1. R-matrix calculations of electron-molecule collisions at low & intermediate energy Jonathan Tennyson Department of Physics and Astronomy University College London IAEA Sept 2005 DC arcjet reactor used to grow diamond films at high rates; University of Bristol, UK

2. Elastic scattering AB + e Electronic excitation AB + e AB* + e Rotational excitation AB(N”) + e AB(N’) + e Vibrational excitation AB(v”=0) + e AB(v’) + e Dissociative attachment / Dissociative recombination AB + e A  + B Impact dissociation AB + e A + B + e Increasing Energy Processes at low impact energies Impact ionisation (e,2e) AB + e AB + + e + e

3. Polyatomic R-matrix method  k   A  i,j a i,j,k  i N  i,j   i b j,k  j N+1  i N = target states = CI target built from nuclear centred GTOs  j N+1 = L 2 functions H ee outer region inner region  i,j = continuum orbitals = GTOs centred on centre of mass (CM) (within the Fixed-Nuclei approximation) a

4. Electron – water rotationally resolved cross sections: Differential cross sections (DCS) at 6 eV  J=1  J=0  J=all * Cho et al (2004) Jung et al (1982)

5. Electron – water (rotationally averaged) elastic cross sections Integral cross section A Faure, JD Gorfinkel & J Tennyson J Phys B, 37, 801 (2004)

6. C 2 states Electron – C 2 : G. Halmova, JD Gorfinkel & J Tennyson J Phys B, to be submitted

13. Intermediate impact energies Ionization and large number of states energetically accessible Ionization AB + e AB + e + e A few semi-rigorous methods used to treat ionization in this energy range (BEB, DM, etc.) provide an analytical expression for the cross section In principle, an infinite number of states is needed in the close-coupling expansion We have developed and implemented a molecular R- matrix with pseudostates method (MRMPS) for electron-molecule collisions

14. R-matrix with pseudostates method (RMPS) Add  i N not true eigenstates of system: represent discretized continuum obtained by diagonalizing target H must do not represent bound states transitions to these states give ionization (projection?)  k   A  i,j  a i,j,k  i N  i,j   i b j,k  j N+1 Pseudostates

15. Example: H 3 + Previous ‘Standard’ calculations for electronic excitation, E < 20 eV Kohn calculation: Orel (1992) R-matrix calculation: Faure and Tennyson (2002) (6 target states) Positive ion, electron density compact  can keep box small (a = 10 a 0 ) In our calculation: Target basis set and continuum basis set (l = 0,1,2,3,4) from standard calculation Different basis sets for PCOs with β=1.3,  0 =0.14, 0.15, 0.16, 0.17 and l = 0,1,2, and others

16. Electron impact ionisation of H 3 + J D Gorfinkiel & J Tennyson, J Phys B, 37, L343 (2004)

17. Quantum defect for resonances increased by about 0.05 Electronic excitation of H 3 +

18. Polarizability of H 3 + (in a.u.) Molecular R-matrix with Pseudostates Method (MRMPS)

19. Electron impact ionisation of H 2 JD Gorfinkiel & J Tennyson, J Phys B, 38, 1607 (2005)

20. extend energy range of calculations treat near threshold ionisation improve representation of polarisation Conclusions With the RMPS method for electron molecule collisions we have: Will allow us to treat excitation to high electronic states and collisions with anions (e.g. C 2  ) Electron impact rotational excitation of ions can be important. Experimental verification?

21. Electron collisions with biomolecules?

22. Electron collisions with tetrahydroforan (THF) C 4 H 8 O Dorra Bouchiha, Laurent Caron, Leon Sanche (Sherbrooke) Jimena D Gorfinkiel (UCL)

23. Guanine Cytosine Thymine Adenine tetrahydrofuran (THF) 3-hydroxy- tetrahydrofuran  -tetrahydrofuryl alcohol + H2O+ H2O Why tetrahydrofuran?

24. Radiation damage/radiation therapy: effect of secondary electrons First R-matrix calculations with a molecule this size (13 nuclei and 40 electrons) C 4 H 8 O (THF)

25. C 2v geometry from semi-empirical calculation (* C 2 not a lot different ) Basis set: DPZ + some diffuse functions (Rydberg character of some states) for C and O. TZ tested for H. Both MOs and averaged pseudo-NOs tested CAS-CI: 32 electrons frozen  around 3500/5000 configurations a = 13,14,15 a 0 up to 14 states in the close-coupling expansion Calculation A variety of models tested

27. E(eV)  (eV) 2A22A2 7.624.6x10 -4 2B12B1 7.642.4x10 -4 2B12B1 7.670.014 2B12B1 8.110.030 Not fitted (yet)

28. Calculations We started with TZ basis for H because it’s slightly more compact. We used a =13,14 a 0 and 8 and 14 states in close-coupling expansion. Results were stable with radius and number of states, but core excited resonances are very sensitive to choice of NOs (averaging). No shape resonance.  Ground state energy:  231.023 Hartree  Ground state dipole moment: 2.06 Debye  Excitation thresholds: around 2.5 eV too high with MOs

29. Some results Total cross section Core-excite resonances

30. Calculations We tried a DZ basis for H to try to improve dipole. We used a =14,15 a 0 and 8 state in close-coupling expansion. Results not stable with radius See a shape resonance!!  Ground state energy:  231.020 Hartree  Ground state dipole moment: 2.13 Debye Excitation thresholds: around 1.5 eV too high with MOs  LUMO has the right symmetry

31. Some results Total cross section Present at SE level E=7.43 eV  =1.42 eV Shape resonance

32. Total inelastic cross section

34. Calculations can be performed with our codes Shape resonance ?? Several core-excited resonances Description of electronic states should be improved More information on electronic excited states is needed !! Conclusion

35. Chiara Piccarreta Jimena Gorfinkiel Gabriela Halmova

36. www.quantemol.com An expert system for running the UK molecular R-matrix codes Demonstrations available