Simulations%20of%20Biological%20Systems%20with%20DFTB%20and%20the%20Divide-and-Conquer%20Linear%20Scaling%20Method%20Weitao%20Yang,%20Duke%20University

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Simulations of Biological Systems with DFTB and
the Divide-and-Conquer Linear Scaling
MethodWeitao Yang, Duke University
Theory Biological Nano Material
Funding NSF NSF-NIRT NIH DARPA SF ACS September
06
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Studies of Biological Systems Y. Zhang,
H.Liu, Z. Lu, A. Cisneros, T. Hori, A. Boone,
J.Parks, H. Hu, S. Burger, M. Wang
Taisung Lee (Minnesota) Darrin York
(Minnesota) Haiyan Liu (USTC) Marcus
Elstner Thomas Frauenheim
Hao Hu
Jan Hermans (UNC) Carter (UNC) Nakatsuji
(Kyoto) Fitzgerald, Rudolph (Duke) Whitman
(TX-Austin)
NIH
Zhengyu Lu
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Outline

• The need of QM for large biological systems
• The SCC-DFTB approach
• The Linear-Scaling Divide-and-Conquer Approach
• Applications
• Challenges

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Motivations

• Biological systems and processes are complex and
  require statistical mechanics for the sampling
  and accurate description of interaction energies.
• Molecular mechanics (force field) model the
  interaction energies empirically, and can be
  limited in applicability.
• Quantum mechanics (electronic structure theory)
  describe potential energy surfaces at different
  levels of approximation, and can reach chemical
  accuracy.

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SCC-DFTB

• Elstner M, Porezag D, Jungnickel G, Elstner J,
  Haugk M, Frauenheim T, Suhai S, Seifert G.
  Self-consistent-charge density functional
  tight-binding method for simulations of complex
  materials properties. Phys Rev 1998B2872607268
• High accuracy
• Transparent construction and appealing derivation

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O(N) Approach to Large System Simulations

• Linear Scaling Quantum Mechanical Method
  Divide-and-Conquer Method, Yang, PRL (1991)
• Before our work, quantum chemistry calculations
  scaled at least as N3
• Our divide-and conquer approach is the first
  linear scaling, O(N) approach. It opened the
  field. Many labs have since joined and extended
  the effort.
• Divide the system into subsystems and calculate
  each subsystem separately.
• Computational effort ? the size of molecule.

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The idea of divide and conquer
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Recent applications of the Divide-and-Conquer
method by other laboratories

• Calculations of micrometer-long carbon nanotubes
  field emission mechanism, GuanHua Chen, Ningsheng
  Xu, et al. Phys. Rev. Lett, 2004 (8000 C atoms)
• Structure, dynamics and quantum properties of
  65,536-atom CdSe nanoparticles, Shimojo, KaliaK,
  Nakano, Vashishta, Computer Physics
  Communication, 2005

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Some Recent Applications of DFTB the
Divide-and-Conquer Method withCollaborators

• Energetics of the electron transfer from
  bacteriopheophytin to ubiquinone in the
  photosynthetic reaction center ofRhodopseu-domonas
  Viridis Theoretical study. JPC B, 2003.
• 400 ps Dynamics simulation of Crambin in water
  with QM forces, Proteins, 2003
• The Complex Mechanical Properties of Single
  Amylose Chains in Water A Quantum Mechanical
  and AFM Study, JACS 2004
• Simulation of bulk water structure with
  SCC-DFTB-QM forces, 2006 (Talk to be given by Dr.
  Hao Hu)

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The Complex Mechanical Properties of Single
Amylose Chains in Water A Quantum Mechanical
and AFM Study
Lu, Nowak, Lee, Marszalek, and Yang, JACS 2004
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• Our simulations reproduce the characteristic
  plateau of amylose in the force-extension curve
  of amylose
• Unravel the mechanism of the extensibility of a
  polysaccharide amylose in water, which displays
  particularly large deviations from the simple
  entropic elasticity
• We find that this deviation coincides with
  force-induced chair-to-boat transitions of the
  glucopyranose rings.

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Challenges to SCC-DFTB from recent developments
in DFT

• The SCC-DFTB is based on GGA
• The importance of self-interaction error in
  approximate DFT
• The new generation of functionals uses KS
  orbitals explicitly (Orbital functionals)

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Self-interaction free-exchange-correlation
functional The Mori-Cohen-Yang functionalJCP,
124, 091102, 2006

• A self-interaction-free exchange-correlation
  functional which is very accurate for
  thermochemistry and kinetics
• Based on the orbital/potential functional
  approach and the adiabatic connection.
• Combine ab initio construction of the functional
  forms through adiabatic connection
• Use the exact exchange, generalized gradient
  appromation (GGA) and meta-GGA functionals

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Non-hydrogen transfer barriers (kcal/mol)
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Summary of the MCY functionals

• SIE free theoretical construction 2 parameters
  fitted to heats of formation
• Computationally efficient, as B3LYP (including
  the exact exchange)
• Better thermodynamics than all the other common
  functionals
• Much Improved Reaction Barriers
• MAE 1.85 kcal/mol for H transfer
• MAE 1.88 kcal/mol for non H transfer
• IP, EA, Molecular Structure improvement over
  B3LYP
• Week interactions similar or slightly worse than
  B3LYP

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The idea of divide and conquer
Key to linear scaling the use of the localized
electronic degrees of freedom --Yang and
Perez-Jorda, in Encyclopedia of Computational
Chemistry, edited by Schleyer, John Wiley Sons
(1998). --Lewis, Carter, Jr., Hermans, Pan, Lee
and Yang, Cytidine Deaminase, JACS (1998).
--Liu, Elstner, Kaxiras,Frauenheim, Hermans and
Yang, Protein Dynamics, PROTEINS, (2001). Lu, et.
al., Mechanics of nano systems, JACS (2004)
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The Divide-and-Conquer Approach

• The first linear scaling method for electronic
  structure calculations
• Yang, Phys. Rev. Lett., 66, 1438 (1991),
• Lee and Yang, J. Chem. Phys., 163, 5674 (1995).
• Implementation for semi-empirical QM approaches
• Lee, York and Yang, J. Chem. Phys. 105, 2744
  (1996)
• Dixon and Merz, J. Chem. Phys. 104, 6643 (1996).
• Implementation for solids and surfaces
• Zhu, Pan and Yang, Phys. Rev. B., 53, 12713
  (1996)
• Warschkow, Dyke Ellis, J. Comp. Phys., 143, 70
  (1998)
• Implementation for electrostatic problems
• Gallant and St-Amant, Chem. Phys. Lett. 256, 569
  (1996).