What is the course about? Part 1 Organic Chemistry: organocatalysis 10-10 (1 Å) - 10-9 m Part 2 Structural Biology: peptide conformations Part 3 10-9 - 10-8 m Photochemistry and Photobiology: olefins & vision > 10-8 m (proteins)
Fate of Light Energy at the Molecular Level LIGHT ENERGY WASTAGE LIGHT ENERGY EXPLOITATION Fluorescent Probes (few ps) Ang. Chem. Int. Ed. 2001 Stereoselectivity in Pericyclic Reactions (100 fs) J. Phys. Chem A 2001 Internal Conversion in Cytosine (100 fs) JACS 2002 Fluorescent proteins (ca. 0.3 ns) JACS 2004 Molecular Motion in Biological Photoreceptors (500 fs) PNAS 2000, 2004, 2005, 2006, 2007
Thermal Reaction Path Energy Transition Structure (TS) TS or activated complex 1935 Eyring, Evans and Polanyi A B Ground State Reaction Coordinate Minimum Energy Path
Photochemical Reaction Path Excited State Conical Intersection (CI) or Photochemical Funnel 1966 Zimmerman, 1972 Michl hν A* Ground State Energy hν A CI B Minimum Energy Paths Excited State Ground State Reaction Coordinate
Photochemical Reaction Path Stationary Point Singularity Transition Vector (X 1 ) Branching (or g-h) plane (X 1, X 2 )! TS CI A* A X 1 X 2 X 1 B One Product B One or More Product A
Benzene Photochemistry (excited state) (primary) (secondary) h ν 254 nm liquid state under N 2 (e.g. Turro 1986) prefulvene benzvalene (q.y. 0.02) N of photoproduct molecules N of absorbed photons Ground state diradical intermediate
Benzene Conical Intersection: Structure unpaired electrons ground state allyl radical 1.4 Å 2.0 Å half-broken bond 1.4 Å This conical intersection defines the "prefulvene" path
Benzene Conical Intersection: Branching Space Ψ A Ψ B CI diradical Kekule Energy Excited State Ground State Reaction Coordinate The wavefunction (electronic structure) does not change when passing through the CI.
Benzene Conical Intersection: Branching Space X 1 = δ ( E 1 E 2 ) δ q Gradient Difference (fastest escape from energy degeneracy) X 2 = ψ 1 δ δ q ψ 2 Derivative Coupling (fastest change in the electronic structure)
Benzene Conical Intersection: Wavefunction Barry phase: the wavefunction (and bonding) changes sign along a loop that contains the intersection! coupled electrons coupled electrons coupled electrons x 1 x 2
Benzene Conical Intersection: the branching space 3! χ unstable 1! x 2 -x 1 χ x 1 3! 1! -x 2 x 1 1! 3! unstable -x 2 x 2 -x 1 Branching space diagram
A bit of History the first computations: 1969 Van der Lugt and Oosteroff and 1975 Devaquet et al. found that the point of return to the ground state (M*) is an energy minimum. State correlation diagram 2A 1 π 12 π 2 π 32 π 4 S 1! S 1 σ 12 π 1 π 22 σ 2 Avoded crossing Suggests that the non-crossing rule applies not only to diatomic but also to polyatomic molecules 1B 2 1A 1 π 12 π 21 π 31 π 4 S 2! M *! π 12 π 22 π 3 π 4 S 0! S 0 σ 12 π 12 π 2 σ 2 C s symmetry! Slow decay (Fermi Golden Rule - coupling of vibrational states) interpolated and symmetric reaction coordinate
A bit of History E. Teller Isr. J. Chem. 7, 227, 1969 in a polyatomic molecule the non-crossing rule, which is rigorously valid for diatomics, fails and two electronic states, even if they have the same symmetry, are allowed to cross at a conical intersection... radiationless decay from the upper to the lower intersecting state occurs within a single vibrational period when the system travels in the vicinity of such intersection points H.C. Longuet-Higgins, The Intersection of Potential Energy Surfaces in Polyatomic Molecules, Proc. R. Soc. Lond. Ser. A., 344, 147-156, 1975 thereby disposing of a recent claim that the non-crossing rule for diatomic molecules applies also to polyatomic molecules....
