Applications of SCC-DFTB method in important chemical systems Hao Hu Dept. Chemistry Duke University

Outline Calculate relative pKa for small organic molecules Simulate liquid water with Divide-and-Conquer method Accurate: bridging low-accuracy MM fields with high-level ab initio QM methods Fast: allowing simulations of large-size molecule systems Elstner, M. et al., Phys. Rev. B. 58:7260, 1998 Frauenheim Th. et al., Phys. Stat. Sol. B 217:357, 2000

pKa simulation Acid dissociation process: BH  B - + H + Important chemical and biological significance protein-ligand, protein-protein interactions Protein/DNA conformational changes Enzyme catalysis Extensive theoretical studies based on MM force fields Continuum solvation model Explicit free energy simulation Toward high-accuracy QM/MM simulations Continuum model (Jensen group) Explicit free energy simulation (Cui group)

pKa simulation Not such a simple problem! Participation of water: BH + x (H 2 O)  B - + H + (H2O) x Unless the precise chemical composition of the hydrated proton is known, no theoretical simulation of this process is accurate.

pKa simulation Simulate relative pKa? Contribution of water is constant Contribution of proton solvation is constant Contribution of zero-point energy is constant B 1 H + x (H 2 O)  B H + (H2O) x B1HB1HB1-B1- G1G1 B 2 H + x (H 2 O)  B H + (H2O) x B2HB2HB2-B2- G2G2  G=?

pKa simulation: A two-step approach 1. Dual-topology/dual-coordinate QM/MM free energy simulation with SCC-DFTB method BH (aq) B - (aq) G4G4 BH (vac) B - (vac) G1G1 G2G2 G3G3  G 4 =  G 3 +  G 1 –  G 2 =  G solv +  G 1 Hu & Yang, J. Chem. Phys. 123:041102, 2005 Similar work by Cui group

pKa simulation: A two-step approach 2. Recover ab initio free energetics from SCC-DFTB simulations BH (aq, DFT) B - (aq, DFT) G8G8 BH (aq,SCC-DFTB) B - (aq,SCC-DFTB) G4G4 G6G6 G7G7  G 8 =  G 7 +  G 4 –  G 6 Convergence of  G 6 and  G 7 can be verified from different samples of the simulations. Reference potential method, Warshel group

pKa simulation Correlation between SCCDFTB and DFT energies MethanolMethoxide Slope=1.38Slope=0.94 Sigma program interfaced with SCC-DFTB (2002), Gaussian03 (2005), and NWChem (2006)

pKa simulation Correlation between SCCDFTB and DFT energies Acetic acidAcetic ion Slope=1.08Slope=0.95

pKa simulation Results moleculepKa  G expr (kcal/mol)  G 4 (kcal/mol)  G 8 (kcal/mol) methanol phenol Acetic acid

pKa simulation Conclusions 1.SCC-DFTB can be applied to long time QM/MM free energy simulations to ensure the convergence of the sampling. 2.High level ab initio QM methods can be successfully applied to improve the accuracy. 3.The solute-water interaction may need further improvements: can we also simulate bulk water with SCC-DFTB method?

Simulating liquid water with the Divide-and-Conquer method

Water simulation Divide-and-Conquer method: A linear-scaling approach Each subsystem contains a central part (solid color) which is a non-overlapping portion of the whole system, plus a buffer region (light color) corresponding to other parts of the system that are within a certain distance of the central part. Methods:Yang, W. Phys. Rev. Lett. 66:1438, 1991 Application to a protein molecule: Liu, H. et al. Proteins 44:484, 2001

Water simulation System setup 360 water molecules in a cubic box of 22.1  22.1  22.1 Å 3 Temperature 298 K Cutoff distance 8 Å Integration step size 1 femtosecond Constant-pressure Some tricks Original SCC-DFTB gives too low density Modified gamma function gives too high density

Water simulation O-O radial distribution function (RDF)  = 982 g/cm 3 E vap = 8.3 kcal/mol

Water simulation Re-examining the water clusters

Water simulation Re-examining the water clusters Maheshwary, S., Patel, N., Sathyamurthy, N., Kulkarni, A. D., & Gadre, S. R., J. Phys. Chem.-A 105, (2001)

Water simulation Re-examining the water clusters

Water simulation Re-examining the water clusters

Water simulation Re-examining the water clusters 614 HF geometry SCC-DFTB annealing

Water simulation O-O radial distribution function (RDF) Too many first-shell neighbors

Conclusions 1.SCC-DFTB can be effectively used as a bridge between expensive, high-accuracy QM methods and low-accuracy MM force fields. SCC-DFTB can to a large extent reproduce the covalent geometries of many organic/biological molecules 2.SCC-DFTB can qualitatively describe the interactions and structure of a liquid water system. However, improvements have to be made to better model the complicated electrostatic interactions in water, including the polarization and short-range dispersion/repulsion interactions

Acknowledgements The organizers of this special symposium: Dr. John McKelvey Dr. Thomas Frauenheim Dr. Marcus Elstner Dr. Weitao Yang Dr. Jan Hermans Dr. Haiyan Liu Dr. Zhenyu Lu Mr. Ruhuai Yun

If you like your graduate student, send him/her to study water; If you hate your graduate student, send him/her to study water.