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Electronic Properties of Flexible Systems Tim Clark

Introduction UNO-CAS FRET SHG in membranes Very large scale MO SAMFETs. Computer- Chemie -Centrum and Excellence Cluster “Engineering of Advanced Materials” Friedrich-Alexander- Universität Erlangen- Nürnberg Tim.Clark@chemie.uni-erlangen.de. Centre for Molecular Design

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Electronic Properties of Flexible Systems Tim Clark

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  1. Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs Computer-Chemie-Centrum and Excellence Cluster “Engineering of Advanced Materials” Friedrich-Alexander-UniversitätErlangen-Nürnberg Tim.Clark@chemie.uni-erlangen.de Centre for Molecular Design University of Portsmouth Tim.Clark@port.ac.uk Electronic Properties of Flexible Systems Tim Clark

  2. Acknowledgements • Dr. Harry Lanig • Dr. Frank Beierlein • Dr. CatalinRusu • Dr. Matthias Hennemann • Dr. Christof Jäger • Dr. Olaf Othersen • Pavlo Dral M.Sc. • Prof. Siegfried Schneider (FRET) • Prof. CarolaKryschi (SHG) • Prof. Nigel Richards (EMPIRE) • Prof. Markus Halik (SAMFETs) • Deutsche Forschungsgemeinschaft (DFG) • Bavarian State Government (KONWIHR) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  3. Modeling • The Hamiltonian • Force field – no electronics, but good sampling and geometries • Semiempirical MO/CI • CC-DFTB/TD-CC-DFTB • DFT/TDDFT • Ab initio • SAMPLING !!!! • Molecular dynamics • QM/MM electronics • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs No good for charge transfer Can‘t do large systems

  4. Semiempirical MO Theory • Is very fast • Can therefore handle either very large systems or very many smaller ones • Generally gives very good one-electron properties • because the semiempirical electron density is good • because the parameterization probably used a related property • Because the MEP is good, solvent effects are also good • Semiempirical CI is good for excited states • Also better for frontier orbital energies than “higher” levels of theory • Is therefore ideal for calculating the properties of many “hot” geometries (snapshots) from MD simulations to obtain ensemble properties • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  5. Topics • UNO-CAS for Band Gaps • Simulating FRET in Biological Systems • Simulating SHG in Biological Membranes • EMPIRE – Very Large massively parallel Semiempirical MO calculations • Self-Assembled Monolayer Field-Effect Transistors (SAMFETs) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  6. Semiempirical UNO-CAS for Optical Band Gaps • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs Pavlo Dral

  7. UNO-CAS • UHF Natural Orbital – Complete Active Space configuration interaction • J. M. Bofill and P. Pulay, J. Chem. Phys. 1989, 90, 3637. • Semiempirical UNO-CAS and UNO-CI: Method and Applications in Nanoelectronics, P. O. Dral and T. Clark, J. Phys. Chem. A,2011, 115, asap (DOI: 10.1021/jp204939x). • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  8. UHF Natural Orbitals (UNOs) • Diagonalize the total ( + ) UHF density matrix • The eigenvectors are the UHF Natural orbitals and the Eigenvalues are the UNO occupation numbers (0 or 2 for RHF, partial values between 0 and 2 for UHF) • Significant Fractional Occupation Numbers (SFONs) between 0.02 and 1.98 define the active space • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  9. Advantages • The active space defined by the SFONs is usually small enough to allow a full CI calculation (UNO-CAS) • A CI-Singles (CIS) or CISD approach can be used for larger active spaces • The active space is defined automatically • UNOs contain some multi-reference information derived from the components of the UHF wavefunction • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  10. Disadvantages • It is sometimes very difficult to find the correct UHF wavefunction (there may be many solutions close in energy) • Only applicable for systems that exhibit RHF/UHF instability (symmetry breaking) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  11. Calculated Band Gaps: Polyynes • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  12. Polyacene band gaps • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  13. Optical Properties • Two examples • Fluorescence resonant energy transfer (FRET) in TetR (S. Schneider) • Second-harmonic generation (SHG) by dyes in biological membranes (C. Kryschi) • A Numerical Self-Consistent Reaction Field (SCRF) Model for Ground and Excited States in NDDO-Based Methods, G. Rauhut, T. Clark and T. Steinke, J. Am. Chem. Soc., 1993, 115, 9174. • NDDO-Based CI Methods for the Prediction of Electronic Spectra and Sum-Over-States Molecular Hyperpolarizabilities, T. Clark and J. Chandrasekhar, Israel J. Chem., 1993, 33, 435. • A Semiempirical QM/MM Implementation and its Application to the Absorption of Organic Molecules in Zeolites, T. Clark, A. Alex, B. Beck, P. Gedeck and H. Lanig, J. Mol. Model. 1999, 5, 1. • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  14. FRET in the Tetracycline Repressor • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs Frank Beierlein, Prof. Siegfried Schneider, Harry Lanig, Olaf Othersen Simulating FRET from Tryptophan: Is the Rotamer Model Correct? , F. R. Beierlein, O. G. Othersen, H. Lanig, S. Schneider and T. Clark, J. Am. Chem. Soc. , 2006 , 128 , 5142-5152.

