Electron - molecule collision calculations using the R-matrix method

1. Electron - molecule collision calculations using the R-matrix method Jonathan Tennyson Department of Physics and Astronomy University College London IAEA. Vienna, December 2003

2. Processes: at low impact energies Elastic scattering AB +eAB +e Electronic excitation AB +eAB*+e Vibrational excitation AB(v”=0)+eAB(v’)+ e Rotational excitation AB(N”)+eAB(N’)+e Dissociative attachment / Dissociative recombination AB +eA+B A +B Impact dissociation AB +eA+B +e All go via (AB-)**. Can also look for bound states

3. Outer region e– Inner region C F Inner region: exchange electron-electron correlation multicentre expansion of  Outer region: exchange and correlation are negligible long-range multipolar interactions are included single centre expansion of  The R-matrix approach C R-matrix boundary r = a: target wavefunction = 0

4. Scattering Wavefunctions Yk= ASi,jai,j,kfiNhi,j + bj,kfjN+1 where fiN N-electron wavefunction of ith target state hi,j1-electron continuum wavefunction fjN+1 (N+1)-electron short-range functions A Antisymmetrizes the wavefunction ai,j,kand bj,kvariationally determined coefficients

5. UK R-matrix codes L.A. Morgan, J. Tennyson and C.J. Gillan, Computer Phys. Comms., 114, 120 (1999).

6. Electron collisions with OClO R-matrix: Baluja et al (2001) Experiment: Gulley et al (1998)

7. Electron - LiH scattering:2S eigenphase sums B Anthony (to be published)

8. Electron impact dissociation of H2 Important for fusion plasma and astrophysics Low energy mechanism: e- + H2(X 1Sg) e- + H2(b 3Su) e- + H + H R-matrix calculations based on adiabatic nuclei approximation extended to dissociation

9. ` • Excess energy of incoming e- over dissociating energy can be split between nuclei and outgoing e- in any proportion. • Fixed nuclei excitation energy changes rapidly with bondlength • Tunnelling effects significant Including nuclear motion (within adiabatic nuclei approximation) in case of dissociation ds(Ein) dEout Determine choice of T-matrices to be averaged

10. The energy balance method D.T. Stibbe and J. Tennyson, New J. Phys.,1, 2.1 (1999).

11. Explicit adiabatic averaging over T-matrices using continuum functions

12. Total cross sections, s(Ein) • Energy differential cross sections, ds(Ein) dEout • Angular differential cross sections, ds(Ein) dq • Double differential cross sections, d2s(Ein) dqdEout Required formulation of the problem Need to Calculate: C.S. Trevisan and J. Tennyson, J. Phys. B: At. Mol. Opt. Phys., 34, 2935 (2001)

13. e- + H2 e- + H + H Integral cross sections Cross section (a02) Incoming electron energy (eV)

14. e- + H2 e- + H + H Angular differential cross sections at 12 eV Differential Cross section (a02) Angle (degrees)

15. e- + H2(v=0)e-+ H + H Energy differential cross sections in a.u. Atom kinetic energy (eV) Incoming electron energy (eV)

16. e- + H2(v>0)e-+ H + H Energy differential cross sections in a.u. V = 2 V = 3 Atom kinetic energy (eV) Incoming electron energy (eV)

17. Electron impact dissociation of H2 Effective threshold about 8 eV for H2(v=0) Thermal rates strongly dependent on initial H2 vibrational state For v=0: Excess energy largely converted to Kinetic Energy of outgoing H atoms For v > 0: Source of cold H atoms ?

18. Quasibound states of H2-: 2Sg+resonances Energy (eV) Internuclear separation (a0) DT Stibbe and J Tennyson, J. Phys. B.,31, 815 (1998).

