Simulations of Biological Systems with DFTB and the Divide-and-Conquer Linear Scaling Method Weitao Yang, Duke University Funding NSF NSF-NIRT NIH DARPA SF ACS September 06 Theory Biological Nano Material

Jan Hermans (UNC) Carter (UNC) Nakatsuji (Kyoto) Fitzgerald, Rudolph (Duke) Whitman (TX-Austin) NIH 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 Zhengyu Lu

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

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.

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 1998;B28:7260–7268 High accuracy Transparent construction and appealing derivation

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 N 3 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.

The idea of divide and conquer

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

Some Recent Applications of DFTB+ the Divide-and-Conquer Method with Collaborators Energetics of the electron transfer from bacteriopheophytin to ubiquinone in the photosynthetic reaction center ofRhodopseu- domonas Viridis: Theoretical study. JPC B, 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)

The Complex Mechanical Properties of Single Amylose Chains in Water: A Quantum Mechanical and AFM Study Lu, Nowak, Lee, Marszalek, and Yang, JACS 2004

–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.

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)

Self-interaction free-exchange-correlation functional: The Mori-Cohen-Yang functional JCP, 124, , 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

Non-hydrogen transfer barriers (kcal/mol)

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

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)

–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, (1996) Warschkow, Dyke & Ellis, J. Comp. Phys., 143, 70 (1998) –Implementation for electrostatic problems Gallant and St-Amant, Chem. Phys. Lett. 256, 569 (1996). The Divide-and-Conquer Approach