theoretical study of charge transfer in ion-molecule collisions
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Theoretical Study of Charge Transfer in Ion-Molecule Collisions
Emese Rozsályi University of Debrecen2012.03.01. Department of Theoretical Physics
C2+ + OH → C+ + OH+
C2+ + HF → C+ + HF+
C2+ + HCl → C+ + HCl+
By the Wigner and von Neumann non-crossing rule, adiabatic potential energy curves for states of the same symmetry cannot cross.
Potential energy curves for states of the same symmetry can approach each other in a narrow region avoided crossing
The charge-transfer process is driven by means of the nonadiabatic interactions in the vicinity of avoided crossings.
Comparison of depth-dose profiles
The dose to normal healthy tissue is the least by using carbon-ion therapy. This depth-dose profile is the closest to the desire profile in diagram (a) in terms of tumour coverage, critical organ avoidance and minimised entry channel dosage.
Ion-diatomic collisional system
B R A
ρ ϴ
C
The projectile follows straight-line trajectories:
X
v
b R ϑ
θ ρ Z Y
The electronic motion is described by the eikonal equation:
Semiclassical treatment
Sudden approximation
No appreciable change in the ro-vibrational wavefunction is effected in the time interval in which the electronic transition takes place.
Molecular close-coupling treatment:
Semiclassical formalism
For a given nuclear trajectory and fixed :
The coefficients are subject to the initial condition:
X
Z’ v
Dynamical couplings: R
ρ Z
X’
Cross sections
The probability for transition to the final state is:
The cross section for transition to state , for each value of ρ is:
The total cross section is a sum of the partial cross sections:
Franck-Condon approximation The coefficients are slowly varying functions of ρ
it is possible to substitute them with values at the equilibrium distance of the diatomic molecule ρ0
F0ν is the Franck-Condon factor between the BC and BC+ vibration wave functions at equilibrium geometry for the vibrational level ν=0 and ν, respectively.
EIKONXSR.J. Allan, C. Courbin, P. Salas, P. Wahnon, J. Phys. B 23, L461 (1990).
LEVEL 7.7 R.J. Le Roy [http://leroy.uwaterloo.ca]
Dissociation limits and their atomic terms
States of HF+
Corresponding symmetry of states within the C2v point group
Asymptotic energies (eV)CASSCF/aug-cc-pVTZ
Asymptotic energies (eV)MRCI/aug-cc-pVTZ
H++F(2P) 2Σ+
2Π2A12B1, 2B2
-99.4658-99.4482
-99.6230-99.6236
H(2S)+F+(3P) 2,4Σ-
2,4Π2B1, 2B22A24B1, 4B24A2
-99.3536-99.3472-99.3350-99.3355
-99.4908-99.4902-99.4896-99.4897
H(2S)+F+(1D) 2Σ+
2Π 2Δ
2A12B1, 2B22A22A1
-99.2661-99.2531-99.2427-99.2391
-99.3940-99.3939-99.3932-99.3933
Dissociation limits and their atomic terms
Energies obtained from NIST database (in eV)
CASSCF/aug-cc-pVTZ energies (in eV)
MRCI/aug-cc-pVTZ energies(in eV)
H++F(2P) 0 0 0
H(2S)+F+(3P) 3.8452 3.1075 3.6246
H(2S)+F+(1D) 6.4123 5.6273 6.2505
States of HF+
NIST H+F+ , H++F
MOLPROH.J. Werner, P. Knowles, MOLPRO (version 2009.1) package of ab initio programs
The quasimolecule CHF2+
E∞(eV) C+-state HF+-state CHF2+-state
1. 0 2P◦ 12Π 1,3Σ+, 1,3Π, 1,3Δ
2. 3.9093 2P◦ 12Σ+ 1,3Σ+, 1,3Π
3. 5.1775 4P 12Π 3,5Σ+, 3,5,Π, 3,5Δ
4. 9.2453 4P 12Σ+ 3,5Σ+, 3,5Π
5. 9.3017 2D 12Π 1,3Σ+, 1,3Π, 1,3Δ, 1,3φ
Comparison of asymptotic energies (in eV):
Configuration This calculation Separated species
C2+(1S) + HF(1+) 8.368 8.279
C+(2P) + HF+(2+) 3.824 3.909
C+(2P) + HF+(2Π) 0 0
Three 1+ states and two 1Π states are considered in the process:
C2+(1s22s2)1S + HF(1+) 1+
C+(1s22s22p)2P + HF+(2+)1+, 1Π
C+(1s22s22p)2P + HF+(2Π)1+, 1Π
C2++HF
1. 1. C+(1s22s22p)2P + HF+(2Π) 1+, 1Π
2. 2. C+(1s22s22p)2P + HF+(2+) 1+, 1Π
3. 3. C2+(1s22s2)1S + HF(1+) 1+
Potential energy curves, θ=0◦, ρHF=eq., 1Σ+, 1Π.
