1. Quantum Chemistry of Complex Systems or Insights into Really Hard Problems with Quantum and Statistical Mechanics Stephan Irle WPI-Institute of Transformative Bio-Molecules & Department of Chemistry, Graduate School of Science Nagoya University The 1st International Symposium on Transformative Bio-Molecules Nagoya University, April 18-19, 2013

2. 2 Complex systems Complex Molecular Systems Large number of atoms and/or functional groups Multiple, equally important components Large number of degrees of freedom Alcohol dehydrogenase PDB: 1ADC, 80 kDa http://en.wikipedia.org/wiki/Photosystem_II 3. 3 How to treat complex systems? QM/MM (Warshel, Karplus JACS 1972) Target region Bystander region IPN Synthase Reality Prioritize cut Approximate Approximate QM (semiempirical QM methods, e.g. CNDO, NDDO, MNDO, AM1, PM3-PM7, DFTB) delocalized systems chaotic reaction systems 4. Density-Functional Tight-Binding (DFTB) Tight Binding (extended-Huckel-like) method with parameters from DFT E(NCC-)DFTB = niei i valence orbitals + 1 2 EAB rep AB atoms E(SCC-)DFTB = E(NCC-)DFTB + 1 2 gABDqA A,B atoms DqB ES( pin-polarized)DFTB = E(SCC-)DFTB + 1 2 pAl pAl'WAll' l'A lA A atoms Marcus Elstner Christof Khler Helmut Eschrig Gotthard Seifert Thomas Frauenheim 4 DFTB Fast QM Method: Approximate DFT Eschrig, Seifert (1980s): 2-center approximation Minimum basis set No integrals, DFTB is roughly 1000 times faster than DFT! Foulke, Haydock (1989): 5. 5 Optimized elemental electronic DFTB parameters now available for Z=1-109! Yoshifumi Nishimura, Chien-Pin Chou Henryk A. Witek, Stephan Irle Nagoya University National Chiao Tung University, Taiwan Henryk A. Witek Yoshifumi Nishimura Chien-Pin Chou DFTB 6. 6 1. Chaotic and Delocalized Systems Simulations of Carbon Nanostructure Formation Collaborators: K. Morokuma and coworkers, A. J. Page (Newcastle, Australia) CREST grant 2006-2011 (KM, SI) 7. Ignis mutat res - Fire transmutes everything Alchimistic maxim 8. Hypothetical mechanisms relying on more or less sound assumptions; no intermediate species experimentally confirmed so far. No experimental or theoretical verification ! C60 (Cn)x Centrally managed C60 formation models Buckminster Fuller 1895-1983 Lego philosophy Fullerene formation 8 9. Giant Fullerene Formation Mechanism from DFTB/MD 0.12 ps 0.35 ps 2.90 ps 59.53 ps S2 Modified from: SI, G. Zheng, Z. Wang, K. Morokuma, J. Phys. Chem. B 110, 14531 (2006) 10 1D2D 2D3D Fullerene formation 10. Giant buckyball shrinking by C2 evaporation J. Chem. Phys. 122, 014708 (2005) J. Nanosci. Nanotechnol. 7, 1662 (2007) Huang et al., Phys. Rev. Lett. 99, 175503 (2007) Predictive power of computer simulations! 11 Fullerene formation Natural Selection 11. C60 fullerene formation is a 2-step process Size-Up + Size-Down = Shrinking Hot Giant (SHG) Road of Fullerene Formation Lego philosophy Fullerene formation 12 12. SCC-DFTB; Te = 10,000 K. MD; t=1 fs. NVT ensemble; Tn= 1,500 K. Nos-Hoover-Chain thermostat. 30 C2 deposited onto fcc-Fe38 surface (1/ps). NVT thermal annealing for 400 ps. Yasuhito Ohta 13 Y. Ohta, Y. Okamoto, A. J. Page, SI, K. Morokuma, ACS Nano 3, 3413 (2009) 10 trajectory replica. C2 shooting and annealing on Fe38 particle Nanotube formation 13. C2 shooting and annealing on Fe38 particle 14 Y. Ohta, Y. Okamoto, A. J. Page, SI, K. Morokuma, ACS Nano 3, 3413 (2009) Nanotube formation Pentagon-first mechanism 14. Growth at base is chaotic Annealing from pentagon to hexagons takes place very slowly (n,m) chirality already established in outer tube area imprints hexagon addition pattern during annealing Nucleation and growth hypothesis: Nanotube formation A. J. Page, Y. Ohta, SI, K. Morokuma, Acc. Chem. Res. 43, 1375 (2010) In sharp contrast to: F. Ding, A. Harutyunyan, B. I. Yakobson, Proc. Natl. Acad. Sci. 106, 2506 (2009) 15 15. 