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

Processes at low impact energies

Elastic scattering AB + e AB + e AB Rotational excitation (N”) + e AB (N’) + e Vibrational excitation AB (v”=0) + e AB (v’) + e Dissociative attachment / Dissociative recombination AB + e A  + B Electronic excitation AB + e AB * + Impact dissociation e AB + e A + B + e Impact ionisation (e,2e) AB + e AB + + e + e

Polyatomic R-matrix method

(within the Fixed-Nuclei approximation) Y

k

= A S

i,j

a

i,j,k

f

i N

h

i,j

+ S

i

b

j,k

f

j N+1

f

i N = target states =

CI target built from nuclear centred GTOs f

j N+1 = L 2 functions

h

i,j = continuum orbitals =

GTOs centred on centre of mass (CM) inner region H H

e

 a outer region

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

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

37

, 801 (2004)

Electron – C 2 :

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

Intermediate impact energies

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

R-matrix with pseudostates method (RMPS)

Y

k

= A S

i,j

a

i,j,k

f

i N

h

i,j

+ S

i

b

j,k

f

j N+1

Add f

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?)

Pseudostates

Example: H

3 +

Positive ion, electron density compact  can keep box small (a = 10 a 0 ) Previous ‘Standard’ calculations for electronic excitation, E < 20 eV • Kohn calculation: Orel (1992) • R-matrix calculation: Faure and Tennyson (2002) (6 target states) 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

Electron impact ionisation of H 3 +

J D Gorfinkiel & J Tennyson, J Phys B,

37

, L343 (2004)

Electronic excitation of H 3 +

Quantum defect for resonances increased by about 0.05

Molecular R-matrix with Pseudostates Method (MRMPS)

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) 64 (E cut =45 eV) 152 (E cut =132 eV) -3.4563 -3.5247 -3.5336 Accurate

ab initio

value -3.5978 -2.0893 -2.2093 -2.2480 -2.2454

Electron impact ionisation of H 2

JD Gorfinkiel & J Tennyson, J Phys B,

38

, 1607 (2005)

Conclusions

Electron impact rotational excitation of ions can be important.

Experimental verification?

With the RMPS method for electron molecule collisions we have : • • • extend energy range of calculations treat near threshold ionisation improve representation of polarisation Will allow us to treat excitation to high electronic states and collisions with anions (e.g. C 2  )

Electron collisions with biomolecules?

Electron collisions with tetrahydroforan (THF) C

4

H

8

O

Dorra Bouchiha, Laurent Caron, Leon Sanche (Sherbrooke) Jimena D Gorfinkiel (UCL)

Why tetrahydrofuran?

tetrahydrofuran (THF) 3-hydroxy tetrahydrofuran  -tetrahydrofuryl alcohol

+ H 2 O

Guanine Thymine Cytosine Adenine

Why tetrahydrofuran?

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

Calculation

A variety of models tested • 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

Not fitted (yet) 2 A 2 2 B 1 2 B 1 2 B 1 E(eV) 7.62

7.64

7.67

8.11

 (eV) 4.6x10

-4 2.4x10

-4 0.014

0.030

Calculations

We started with TZ basis for H because it’s slightly more compact. We used

a

=13,14 a 0 close-coupling expansion.

and 8 and 14 states in  Ground state energy:  231.023 Hartree  Ground state dipole moment: 2.06 Debye  Excitation thresholds: around 2.5 eV too high with MOs Results were stable with radius and number of states, but core excited resonances are very sensitive to choice of NOs (averaging). No shape resonance .

Some results

Total cross section Core-excite resonances

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.

 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 Results not stable with radius See a shape resonance !!

Some results

Total cross section Shape resonance Present at SE level E=7.43 eV  =1.42 eV

Total inelastic cross section

Total inelastic cross section

Conclusion

• 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 !!

Chiara Piccarreta Jimena Gorfinkiel Gabriela Halmova

An expert system for running the UK molecular R-matrix codes

Demonstrations available

www.quantemol.com