Radial coupling matrix elements between 1+ states, θ=0◦, ρHF=eq.
Rotational coupling matrix elements between 1+ and 1Π states, θ=0◦, ρHF=eq.
C2++HF
Total and partial charge transfer cross sections at equilibrium, ϴ=0° ; full line: with translation factors; broken line: without translation factors.
Total and partial charge transfer cross-sections for the vibration coordinate rHF=1.5 a.u., θ=0°.
Radial coupling matrix elements between 1+ states, θ=0°, Dotted line, rHF=2.0 a.u.; full line, rHF=1.73836832 a.u. (equilibrium); dashed line, rHF=1.5 a.u.
Total and partial charge transfer cross-sections for the vibration coordinate rHF=2.0 a.u., θ=0°.
Total charge transfer cross-sections, θ=0°, for different values of the vibration coordinate rHF.
C2++HF/ C2++OH
ν V=0.15 V=0.15 V=0.15 V=0.15 V=0.15
0 14.260 14.424 15.379 15.339 17.071
1 5.007 5.064 5.400 5.385 5.994
2 1.279 1.293 1.379 1.375 1.531
3 0.305 0.308 0.329 0.328 0.365
4 0.073 0.075 0.080 0.079 0.088
Total charge transfer cross-sections for the C2+- HF system in the linear approach, θ=0°, for different values of the vibration coordinate rHF.
Total charge transfer cross-sections for the C2+- OH system in the linear approach, θ=180°, for different geometries of the OH radical.
Total cross sections for the C2+ + HF(=0) →C+ + HF+
() charge transfer process (in 10-16 cm2) for different velocities v (in a.u.).
— ϴ = 0o — ϴ = 20o— ϴ = 45o— ϴ = 90o ····· ϴ = 135o ····· ϴ = 160o ····· ϴ = 180o
Potential energy curves,ρHF=eq., 1Σ+, 1Π.
θ=90◦ θ=180◦
Evolution of the radial couplings for different orientations.
rad23rad12
C2++HF
Total charge transfer cross-sections at equilibrium, for different orientations θ from 0° to 180°.
Radial coupling matrix elements between 1+ states for different orientations θ from 0° to 180°. Dotted line, θ=90°; dotted-dashed line, θ=45°; dashed line, θ=135°; thin full line, θ=0°; full line, θ=180°.
C2++HF
Velocity(a.u.)
Elab
(keV)
sec3231Σ+ - 21Σ+
secpi3231Σ+ - 21Π
sec3131Σ+ - 11Σ+
secpi3131Σ+ - 11Π
sectot
0.05 0.75 7.04 2.68 0.48 0.34 10.54
0.1 3 8.41 3.99 0.86 0.96 14.22
0.15 6.75 8.78 4.79 1.04 1.48 16.10
0.2 12 8.75 5.31 1.24 1.33 16.64
0.25 18.75 8.56 6.04 1.76 1.53 17.89
0.3 27 8.13 6.97 2.19 1.81 19.10
0.35 36.75 8.18 7.68 2.52 2.10 20.51
0.4 48 8.25 8.10 2.89 2.25 21.49
0.45 60.75 8.16 8.22 3.38 2.24 22.01
0.5 75 7.94 8.15 3.96 2.15 22.20
0.6 108 7.37 7.64 5.25 1.96 22.23
Charge transfer cross sections averaged over the different orientations.
C2++HCl
Potential energy curves for the 1+ (full line) and 1Π (broken line) states of the C2+-HCl molecular system at equilibrium, θ=0°.