19. Can one calculate resonance positions with a standard quantum chemistry code? R-matrix Resonance position H2- potential curves calculated with Gaussian by Mebel et al. Energy (eV) No! R (a0) D T Stibbe and J Tennyson, Chem. Phys. Lett., 308, 532 (1999)

20. Electron collision with CFx radicals extremely high global warming potential C2F6and CF4 practically infinite atmospheric lifetimes CF3Ilow global warming potential C2F4strong source of CFx radicals new feedstock gases no information on how they interact with low E e– CFx radicals highly reactive, difficult species to work with in labs Theoretical approaches – attractive source of information

21. Twin-track approach Joint experimental and theoretical project e– interactions with the CF3I and C2F4 e– collisions with the CF, CF2 and CF3 N.J. Mason, P. Limao-Vieira and S. Eden I. Rozum and J. Tennyson

22. Electron collisions with the CF Target model • X1, 4–, 2+, 2, 2– and 4 • Slater type basis set: (24,14) + (,) valence target states2+ Rydberg state valence NORydberg NO () (24,14)(7…14 3…6) C F single + double excitation single excitation (12)4(3 …6 1 2)11 (12)4(3 …6 1 2)10(73)1 final model

23. Electron collisions with the CF • Resonances 1Ee = 0.91 eV e = 0.75 eV 1+Ee = 2.19 eV e = 1.73 eV 3–Ee~ 0 eV 22

24. Electron collisions with the CF • Bound states 1 Eb(Re) = 0.23 eV 3 Eb(Re) = 0.26 eV shape resonances E(1) = 0.054 eV E(3) = 0.049 eV 3– at R > 2.5 a0 1 at R > 3.3 a0 • 3– and 3 C(3P) + F–(1S) 1 and 1 C(1D) + F–(1S) unbound at R = 2.6 a0 27 become bound

25. Electron collisions with the CF 2 Resonances • shape resonances: 2B1(2A’’) Ee=0.95 eV e = 0.18 eV 2A1(2A’) Ee= 5.61 eV e = 2.87 eV • bound state at R > 3.2 a0 2B1 CF(2P) + F–(1S) 3b1 7a1

26. Electron collisions with the CF3 C F3 110.7o F1 F2 Target representation • Cs symmetry group • X2A’, 12A”, 22A’, 22A”, 32A’, 32A” • Models 1. (1a’2a’3a’1a”)8 (4a’…13a’2a”…7a”)25 240 000 CSF (Ra) 2. (1a’…6a’1a”2a”)16 (7a’…13a’3a”…7a”)17 28 000 CSF 3. (1a’…5a’1a”2a”)14 (6a’…13a’3a”…7a”)19 50 000 CSF 2.53 ao a = 10 ao

27. Electron collisions with the CF3 Electron impact excitation cross sections • Bound state E(1A’) ~ 0.6 eV No (low-energy) resonances!

28. Dissociative recombination of NO+ NO+ important ion in ionosphere of Earth and thermosphere of Venus Mainly destroyed by NO+ + e- N + O Need T-dependent rates for models Recent storage ring experiments show unexplained peak at 5 eV • Calculations: • resonance curves from R-matrix calculation • nuclear motion with multichannel quantum defect theory

29. NO+ dissociation recombination: potential energy curves Spectroscopically determined R-matrix ab initio R-matrix calibrated

30. NO+ dissociation recombination: Direct and indirect contributions

31. NO+ dissociation recombination: comparison with storage ring experiments IF Schneider, I Rabadan, L Carata, LH Andersen, A Suzor-Weiner & J Tennyson, J. Phys. B, 33, 4849 (2000)

32. NO+ dissociation recombination: Temperature dependent rates Experiment Mostefaoui et al (1999)) Rate coefficient (cm3 s-1) Calculation Electron temperature, Te (K)

33. Electon-H3+ at intermediate energies Jimena Gorfinkiel

34. Conclusion • R-matrix method provides a general method for treating low-energy electron collisions with neutrals, ions and radicals • Results should be reliable for the energies above 100 meV (previous studies of Baluja et al 2001 on OClO). • Total elastic and electron impact excitation cross sections. • Being extended to intermediate energy and ionisation.

35. Chiara Piccarreta Natalia Vinci Jimena Gorfinkiel Iryna Rozum