Electron - molecule collision
calculations using the R-matrix
method
Jonathan Tennyson
Department of Physics and Astronomy
University College London
IAEA. Vienna,
December 2003
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 + BImpact dissociation
AB + e
A+B+e
All go via (AB-)** . Can also look for bound states
The R-matrix approach
Inner region:
Outer region
e–
• exchange
• electron-electron correlation
• multicentre expansion of 
Inner region
Outer region:
C
C
F
R-matrix boundary r = a:
target wavefunction = 0
• exchange and correlation are
negligible
• long-range multipolar
interactions are included
• single centre expansion of 
Scattering Wavefunctions
k = A
N
Si,j ai,j,k fi
hi,j +
N+1
bj,k fj
where
N
fi N-electron wavefunction of ith target state
hi,j 1-electron continuum wavefunction
N+1
fj (N+1)-electron short-range functions
A Antisymmetrizes the wavefunction
ai,j,k and bj,k variationally determined coefficients
UK R-matrix codes
L.A. Morgan, J. Tennyson and C.J. Gillan, Computer Phys. Comms., 114, 120 (1999).
Electron collisions with OClO
R-matrix: Baluja et al (2001)
Experiment: Gulley et al (1998)
Electron - LiH scattering:
2S
eigenphase sums
B Anthony (to be published)
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
Including nuclear motion` (within adiabatic nuclei
approximation) in case of dissociation
• Excess energy of incoming eover dissociating energy can be
split between nuclei and outgoing
e- in any proportion.
• Fixed nuclei excitation energy
changes rapidly with bondlength
• Tunnelling effects significant
ds(Ein)
dEout
Determine choice of Tmatrices to be averaged
The energy balance method
D.T. Stibbe and J. Tennyson, New J. Phys., 1, 2.1 (1999).
Explicit adiabatic averaging over T-matrices using continuum functions
Need to Calculate:
• 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
C.S. Trevisan and J. Tennyson, J. Phys. B: At. Mol. Opt. Phys., 34, 2935 (2001)
e- + H2
e- + H + H
Cross section (a02)
Integral cross sections
Incoming electron energy (eV)
e- + H2
e- + H + H
Differential Cross section (a02)
Angular differential cross sections at 12 eV
Angle (degrees)
e- + H2(v=0)
e- + H + H
Atom kinetic energy (eV)
Energy differential cross sections in a.u.
Incoming electron energy (eV)
e- + H2(v>0)
e- + H + H
Atom kinetic energy (eV)
Energy differential cross sections in a.u.
V=2
V=3
Incoming electron energy (eV)
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 ?
Energy (eV)
Quasibound states of H2-: 2Sg+ resonances
Internuclear separation (a0)
DT Stibbe and J Tennyson, J. Phys. B., 31, 815 (1998).
Can one calculate resonance positions with
a standard quantum chemistry code?
Energy (eV)
R-matrix Resonance position
H2- potential curves calculated
with Gaussian by Mebel et al.
R (a0)
No!
D T Stibbe and J Tennyson, Chem. Phys. Lett., 308, 532 (1999)
Electron collision with CFx radicals
extremely high global warming potential
C2F6 and CF4
practically infinite atmospheric lifetimes
CF3I
C2F4
new feedstock gases
low global warming potential
strong source of CFx radicals
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
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
Electron collisions with the CF
Target model
• X1, 4S–, 2S+, 2, 2S– and 4
• Slater type basis set: (24s,14) + (s, )
C
valence target states
valence NO
single + double
excitation
(24s,14)
final model
2S+
Rydberg state
Rydberg NO (S)
single excitation
(7s…14s 3…6)
(1s 2s)4(3s …6s 1 2)11
(1s 2s)4(3s …6s 1 2)10(7s 3)1
F
Electron collisions with the CF
• Resonances
1
Ee = 0.91 eV
e = 0.75 eV
1S +
Ee = 2.19 eV
e = 1.73 eV
3S –
Ee ~ 0 eV
22
Electron collisions with the CF
• Bound states
1
Eb(Re) = 0.23 eV
3 E (R ) = 0.26 eV
b e
unbound at R = 2.6 a0
shape resonances E(1) = 0.054 eV
E(3) = 0.049 eV
3S–
at R > 2.5 a0
1 at R > 3.3 a
0
•
3S–
and 3
1 and 1
become bound
C(3P) + F–(1S)
C(1D) + F–(1S)
27s
Electron collisions with the CF
Resonances
•
shape resonances:
2B (2A’’) E = 0.95 eV
1
e
e = 0.18 eV
2A (2A’)
1
Ee = 5.61 eV
e = 2.87 eV
3b1
7a1
• bound state at R > 3.2 a0
2B
1
CF(2P) + F–(1S)
2
Electron collisions with the CF3
Target representation
C
2.53 ao
• Cs symmetry group
• X2A’, 12A”, 22A’, 22A”, 32A’, 32A”
F1
• Models
F3
110.7o
F2
a = 10 ao
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
Electron collisions with the CF3
Electron impact excitation cross sections
• Bound state
E(1A’) ~ 0.6 eV
No (low-energy)
resonances!
Dissociative recombination of NO+
NO+ important ion in ionosphere of Earth
and thermosphere of Venus
Mainly destroyed by
NO+ + eN +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
NO+ dissociation recombination: potential energy curves
Spectroscopically determined
R-matrix ab initio
R-matrix calibrated
NO+ dissociation recombination:
Direct and indirect contributions
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)
Rate coefficient (cm3 s-1)
NO+ dissociation recombination:
Temperature dependent rates
Experiment
Mostefaoui et al (1999))
Calculation
Electron temperature, Te (K)
Electon-H3+ at intermediate energies
Jimena Gorfinkiel
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.
Chiara
Piccarreta
Natalia Vinci
Jimena Gorfinkiel
Iryna Rozum