jones X Li CS Trevisan AE Orel B Abeln Z Walters

45. Complex Kohn Method for Electron-Molecule Scattering