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
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.
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
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 9 10 11 12 13 14 15 16 16 17 18 19 Binding energy ev Application to benzene: 2 2 E = E = A + E 1g 2g 1g 2g Example of Jahn-Teller JT active mode schematic
The X 2 E 1g - E 2 B 2u potential energy curves for the benzene cation 20 a D 2h 20 a D 2h 18 18 V[eV] 16 14 Ẽ 2 B 2u D 2 E 1u C 2 A 2u V[eV] 16 14 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 16 10 B 3g X 2 E 1g B 2g Q 18 b C 2h b C 2h 18 18 V[eV] 16 14 Ẽ 2 B 2u D 2 E 1u C 2 A 2u V[eV] 16 14 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 16-6 -4-2 0 2 4 6 8 10 X 2 E 1g B g B g Q 18-10 -5 0 5 10
The B2E2g - C2A2u triple conical intersection in the benzene cation
Calculated bands of the photoelectron spectrum of benzene 2 2 2 Multi-mode JT effect in the X E1g band JT and PJT effects in the B E / C A bands 2g 2u 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 11.5 12.0 12.5 a 0 86 159 190 194 235 225 293 16 + 17 + 18 a E 2g Intensity b c 0 0-75 -31 86 123 159 190 194 209 225 235 83 120 157 193 204 222 234 16 + 17 + 18 + 2 293 280 294 Experiment Baltzer et al. INTENSITY b A 2u 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 Energy ev 11.5 12.0 12.5 ENERGY ev
. Points to efficient subpicosecond B/ C X internal conversion process.
0 20 40 60 80 10 0 1 20 140 160 180 20 Time fs 0 20 40 60 80 10 0 1 20 140 160 180 20 Time-dependent electronic populations for three vibronically coupled electronic states of the benzene cation 2 2 2 The B E, D E and E B states 2 2 2 The X E, B E and C A states 1g 2g 2u 2g 1u 2u PROBABILITY 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 50 100 150 200 a b X state B state C state Without degeneracies 0 0 50 100 150 200 TIME fs Probability 0.8 0.4 0 0.8 0.4 0 0.8 0.4 B B B D D E D 0 0 50 100 150 200 Time fs Benchmark calculations for multi-state non-adiabatic dynamics E E a b c
MCTDH method Wave-packet dynamics Multi-Configuration Time-Dependent Hartree Multi-set formulation for non-adiabatic problem: ϕ σ 1, 1 1 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 = = = =
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
Correlation of Vertical Ionization Potentials IPs
Minima of conical intersection seams o-difluorobenzene m-difluorobenzene p-difluorobenzene
Photoelectron spectra Fourier transformation of the autocorrelation function
Time-dependent electronic populations Wave-packet propagation by MCTDH o-difluorobenzene m-difluorobenzene p-difluorobenzene
Time-dependent electronic populations Wave-packet propagation by MCTDH o-difluorobenzene m-difluorobenzene p-difluorobenzene Encircled: excited state with large transition dipole fluorescing: meta
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.
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 252 25th - 29th August 2008. 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 2008. We look forward to welcoming you in Heidelberg in August 2008. For the organizing committee: Prof. Dr. H. Köppel Chair Theoretical Chemistry University of Heidelberg Im Neuenheimer Feld 229 D-69120 Heidelberg, Germany Phone: +49-6221-545214 Fax: +49-6221-545221 Email: Horst.Koeppel@pci.uni-hd.de Web address: http://jt2008.uni-hd.de