Electron molecule collision calculations using the R-matrix method Jonathan Tennyson Department of...

Electron molecule collision calculations using the R-matrix

method

Jonathan TennysonDepartment of Physics and Astronomy

University College London

IAEA. Vienna,

December 2003

Processes: at low impact energies

Elastic scattering AB + e AB + eElectronic excitation

AB + e AB* + e

Dissociative attachment / Dissociative recombination AB + e A + B A + B

Vibrational excitation

AB(v”=0) + e AB(v’) + e

Rotational excitation

AB(N”) + e AB(N’) + e

Impact dissociation

AB + e A + B + e

All go via (AB)** . Can also look for bound states

The R-matrix approach

C

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

R-matrix boundary r = a: target wavefunction = 0

Scattering Wavefunctions

kA i,jai,j,kiNi,jbj,kj

N+1wherei

N N-electron wavefunction of ith target state

i,j1-electron continuum wavefunction

jN+1 (N+1)-electron short-range functions

A Antisymmetrizes the wavefunctionai,j,kand bj,kvariationally 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: 2 eigenphase sums

B Anthony (to be published)

Electron impact dissociation of H2

Important for fusion plasma and astrophysics

Low energy mechanism:e + H2(X 1g) e + H2(b 3u) e + H + H

R-matrix calculations based onadiabatic nuclei approximation

extended to dissociation

` Including nuclear motion (within adiabatic nuclei approximation) in case of dissociation

dEout

d(Ein)

• 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

Determine choice of T-matrices to be averaged

D.T. Stibbe and J. Tennyson, New J. Phys., 1, 2.1 (1999).

The energy balance method

Explicit adiabatic averaging over T-matrices using continuum functions

Need to Calculate:

• Total cross sections, (Ein)

• Energy differential cross sections, d(Ein)

dEout

• Angular differential cross sections, d(Ein)

d

• Double differential cross sections, d2(Ein)

ddEout

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 Integral cross sections

Incoming electron energy (eV)

Cro

ss s

ecti

on (

a 02 )

e + H2 e + H + H Angular differential cross sections at 12 eV

Angle (degrees)

Dif

fere

ntia

l Cro

ss s

ecti

on (

a 02 )

e + H2(v=0) e+ H + H Energy differential cross sections in a.u.

Ato

m k

inet

ic e

nerg

y (e

V)

Incoming electron energy (eV)

e + H2(v>0) e+ H + H Energy differential cross sections in a.u.

Ato

m k

inet

ic e

nerg

y (e

V)

Incoming electron energy (eV)

V = 2 V = 3

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 atomsFor v > 0: Source of cold H atoms ?

Ene

rgy

(eV

)

Internuclear separation (a0)

DT Stibbe and J Tennyson, J. Phys. B., 31, 815 (1998).

Quasibound states of H2: g

+resonances

Can one calculate resonance positions with a standard quantum chemistry code?

R (a0)

Ene

rgy

(eV

)

R-matrix Resonance position

H2- potential curves calculated

with Gaussian by Mebel et al.

D T Stibbe and J Tennyson, Chem. Phys. Lett., 308, 532 (1999)

No!

Electron collision with CFx radicals

extremely high global warming potential

C2F6 and CF4

practically infinite atmospheric lifetimes

CF3I low global warming potential

C2F4 strong 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

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, 4–, 2+, 2, 2– and 4• Slater type basis set: (24,14) + (, )

valence target states 2+ Rydberg state

valence NO Rydberg NO ()

(24,14) (7…14 3…6)

C F

(1 2)4(3 …6 1 2)11

(1 2)4(3 …6 1 2)10(7 3)1final model

single

excitation

single + double

excitation

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

22

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

27

become bound

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

Electron collisions with the CF3

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

C

F3

110.7o

F1 F2

a = 10 ao

2.53 ao

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 Earthand thermosphere of Venus

Mainly destroyed byNO+ + e N + O

Recent storage ring experiments show unexplained peak at 5 eV

Need T-dependent rates for models

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)

NO+ dissociation recombination: Temperature dependent rates

Electron temperature, Te (K)

Rat

e co

effi

cien

t (cm

3 s

1 )

ExperimentMostefaoui et al (1999))

Calculation

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.

Natalia Vinci

Iryna Rozum

Jimena Gorfinkiel

ChiaraPiccarreta