daniel haxton atomic, molecular, and optical theory group, lawrence berkeley national lab

Daniel HaxtonAtomic, Molecular, and Optical theory group, Lawrence Berkeley National Lab

Joint Workshop with IAEA on Uncertainty Assessment for Atomic and Molecular DataITAMP, July 8 2014

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-

H2 + e- H + H-

CHOOH + e- CHO2- + H

DEA leads to damage in technological and biological

systems.

D.E.A. : AB + e- A- + B

Calculation of dissociative electron attachment cross sections

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.

Basic Mechanism

1. e- + AB AB- (attachment)

2. AB- A + B- (dissociation)

Reverse of process 1 competes with process 2.

R

V A + B

A + B-

Dissociative Attachment

Resonant processes include DEA

Basic Mechanism

Nonresonant processes

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

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

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 )

Summary - Basics

DEA to H2O occurs via three different states and leads to different final channels with VASTLY different cross sections

Different initial and final states, different uncertainty

H-

O-

OH-

1500

200

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Can get within 5%

Don’t even have a theory

Within 50%

1/100th experimental result

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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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Our interest currently is in angular distributions because they can tell us about dynamics.


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AXIAL RECOIL

30 DEGREES

Acetylene


Calculations / experiment indicate breakup at ~30 degrees H-C-C bond angleconsistent with Orel and Chorou PRA 77 042709

MORE ELABORATE TREATMENT

Complex Kohn Electron-Molecule Scattering Code: Developed

1987-1995

T. N. Rescigno, A. E. Orel, B. Lengsfield, C.W. McCurdyLawrence Livermore National Lab, Lawrence Berkeley

National Lab

,,i

ll jh ,

Complex Kohn Variational Method: Stationary principle for the T-Matrix (scattering amplitude), Walter Kohn

QuantumChemistry

ContinuumFunctionsThe “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

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.

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 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)



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.

Dissociative Attachment to CO2

e- - CO2 DEA and vibrational excitation have been studied since

the 1970s

4 eV 2Πu shape resonance produces O- and vib excitation

8.2 eV 2Πg Feshbach resonance produces O- 13 eV Feshbach 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)

McCurdy Isaacs Meyer Rescigno PRA 67, 042708 (2003)

DEA is minor channel; mostly vibrational excitation.

1.5 x 10-16 cm2 vibrational excitation1.5 x 10-15 cm2 total cross section

DEA cross section: 1.5 x 10-19 cm2


McCurdy Isaacs Meyer Rescigno PRA 67, 042708 (2003)


Width of (one component of the) resonance is very large when molecule is bent.

STRONG effect of lifetime on final breakup channel.

3 components of O- 2P make a 2Π resonance and a 2Σ virtual state

CO2 ground state

CO2- shape

resonance

Feshbach resonance conical

intersection

(CAS + single and doubles CI on both neutral and anion states)Dashed = neutral, solid colored = anion


Proposed Mechanism: Bend to stay on lower cone and dissociate to ground

state products

θOCO = 180o θOCO = 140o

2Πu → 2A’ + 2A” states upon bending and stretching

dissociation on 2A’

Moradmand et al. Phys. Rev. A 88, 032703 (2013)

Calculation done blind, no experiment now or then

Step 1: Identify candidate states!

Attachment at zero electron energy.

Dissociative Recombination of NO2+ + e-

NO2+ ground neutral

NO2 excited states

Work done with Chris Greene at JILA, University of Colorado Boulder

Candidates for direct DR


Simple estimate of cross section as function of energy


Put the pieces together


The result


Highly sensitive to position ofresonant states in this case.

3 resonance states, with multiple products from each

C. E. Melton, J. Chem. Phys., 57, 4218 (1972)

O- production

2B1

2B2

2A1

H- production

2B1

2A1

H2O + e- H2O- (2B1, 2A1, 2B2) {H- + OH (2)H- + OH (2)H + H + O-

H2 + O-

Dissociative Attachment to H2O

1. H- is produced from the 2B1 resonance directly

2. O- production from 2B2 resonance comes from passage through conical intersection to 2A1 surface.

3. O- production from 2A1 comes from three body breakup O- + H + H .

Calculations have Revealed Different Dynamics of the

Resonances in H2O


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

2. 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

),,( γRrER

2/),,(),,( γγ RriRrEV Ranion −=

),,( γRr


Complex Potential Energy SurfacesV(r1, r2, ) = ER - i/2

G = h/ is lifetime

r1 r2


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:


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

Local complex potential model:

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q = 00 150 350

700104.50 1250

1500 1800

OH +H-

OH +H-

O- + H2

O

H H

r2r1

q

Complete 2B1 (2A’’) Potential Surface

Triatomic rovibrational dynamics calculated withMulticonfiguration Time-Dependent Hartree Method


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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Cross Sections for OH vibrational states compared with experiment

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Calc. Shifted by in incident energy by +0.34 eVD. S. Belic, M. Landau and R. I. Hall, Journal of Physics B 14, pp.175-90 (1981)

5.99 vs 6.5 10-18 cm2

2B1

2A1

H- from 2A1 (middle peak)


~5 x 10-19 cm2

~1 x 10-18 cm2 but overlaps 2B1


Very little O- from 2B1. . . even with Renner-Teller coupling to 2A1. . . subtleties of PES?

Very happy with this level of agreement for 2A1

We got lucky with 2B2

Total O- production all states

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

daniel haxton atomic, molecular, and optical theory group, lawrence berkeley national lab

Documents

ab e

step attachment

bdissociative attachment

ratio of dea

different states

total cross section

lowenergy dea

detachment probability