16 2. Delocalized Systems Vibrational Spectra of Extended Systems Collaborators: Henryk A. Witek (NCTU) 16. Periodic boundary conditions (PBC) Ignoring edge effect Repeating unit cell Finite molecular models Larger structures (> 200 atoms) Computational cost SCC-DFTB method allows transitions from molecule to solids (Self-Consistent-Charge Density-Functional Tight-Binding) M. Elstner et al., Phys. Rev. B, 58, 7260, (1998). Dilemma of conventional quantum chemistry Vibrational spectra 17 17. Analytical Hessian for (SCC-)DFTB: H. A. Witek et al., J. Chem. Phys., 121, 5163, (2004). Modeling Raman spectra: H. A. Witek et al., J. Chem. Phys., 121, 5171, (2004). Modeling Infrared (IR) spectra: H. A. Witek et al., J. Theor. Comput. Chem., 4, 639, (2005). Benchmark of harmonic frequency: H. A. Witek et al., J. Comput. Chem., 25, 1858, (2004). Set of 66 small/medium-size molecules, 1304 distinct vibrational modes SCC-DFTB is better than other semi-empirical methods (AM1 and PM3) (0.9933) (0.9917) (0.9762) (0.9704) (0.9566) (1.0043) (0.9102) (scaling factor) Accuracy of SCC-DFTB Frequencies Vibrational spectra 18 18. Suitable performance for large nanomolecular systems Fullerene C60 (Ih) H. A. Witek et al., J. Chem. Phys., 125, 214706, (2006). W. Li et al., ACS Nano, 4, 4475, (2010). Comparable with DFT results Nanodiamonds Size evolution of Raman spectra Octahedral models Analytical 2nd derivatives (H. A. Witek et al., JCP, 121, 5163, (2006).) Optimized parameters for frequency (E. Malolepsza et al., CPL, 412, 237 (2005).) Vibrational spectra 19 19. d = 6.1 []1 nm: C80H18 2 nm: C160H18 3 nm: C230H18 4 nm: C300H18 5 nm: C380H18 6 nm: C450H18 7 nm: C520H18 8 nm: C600H18 9 nm: C670H18 10 nm: C740H18 L SCC-DFTB can treat vibrational analysis of ~1000 atoms Raman (5,4) SWCNTs with lengths from 1-10 nm Vibrational spectra 20 20. Increasing tube length L Reduced Raman D-band intensity peak (SCC-DFTB) [cm-1] RBM ~380 D-band ~1250 G-band ~1550 RelativeRamanIntensity (RamanG-band=1) Vibrational spectra 21 21. 22 3. Delocalized and Flexible Systems Origin of the fluorescence blueshift in [n]cycloparaphenylenes Collaborators: K. Itami, Y. Segawa, and coworkers, S. Yamaguchi, A. Fukazawa, S. Saito, and coworkers CREST grant 2012-2015 (SY, SI) C. Camacho, K. Itami, Th. Niehaus, SI, Chem. Sci. 4, 187 (2013) 22. Optical spectraAbsorption and Emission Spectra 23 1E1 Absorption: 1 peak Emission: at least 2 peaks! Iwamoto, Watanabe, Sakomoto, Suzuki, Yamago, JACS 133, 8354 (2011) 23. 24 CAM-B3LYPTD-DFTB/MD Electron Dynamics in Complex Systems Group, Universitt Regensburg Linear response TD-DFTB: Thomas Niehaus Method TD-DFTB w/mio-1-1 parameters 8 states considered, dynamics performed for S0, S1, S2/S3 MD: 1. starting from optimized geometries 2. NVT 0.5 ps equilibration at 298 K 3. NVE for 4.7 ps, production runs 4. CAM-B3LYP/SV(P) single point excited state calculations (up to 32 sample points) Optical spectra 24. Optical spectra 25 Simulated [n]CPP UV/Vis spectra CAM-B3LYP/SV(P)TD- DFTB-MD snapshots Energy Energy Yes blueshift! Yes blueshift! Yes blueshift! 25. Absorption and Emission Spectra Explained 26 Absorption: 1 peak Dynamic blue-shift, emission from S2/S3 Static blue-shift, emission from S1 C. Camacho, K. Itami, Th. Niehaus, SI, Chem. Sci. 4, 187 (2013) 26. 