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Renner-Teller Coupling in H2S+: Comparison of theory with optical spectra an PFI and MATI results

G. Duxbury1, Christian Jungen2 and Alex Alijah3

1Physics Department, University of Strathclyde, Glasgow, G4 0NG, UK

2LAC, Laboratoire Aime Cotton du CNRS, Universite de Paris -Sud, 91405 Orsay France

3GSMA, UMR CNRS 6089, Universite de Reims Champagne-Ardenne, B.P. 1039, 51687 Reims Cedex2, France

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Outline of presentation• Resumé of the transformed Hamiltonian• Example 1• NH2, small energy gap, large number of ro-vibronic

states identified, little ambiguity in assignment• Example 2• H2S+, large energy gap between ground and excited

states, large spin orbit coupling constant, ca 400 cm-1

• Potential ambiguity in the assignments.• Analysis of models used to fit the emission spectra,

PFI and MATI spectra

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NH2 P.E. curves and energy levels, 1980 and 2002

1980 JHM,

2002, Alijah and Duxbury

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Sawtooth Diagrams2 parent, spin-orbit splitting proportional to

• Jungen, Hallin and Merer (1980

Lz

Below barrier, K-dependent, above the barrier strong localised resonances.

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Sawtooth Diagrams for NH2, including Fermi Resonance, K=1.

• No Fermi resonance: non-interacting sawtooth curves

• Fermi resonance:distorted sawtooth curves. Experimental points added.

• Alijah and Duxbury, J .Mol. Spec. 2002

Lz

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H2S+

• Large energy gap between the minima of the potential energy curves

• In the original spectra very few lower state levels identified, long extrapolation

• BUT, strong resonances between upper-state and lower state levels. These are clearly seen on the photographic plate spectra recorded in Sydney Leach’s Lab at Orsay (then PPM)

• Displacements of up to 400 cm-1 demonstrate the strength of the interactions (see next slide).

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Unification H2S+ (1983)

• Duxbury, Jungen and Rostas (1983)

• 1972, only half the resonances in v’ = 5 and 6 identified by Duxbury, Horani and Rostas.

• New D,J,R• calculations allow

details of resonances to be calculated.

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Recent work on H2S+

• In the original analysis of the electronic spectra of H2S+ and D2S+ there was little information available about the higher bending levels of the state, so that in the second analysis paper the vibrational numbering of the lower state levels in the region where they interact strongly with levels of the excited state was obtained by extrapolation.

• The paper describing the pulsed-field ionization –photoelectron (PFI-PE) study of H2S+ by Hochlaf et al. 9 contains extensive measurements of the vibrational PFI-PE bands of the state.

• But Hochlaf et al. used an asymmetric-rotor model to fit the rotational structure above the barrier to linearity.

%X 2B

1

%X 2B

1

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Lower resolution and asymmetric rotor assumption

Equivalent region of the pfi spectrum of H2S+ recorded by Hochlaf et. al. 8. Note that the same asymmetric rotor analysis was used below, 0,4,0 and also above, 0,5,0 and 0,6,0 the onset of the massive RT perturbation. Note also the second K = 1 sub-band of A(0,6,0) is labelled as K = 4 not K = 1. An earlier PES paper by Balzer et al10 gave the correct assignment.

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Original Potential curves 1972

Original P.E. curves H2S+

G.Duxbury,M. Horani and J. Rostas. Proc. R. Soc. Lond. A331 109-137 (1972). Upper

2A1state vibrational numbering derived from the isotope shift when H is replaced by D.

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Recent work on H2S+

In the original analysis 4,5 of the electronic spectra of H2S+ and D2S+ there was little information available about the higher bending levels of the state. The vibrational numbering of the lower state levels in the region where they interact strongly with levels of the excited state was obtained by extrapolation. The paper describing the pulsed-field ionization –photoelectron (PFI-PE) study of H2S+ by Hochlaf et al. 9 contains extensive measurements of the vibrational PFI-PE bands of the state. We have extrapolated from their vibrational numbering to the interaction region, and have renumbered the lower state vibrational levels in the strongly interacting region accordingly. The new assignments are given in the next figure.

