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Holding Computations of Conical Intersections to a Gold Standard

Holding Computations of Conical Intersections to a Gold Standard. Conical Intersections in Chemistry. M. A. Robb and co-workers. CONICAL INTERSECTIONS. The Electronic Hamiltonian Near the Conical Intersection in ( φ 1 , φ 2 ) Basis. with. General Eigenpairs.

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Holding Computations of Conical Intersections to a Gold Standard

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  1. Holding Computations of Conical Intersections to a Gold Standard

  2. Conical Intersections in Chemistry M. A. Robb and co-workers.

  3. CONICAL INTERSECTIONS

  4. The Electronic Hamiltonian Near the Conical Intersection in (φ1, φ2) Basis with General Eigenpairs

  5. The Jahn-Teller Conical Intersection where and real, electronic eigenfunctions calculable with by standard quantum chemistry programs For the Jahn-Teller casea, and a U. Höper, P. Botschwina, H. Köppel, J. Chem. Phys. 112, 4132 (2000).

  6. Power Series Expansions of matrix elements over p linear Jahn-Teller modes, and s quadratic Jahn-Teller active modes

  7. where has been neglected and spin-orbit coupling, added as necessary Relation to PES Derivatives Typical Spectroscopic Hamiltonian

  8. Connecting the Jahn-Teller Parameters and the PES Equilibrium vibrational frequency (cm-1) of mode i Linear J-T coupling constant of mode i Quadratic J-T coupling constant of mode i Spin-orbit coupling parameter (cm-1) J-T stabilization energy due to mode i Total J-T stabilization energy with Barrier to pseudorotation

  9. Vibronic Eigenvalues and Eigenfunction Solution of

  10. Vibronic Eigenvalues and Eigenfunction Solution of If is neglected and T is set to zero, then one achieves the usual Jahn-Teller PES, where

  11. Quantities Calculated on the Potential Energy Surface E0, X0 Emin, Xmin xd εtotal εB E0, X0 energy and geometry at the symmetric point Emin, Xmin energy and geometry at the distorted minimum xd distortion vector Qi, etc. normal coordinates and first derivatives at X0 εtotal, εB Jahn-Teller stabilization energy and barrier to pseudorotation

  12. Computational methods

  13. Jahn-Teller Active Molecules • Linear Jahn – Teller coupling - h(ωe)+ l (D) • Quadratic Jahn – Teller coupling - q (K) • Spin-orbit coupling - SO (aξe) • Quantizing the nuclear moton - T • Multi-mode effects – Di, Ki, ωei

  14. Jahn-Teller Active Radicals ~ ~ + ~ ~ 1 ~

  15. PES, REMPI, ZEKE SPECTROSCOPY

  16. Brief History of Studies of Jahn-Teller Effect in Cyclopentadienyl

  17. Diene Distortion Allyl Distortion Molecular Orbitals involved in Jahn-Teller Distortion of C5H5 C2v D5h C2v

  18. Pseudorotation around the C5H5 PES E Ra Ra Rb Rb E

  19. C5H5E2' Vibrational Mode n12 (815) n11 (1058) n10 (1411) n9 (3030)

  20. C5H5A1 Vibrational Mode n1 (3060) n2 (1098)

  21. Cyclopentadienyl Excitation Spectrum C5H5 C5D5

  22. C5H5 Emission from 111 Experimental Ab initio fundamentals and overtones Fit fundamentals and overtones Ab initio Jahn-Teller Fit Jahn-Teller Simulation Experimental

  23. C5H5 Emission from Origin Experimental Ab initio fundamentals and overtones Fit fundamentals and overtones Ab initio Jahn-Teller Fit Jahn-Teller Simulation Experimental

  24. C5H5 Emission from 121 Experimental Ab initio fundamentals and overtones Fit fundamentals and overtones Ab initio Jahn-Teller Fit Jahn-Teller Simulation Experimental

  25. C5D5 Emission From Origin Experimental Ab initio fundamentals and overtones Fit fundamentals and overtones Ab initio Jahn-Teller Fit Jahn-Teller Simulation Experimental

  26. Jahn-Teller Parameters

  27. Cyclopentadienyl Geometric Distortion exp calc ~ ~ ~

  28. Benzene Cation Experimental Results

  29. BENZENE CATION PES

  30. Benzene Cation Pseudorotation

  31. Benzene Cation e2g Vibrational Modes n18 (573) n17 (1152) n15 (3017) n16 (1571)

  32. C6H6+ ZEKE Spectrum Ab initio fundamentals and overtones Fit fundamentals and overtones Ab initio quadratic Jahn-Teller (e1g, e1u, e2u) Fit and split quadratic Jahn-Teller Ab initio linear Jahn- Teller (e2g) Fit linear Jahn-Teller Simulation Experimental

  33. C6D6+ ZEKE Spectrum Ab initio fundamentals and overtones Fit fundamentals and overtones Ab initio quadratic Jahn-Teller (e1g, e1u, e2u) Fit and split quadratic Jahn-Teller Ab initio linear Jahn- Teller (e2g) Fit linear Jahn-Teller Simulation Experimental

  34. Benzene Cation IR Spectra

  35. Benzene Cation Jahn-Teller Energy Stabilization and Geometric Distortion Exp

  36. Jahn-Teller Parameters

  37. PES Scans a Net barrier to B3g(Φ=π/3) geometry with respect to B2g(Φ=0) geometry

  38. CH3OA1 Vibrational Modes n3 (1040) n2(1422) n1 (2822)

  39. CH3OE Vibrational Mode n6(1082) n5 (1434) n4 (2891)

  40. Methoxy Dispersed Fluorescence

  41. ~ SPIN-VIBRONIC CONSTANTS OF THE X2E STATES OF THE METHOXY FAMILY OF RADICALS aFixed at ab initio value bFor CF3O an anharmonicity in 6 was observed, exe=8cm-1

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