Introduction to Quantum & Computational Chemistry for Electronically Excited States Lecture 4 Target: Computer simulations are employed to study the structure and reactivity of single molecules and molecular systems (molecule in solution on in a macromolecular cavity). Tools: We need a series of software technologies to describe the electronic and geometrical structure of molecules and their time evolution. (visit http://www.lcpp.bgsu.edu) The (3N-6 Dimensional) Potential Energy Surface of a Chemical Reaction [T (R) + Vnn(R) + Eel(R)] Photochemical Reaction Path Excited State Conical Intersection (CI) or A* “Photochemical Funnel” 1966 Zimmerman, 1972 Michl B hν A* Ground State CI hν B Energy A A Excited State Ground State Minimum Energy Paths Reaction Coordinate Photochemical Reaction Path Stationary Point Singularity Transition Vector (X 1) Branching (or g-h) plane (X1, X2) TS CI A* A X X1 2 X1 B B A One Product One or More Product Benzene Photochemistry (excited state) (primary) (secondary) h ν 254 nm liquid state prefulvene benzvalene under N2 (q.y. 0.02) (e.g. Turro 1986) N of photoproduct molecules N of absorbed photons Ground state diradical intermediate Benzene Conical Intersection: Structure unpaired electrons ground state 1.4 Å allyl radical 2.0 Å half-broken bond 1.4 Å This conical intersection defines the "prefulvene" path Benzene Conical Intersection:Branching Space ΨB ΨA diradical CI Energy Kekule Excited State Ground State Reaction Coordinate The wavefunction (electronic structure) does not change when passing through the CI. Benzene Conical Intersection:Branching Space δ( E 2 − E1 ) δ X1 = X2 = ψ1 ψ2 δ q δq Gradient Difference Derivative Coupling (fastest escape from energy degeneracy) (fastest change in the electronic structure) Benzene Conical Intersection: Wavefunction A consequence of the Geometric Phase theorem: the wavefunction (and bonding) changes sign along a loop that contains the intersection ! coupled electrons coupled electrons coupled electrons x 1 x2 Benzene Conical Intersection: the branching space χ unstable 3 1 x2 χ -x1 x1 3 1 -x2 3 1 unstable x1 -x2 -x1 x2 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. 2 2 S1 σ1 π1π2 σ2 State correlation π 2 π π 2π S diagram 2A1 1 2 3 4 1 2 1 1 1B2 π1 π2 π3 π4 S2 M* Slow decay (Fermi Golden Avoded crossing h ν Rule - coupling of Suggests that the non- vibrational states) crossing rule applies not only to diatomic but also 2 2 1A π1 π2 π3π4 S0 S σ 2 π 2π σ to polyatomic molecules 1 0 1 1 2 2 Cs symmetry 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* hν’ CI hν B Energy A 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 A bit of History 1982-1988 CASSCF Gradients of the Excited State Energy (Robb, Bernardi, Schlegel and Olivucci). Structure Predicted from Valence Bond Theory allow the use optimization methods (eg pseudo Newton-Raphson) allow to draw guess structures (eg for pericyclic reactions) ! 