Four 1+ states and three 1Π states are considered in the process:
1.C+(1s22s22p)2P° + HCl+(2Π) 1+, 1Π
2. C+(1s22s22p)2P° + HCl+(2+) 1+, 1Π
3. C+(1s22s22p)2D + HCl+(2Π) 1+, 1Π
4. C2+(1s22s2)1S + HCl(1+) 1+
C2++HCl
Total and partial charge transfer cross sections at equilibrium, ϴ=0° ;
Radial coupling matrix elements between 1+ states, θ=0◦, ρHCl=eq.
Rotational coupling matrix elements between 1+ and 1Π states, θ=0◦, ρHCl=eq.
C2++HCl Velocit
y
(a.u.)
Elab
(keV)
sec43
41Σ+31
Σ+
secpi43
41Σ+31
Π
sec42
41Σ+21Σ+
secpi42
41Σ+21
Π
sec41
41Σ+11Σ+
secpi41
41Σ+11
Π
Sectot
C 2++HCl
Sectot
C 2++HF
0.05 0.75 6.99 1.78 0.14 0.22 0.17 0.09 9.38 10.54
0.1 3 12.22 2.80 0.39 0.77 0.14 0.27 16.58 14.22
0.15 6.75 7.48 4.78 0.36 1.14 0.27 0.23 14.26 16.10
0.2 12 3.73 4.99 1.80 1.38 0.73 0.42 13.05 16.64
0.25 18.75 2.84 3.86 3.50 0.99 0.57 0.82 12.59 17.89
0.3 27 2.36 2.91 3.91 0.95 0.77 0.81 11.70 19.10
0.35 36.75 2.14 2.34 3.43 1.07 0.88 0.66 10.52 20.51
0.4 48 2.08 2.03 2.72 1.16 0.77 0.55 9.32 21.49
0.45 60.75 2.07 1.86 2.14 1.21 0.68 0.47 8.42 22.01
0.5 75 2.06 1.74 1.77 1.21 0.65 0.43 7.87 22.20
0.6 108 2.07 1.57 1.44 1.15 0.67 0.48 7.37 22.23
The comparative results show that the charge-transfer mechanism is fundamentally dependent of the specific nonadiabatic interactions involved in each system.
Publication list The presentation is based on the following papers: 1. E. Bene, E. Rozsályi, Á. Vibók, G. J. Halász, M. C. Bacchus-Montabonel: Theoretical treatment of direct
and indirect processes in ion-biomolecule collisions, AIP Conf. Proc. 1080, 59-70 (2008). 2. E. Rozsályi, E. Bene, G. J. Halász, Á. Vibók, M. C. Bacchus-Montabonel: Theoretical treatment of charge
transfer in collisions of C2+ ions with HF: Anisotropic and vibrational effect, Phys. Rev. A 81, 062711 (2010). 3. E. Rozsályi, E. Bene, G. J. Halász, Á. Vibók, M. C. Bacchus-Montabonel: Ab initio molecular treatment of
C2+ + HF collision system, Acta Physica Debrecina, XLIV, 118 (2010). 4. E. Rozsályi, E. Bene, G. J. Halász, Á. Vibók, M. C. Bacchus-Montabonel: Ab initio study of charge transfer
dynamics in collisions of C2+ ions with hydrogen chloride, Phys. Rev. A 83, 052713 (2011). 5. E. Rozsályi: Charge transfer in collisions of C2+ ions with HCl molecule, Acta Physica Debrecina, XLV, 166
(2011). 6. E. Rozsályi, E. Bene, G. J. Halász, Á. Vibók, M. C. Bacchus-Montabonel: Analysis of charge transfer
mechanism in ion-biomolecule collisions. Advances in the Theory of Quantum Systems in Chemistry and Physics; Progress in Theoretical Chemistry and Physics; 22, (355-368), 2012, ISBN 978-94-007-2075-6, Springer.
Thanks to...
Dr. Ágnes Vibók, Dr. Halász Gábor and Dr. Marie-Christine Bacchus-Montabonel for their support, inspiring comments and patience during the research.
The presentation is supported by the TÁMOP-4.2.2/B-10/1-2010-0024 project.The project is co-financed by the European Union and the European Social Fund.
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