Quantum Dynamics of Electronically Excited Molecules: Current Developments and Future Challenges

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1 Quantum Dynamics of Electronically Excited Molecules: Current Developments and Future Challenges Susanta Mahapatra School of Chemistry University of Hyderabad, Hyderabad Tel: ; URL: Indo-German workshop, September 7-8, 2009, Neuss, Germany

2 Central Theme Electron-Nuclear Coupling f hγ i Entanglement electronic and nuclear motion in molecules; ubiquitous, dynamics of excited electronic states of Polyatomic Molecules Crossings of electronic potential energy surfaces Nuclear motion is quantum mechanical A central quest in the new vista of chemical dynamics

3 Noncrossing Rule : von Neumann and Wigner Electronic states of a diatomic molecule do not cross, unless permitted by symmetry J. von Neumann and E. Wigner, Physik. Z. 30, 467 (1929) E. Teller, J. Phys. Chem. 41, 109 (1937) Landau & Lifshitz, Quantum Mechanics: Nonrelativistic Theory, 1965 H. C. Longuet Higgins, Proc. R. Soc. (London) Ser. A 344, 147 (1975) G. Herzberg and H. C. Longuet Higgins, Discuss. Faraday Soc. 35, 77 (1963) C. A. Mead, J. Chem. Phys. 70, 2276 (1979) It does not apply to Polyatomic systems!!

4 Review of basic concepts Diabatic (?) Adiabatic (?) Equation of a elliptical Double cone 22 Λ = Linear coupling vector δ = Gradient difference vector Coordinates Surfaces are degenerate when Δ 2 = 0 ; H 122 = 0 X 1 =X 2 =0 This happens when these terms are independent i.e. they are function of different coordinates

5 Diatomics : Only one coordinate If the two states have same symmetry they do not cross Non crossing rule If the states have different symmetry then H 12 = 0 ; they can cross J. von Neumann and E. Wigner, Physik. Z. 30, 467 (1929); C. A. Mead, J. Chem. Phys. 70, 2276 (1979) Polyatomics : Degrees of freedom n > 1 States can always cross in principle, irrespective of symmetry Near the degeneracy Δ = δ R H 12 = λ R Degeneracy is lifted to first order in the space spanned by the vectors δ and λ

6 Intersections of molecular potential energy surfaces Conical Intersection Glancing Intersection n-2 dimensional intersection space For linear systems Herzberg & Teller, Z. Phys. Chemie B21, 410 (1933); E. Renner, 92, 172 (1934) 2 dimensional branching space x2 Teller, J Phys. Chem. 41, 109 (1937); Herzberg & Longuet-Higgins, Discuss. Faraday Soc. 35, 77 (1963); Carrington, ibid. 53, 27 (1972) Consequences: Break-down of the Born-Oppenheimer approximation x 1 Crucial: paradigm for signaling ULTRAFAST decay of excited molecular states Nuclear motion no longer remain confined on a (scalar) adiabatic PES a nonadiabatic situation

7 Complexities in Theoretical Treatments: Singular nonadiabatic coupling terms in the adiabatic representation Born-Huang term Derivative coupling vector Adiabatic Diabatic cusp H 11 H 12 H 21 H 22 Smooth Adiabatic electronic wavefunction changes sign Topological effect / Geometric phase effect G. Herzberg and H. C. Longuet-Higgins, Discuss. Faraday Soc. 35, 77 (1963) H. C. Longuet-Higgins, Proc. Roy. Soc. London, Ser. A, 344, 147 (1975) M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984) C. A. Mead, Rev. Mod. Phys. 64, 51 (1992) Quite Tricky! Lichten, Phys. Rev. 131, 229 (1963); Smith, Phys. Rev. 179, 111 (1969)

8 Indo-German Collaborations: Highlights 1. Conical intersections in H 3 2. The Jahn-Teller and pseudo-jahn-teller effects in the radical cations of cyclopropane and methyl fluoride 3. Photophysics/chemistry of phenol and pyrrole 4. Photodetachment spectroscopy of NO 3 - Construction of theoretical models and algorithms ab initio electronic structure calculations and quantum dynamical simulations Matrix diagonalization Traditional wave packet and also MCTDH

9 The Jahn-Teller effect All non-linear nuclear configurations are unstable on an orbitally degenerate electronic state Tend to distort in such a way as to remove the electronic degeneracy ---- H. A. Jahn & E. Teller 1937 E σ E σ I II E σ E σ Four fold axial symmetry reduces to two fold E σ (I) = E σ (II) Energy levels cross at E E 0 σ (II) = E σ (I)

10 JT Interactions in the Electronic Ground State of H 3 H D 3h V c min = 2.74 ev H γ r R H V + H + H 2 V - H 2 + H Adiabatic to diabatic transformation angle DMBE PES: Varandas et al. J. Chem. Phys. 86, 6258 (1987).

