Multiple conical intersections and multi-state nonadiabatic dynamics in benzenoid cations

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1 Multiple conical intersections and multi-state nonadiabatic dynamics in benzenoid cations Horst Köppel Theoretische Chemie Physikalisch-Chemisches Institut, Universität Heidelberg - Benzene cation M. Döscher, I. Baldea, P. Szalay - Fluorinated derivatives J. Franz, E. Gindensperger, S. Faraji - MCTDH H.-D. Meyer

2 Issues and perspectives Identify new coupling phenomena and expand limits of applications of vibronic coupling theory and related JT theory. Beyond two-state model: nonadiabatic couplings in different electronic function spaces, simultaneous JT and PJT interactions. Symmetry lowering through asymmetric substitution. Chemical effects of substitution fluorination. Low-order Taylor series approach to vibronic problem diabatic electronic basis: feasability and importance of specific coupling terms. Consider electronic spectra and photoinduced internal conversion dynamics; dynamics through MCTDH.

3 Divergent nonadiabatic couplings at conical intersections d 3N rφ n φm Q i = d 3N rφ n r, Q H el Q i φm r, Q V m Q V n Q for V m Q V n Q Note elliptical double cone Branching space: d = 2 Intersection space: d = N 2 W. Domcke, D. Yarkony, H. Köppel Eds. Conical Intersections. Electronic Structure, Dynamics and Spectroscopy World Scientific, Singapore, 2004

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5 Multi-state and multi-mode non-adiabatic coupling effects in the benzene cation Experimental photoelectron spectrum of benzene Siegbahn et al. Intensity E 1g E 2g A 2u E 1u B 2u B 1u A 1g E 2g The approximation of linear and quadratic vibronic coupling H =T 1 + W N n n W Q = V Q + k Q Q Q +... nn 0 W Q = W 0 + nn' nn' +... n n' with Q : normal coordinate of V Q i 0 Symmetry selection rule for : x x i n Q n' A i i i nn ' i Q i, j i ij nn' i i j Binding energy ev Application to benzene: 2 2 E = E = A + E 1g 2g 1g 2g Example of Jahn-Teller JT active mode schematic

6 The X 2 E 1g - E 2 B 2u potential energy curves for the benzene cation 20 a D 2h 20 a D 2h V[eV] Ẽ 2 B 2u D 2 E 1u C 2 A 2u V[eV] B 2u Ẽ 2 B 2u D 2 E 1u C 2 A 2u B 3u 12 A g B 2 E 2g B 1g 12 B 1g B 2 E 2g A g 10 B 3g X 2 E 1g B 2g Q B 3g X 2 E 1g B 2g Q 18 b C 2h b C 2h V[eV] Ẽ 2 B 2u D 2 E 1u C 2 A 2u V[eV] B u Ẽ 2 B 2u D 2 E 1u C 2 A 2u B u 12 A g B 2 E 2g A g 12 A g B 2 E 2g A g 10 X 2 E 1g B g B g Q X 2 E 1g B g B g Q

7 The B2E2g - C2A2u triple conical intersection in the benzene cation

8 Calculated bands of the photoelectron spectrum of benzene Multi-mode JT effect in the X E1g band JT and PJT effects in the B E / C A bands 2g 2u a a E 2g Intensity b c Experiment Baltzer et al. INTENSITY b A 2u Energy ev ENERGY ev

9 . Points to efficient subpicosecond B/ C X internal conversion process.

10 Time fs Time-dependent electronic populations for three vibronically coupled electronic states of the benzene cation The B E, D E and E B states The X E, B E and C A states 1g 2g 2u 2g 1u 2u PROBABILITY a b X state B state C state Without degeneracies TIME fs Probability B B B D D E D Time fs Benchmark calculations for multi-state non-adiabatic dynamics E E a b c

11 MCTDH method Wave-packet dynamics Multi-Configuration Time-Dependent Hartree Multi-set formulation for non-adiabatic problem: ϕ σ 1, 1 1 1,..., 1,...,,..., J J J p k k k j n j n j j j p A t q t A t q q k p p p Φ = = Ψ = = = =

12 Fluorinated benzene radical cations C 2v C 2v C 2v D 2h Changes introduced by fluorination Symmetry lowering: no JTE Chemical effects: increase in σ-type IPs VeV Electronic structure calculations EOM-CCSD

13 Correlation of Vertical Ionization Potentials IPs

14 Minima of conical intersection seams o-difluorobenzene m-difluorobenzene p-difluorobenzene

15 Photoelectron spectra Fourier transformation of the autocorrelation function

16 Time-dependent electronic populations Wave-packet propagation by MCTDH o-difluorobenzene m-difluorobenzene p-difluorobenzene

17 Time-dependent electronic populations Wave-packet propagation by MCTDH o-difluorobenzene m-difluorobenzene p-difluorobenzene Encircled: excited state with large transition dipole fluorescing: meta

18 Summary and conclusions Simultaneous JT and PJT interactions with 10 vibrational degrees of freedom can be treated MCTDH. Modelling through low-order Taylor series often feasible; specific 2ndorder coupling terms often important. Complex intersecting seams of conical intersections in benzene cation; relevant to fluorescence and fragmentation dynamics. Partial substitution fluorination transforms JT intersections to less symmetric i.e. more generic ones. Chemical effects of fluorination with implications for vibronic dynamics. In multi-surface problems IVR-type energy redistribution not completely understood.

19 XIX International Symposium on the Jahn-Teller Effect: Vibronic Interactions and Orbital Physics in Molecules and in the Condensed Phase Heidelberg, University Campus, Chemistry Lecture Hall INF th - 29th August Topics covered: Basic Jahn-Teller theory History of Jahn-Teller theory and applications Cooperative Jahn-Teller effect and orbital ordering Conical Intersections, their location and characterization Vibronic interactions and spin-orbit coupling Dynamics on intersecting potential energy surfaces quantum and classical Fullerenes and Fullerides High-resolution spectroscopy of Jahn-Teller active systems Jahn-Teller effect and structural phase transitions Jahn-Teller effect in molecular magnets Preliminary List of Invited Speakers: I. Bersuker Austin W. Domcke Munich J. Dunn Nottingham A. Fishman Ekatarinburg K. Kamaras Budapest B. Keimer Stuttgart S. Matsika Philadelphia F. Merkt Zürich T. A. Miller Columbus V. Polinger Seattle M. A. Robb London B. Tsukerblat Beer-Sheva Y. Wang Berkeley G. Worth Birmingham The conference is open to students, postdocs and all colleagues interested in the field. Contributions of all participants are encouraged. Registration will start in late April or early May We look forward to welcoming you in Heidelberg in August For the organizing committee: Prof. Dr. H. Köppel Chair Theoretical Chemistry University of Heidelberg Im Neuenheimer Feld 229 D Heidelberg, Germany Phone: Fax: Horst.Koeppel@pci.uni-hd.de Web address: