Elstner_ApproximateMethods - Approximate methods for large...

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Unformatted text preview: Approximate methods for large molecular Approximate methods for large molecular systems systems Marcus Elstner Physical and Theoretical Chemistry, Technical University of Braunschweig Motivation Motivation Structure-formation, atomic-scale related properties and processes Si21 C60-trimer defects, doping Si1600 MoS2 4H-SiC-surfaces a-SiCN-ceramics GaN-devices Reactions in biological Systems Reactions in biological Systems Alcohol DeHydrogenase Aquaporin Photosynthetic Reaction Center Catalysis bR Photochemistry Proton Transfer Photochemistry Electron/Energy Transfer Need QM description Computational challange Computational challange ~ 1.000-10.000 atoms ~ ns molecular dynamics simulation (MD, umbrella sampling) - weak bonding forces - chemical reactions - treatment of excited states ‚‚multiscalebusiness‘ multiscale business‘ Continuum electrostatics Continuum electrostatics ns Molecular Mechanics Molecular Mechanics ps SE-QM SE-QM approx-DFT approx-DFT time fs HF, DFT HF, DFT CI, MP CI, MP CASPT2 CASPT2 predictivity nm Length scale Size problem:: Size problem number of structures MD, MC, GA time scale of process MD, MC -- RP, TST ab initio, SE MM size of system: number of atoms Size problem::QM-Methods Size problem QM-Methods Hybride methods: QM/MM, QM/QM Linear scaling: O(N) SE/approx. Methods Semi-empirical /approximate methods Semi-empirical /approximate methods approximation, neglect and parametrization of interaction integrals from ab-initio and DFT methods -HF-based: CNDO, INDO, MNDO, AM1, PM3, MNDO/d, OM1,OM2 -DFT-based: SCC-DFTB, DFT- 3center- tight binding (Sankey) Fireballs --- > Siesta DFT code ~ 1000 atoms, ~ 100 ps MD Approximate density-functional theory: Approximate density-functional theory: SCC-DFTB SCC-DFTB Self cconsistent--cchargedensity ffunctionalttight-binding Self onsistent harge density unctional ight-binding • Seifert (1980-86): Int. J. Quant Chem., 58, 185 (1996). O-LCAO; 2-center approximation: approximate DFT http://theory.chm.tu-dresden.de • Frauenheim et al. (1995): Phys. Rev. B 51, 12947 (1995). efficient parametrization scheme: DFTB www.bccms.uni-bremen.de • Elstner et al. (1998): Phys. Rev. B 58, 7260 (1998). charge self-consistency: SCC-DFTB www.tu-bs.de/pci approximate DFT Extensions and Combinations:: Extensions and Combinations O(N)-QM/MM TD-DFTB-LR QM/MM divide+conquer AMBER: Han, Suhai DKFZ CHARMM: Cui, Karplus; Harvard TINKER: Liu, Yang; Duke CEDAR: Hu, Hermans; NC Univ H. Liu W. Yang Duke Univ SCC-DFTB Solvent Cosmo: W. Yang GB: H. Liu DISPERSION P. Hobza, Prague Electron Transport A. Di Carlo TD-DFTB R. Allen Texas A&M SCC-DFTB:: SCC-DFTB available for H C N O S P Zn (Si, ...) all parameters calculated from DFT computational efficiency as NDO-type methods (solution of gen. eigenvalue problem for valence electrons in minimal basis) SCC-DFTB::Tests SCC-DFTB Tests 1) Small molecules: covalent bond reaction energies for organic molecules geometries of large set of molecules vibrational frequencies, 2) non-covalent interactions H bonding VdW 3) Large molecules (this makes a difference!) Peptides DNA bases SCC-DFTB::Tests SCC-DFTB Tests 4) Transition metal complexes 5) Properties IR, Raman, NMR excited states with TD-DFT Transport calculations SCC-DFTB: Reviews SCC-DFTB: Reviews 1) Application to biological molecules M. Elstner, et al. ,A self-consistent carge density-functional based tight-binding scheme for large biomolecules, phys. stat. sol. (b) 217 (2000) 357. Elstner, et al. An approximate DFT method for QM/MM simulations of biological structures and processes. J. Mol. Struc. (THEOCHEM), 632 (2003) 29. M. Elstner, The SCC-DFTB method and its application to biological systems, Theoretical Chemistry Accounts, in print 2006. 2) Focus on solids and nanostructures T. Frauenheim, et al., Atomistic Simulations of complex materials: ground and excited state properties, J. Phys. : Condens. Matter 14 (2002) 3015. Th. Frauenheim et al. A self-consistent carge density-functional based tightbinding method for predictive materials simulations in physics, chemistry and biology, phys. stat. sol. (b) 217 (2000) 41. G. Seifert, in: Encyclopedia of Computational Chemistry (Wiley&Sons 2004 ) SCC-DFTB Tests 1:: Elstner et al., PRB 58 (1998) 7260 SCC-DFTB Tests 1 Elstner et al., PRB 58 (1998) 7260 Performance for small organic molecules (mean absolut deviations) • Reaction energiesa): ~ 5 kcal/mole • Bond-lenghtsa) : ~ 0.014 A° • Bond anglesb): ~ 2° •Vib. Frequenciesc): ~6-7 % a) J. Andzelm and E. Wimmer, J. Chem. Phys. 96, 1280 1992. b) J. S. Dewar, E. Zoebisch, E. F. Healy, and J. J. P. Stewart, J. Am. Chem. Soc. 107, 3902 1985. c) J. A. Pople, et al., Int. J. Quantum Chem., Quantum Chem. Symp. 15, 269 1981. SCC-DFTB Tests 2::T..Krueger, et al., J. SCC-DFTB Tests 2 T Krueger, et al., J. Chem. Phys. 122 (2005) 114110. Chem. Phys. 122 (2005) 114110. With respect to G2: mean ave. dev.: 4.3 kcal/mole mean dev.: 1.5 kcal/mole SCC-DFTB Tests: SCC-DFTB Tests: Accuracy for vib. freq., problematic case e.g.: Special fit for vib. Frequencies: Mean av. Err.: 59 cm-1 33 cm-1 Malolepsza, Witek & Morokuma: CPL 412 (2005) 237. Witek & Morokuma, J Comp Chem. 25 (2004) 1858. for CH H-bonded systems: water H-bonded systems: water CCSD(T): 5.0 kcal/mole (Klopper et al PCCP 2000 2, 2227) BLYP: 4.2 kcal/mole PBE: 5.1 kcal/mole B3LYP: 4.6 kcal/mole HF: 3.7 kcal/mole (from Xu&Goddard, JCPA 2004) For larger systems: DFTB: 3.3 kcal/mole HF: 5.7 kcal/mole @ 6-31G* B3LYP: 6.8 kcal/mole @ 6-31G* ~2 kcal/mole BSSE (BSIE) H-bonds H-bonds Han et al. Int. J. Quant. Chem.,78 (2000) 459. Han et al. Int. J. Quant. Chem.,78 (2000) 459. Elstner et al. phys. stat. sol. (b) 217 (2000) 357. Elstner et al. phys. stat. sol. (b) 217 (2000) 357. Elstner et al. J. Chem. Phys. 114 (2001) 5149. Elstner et al. J. Chem. Phys. 114 (2001) 5149. Yang et al., to be published. Yang et al., to be published. -~1-2kcal/mole too weak - relative energies reasonable Coulomb interaction - structures well reproduced H2O-dimer complexes Cs, C2v NH3-NH3- and NH3-H2O-dimer Model peptides: N-Acetyl-(L-Ala)n N‘-Methylamide (AAMA) + 4 H2O Secondary-structure elements for Glycine und Secondary-structure elements for Glycine und Alanine-based polypeptides Alanine-based polypeptides Elstner, et al.. Chem. Phys. 256 (2000) 15 Elstner, et al.. Chem. Phys. 256 (2000) 15 N = 1 (6 stable conformers) 310 - helix αR-helix stabilization by internal H-bonds between i and i+3 between i and i+4 N DFTB very good for: main problem for DFT(B): dispersion! - relative energies AM1, PM3, MNDO quite bad - geometries OM2 much improved (JCC 22 (2001) 509) - vib. freq. o.k.! Glycine and Alanine based polypeptides in vacuo Glycine and Alanine based polypeptides in vacuo Elstner et al., Chem. Phys. 256 (2000) 15 Elstner et al., Chem. Phys. 256 (2000) 15 Elstner et al. Chem. Phys. 263 (2001) 203 Elstner et al. Chem. Phys. 263 (2001) 203 Bohr et al., Chem. Phys. 246 (1999) 13 Bohr et al., Chem. Phys. 246 (1999) 13 Relative energies, structures and vibrational properties: N=1-8 N=1 (6 stable conformers) ∆ relative energies (kcal/mole) E B3LYP (6-31G*) MP2 MP4-BSSE SCC-DFTB φ N ψ Ace-Ala-Nme C7eq C5ext C7ax β2 αR MP4-BSSE: Beachy et al, BSSE corrected at MP2 level αP Strength of SCC-DFTB Strength of SCC-DFTB Structure of large molecules - dynamics - relative energies DNA: A. V. Shiskin, et al., Int. J. Mol. Sci. 4 (2003) 537. O. V. Shishkin, et al., J. Mol. Struc. (THEOCHEM) 625 (2003) 295. Problems: Problems: same Problems as DFT additional Problems: - except for geometries, in general lower accuracy than DFT - slight overbinding (probably too low reaction barriers?!) - too weak Pauli repulsion - H-bonding (will be improved) - hypervalent species, e.g. HPO4 or sulfur compounds - transition metals: probably good geometries, ... ? - molecular polarizability (minimal basis method!) SCC-DFTB vs. NDDO (MNDO, AM1, PM3) SCC-DFTB vs. NDDO (MNDO, AM1, PM3) DFTB: energetics of ONCH ok, S, P problematic very good for structures of larger Molecules vibrational frequencies mostly sufficient (less accurate than DFT) NDDO: very good for energetics of ONCH (and others, even better than DFT) structures of larger Molecules often problematic !!! do NOT suffer from DFT problems e.g. excited states Mix of DFTB and NDDO to combine strengths of both worlds DFT Problems: DFT Problems: J- Ex = 0 !: Band gaps, barriers (2) Ex: wrong asymptotic form; - ε (1) Ex: Self interaction error. HOMO << Ip: virtual KS orbitals (3) Ex: ‚somehow too local‘; overpolarizability, CT excitations (4) Ec: ‚too local‘: Dispersion forces missing (5) Ec: even much more ‚too local‘: isomerization reactions (6) Multi-reference problem (1) –(3) of course related, cure: exact exchange! DFT Problems: ((very)selective publications DFT Problems: very) selective publications (1) Ex: PRB 23 (1981) 5048, JCP 109 (1998) 2604 (2) Ex: JCP 113 (2000) 8918, Mol. Phys. 97 (1999) 859. (3) Ex: JPCA 104 (2000) 4755, JCP 119 (2003) 2943. (4) Ec: JCP 114 (2001) 5149 (5) Ec: Angew. Chem. Int. Ed. 2006, 45, 4460 –4464 (6) Koch, Wolfram / Holthausen, Max C. A Chemist's Guide to Density Functional Theory, Wiley Problems of DFT-GGA Problems of DFT-GGA - overbinding of small molecules: CO... B3LYP, rev-PBE 10 kcal - transition metals: B3LYP, PB86 ..., spin states, energetics 10-20 kcal - vib. Freqencies: - conjugate systems: GGAs overpolarize PA‘s of respective proton donors 10 kcal - H-bonds: ok with DFT, HF (cancellation of errors), water structure? - proton transfer (PT) barriers: GGA< B3LYP < MP2< CCSD 2-4 kcal with B3LYP! Solution1: don‘t worry or don‘t care different functionals VERY different accuracy Solution2: use something else -VdW- problem (dispersion) complete failure ‚Solution‘: empirical dispersion for GGAs -excited states within TD-DFT: ionic, CT states, double excitations, Rydberg states Solution: exact exchange or CI-based methods ...
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