TDDFT as a tool in biophysics

Transcription

1 TDDFT as a tool in biophysics The primary event in vision Robert Send Universität Karlsruhe Robert Send TDDFT as a tool in biophysics / 28

2 Outline 1 Human vision 2 The methods 3 The photoreaction mechanism: Three methods two results Robert Send TDDFT as a tool in biophysics / 28

3 Human vision Robert Send TDDFT as a tool in biophysics / 28

4 Human vision Robert Send TDDFT as a tool in biophysics / 28

5 Human vision Robert Send TDDFT as a tool in biophysics / 28

6 Human vision The chromophor: 11-cis retinal Robert Send TDDFT as a tool in biophysics / 28

7 Human vision The photoproduct: all-trans retinal Robert Send TDDFT as a tool in biophysics / 28

8 Human vision Photoreaction to all-trans retinal 1 Extremely fast (200 fs) Very efficient (quantum yield of 0.67) Very selective Tunable absorption maximum 1 P.Kukura et al. Science (2005) and references therein Robert Send TDDFT as a tool in biophysics / 28

9 Human vision The chromophor: 11-cis retinal Polyene chain Protonated Schiff base: NH + 2 β-ionone ring Charge-transfer upon excitation 1 1 R. Mathies and L. Stryer Proc. Natl. Acad. Sci. USA (1967) Robert Send TDDFT as a tool in biophysics / 28

10 TDDFT Ansatz: γ α (x, x ) = ia ( X α ia φ a (x)φ i (x ) + Y α ia φ i (x)φ a (x ) ) Robert Send TDDFT as a tool in biophysics / 28

11 TDDFT Ansatz: γ α (x, x ) = ia ( X α ia φ a (x)φ i (x ) + Y α ia φ i (x)φ a (x ) ) Casida s equation: [( A(ωn ) B(ω n ) B(ω n ) A(ω n ) ) ω n ( )] ( Xn Y n ) = 0 Robert Send TDDFT as a tool in biophysics / 28

12 TDDFT Ansatz: γ α (x, x ) = ia ( X α ia φ a (x)φ i (x ) + Y α ia φ i (x)φ a (x ) ) Casida s equation: [( A(ωn ) B(ω n ) B(ω n ) A(ω n ) ) ω n ( )] ( Xn Y n ) = 0 with C iajb (ω) = (A(ω) + B(ω)) iajb = (ɛ a ɛ i )δ ij δ ab (A(ω) B(ω)) iajb = (A(ω) + B(ω)) iajb + 2C iajb (ω) ( ) 1 dxdx φ i (x)φ a (x) r r + f xc(ω, x, x ) φ j (x )φ b (x ) Robert Send TDDFT as a tool in biophysics / 28

13 Coupled Cluster methods Ground state energy: E = E HF + Φ HF Ĥe ˆT Φ HF with exp( ˆT 1 + ˆT 2 + ˆT 3...) = 1 + ˆT 1 + ˆT ˆT ˆT 1 ˆT ˆT Robert Send TDDFT as a tool in biophysics / 28

14 Coupled Cluster methods Ground state energy: with E = E HF + Φ HF Ĥe ˆT Φ HF exp( ˆT 1 + ˆT 2 + ˆT 3...) = 1 + ˆT 1 + ˆT ˆT ˆT 1 ˆT ˆT Excitation energy: with (A ω n I) X n = 0 A µν = Φ HF ˆτ + µ e ˆT [ Ĥ, ˆτ ν ] e ˆT Φ HF T I µν = Φ HF τ ˆ µ e ˆ ˆτ ν e T Φ HF = δ µν Robert Send TDDFT as a tool in biophysics / 28

15 Complete Active Space Self-Consistent Field (CASSCF) Choose: m active orbitals, n α,β active electrons Form Φ CAS with ( ) ( m m n α n β ) determinants Optimize coefficients and orbitals E = min ω i Ψ SA c 0,cs r,...,{φ i Ĥ Ψ SA i i } (12,12): Slater determinants Multireference: important for bond twists i Robert Send TDDFT as a tool in biophysics / 28

