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)
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
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)
• 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 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
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
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
• 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