11 H 3 Vibrations: A 1 Q x e Q y Q y R χ Pseudorotation angle Q x S. Mahapatra and H. Köppel, J. Chem. Phys. 109, 1721 (1998). A. Thiel and H. Köppel, J. Chem. Phys. 110, 9371 (1999).

12 Theory Time-dependent Wave Packet ~ 1.2 ev V - ~ 2.95 ev ~ 4.15 ev V + Crossing at E = ev (V c min = 2.74 ev) wave packet terminates at the immediate neighborhood of the conical intersections of the final electronic state. Large shift from the vertical transition energy Huge ZPE (~ 0.7 ev) due to the cusp of the JT split PESs R. Bruckmeier, Ch. Wunderlich, and H. Figger. Phys. Rev. Lett (1994) Mahapatra and Köppel, Phys. Rev. Lett. 81, 3116 (1998); J. Chem. Phys. 109, 1721 (1998); Faraday Discuss, 110, 248 (1998)

13 Nonradiative decay How fast? Time-dependent electronic population of the upper adiabatic ( V + ) sheet To within 3-6 fs. Perhaps the fastest femtosecond decay process treated in the literature!! Mahapatra and Köppel, Phys. Rev. Lett. 81, 3116 (1998)

14 Dissociative Recombination (DR) of H 3 DR mechanism is important to the interstellar chemistry DR mechanism is complex and not yet understood Various nonadiabatic transitions are anticipated to contribute to the observed DR rate Rydberg electronic states are coupled to the ground electronic state in the DR process

15 Jahn-Teller conical intersections in 3p (E ) and 3d (E ) The Rydberg excited H 3 undergoes various nonadiabatic transitions and dissociates on the repulsive lower adiabatic sheet of its ground electronic state The (E e)-jt CIs in these electronic states influence the nuclear dynamics in the DR processes Study of JT CIs is important in understanding the DR processes Static aspects are studied in terms of ab initio quantum chemistry calculations Dynamic aspects are studied in terms of vibronic spectra and nonradiative decay behavior of these electronic states

16 Potential energy surfaces PES Contours Raw Spline JT CIs in 3p (E ) 3p (E ) JT interactions are low in 3d (E ) JT CIs in 3d (E ) 3d (E ) M. Jungen and coworkers, Khim. Fiz., 23(2), 71 (2004) Rao, Mahapatra, Köppel, Jungen, J. Chem. Phys. 123, (2005)

17 Vibronic Coupling Model : E 2 0 E 3 0 κ N E 1 0 Harmonic Hamiltonian to be invariant under the symmetry operation of the corresponding point group Determines the relative signs of the coupling constants KÖppel, Domcke and Cederbaum, Adv. Chem. Phys. 57, 59, (1984); Parameters are obtained by computing potential energy surfaces

18 Dynamical Observables Multi-Configuration Time-Dependent Hartree (MCTDH) scheme The photoelectron spectrum Fermi s golden rule: of the autocorrelation function Nonradiative decay of electronic populations Meyer, Manthe, Cederbaum, Chem. Phys. Lett. 165, 73 (1990); Meyer, Manthe, Cederbaum, Chem. Phys. 97, 3199 (1992); Beck, Jäckle, Worth, Meyer, Phys. Rep. 324, 1 (2000). Worth, Beck, Jäckle, Meyer, The MCTDH Package, Version 8.2, 2000, University of Heidelberg, Germany.Mayer, Version 8.3, See

19 Jahn-Teller and pseudo-jahn-teller effects in cyclopropane radical cation Cyclopropane Radical Cation hγ + Eqm. Geometry : D 3h D 3h MP2/cc-PVTZ Expt Holland et. al. J. Elect. Spect. 125, 2002, Mean Spacing 60.0 mev E 2.59 ev 2.43 ev Γ vib =3A 1 +A 2 +4E +A 1 +2A 2 +3E ~ B 2 A 1 ~ A 2 E ~ X 2 E (E e) -JT r C-C A r C-H A CCC HCH [E ΧE ] = [E Χ E ] = A 1 +E [E ΧE ] =A 1 + A 2 +E JT Active Condon Active Pseudo- JT Active

20 Important vibrational modes

21 Adiabatic Potential Energy cuts of X 2 E -A 2 E electronic manifold Symmetric modes Degenerate modes

22 X 2 E' band of CP + : LVC Model V c min = ev V 0 - = 9.66 ev 0.15 ev ν ev ν 2 Expt ΔE JT = 0.98 ev 0.78 ev Theory (Sym JT) ev ν ev ν ev T. S. Venkatesan et. al, J. Phys. Chem. A (2004) Slonczewski resonances J.C.Slonczewski, Phys. Rev. 131,1596 (1963)