16 Complete Active Space Self-Consistent Field (CASSCF) Choose: m active orbitals, n α,β active electrons Form Φ CAS with ( ) ( m m n α n β ) determinants Optimize coefficients and orbitals E = min ω i Ψ SA c 0,cs r,...,{φ i Ĥ Ψ SA i i } (12,12): Slater determinants Multireference: important for bond twists i Robert Send TDDFT as a tool in biophysics / 28

17 CASPT2: CASSCF includes static correlation Dynamic correlation missing CASPT2: Perturbation theory for the inactive space CASPT2 energy: Second order estimate for E(FCI ) E(CASSCF ) Accurate excitation energies for small molecules PT: correction for correlation energy Robert Send TDDFT as a tool in biophysics / 28

18 Method overview TDDFT CC2 CAS single reference single reference multireference linear response linear response state averaged CT: f 2 xc CT: lin. response CT: reliable 3 large molecules large molecules limited active space 2 A. Dreuw, J.L. Weisman, and M. Head-Gordon J. Chem. Phys (2003) 3 M. Wanko et al. J. Chem. Phys (2004) Robert Send TDDFT as a tool in biophysics / 28

19 Three methods two results CAS as a reference method CASPT2 reliable for small molecules Reliable for charge-transfer states Multireference for strongly twisted bonds and at conical intersections TDDFT applicable? Charge-transfer issue TDDFT results contradict CASPT2 results Robert Send TDDFT as a tool in biophysics / 28

20 Back to the chromophore Vertical excitation energies (in ev) Method 1a 2a Ref. BP86/TZVP B3LYP/TZVP [1] CC2/TZVPP [2] CASPT2/6-31G* [3] CASPT2/ANO [4] Experiment [5] [1] R. S. and D. Sundholm J. Phys. Chem. A (2007) [2] R. S. and D. Sundholm Phys. Chem. Chem. Phys (2007) [3] A. Cembran et al. J. Phys. Chem. A (2005) [4] S. Sekharan et al. Biophys. J. 91 L07 (2006) [5] I.B. Nielsen et al. Phys. Rev. Lett (2006) Robert Send TDDFT as a tool in biophysics / 28

21 Back to the chromophore Vertical excitation energies (in ev) Method 1a 2a Ref. BP86/TZVP B3LYP/TZVP [1] CC2/TZVPP [2] CASPT2/6-31G* [3] CASPT2/ANO [4] Experiment [5] Charge-transfer problems Coupled cluster-series convergence Basis sets Active space CAS as a reference? [1] R. S. and D. Sundholm J. Phys. Chem. A (2007) [2] R. S. and D. Sundholm Phys. Chem. Chem. Phys (2007) [3] A. Cembran et al. J. Phys. Chem. A (2005) [4] S. Sekharan et al. Biophys. J. 91 L07 (2006) [5] I.B. Nielsen et al. Phys. Rev. Lett (2006) Robert Send TDDFT as a tool in biophysics / 28

22 Applicability of TDDFT Do charge-transfer problems occur? Check and compare: Optimization with hybrid/non-hybrid functionals Stabilization with point charges Stabilization with polar molecules Optimization with CC2 Convergence of the CC series Robert Send TDDFT as a tool in biophysics / 28

23 Applicability of TDDFT Do charge-transfer problems occur? Check and compare: Optimization with hybrid/non-hybrid functionals Stabilization with point charges Stabilization with polar molecules Optimization with CC2 Convergence of the CC series 11-cis retinal: all optimization results agree exception: angle of the β-ionone ring Robert Send TDDFT as a tool in biophysics / 28

24 Optimizing the excited state Bond length alternation ground state 1a TDDFT 1a CASSCF(12,12) pm C6-C7 C7-C8 C8-C9 C9-C10 C10-C11 C11-C12 C12-C13 C13-C14 C14-C15 C15-N16 4 A. Cembran et al. J. Phys. Chem. A (2005) 5 R. S. and D. Sundholm Phys. Chem. Chem. Phys (2007) Robert Send TDDFT as a tool in biophysics / 28