27 4. Delocalized Huge Systems Molecular and electronic structure of covalent organic frameworks (COFs) Collaborators: D. Jiang and coworkers (IMS, Okazaki) 27. XRD Simulations of Covalent Organic Frameworks AA stacking results match the experimental data SCC-DFTB-D confirmed the AA stacking is more preferable! 2D COFs 28 SCC-DFTB-D X. Feng, L. Liu, Y. Honsho, A. Saeki, S. Seki, SI, Y. Dong, A. Nagai, D. Jiang, Angew. Chem. Int. Ed. 51, 2618 (2012) 28. Biosystems QM/MM (Warshel, Karplus JACS 1972) Target region Bystander region IPN Synthase Reality Prioritize cut Approximate Approximate QM (DFTB3-D/MD) 29. 30 Failure of MM Failure of MM may give wrong X-ray structure! N sp3 N sp2 modeled - wrong input correct - crystal structure and quantum calculation Y. Tanaka, V. Sychrovsky et al., J. Phys. Chem. B 116, 12535 (2012) 30. 31 DFTB for protein backbone Performance of DFTB: Conformations of peptides f Alanine Dimer {f, y} are rotated by 15 degrees Ramachandran Plot http://upload.wikimedia.org/wikipedia/commons/thumb/9/90/Ramachand ran_plot_general_100K.jpg/671px-Ramachandran_plot_general_100K.jpg y 31. 32 DFTB for protein backbone Performance of DFTB: Conformations of peptides MP2/cc-pVDZ (reference) y f DFTB3-D UFF AMBER Failure of MM force fields to correcly describe peptide backbone in gas phase! 32. 33 FMO-DFTB What is Fragment Molecular Orbital (FMO)? A molecule is divided into N fragments and ab initio MO calculations on the fragments (monomers) and fragment pairs (dimers) are performed under electrostatic potential from other monomers. The total energy of a molecule (E) is calculated using the energies of the monomer (EI) and dimer (EIJ); EEI+(EIJ-EI-EJ) Advantage of the method: reproduces ab initio properties with good accuracy, is efficient on massively parallel computers. FMO is a fragment-based MO method for large molecules. Several fragment-based methods have been proposed. A brief review is given in Fedorov & Kitaura, Chapter 1 in Modern Methods for Theoretical Physical Chemistry of Biopolymers, E. Starikov J. Lewis S. Tanaka, Eds, Elsevier (2006). D. Fedorov (AIST) K. Kitaura (AICS) 33. 34 FMO-DFTB Implementation of FMO-DFTB D. Fedorov (AIST) Full SCC-DFTB (reference) : -18.9190503342 H FMO-DFTB with SCI : -18.9190404398 H (+0.006 kcal/mol error) FMO-DFTB without SCI : -18.9169093952 H (+1.34 kcal/mol error) Fragment 1 Fragment 2Fragment 3 -0.207 -0.154 0.288 -0.144 -0.196 -1.283 -0.137 -0.093 0.263 -0.097 -0.150 -1.062 3-hexanol Y. Nishimoto SCI: Superposed charge interaction 34. 35 ITbM Research QM for Bio (Part 1) Bio-imaging, biofluorescence Aldol-type condensation with Rh(I) (Y. Nishimoto, S. Saito) (Bio)catalysis Weakly fluorescent Strongly fluorescent UV light irradiation PRPG Photoremovable protecing group (PRPG) (D. Yokogawa) 35. 36 ITbM Research QM for Bio (Part 2) Vibrational spectropscopy of proteins Substrate-enzyme binding (Yoshimura/Crudden/Irle, etc.) K. Welke et al., Phys. Chem. Chem. Phys. 15, 6651 (2013) Others, e.g. sugar conformations, protein-membrane, etc. 36. 37 Acknowledgments Back row: Yoshifumi Nishimura (D3), Kosuke Usui (M2), Jun Kato (B4), Tim Kowalczyk (JSPS, PhD,), Cristopher Camacho-Leandro (PhD), Yoshio Nishimoto (D1) Front row: Takayo Noguchi (secty), Naoto Baba (B4), Matt Addicoat (JSPS, PhD), SI, Arifin (G30, D1), Daisuke Yokogawa (Assist. Prof.) 37. Energy E- (S2, B 1B) E+ (S3,C 1B) Absorption and Emission Spectra 38 1E1 Emission: at least 2 intensive peaks!