Photophysics of octatetraene Ultrafast deactivation channels are not consistent with stable M* intermediate. A* Energy hν hν A CI B Excited State Ground State Reaction Coordinate
A bit of History Zimmerman, Michl and Salem were the first to suggest that, in photochemical organic reactions, the point of return M* may correspond to a conical intersection. Zimmerman and Michl call it photochemical funnel. 1966, Howard Zimmerman 1970, Josef Michl 1974, Lionel Salem
1982-1988 CASSCF Gradients of the Excited State Energy (Robb, Bernardi, Schlegel and Olivucci). Structure Predicted from Valence Bond Theory allow to draw guess structures (eg for pericyclic reactions)! A bit of History allow the use optimization methods (eg pseudo Newton-Raphson) 1990 First Conical Intersection Detected for the Ethylene Dimerization (Bernardi, Olivucci, Robb). Computation is carried out on the CRAY-XMP in London. 2.17 Å 1.47 Å 2.08 Å 1990-2000 with M. A. Robb and F. Bernardi: 25 different organic chromophores undergoing 16 different reactions statistical demonstration using quantum chemistry
A bit of History The Norfolk Building King s College London 1989-1992 Michael Robb
A bit of History First application of ab initio CASPT2//CASSCF: s-cis buta-1,3-diene J. Chem. Phys. 1995! 2A 1 excited state minimum energy path S 2 40 1B 2 S 2 /S 1 2A 1 S 1! S 2 /S 1 20 S 2! 1B 2 S2 M *! 0 hν S 1 /S 0 S 1 /S 0 1A 1 S 0! S 0 C s symmetry! 0.0 1A 1 real crossing between states of the same (A 1 ) symmetry
A bit of History the van der Lugt and Oosteroff result is consistent with the existence of a conical intersection at the bottom of the S 1 energy surfaces S 1 σ 12 π 1 π 22 σ 2 π 12 π 2 π 32 π 4 S 1! S 1 FC! S 2 σ 12 π 11 π 21 σ 2 π 12 π 21 π 31 π 4 S 2! M *! CI! π 12 π 22 π 3 π 4 S 0! S 0 σ 12 π 12 π 2 σ 2 S 0 Gradient Based Coordinate! Symmetry Based Coordinate!
Computational Tools Intrinsic Reaction Coordinate (IRC) Conical Interersection Optimization (CIO) Initial Relaxation Direction (IRD) Trajectory (Classical or Semi-classical) Energy Minimum and Transition State Optimization
Construction of a Photochemical Reaction Path FC! CI IRD! TS 2 M 2 TS 1 IRD! CIO! M 1 X 2 X 1 IRC! reactant! Upper state! Lower state! Thermal! product! TSO! TS!
Construction of Photochemical Reaction Path Caltech 1999 Nobel Prize for Chemistry
Photochemical Reaction Path in Textbooks 2001
Photochemical Reaction Path in Textbooks 1990 the use of computational methods to elucidate reaction mechanisms has not really made a major impact on the way in which organic photochemist think about such mechanisms Turro, N. J. (1990). J. Photochem. Photobiol., A: Chemistry 51 63. 2008 5.6 Conical Intersections near Zero-Order Surface Crossings 6.12 The Non-Crossing Rule and Its Violations: Conical Intersections and their Visualization 6.13 Some Important and Unique Properties of Conical Intersections 6.30 Concerted Photochemical Pericyclic Reactions and Conical Intersections
Computational Photochemistry optimization of a singularity wavefunction/density (orbital occupancies) MOLECULAR AND ELECTRONIC STRUCTURE OF THE CROSSING: NATURE OF THE PHOTOCHEMICAL FUNNEL equilibrium geometries and transition states EXCITED STATE REACTION PATHS: EXCITED STATE DECAY branching plane almost routine GROUND STATE RELAXATION PATHS: PHOTOPRODUCT SELECTIVITY Newton equations of motion feasible since 2007! TRAJECTORIES: REACTION TIME SCALES AND QUANTUM YIELDS still unpractical or impossible
