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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 Calculation of dissociative electron attachment cross sections

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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 - H 2 + e - H + H - CHOOH + e - CHO H DEA leads to damage in technological and biological systems. D.E.A. : AB + e - A - + B Calculation of dissociative electron attachment cross sections

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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 DNA damage via double strand breaks There has been a resurgence of interest in low-energy DEA to biologically relevant systems - water, alchohols, organic acids, tetrahydrofuran, DNA base pairs, etc.

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

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Resonant processes include DEA Basic Mechanism Nonresonant processes

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V A + B A + B - Vibrational Excitation “Boomerang Model” R R V A + B - Dissociative Attachment A + B 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* 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

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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 t diss to dissociate, the cross section depends on the width as Summary - Basics

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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 ) Summary - Basics

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DEA to H 2 O occurs via three different states and leads to different final channels with VASTLY different cross sections Different initial and final states, different uncertainty H-H- O-O- OH Can get within 5% Don’t even have a theory Within 50% 1/100 th experimental result

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

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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

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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

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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

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

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Complex Kohn Electron-Molecule Scattering Code: Developed T. N. Rescigno, A. E. Orel, B. Lengsfield, C.W. McCurdy Lawrence Livermore National Lab, Lawrence Berkeley National Lab Complex Kohn Variational Method: Stationary principle for the T-Matrix (scattering amplitude), Walter Kohn Quantum Chemistry 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. Complex Kohn Method for Electron-Molecule Scattering

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

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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 configurations Energies < ≈ 50 eV and low asymptotic angular momentumset for 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) Complex Kohn Method for Electron-Molecule Scattering

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But the future looks promising for calculating total widths (lifetimes). Advancements in Kohn suite – McCurdy Rescigno Lucchese Electronic structure methods for metastable states (SciDAC project) It’s the survival probability that’s the problem.

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Dissociative Attachment to CO 2 e - - CO 2 DEA and vibrational excitation have been studied since the 1970s 4 eV 2 Π u shape resonance produces O - and vib excitation 8.2 eV 2 Π g Feshbach resonance produces O - 13 eV Feshbach resonance produces O - Schulz measured O 2 - from an 11.2 eV resonance in 1970s Three DEA peaks identified by Sanche in CO 2 films at 8.2 eV 11.2 eV and 15 eV in 2004 Chantry (1972) and Fayard (1976)

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McCurdy Isaacs Meyer Rescigno PRA 67, (2003) DEA is minor channel; mostly vibrational excitation. 1.5 x cm 2 vibrational excitation 1.5 x cm 2 total cross section DEA cross section: 1.5 x cm 2 Dissociative Attachment to CO 2

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McCurdy Isaacs Meyer Rescigno PRA 67, (2003) Dissociative Attachment to CO 2 Width of (one component of the) resonance is very large when molecule is bent. STRONG effect of lifetime on final breakup channel.

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

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

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NO 2

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Calculation done blind, no experiment now or then Step 1: Identify candidate states! Attachment at zero electron energy. Dissociative Recombination of NO e - NO 2 + ground neutral NO 2 excited states Work done with Chris Greene at JILA, University of Colorado Boulder

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Candidates for direct DR Dissociative Recombination of NO e -

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Simple estimate of cross section as function of energy Dissociative Recombination of NO e -

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Put the pieces together Dissociative Recombination of NO e -

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The result Dissociative Recombination of NO e - Highly sensitive to position of resonant states in this case.

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3 resonance states, with multiple products from each C. E. Melton, J. Chem. Phys., 57, 4218 (1972) O - production 2B12B1 2B22B2 2A12A1 H - production 2B12B1 2A12A1 H 2 O + e - H 2 O - ( 2 B 1, 2 A 1, 2 B 2 ) { H - + OH ( 2 ) H - + OH ( 2 ) H + H + O - H 2 + O - Dissociative Attachment to H 2 O

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1.H - is produced from the 2 B 1 resonance directly 1.O - production from 2 B 2 resonance comes from passage through conical intersection to 2 A 1 surface. 2.O - production from 2 A 1 comes from three body breakup O - + H + H. Calculations have Revealed Different Dynamics of the Resonances in H 2 O Dissociative Attachment to H 2 O

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A Complete ab initio Treatment of Polyatomic Dissociative Attachment 1.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 1.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 Dissociative Attachment to H 2 O

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Complex Potential Energy Surfaces V(r 1, r 2, ) = E R - i /2 = h/ is lifetime r1r1 r2r2 Dissociative Attachment to H 2 O

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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: Dissociative Attachment to H 2 O

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HOWEVER are many systems requiring more elaborate (nonlocal) treatment of effective operator – Horacek, Houfek, Domcke, others, e.g. Dissociative Attachment to H 2 O Electron scattering in HCl: An improved nonlocal resonance model Phys. Rev. A 81, (2010) J. Fedor, C. Winstead, V. McKoy, M. Čížek, K. Houfek, P. Kolorenč, and J. Horáček Local complex potential model:

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38 = OH +H - O - + H 2 O HH r2r2 r1r1 Complete 2 B 1 ( 2 A ’’ ) Potential Surface

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Triatomic rovibrational dynamics calculated with Multiconfiguration Time-Dependent Hartree Method Dissociative Attachment to H 2 O Cross section from energy resolved projected flux. Significant but manageable expense involved in computing a double Fourier transform. Adaptive method capable of handling multidimensional vibrational dynamics E.g. malonaldehyde 24 atoms H.D. Meyer et al, University of Heidelberg

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40 Cross Sections for OH vibrational states compared with experiment Calc. Shifted by in incident energy by eV D. S. Belic, M. Landau and R. I. Hall, Journal of Physics B 14, pp (1981) 5.99 vs cm 2

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Dissociative Attachment to H 2 O

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2B12B1 2A12A1 H - from 2 A 1 (middle peak) Dissociative Attachment to H 2 O ~5 x cm 2 ~1 x cm 2 but overlaps 2 B 1

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Dissociative Attachment to H 2 O Very little O - from 2 B 1... even with Renner-Teller coupling to 2 A 1... subtleties of PES? Very happy with this level of agreement for 2 A 1 We got lucky with 2 B 2 Total O - production all states

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Atomic, molecular, and optical theory group at LBNL 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 of vibrational excitation 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 CW McCurdy TN Rescigno CY Lin J Jones X Li CS Trevisan AE Orel B Abeln Z Walters

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45 Complex Kohn Method for Electron-Molecule Scattering

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