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Toward the treatment of Renner-Teller effect in medium sized molecular systems Majdi HOCHLAF Laboratoire Modélisation et Simulation Multi Echelle (MSME UMR 8208 CNRS), Université Paris-Est Marne-La-Vallée
Why? • Molecular systems are present in diverse media: Astrophysical media, Earth atmosphere, planetary atmospheres, combustion, plasmas • State-to-the-art experimental techniques can produce and record such rovibronic spectra Importance of the precise characterization of these species for modeling these media, their reactivity and for applications (environment, …)
Problematic/definition? G. Herzberg, Electronic Spectra and Electronic Structure of Polyatomic Molecules, Van Nostrand, Toronto, ON, 1966. M. Peric, B. Ostojic, J. Radic-Peric. Phys. Reports 290, 283 (1997). Ch. Jungen, A.J. Merer, in: K.N. Rao (Ed.), Molecular Spectroscopy: Modem Research, vol. 2, Academic Press, New York, 1976, p. 127. G. Duxbury, Molecular Spectroscopy, vol. 3, Billing and Sons, Guildford and London, 1975, p. 497. J.M. Brown, F. Jorgensen, in: I. Prigogine, S.A. Rice (Eds.), Advances in Chemical Physics, Wiley, New York, 1983, vol. 52, p. 117. H. Köppel, W. Domcke, L.S. Cederbaum, in: I. Prigogine, S.A. Rice (Eds.), Advances in Chemical Physics, Wiley, New York, 1984, vol. 72, p. 59.
Couplings between electronic (degenerate electronic state at linearity) vibrational, rotational, spin-orbit angular momenta. • The Renner-Teller effect can be considered: • In the neighborhood of the linear geometry as a consequence of the electrostatic interaction between two components of an electronic state with a non-zero angular momentum. • At stronglybentgeometries, it is more plausible to think about two different electronic states coupled with each other through the electronic-rotational Coriolis interaction • Diversity and complexity of spin-rovibronic spectra and of “cases” to treat
Triatomics CCN+ A1P CS2+ A2Pu Unique levels=Non Born-Oppenheimer description
Barrier to linearity K-reordering H2S+ A2Pu H2S + hn H2S+ + e-(pfi)
Tetratomics HCCH+ X2Pu Vibrational modes Electronic motions
One quantum in bending modes DifferenceExp. / Theory : ~1%Jutier et al (JCP, 2009)
Pentatomics bending coordinates
Methodologies and benchmarks to solve the nuclear motions problem • Perturbative approaches: Renner, Merer, Jungen… • Variational approaches: Born-Oppenheimer approximation: Generation of the potentials energy surfaces then treatment of nuclear motions Y= a Y- + b Y+ • Triatomics: we adopt the variational approaches developed by Carter and co-workers for triatomics[1-3]. • Tetraatomics: extension by Jutier and co-workers is also available [4,5]. • These treatments are performed in internal coordinates or in Jacobi coordinates. • Hamiltonians exhibit complex forms. 1. S. Carter, N. C. Handy, Mol. Phys. 52, 1367 (1984). 2. S. Carter, N. C. Handy, P. Rosmus, G. Chambaud, Mol. Phys. 71, 605 (1990). 3. W. Gabriel, G. Chambaud, P. Rosmus, S. Carter, N. C. Handy, Mol. Phys. 81, 1445 (1994). 4. L. Jutier, C. Léonard, F. Gatti. J. Chem. Phys. 130, 134301 (2009).5. 5. L. Jutier, C. Léonard, F. Gatti. J. Chem. Phys. 130, 134302 (2009).
These hamiltonians are expressed on specific basis sets for the stretchings (e.g. Hermit polynomes), the bending (e.g. Legendre polynomes) and torsions (Fourier transform expansions). The energies and the rovibronic wave functions are optimized variationally. • Sizes of the corresponding matrices grow rapidly and become too large, so that they are hard to handle (contractions). • This limits the extension of such approaches to larger polyatomic systems. • Bunker and co-worker and Peric and co-workers developed a simpler approach in reduced dimensionality where only bendings modes (subject to strong modified patterns) are treated (variationally). • Prediction of spectra of tri-, tetra and even hexa-atomic Renner-Teller systems (mostly of linear/linear cases) . 1. M. Peric, B. Ostojic, J. Radic-Peric. Phys. Reports 290, 283 (1997).
SNO: “Heavy atoms” + Conical intersection Anharmonic resonnancs
General comments and conclusions To treat Renner-Teller systems of large or medium sizes (complex), we have to develop new approaches. This remains an open question for discussion. HOW?
Acknowledgments EC: H2020 EC: H2020 http://cost-molim.eu/