R-matrix calculations of electron-molecule collisions at low & intermediate energy

Jonathan TennysonDepartment 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

Elastic scattering AB + e AB + e

Electronic excitation AB + e AB* + e

Rotational excitation

AB(N”) + e AB(N’) + eVibrational excitation

AB(v”=0) + e AB(v’) + e

Dissociative attachment / Dissociative recombination AB + e A + B

Impact dissociation

AB + e A + B + e

Incr

easi

ng

En

ergy

Processes at low impact energies

Impact ionisation (e,2e) AB + e AB+ + e + e

Polyatomic R-matrix method

kA i,j ai,j,kiNi,jibj,kj

N+1

iN= target states = CI target built from nuclear centred GTOs

jN+1= L2 functions

H H

e

outer region

inner regioni,j = continuum orbitals = GTOs centred on centre of mass (CM)

(within the Fixed-Nuclei approximation)

a

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)

Electron – water (rotationally averaged) elastic cross sections

Integral cross section

A Faure, JD Gorfinkel & J Tennyson J Phys B, 37, 801 (2004)

C2 statesElectron – C2:

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

Intermediate impact energies

Ionization and large number of states energetically accessible

IonizationAB + 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

R-matrix with pseudostates method (RMPS)

Add iN 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?)

kA i,jai,j,kiNi,ji bj,kj

N+1

Pseudostates

Example: H3+

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 a0)

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 H3+

J D Gorfinkiel & J Tennyson, J Phys B, 37, L343 (2004)

Quantum defect for resonances increased by about 0.05

Electronic excitation of H3+

States in close-coupling expansion parallel perpendicular

6 (physical target states) -3.2848 -0.0638

28 (Ecut= 33.47 eV) -3.4563 -2.0893

64 (Ecut=45 eV) -3.5247 -2.2093

152 (Ecut=132 eV) -3.5336 -2.2480

Accurate ab initio value -3.5978 -2.2454

Polarizability of H3+ (in a.u.)

Molecular R-matrix with Pseudostates Method (MRMPS)

Electron impact ionisation of H2

JD Gorfinkiel & J Tennyson, J Phys B, 38, 1607 (2005)

• 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. C2

)

Electron impact rotational excitation of ions can be important.Experimental verification?

Electron collisions with biomolecules?

Electron collisions with tetrahydroforan (THF) C4H8O

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

N N

N C6 N

NH2

Guanine

Cytosine

Thymine

Adenine

tetrahydrofuran(THF)

3-hydroxy-tetrahydrofuran

-tetrahydrofurylalcohol

+ H2O

Why tetrahydrofuran?

Why tetrahydrofuran?

• Radiation damage/radiation therapy: effect of

secondary electrons• First R-matrix calculations with a molecule this size

(13 nuclei and 40 electrons)

C4H8O (THF)

• C2v geometry from semi-empirical calculation (* C2 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 a0

• up to 14 states in the close-coupling expansion

Calculation

A variety of models tested

E(eV) (eV)

2A2 7.62 4.6x10-4

2B1 7.64 2.4x10-4

2B1 7.67 0.014

2B1 8.11 0.030

Not fitted (yet)

Calculations

We started with TZ basis for H because it’s slightly more compact. We used a =13,14 a0 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

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 a0 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

Some results

Total cross section

Present at SE level E=7.43 eV =1.42 eVShape resonance

Total inelastic cross section

Total inelastic cross section

• 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

ChiaraPiccarreta

Jimena Gorfinkiel

Gabriela Halmova

www.quantemol.com

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

Demonstrations available