1. Theoretical study of Group 14 C+(2PJ)-RG and Si +(2PJ)-RG complexes (RG = He –Xe)
William D. Tuttle, Rebecca L. Thorington, Larry A. Viehland and Timothy G. Wright
ISMS 2017, Clusters/Complexes, RH June 22nd 2017

2. Why C+-RG and Si+-RG?
Extension of work on M+-RG complexes from Groups 1, 2, 11, 12 and 13.
Generating accurate interatomic potentials for use in calculation of ion transport data, useful for reaction kinetics involving ions.
C+-He proposed as a cooling mechanism for C+ in the interstellar medium.1
Si+ ions of atmospheric importance; presence in upper atmosphere from meteoroids, important in understanding their rapid depletion with altitude.2
1N. Toshima, J. Phys. Soc. Jpn. 38, 1464 (1975). 2J. M. C. Plane et al., J. Geophys. Res. Atmos. 121, 3718 (2016).

3. Computational methodology
RCCSD(T) interaction potentials arising from the non-SO terms and SO levels correlating with the C+,Si+(2PJ)-RG(1S0) asymptote computed in MOLPRO.
Counterpoise-corrected at over 80 internuclear separations from short- to long-R.
aug-cc-pwCVXZ (X=Q,5) basis sets for all atoms (except He, aug-cc-pVXZ), extrapolated to basis set limit. ECPs for Kr, Xe.
CP-corrected interaction energies used as unperturbed eigenvalues of the Breit- Pauli SO matrix for SO-inclusive potentials.

4. C+-He : An illustrative example
2Σ+ 2Π

5. C+-He : An illustrative example
2Σ1/2+
2Π3/2
2Π1/2

6. C+-He : An illustrative example
Let’s look at some trends in Re, De, ωe and k!

7. 2Πnon-SO

8. What about the influence of the SO effect?

9. 2Π1/2 and 2Π3/2

10. What about the influence of the SO effect?
Hund’s case (a): expected asymptotic 2PJ splitting is ~3/2 the molecular 2ΠΩ splitting (all below values in cm-1)
C+-He
C+-Ne
C+-Ar
Experiment
Asymptotic splitting
61.2
63.42
Predicted Hund’s case (a) splitting at Re
40.8
Splitting at Re
41.3
41.4
59.8
(Re split./pred.)*100
101%
102%
147%
Si+-He
Si+-Ne
Si+-Ar
261.7
287.24
174.5
187.0
183.5
178.0
107%
105%

11. What about the influence of the SO effect?
Hund’s case (a): expected asymptotic 2PJ splitting is ~3/2 the molecular 2ΠΩ splitting (all below values in cm-1)
C+-He
C+-Ne
C+-Ar
C+-Kr
C+-Xe
Asymptotic splitting
61.2
Predicted Hund’s case (a) splitting at Re
40.8
Splitting at Re
41.3
41.4
59.8
162.8
450.3
(Re split./pred.)*100
101%
102%
147%
400%
1104%
Si+-He
Si+-Ne
Si+-Ar
257.3
261.7
171.5
174.5
187.0
183.5
178.0
109%
105%
RG C+ Charge transfer?

12. MRCI/aug-cc-pwCVQZ calculations (non-CP corrected, no SO effect) to compare to CCSD(T)/aug-cc-pwCVQZ potentials for the Ar, Kr and Xe complexes. ECPs for Kr, Xe. 2Π
C+-Ar
C+-Kr
C+-Xe
CCSD(T)/QZ
MRCI/QZ
Re / Å
2.003
1.999
2.079
2.082
2.206
2.215
De / cm-1
7876
8025
11772
12043
17059
17417
ωe / cm-1
408
413
433
435
447
445
k / cm-1 91 93
116
117
130
128
2Σ+
C+-Ar
C+-Kr
C+-Xe
CCSD(T)/QZ
MRCI/QZ
Re / Å
3.009
2.997
2.912
2.910
2.803
2.797
De / cm-1
902
1006
1544
1703
3452
3783
ωe / cm-1
116
121
142
147
218
223
k / cm-1 7 8 13 31 32

13. Evidence of charge transfer from MRCI coefficients?
Atom
Ionisation energy / eV C
11.260 Si
8.1517 He
24.587 Ne
21.565 Ar
15.760 Kr
14.000 Xe
12.130
Atom
Atom+(2PJ) splitting / cm-1 C
63.42 Si
287.24 He - Ne
780.42 Ar Kr Xe
Ionisation energy approaching carbon down the RG series
RG+ atomic splitting increasing significantly down RG series

14. Summary
We have calculated accurate CCSD(T)/EBS interaction potentials for C+(2PJ)-RG(1S0) (RG = He – Xe) and Si+(2PJ)-RG(1S0) (RG = He – Ar).
The influence of the spin-orbit interaction on the spectroscopic constants (and calculated ion transport properties) has been investigated.
Significant deviations from Hund’s case (a) molecular spin-orbit splitting behaviour have been attributed to charge transfer in the heavier C+-RG species.

15. Future work
Continuation to the heavier Si+-RG (RG = Kr, Xe) species to investigate charge transfer in those cases.
Heavier Group 14 cations, where the SO splitting will be larger.
Ion transport calculations (Larry Viehland) using these potentials, some of which is already published, alongside the spectroscopic constants.3,4
3William D. Tuttle, Rebecca L. Thorington, Larry A. Viehland and Timothy G. Wright, Mol. Phys., 113, 3767 (2015).
4William D. Tuttle, Rebecca L. Thorington, Larry A. Viehland and Timothy G. Wright, Mol. Phys., 115, 437 (2017).

16. Acknowledgements Thanks for your attention!
Professor Timothy G. Wright
Professor Larry A. Viehland
Rebecca L. Thorington
Dr Adrian M. Gardner
Thanks for your attention!
University of Nottingham HPC facility

17. 2Σ+non-SO

18. 2Σ+1/2

19. 2Σ+1/2
Big influence on Re for Si+-RG complexes; due to proximity of 2Sig+ minimum to the 2Pi potential; interaction between 2Sig+1/2 and 2Pi1/2 serves to reduce bond length in the 2Sig+1/2 level, increasing interactions so higher De/k and higher ωe accompany this. Note that although this also mixes some 2Sig+ character into the 2Pi1/2 level, the 2Pi minimum is significantly separated from the 2Sig+1/2 potential, so this mixing is lessened near Re.
The levels are further apart in the C+ complex due to the greater dissociation energies.