23 Linear vibronic coupling X 2 E band of CP ev 0.80 ev

24 A2E" band of CP + (LVC Model) ΔE JT = ev υ mev υ mev υ mev υ mev Irregular spacing is due to multimode JT effect. Dominant progressions due to υ 2, υ 3, υ 4, and υ 6 vibrational modes

25 Vibronic Spectrum of Coupled X2E -A2E Manifold 4 states and 14 modes quadratic JT plus linear PJT model. Huge impact of PJT coupling via a 1 and e vibrational modes V PJT (min) = ev ~ 1.47 ev above and ~ 0.62 ev below the minimum of X and A JT conical intersections. T. S. Venkatesan et. al, J. Phys. Chem. A, 111, 1746 (2007); J. Mol. Struct. 838, 100 (2007).

26 Vibronic Coupling in Methyl Halides Cation ~ 4.81eV ~ B 2 E A ~ 2 A 1 ~ X 2 E H F C H (C 3V ) H Γ vib = 3A 1 +3E [E x E] = A 1 + E Condon Active JT + PJT Active Karlsson et al. Phys. Scrip. 16, 225 (1977) Mode Frequency/ ev Description ν 1 (A 1 ) C-F Stretch ν 2 (A 1 ) CH 3 Bend ν 3 (A 1 ) C-H Stretch ν 4 (E) C-F Bend ν 5 (E) CH 3 Deformation ν 6 (E) C-H Stretch

27 CH 3 F + Adiabatic Potential Energy Surface CASSCF/MRCI ; aug-cc-pvtz with ECP for Fluorine CAS (11,16) Mahapatra, Vallet, Woywod, Köppel and Domcke, Chem. Phys. 304, 17 (2004).

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29 CH 3 F + Vibronic Structure of the X 2 E State Linear Model Quadratic Model Sym ν 1 ν (Very weak) 2 ν 5 ν 4 JT ν 1 ν 2 ν 5 + ν 4 Sym γ (Very weak) JT Sym JT ν 1 +ν 4 +ν 5 Sym JT

30 X 2 E Band CH 3 F + Expt JT + PJT

31 CH 3 F + Vibronic Structure of the B 2 E State Linear Model Sym ν 1 + ν 3 (weak) JT ν 5 + ν 6 (weak) Quadratic Model Sym γ ν 1 = γ ν 3 = JT γ ν 6 = Sym JT ν 1 + ν 5 Sym JT η 10-3 or less

32 CP, 304, 17 (2004) CH 3 F + A 2 A 1 + B 2 E Band Expt B 2 E + A 2 A 1 (2 : 1) JT + PJT

33 Impact of the intermode (a 1 -e) bilinear coupling terms Mahapatra, Vallet, Woywod, Koeppel and Domcke, J. Chem. Phys. 123, (2005) Schmidt-Kluegmann, Koeppel, Schmatz and Botschwina, Chem. Phys. Lett. 369, 21 (2003)

34 Photostability & nonadiabatic transitions Photochemistry of DNA building blocks: chromophores H O Extremely low quantum yield of fluorescence of the strongly UV absorbing excited singlet ππ* state Very fast nonradiative processes Conversion back to the ground state Photochemical Funnel The photon energy quickly dissipated before more profound chemical rearrangements Photostability hγ Lower diabatic Upper diabatic Faraday Discuss. 127, 283 (2004) J. Chem. Phys. 122, (2005) 123, (2005) J. Photochem. Photobio. A 190, 177 (2007)

35 1 πσ* Optically dark Two curve crossings which become conical intersections when out-of-plane modes (e.g. CCOH dihedral angle) are considered Both CIs have same coupling coordinate CCOH dihedral angle θ (torsion) The photo induced dynamics is simulated by time-dependent WP method

36 Wave packet dynamics P 1 P 2 P 3 S 0 1 πσ* Diabatic 1 ππ* Upper diabatic Lower diabatic

37 Acknowledgement Coworkers: Funding: DST, CSIR-New Delhi VWS and AvH Stiftung, Germany Computational Facilities: CMSD, University of Hyderabad Dr. R. Padmanaban Dr. T. S. Venkatesan Dr. S. Ghosal Mr. B. Jayachander Rao Mr. V. Sivaranjana Reddy Mr. T. Mondal Mr. S. Ghanta Mr. T. Rajagopala Rao Mr. S. Rajagopala Reddy Mr. T. Roy

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