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: 25 different organic chromophores undergoing 16 different reactions “statistical” demonstration using quantum chemistry A bit of History First application of ab initio CASPT2//CASSCF: s-cis buta-1,3-diene J. Chem. Phys. 1995 excited state minimum energy path 2A1 S2 40 S2/S1 1B 2A 2 1 S1 S2/S1 1B 2 * S2 S2 M 20 h ν S1/S0 0 hν S1/S0 1A S 1 0 S0 Cs symmetry 1A 1 real crossing between 0.0 states of the same (A1) 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 S1 energy surfaces 2 2 S1 σ1 π1π2 σ2 π 2 π π 2π S 1 2 3 4 1 S1 FC 2 1 1 S2 σ1 π1 π2 σ2 2 1 1 π1 π2 π3 π4 S2 M* CI h ν S0 Gradient Based Coordinate π 2 π 2π π S 2 2 1 2 3 4 0 S0 σ1 π1 π2σ2 Symmetry Based Coordinate Computational Tools Intrinsic Reaction Coordinate (IRC) A* Conical Interersection Optimization (CIO) Initial Relaxation Direction (IRD) B Trajectory (Classical or Semi-classical) Energy Minimum and Transition State A Optimization 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,transition states and minimum energy paths EXCITED STATE REACTION PATHS: EXCITED STATE DECAY almost routine branching plane GROUND STATE RELAXATION PATHS: PHOTOPRODUCT SELECTIVITY feasible ! Newton equations of motion TRAJECTORIES: REACTION TIME SCALES AND QUANTUM YIELDS still unpractical or impossible Different Electronic States = Different Conical Intersection Structure = Different Chemistry Hydrocarbons Schiff bases S2 Avoided Crossing rule valid ! S 2 2A 1 S2 S2/S1 2A S1 1B 1 2 S1 S1 1B * 2 S2 M * Avoided Crossing rule invalid M - + S1/S0 S1/S0 h ν Avoided Crossing h ν rule invalid 1A S 1 0 S0 1A S 1 0 S0 + NH2 + NH2 (π π*)2 π π* The Chemistry of Conical Intersections: Bond-Making, Bond Breaking and Group Transfer 6 6 1 3 3 1 σ-Bond Making C Group (or σ-Bond) Exchange σ-Bond Breaking 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 π∗ S Polyenes (and polyene radicals) 1 π π∗ S0 π Benzene Cyclohexadienes The Chemistry of Conical Intersections: Conjugated Hydrocarbons The Chemistry of Conical Intersections: Conjugated Hydrocarbons Selectivity may be due to differences in energy 40 30 S1 -1 S0 20 E / kcalmol E / 10 90° 0 cyclizations 3 5 7 9 Z/E isomerization The Chemistry of Conical Intersections: Protonated Schiff Bases - + 1 NH2 (+) 3 2 3 2 NH (+) 5 4 1 2 5 4 cis trans Retinal Rhodopsin 11 Light 11 + + NH NH Trans Form Cis Form (Appears in ca. 200 fs) The Chemistry of Conical Intersections: Protonated Schiff Bases Crossing between the ground state and a (π-π*) singly 1.46 Å excited state 1.38 Å π∗ + 1.38 Å 1.40 Å π N 1.33 Å 90° S1 hν + e- π∗ 90° π S0 Newman projection The Chemistry of Conical Intersections: Protonated Schiff Bases Motion Coupled to Unstable (TS) the Torsion + NH2 N x2 X1 χ -x1 x1 + NH2 + NH2 NH2 -x2 N Stretching X + 2 NH2 Unstable (TS) The Chemistry of Conical Intersections: Protonated Schiff Bases χ + NH2 breaks the double bond hetherolitically + + NH2 NH2 breaks the double bond homolitically + + NH2 NH2 x1 -x2 -x1 x2 The Chemistry of Conical Intersections: Protonated Schiff Bases 0.0 1.46 1.43 12.5 π∗ 1.36 1.35 1.29 1.37 1.37 FC π 1.5 1.41 1.35 24.7 120 1.37 S2 1.37 1.35 π∗ 1.53 1.42 π 100 76.8 ) 1.42 1.30 -1 80 1.39 1.46 S1 1.39 CI 60 91.2 1.43 1.30 1.43 hν (291 nm) 40 1.42 1.36 Energy (kcal mol Energy (kcal S0 180.0 1.43 20 1.45 1.29 1.36 1.35 trans 0 0.0 5.0 10.0 15.0 20.0 MEP co-ordinate (a. u.) Structure of Bovine (rod) Rhodopsin Cα W1 11 12 O HN Glu113 O W2 Lys296 Cα Glu113 Lys296 Try265 S. T. Menon, M. Han, T. P. Sakmar, Physiological reviews 2001, 81, 1659. Low Temperature Photochromism in Bovine Rhodopsin 580 nm irradiation at 77 K -8° (11-cis) Opsin -144° (all-trans) HN HN 0.67 q.y. Opsin Rh (λmax 498 nm) bathoRh (λmax 543 nm) Spalink, J.