  15. Tetracycline Tryptophan FRET (SFB 473) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs One monomer of the Tetracycline Repressor (TetR) Protein

  16. The Experimental Problem • Fluorescence decay in the protein is biexponential • Usually treated using the “rotamer model” • Each individual exponential decay process can be attributed to a corresponding tryptophan rotamer • Differences in distance and, above all orientation, relative to the acceptor (tetracycline) give different decay rates (Förster theory) • Is this model correct? • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  17. Chromophores Tryptophan Two low-lying excited states 1La, polar, solvent sensitive, usually the emitting state (~350nM) 1Lb, non-polar • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs Tetracycline:Mg2+ “BCD” Chromopohore Absorption overlaps with tryptophan emission, making FRET possible

  18. Glycyltryptophan Absorbance Spectra (H2O) • Experimental • SCRF ( = 78.36) • QM/MM (explicit water) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  19. Tryptophan Transition Dipoles • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs In the ring plane From above the ring 10% of the calculated snapshots shown

  20. Rotamer Distribution • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  21. Einstein Coefficients (no FRET) • Total • Rotamer 1 • Rotamer 2 • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  22. FRET Rate Constants (Förster theory) • Total • Rotamer 1 • Rotamer 2 • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  23. Exponential Fits • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs Fit for the total is approximated well by the weighted average of the parameters for the individual rotamers, not as two individual decay components.

  24. FRET Conclusions • Individual rotamers with significant lifetimes can be identified in the MD simulations • Including FRET makes the decay curves biexponentialfor each rotamer • Biexponentiality is caused by the distribution of the FRET rates, rather than by individual rotamers • “Spectroscopic Ruler” distances may be in error by as much as 6 Å if the orientation factor is not considered explicitly • Simulating FRET from Tryptophan: Is the Rotamer Model Correct?, F. R. Beierlein, O. G. Othersen, H. Lanig, S. Schneider and T. Clark, J. Am. Chem. Soc., 2006, 128, 5142-5152. • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  25. SHG in Biological Membranes • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs Catalin Rusu, Prof. Carola Kryschi, Harry Lanig Monitoring Biological Membrane-Potential Changes: a CI QM/MM Study C. Rusu, H. Lanig, T. Clark and C. Kryschi, J. Phys. Chem. B , 2008 , 112 , 2445-2455

  26. SHG in Membranes • Second-harmonic generation (SHG) has been used recently to monitor action potentials (AP) in cardiomyocytes or neurons • The intensity of the SHG (ISHG) is monitored as a function of the trans-membrane potential • Di-8-ANEPPS was used as a typical lipophilic dye that is incorporated into the membrane • The simulation system consisted of one dye molecule, 63 DPCC lipid molecules and 3,840 water molecules • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  27. The Simulation System • Water: blue • Lipids: green (head groups bold) • Dye: red • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs • GROMOS force field with optimized Lennard-Jones parameters for lipids • Periodic boundary conditions • PME electrostatics, NPT ensemble • 10 ns equilibration + 10 ns production MD • 700 snapshots per trajectory (last 7 ns of the production phase)

