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Quantum Chemistry of Complex Systems

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Accurate theoretical studies of chemical systems with predictive power, relevant to experimental research, have only recently become possible by methodological and technological advances. In …

Accurate theoretical studies of chemical systems with predictive power, relevant to experimental research, have only recently become possible by methodological and technological advances. In particular, multiscaling methods such as QM/MM and ONIOM have greatly contributed to understanding and enhanced control of chemical reactions in cases where a system can be partitioned into “active” and “bystander” regions [1]. However, such partitioning schemes are obviously problematic when a system is either composed of regions that are highly correlated due to quantum correlation, or consists of a large number of chemically reactive fragments creating a complex chemical reaction environment. The former situation is encountered in metals and semiconductors, π−conjugated systems such as carbon nanomaterials and large photoactive molecules, whereas the latter often occurs in modern nanomaterials synthesis or chemical sputtering processes. For the theoretical study of such complex systems without obvious spatial partitioning, we found it effective to employ approximate density functional theory (DFT) methods based on density-functional tight-binding (DFTB) approximations. In the first part of this talk, we give a brief overview of our past quantum chemical studies of complex systems ranging from carbon nanostructure formation [2] over the simulation of vibrational [3] and optical [4] spectra to the study of molecular and electronic structures of COFs [5]. In the second part of this talk, we lay out our vision for the fully quantum chemical study of enzyme reactions and bioimaging processes, and present preliminary results for the merger of the fragment molecular orbital (FMO) method with DFTB for free energy calculations.

References:
[1] S. Irle and K. Morokuma, “Integrated Methods: Applications in Nanoscale Quantum Chemistry”, in: J. A. Schwarz, C. Contescu, and K. Putyera, Eds., Dekker Encyclopedia of Nanoscience and Nanotechnology, Marcel Dekker, New York, 2004.
[2] A. J. Page, Y. Ohta, Y. Okamoto, S. Irle, and K. Morokuma, “Mechanisms of Single-Walled Carbon Nanotube Nucleation, Growth and Healing Determined Using QM/MD Methods”, Acc. Chem. Res. 43, 1375-1385 (2010).
[3] D. V. Kazachkin, Y. Nishimura, H. A. Witek, S. Irle, and E. Borguet, “Dramatic reduction of IR vibrational cross-sections of molecules encapsulated in carbon nanotubes”, J. Am. Chem. Soc. 133, 8191-8198 (2011).
[4] C. Camacho, Th. Niehaus, K. Itami, S. Irle, “Origin of the size-dependent fluorescence blueshift in [n]cycloparaphenylenes”, Chem. Sci. 4, 187-195 (2013).
[5] X. Feng, M. A. Addicoat, S. Irle, A. Nagai, D. Jiang D. Jiang, “Control Crystallinity and Porosity of Covalent Organic Frameworks through Managing Interlayer Interactions Based on Self-Complementary π−Electronic Force”, J. Am. Chem. Soc. 135, 546-549 (2013).

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  • 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 å + 1 2 EAB rep A¹B atoms å E(SCC-)DFTB = E(NCC-)DFTB + 1 2 gABDqA A,B atoms å DqB ES( pin-polarized)DFTB = E(SCC-)DFTB + 1 2 pAl pAl'WAll' l'ÎA å lÎA å A atoms å Marcus Elstner Christof Köhler Helmut Eschrig Gotthard Seifert Thomas Frauenheim 4 DFTB Fast QM Method: Approximate DFT Eschrig, Seifert (1980’s): • 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 1D2D 2D3D 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. • Nosé-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 [Å]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 ω(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-B3LYPTD-DFTB/MD Electron Dynamics in Complex Systems Group, Universität 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); E=ΣEI+Σ(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!