e - Errors in electron - molecule collision calculations (at low energies) Jonathan Tennyson University College London Outer region Inner region IAEA May 2013
Electron processes: at low impact energies Elastic scattering AB + e AB + e Electronic excitation AB + e AB* + e Vibrational excitation AB(v =0) + e AB(v ) + e Rotational excitation AB(N ) + e AB(N ) + e Dissociative attachment / Dissociative recombination AB + e A + B A + B Impact dissociation AB + e A + B + e Impact ionisiation AB + e AB + 2e
Errors in electron molecule collision calculations Errors are systematic Generally reduce with increasing energy ie problem simplifies at high energy limit Physics of electrons collisions with ions and neutrals very different No single method treats all processes simultaneously So no complete, self-consistent data sets
Models Static exchange (SE) Static plus polarisation(sep) Close-Coupling (CC) Complete close-coupling ( C CC) eg CCC, RMPS Single-centre expansion Semi-empirical: BEB, BEf, etc. For ions: MCQDT Model more important for determining accuracy than method of solution Eg comparison between (UK) R-matrix, Kohn, Schwinger...
Model vs Method Eg Resonances in electron H 3 + (in ev) Method Schwinger R-matrix RMPS Orel & Kulander (1993) Faure & Tennyson (2002) Gorfinkiel & Tennyson (2005) E res G E res G E res G 2 E 9.1 0.64 9.12 0.64 8.74 0.47 2 A 1 10.3 0.18 10.14 0.19 9.57 0.16 2 A 2 ~11.2 -- 11.11 0.09 10.79 0.14 Different methods: similar answers for same model Results very dependent on the model
R-matrix with Pseudostates Method (RMPS) Polarizability of H 3 + (in a.u.) States in close-coupling expansion parallel perpendicular 6 (physical target states) -3.2848-0.0638 28 (E cut = 33.47 ev) -3.4563-2.0893 64 (E cut =45 ev) -3.5247-2.2093 152 (E cut =132 ev) -3.5336-2.2480 Accurate ab initio value -3.5978-2.2454
Mean polarizability of H 2 O (in a.u.) RMPS Measured standard M Jones & J Tennyson, J. Phys. B, 43, 045101 (2010) Reliable treatment of polarisation effects is biggest problem in low-energy electron-molecule collision calculations
Problems with experimental benchmarks Issues with low and high angle scattering Issues with what is being measured (eg cascade) Heavily biased sample: closed shell molecules
Elastic scattering AB + e AB + e Models: SEP, CC, C CC, single centre SE good at higher energy Treated well theoretically. Theory MUST be used to correct measured cross sections for electron polar molecules.
Electron water rotationally resolved cross sections: Differential cross sections (DCS) at 6 ev * Cho et al (2004) Jung et al (1982) DJ=1 DJ=all DJ=0
Electron water (rotationally averaged) elastic cross sections Integral cross section A Faure, JD Gorfinkel & J Tennyson J Phys B, 37, 801 (2004)
Rotational excitation AB(N ) + e AB(N ) + e Models: SEP, CC ( C CC), single centre (all assume rigid rotors: validated against MCQDT for ions) Calculated rotational excitation cross sections seem reliable. Urgent need for experimental data
Vibrational excitation AB(v ) + e AB(v ) + e Two mechanisms: A.Non resonant. Small contribution but fairly straightforward to compute; Models: So far single centre only Adiabatic treatment of nuclear motion B. Resonant process Requires good resonance positions and target curves Models: SEP, CC, single centre Detailed (non-adiabatic?) treatment of nuclear motion Mainly diatomics. Results largely guided by experiment,
Electronic excitation AB + e AB* + e Model: CC or C CC only (BEf good for high energy) Requires good multistate targets Agreement with experiment: Acceptable in many cases for total cross sections; Issues with theory versus expt for DCS Recommend many more studies with C CC methods Experimentally, what is being measured? Cascade and other issue. What do the modellers actually want? (see also electron impact dissociation)
Dissociative attachment / Dissociative recombination AB + e A + B A + B Models DA: SEP, CC ( C CC), Models DR: CC ( C CC) Need: Accurate resonance curves (and widths) Detailed treatment of nuclear motion (MQDT, wavepackets) Ab initio calculation of precise positions of resonance curves Is very difficult
Dissociation recombination: NO + potential energy curves AB + + e A + B Theory VERY sensitive to precise location of curve crossings Spectroscopically determined Struggles to get reliable branching ratios Best one can hope for at this stage is rough sensitivity analysis rather than actual errors R-matrix ab initio R-matrix calibrated IF Schneider, I Rabadan, L Carata, LH Andersen, A Suzor-Weiner & J Tennyson, J. Phys. B, 33, 4849 (2000)
3 P u symmetry states of N 2 in red Other curves are N 2 + D. Little and J.Tennyson, J Phys B (submitted)
Impact dissociation AB + e A + B + e Mechanism: Proceeds via electon impact electronic exciation to electronically excited states Model: CC or C CC Detailed treatment of nuclear motion required Issues about precise formulation of the problem Only limited studies so far.
Impact ionisiation AB + e AB + 2e Models: C CC or BEB Recommendation: use BEB or equivalent
Spectroscopy Transition intensities for water Ab initio dipole moment, m(q) Computed using large basis, MRCI correlation with large active space Core correction Relativistic correction Converged to 1% L. Lodi, J. Tennyson and O.L. Polyansky, J. Chem. Phys., 135, 034113 (2011).
Transition intensities S if = < i m f > 2 Biggest uncertainty due to wavefunctions Repeat calculations 4 times Stability analysis to identify problem transitions H 2 18 O About 100 000 lines analysed Replace measurements in HITRAN 2012 L. Lodi and J. Tennyson, J. Quant. Spectrosc. Rad. Transf., 113, 850 (2012)
Uncertainties in scattering calculations Usually very hard to quantify Mixture of background systematic errors And large hard-predict contributions (resonances) Urgent need for well-defined error protocols C CC methods seem most promising as: Higher accuracy Can be systematically varied But computationally expensive