25 CASSCF: Ionic states vs. tetraradicals 6 Polyene isomerization via tetraradicals 6 M. Garavelli et al. J. Photochem. Photobiol. A (1998) Robert Send TDDFT as a tool in biophysics / 28

26 CASSCF: Ionic states vs. tetraradicals 6 Polyene isomerization via tetraradicals PSB isomerization via ionic states with bond length inversion 6 M. Garavelli et al. J. Photochem. Photobiol. A (1998) Robert Send TDDFT as a tool in biophysics / 28

27 CAS: Conical intersection region 7 8 C-C stretch vibrations Torsion twist around the double bond 7 R. Gonzalez-Luque Proc. Nat. Acad. Sci (2000) 8 A. Cembran et al. J. Phys. Chem. A (2005) Robert Send TDDFT as a tool in biophysics / 28

28 TDDFT: The β-ionone ring twist 9 9 R. S. and D. Sundholm J. Phys. Chem. A (2007) Robert Send TDDFT as a tool in biophysics / 28

29 TDDFT: The β-ionone ring twist 9 9 R. S. and D. Sundholm J. Phys. Chem. A (2007) Robert Send TDDFT as a tool in biophysics / 28

30 TDDFT: The β-ionone ring twist 10 Three ground state isomers Excitation energy dependent on ring-torsion Single-bond barriers dependent on ring-torsion Not entirely supported at CC2 level 10 R. S. and D. Sundholm J. Phys. Chem. A (2007) Robert Send TDDFT as a tool in biophysics / 28

31 TDDFT: The conical intersection Twist around the single bond Two methyl groups block each other Relaxation to the curl isomer 11 R. S. and D. Sundholm J. Phys. Chem. A (2007) 12 R. S. and D. Sundholm J. Mol. Model (2008) Robert Send TDDFT as a tool in biophysics / 28

32 Soft experimental evidence Inside the protein pocket The double bond isomerization starts after 20 fs 13 The isomerization takes place in the ground state 14 There is an intermediate called photorhodopsin 15 Electron density at the ring changes upon isomerization 15 The isomerization does not happen when the ring is removed T. Kakitani et al. J. Phys. Chem. A (1998) 14 P. Kukura et al. Science (2005) 15 H. Nakamichi and T. Okada Angew. Chem (2006) 16 F. Bartl et al. J. Biol. Chem (2005) Robert Send TDDFT as a tool in biophysics / 28

33 Conclusions Applicability of TDDFT in retinal calculations New isomerization mechanism Robert Send TDDFT as a tool in biophysics / 28

34 Conclusions Applicability of TDDFT in retinal calculations New isomerization mechanism Importance of single bond twists Importance of electrons in the β-ionone ring Robert Send TDDFT as a tool in biophysics / 28

35 Conclusions Applicability of TDDFT in retinal calculations New isomerization mechanism Importance of single bond twists Importance of electrons in the β-ionone ring Doubts about CAS (12,12)-reliability Doubts about basis sets used in CAS calculations CAS might not be applicable in retinal calculations Robert Send TDDFT as a tool in biophysics / 28

36 Problems Three methods with different weaknesses Two different results in agreement with experiment Robert Send TDDFT as a tool in biophysics / 28

37 Problems Three methods with different weaknesses Two different results in agreement with experiment New evaluation of the methods needed New experiments to evaluate the methods needed Robert Send TDDFT as a tool in biophysics / 28

38 Problems Three methods with different weaknesses Two different results in agreement with experiment New evaluation of the methods needed New experiments to evaluate the methods needed No reliability close to conical intersections Dynamical treatment needed Robert Send TDDFT as a tool in biophysics / 28

39 Problems Three methods with different weaknesses Two different results in agreement with experiment New evaluation of the methods needed New experiments to evaluate the methods needed No reliability close to conical intersections Dynamical treatment needed Too many publications on retinal The major questions remain unanswered Robert Send TDDFT as a tool in biophysics / 28

40 Acknowledgements Dage Sundholm (Helsinki) Filipp Furche (Irvine) Reinhart Ahlrichs (Karlsruhe) TURBOMOLE Robert Send TDDFT as a tool in biophysics / 28