Computational Photochemistry (further info http://www.lcpp.bgsu.edu) M. Olivucci, Ed. Computational Photochemistry, Elsevier 2005
Different Electronic States = Different Conical Intersection Structure = Different Chemistry Hydrocarbons Schiff bases Avoided Crossing rule valid! 2A 1 S 1! S 2 /S 1 S 2 2A 1 S 2 1B 2 S 1! S 2 - + 1B 2 S 2 M *! Avoided Crossing rule invalid S 1 /S 0 M *! S 1 /S 0 Avoided Crossing rule invalid 1A 1 S 0! S 0 1A 1 S 0! S 0 (π π*) 2 π π* - +
The Chemistry of Conical Intersections: Bond-Making, Bond Breaking and Group Transfer 6 1 6 3 3 σ-bond Making C 1 σ-bond Breaking Group (or σ-bond) Exchange
The Chemistry of Conical Intersections: Conjugated Hydrocarbons J. Am. Chem. Soc. 1995, 117, 11584-11585 Crossing between the ground state and a (π-π*) doubly excited state 2. 0 1. 4 1. 4 S 1 π π Polyenes (and polyene radicals) S 0 π π Benzene Cyclohexadienes
The Chemistry of Conical Intersections: Multiple conical intersections
The Chemistry of Conical Intersections: Selectivity Selectivity may be due to differences in energy 40 E / kcal mol -1 30 20 10 S 1 S 0 90 0 cyclizations Z/E isomerization 3 5 7 9
The Chemistry of Conical Intersections: Cyclohexadiene/Hexatriene hν + + Allyl radical moiety 2.22 2.12 triradical moiety
The Chemistry of Conical Intersections: Multiple products X 1 X 2
The Chemistry of Conical Intersections: Change in bonding Selectivity may be affected by the excited state dynamics 5! 6! x 2 -x 1 5! χ x 1 5! 6! 6! 5! 6! -x 2 unstable
The Chemistry of Conical Intersections: Protonated Schiff Bases - + 5 4 3 cis 2 1 N H 2 ( + ) 5 4 3 2 1 trans N H 2 ( + ) Retinal Rhodopsin 1 1 + NH Light 1 1 + NH Cis Form Trans Form (Appears in ca. 200 fs)
The Chemistry of Conical Intersections: Charge Transfer Crossing between the ground state and a (π-π*) singly excited state 1.46 Å 1.38 Å π π hν S 1 + 1.38 Å N 1.33 Å 90 1.40 Å π π + e - 90 S 0 Newman projection
The Chemistry of Conical Intersections: Charge Transfer Motion Coupled to the Torsion + Unstable (TS) N H 2 N x 2 X 1 + N H 2 -x 1 N H 2 χ x 1 + N H 2 N -x 2 X 2 Stretching + N H 2 Unstable (TS)
The Chemistry of Conical Intersections: Charge Transfer χ breaks the double bond hetherolitically + + N H 2 + N H 2 + N H 2 N H 2 breaks the double bond homolitically + N H 2 -x 2 x 2 -x 1 x 1
Energy (kcal mol -1 ) The Chemistry of Conical Intersections: Barrierless Photoisomerization Path 0.0 π π 1.46 1.35 FC 1.36 1.43 1.29 1.41 1.37 12.5 1.5 1.37 1.35 π π 120 100 80 60 S 2 S 1 CI 24.7 1.37 1.37 1.35 1.53 1.42 76.8 1.42 1.30 1.39 1.46 1.39 91.2 40 hν (291 nm) 1.43 1.36 1.43 1.30 1.42 20 0 S 0 180.0 1.45 1.35 0.0 5.0 10.0 15.0 20.0 1.43 1.36 trans 1.29 MEP co-ordinate (a. u.)
The Chemistry of Conical Intersections: Azoalkane Fluorescence Quenching τ=930 nsec, Φ f =0.56 N N N N Cl H Cl Cl τ=13 nsec, Φ f =0.01 Crossing between the ground state and a (n-π*) singly excited state S 1 π n! hν π N n! O O S 0 π n N
The Chemistry of Conical Intersections: Azoalkane Fluorescence Quenching S 1 π n! Cl S 0 π n hν N N Azoalkane (pyrazoline) Cl CH 2 Cl 2 N N N N X 1 (coupled electron-proton transfer) X 2 (ring-puckering)
The Chemistry of Conical Intersections: Electron Transfer δ+ δ + δ+ δ Cl N H C N + - Cl N H C H Cl x 2 N H Cl Rαδιχαλ Παιρ! Ion Παιρ! x 1 TS (electron transfer)!