%X 2B

1

%X 2B

1

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2010 Potential curves of H2S+

New P.E curves H2S+, calculations based on Hochlaf et al data.J.Chem. Phys. 120, 6944 (2004) (ref 9.)

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Variation of band origin separations

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Mati results Han, Kang and Kim 2010These results from Han11 and his colleagues may be compared with electronic emission spectra shown earlier.

The sub- band studied is part of the 0,6,0 to 0,0,0 band system shown in the earlier slide. Their numbering has been revised to 0,6,0.

The K=2 sub-band was not assigned in our earlier work as the emission spectrum breaks off due to predissociation

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A comparison of the the analysis of the fluorescence (DJR) and MATI (HKK)spectra

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ConclusionThe main points of this presentation are:

The comparison between the different experimental methods of investigating the spectrum of the hydrogen sulphide ion.

The need to use an appropriate partitioning of the large amplitude Hamiltonian. The rapid increase of the splitting of the the K’=0 and K’=1 subbands after the barrier to linearity is reached demonstrates the changeover to quasilinear behaviour for v2

’=5 and above.

The high resolution MATI spectra of Han, Kang and Kim11 allow higher ro-vibronic levels levels to be seen above the predissociation threshold, in particular for v2

’= 7 and above.

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Acknowledgements

I wish to acknowledge all the help that I have received over the years from Joëlle Rostas, Christian Jungen and Alex Alijah in developing appropriate models of Renner-Teller coupling, and in particular, Richard Dixon, for starting it all off (as well as continuing in his own right, see 12, 13).

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Parameters used for calculations

TABLE 1. Main parameters for Renner-Teller calculation. Parameter type

_X

2

B1

_A

2

A1

Bond length Linear 1.3274 1.3274 Coefft. of tan2 /2 0.0147 0.0147 Potential parameters , se e Re [9]f Barrier height/cm-1 23195.9 4612.4 = m min 87.06 54.053 Force const, f /cm-1 34755.5 24381.9 c2 correction term /cm-1 200 k2 correction term /cm-1 100 Spin orbi t couplin gconst. A SO/cm-1 367.1 367.1 Remaining parameters, and th eirderivatio ,n see Ref.s [1,2,16]

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References1 Barrow, T, Dixon, R.N and Duxbury, G, Mol. Phys. 27, 1217-1124 (1974)2 Duxbury, G and Dixon, R.N,Mol. Phys. 43, 255-274 (1974)3 Jungen, Ch and Merer, A.J. Mol. Phys. 40, 1-23 (1980), 4 Duxbury, G, Horani, M and Rostas, J., Proc. Roy. Soc.A 331,109-137, (1972) 5 Duxbury, G, Jungen, Ch and Rostas, J., Mol Phys. 48, 719-752 (1983)6 Duxbury, McDonald, Van Gogh, Alijah, Jungen and Palivan, J.Chem Phys 108, 2336, (1998)7 Alijah, A. and Duxbury, G. J. Mol. Spectrosc. 211, 1 (2002)8 Duxbury, G. and Reid, J.P. Mol. Phys. 105, 1603 (2007) 10.9 Hochlaf, M, Wietzel, K.-M. and Ng, C.Y., J. Chem. Phys. 120, 6944 (2004)10 Balzer, L. Karlsson, M. Lundquist, B. Wannberg, D.M.P. Holland and M.A. MacDonald, Chem. Phys. 195, 403-422 (1995)11 Han, S., Kang, T.Y. and Kim, S.K., J. Chem. Phys. 132, 124304 (2010)12 Webb, A.D., Dixon, R.N and Ashfold, M.N.R. J. Chem Phys. 127, 224307 (2007)13 Webb, A.D., Kawanaga, N., Dixon and Ashfold. J. Chem Phys.127, 224308 (2007)