  28. QM-CI/MM Snapshots • Di-8-ANEPPS used as the QM-part (chromophore, 91 atoms) • MM surroundings (DCCP + water) consisted of 14,700 atoms • 18 active orbitals • 18 active electrons • Single + pair-double excitations • QM/MM = 4.0 • Excitation energy = 1.17 eV (for sum-over-states ) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  29. Trans-Membrane Potential • External potential applied to the QM-CI/MM calculations • Change in dye dipole moment in vacuo used to calibrate the system • External potential then adjusted to give a local potential at the dye of  0.1 V • Three calculations at +0.1, 0.0 and 0.1 V for each snapshot • Total simulated AP is therefore 0.2 V (about twice as large as in the experiment) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  30. Dye – Vertical Stability • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  31. Calculated ISHG (V = 0.2V) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs Simulation 1:ISHG = 41.6  11.1 % Simulation 2:ISHG = 43.2  13.0 % Experiment: ISHG 40 %

  32. SHG Conclusions • The qualitative picture of the dye in the membrane is correct • The MD simulations give lateral diffusion rates several orders of magnitude higher than those deduced from experiment • Force-field problem (van der Waals)? • Experimental interpretation ? • SHG enhancement of the order found in the experimental studies is also found in the simulations • C. F. Rusu, H. Lanig, O. G. Othersen, C. Kryschi and T. Clark, to be submitted to J. Am. Chem. Soc.(2007) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  33. EMPIRE: A Very Large Scale Parallel Semiempirical SCF Program • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs Matthias Hennemann

  34. The Big Hammer Approach Develop a completely new semiempirical MO Program (EMPIRE) ; design specifications: • Neither LMO nor D&C • Need to treat conjugated systems • Massively parallel: • SCF50,000 Atoms using 1,000 cores • Configuration Interaction (CI)5,000 Atoms using 1,000 cores • Program • Direct on-the-fly calculation of the 2-electron integrals and the one-electron matrix • Avoid matrix diagonalization • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  35. Comparison with VAMP 910 Atoms 1,960 Orbitals VAMP 11 Cycles 59 Seconds (1 Core) EMPIRE 16 Cycles 58 Seconds (1 Core) 7.8 Seconds (12 Cores) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  36. Scaling on one Node • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs Dual-Hex-Core Xeon 5650 “Westmere” 2.66 GHz (@ 2.93 GHz) with 12 MB cache per chip und 24 GB RAM.

  37. Benchmark results: Adamantane 666 11,232 Atoms 24,192 Orbitals 412 Cores: 78.4 Minutes 812 Cores: 44.3 Minuten 1612 Cores: 25.6 Minuten 22 Cycles • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  38. Benchmark-Results: HLRB II • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs HLRB II:9,728 Cores - 512 per Partition: 1.6 GHz dual core Itanium 2 “Montecito”, 4 GB RAM per Core, NUMAlink 4 with 6,4 GByte/s per link und direction

  39. Hard Scaling (LiMa) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs LiMa 500 Dual-Hex-Core Xeon 5650 “Westmere” 2,66 GHz (@ 2.93 GHz) 12 MB Cache per Chip 24 GB RAM per Node Infiniband with 40 Gbit/s per link and direction

  40. Application: Organic Field-Effect Transistors • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs 0 • molecular scale electronic devices with pure and mixed SAMs • relation of device characteristics on molecular structure and SAM composition • SAMs as important dielectric and bifunctional layers in condensers and FETs

  41. Application: Organic Field-Effect Transistors • Constructed of self-assembled monolayers (SAMs) • Head groups such as fullerenes can function as the semiconductor • No additional semiconductor layer necessary • Properties vary widely • Can an adequate permanent semiconductor layer be attained? • Classical MD simulations with AM1 single-points on snapshots • Prof. Marcus Halik • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs C10PA + C60C18PA C60C18PA

  42. C10PA + C60C18PA - Monolayer 6,050 Atoms 15,950 Orbitals 25 Minutes (812 Cores) 36 Cycles At the moment: 50 Snapshots • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  43. Local Electron Affinity (EAL) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  44. Section through the SAM (EAL) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

  45. Section through the SAM (EAL) • Introduction • UNO-CAS • FRET • SHG in membranes • Very large scale MO • SAMFETs

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