Applications of SCC-DFTB method in important chemical systems

Hao HuDept. 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, 1998Frauenheim 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(H2O) 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

B1H + x(H2O) B1- + H+(H2O)x B1H B1

-G1

B2H + x(H2O) B2- + H+(H2O)x B2H B2

-

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

BH(vac) B-(vac)G1

G2 G3

G4 = G3 +G1 – G2 = Gsolv +G1

Hu & Yang, J. Chem. Phys. 123:041102, 2005Similar 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

BH(aq,SCC-DFTB) B-(aq,SCC-DFTB)G4

G6 G7

G8 = G7 +G4 – G6

Convergence of G6 and G7 can be verified from different samples of the simulations.

6 ln exp DFT SCC DFTB SCC DFTBG kT E E

Reference potential method, Warshel group

pKa simulation

Correlation between SCCDFTB and DFT energies

Methanol Methoxide

Slope=1.38 Slope=0.94

Sigma program interfaced with SCC-DFTB (2002), Gaussian03 (2005), and NWChem (2006)

pKa simulation

Correlation between SCCDFTB and DFT energies

Acetic acid Acetic ion

Slope=1.08 Slope=0.95

pKa simulation

Results

molecule pKaGexpr

(kcal/mol)

G4

(kcal/mol)

G8

(kcal/mol)

methanol 15.54 0.00 0.00 0.00

phenol 9.95 -7.67 -5.41 -7.22

Acetic acid 4.76 -14.79 -13.21 -16.68

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 Å3

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) 6 60 11 exp /OOV a r a r

= 982 g/cm3 Evap = 8.3 kcal/mol

Water simulation

Re-examining the water clusters

Water simulation

Re-examining the water clusters

http://www-wales.ch.cam.ac.uk/~wales/CCD/anant-watcl.htmlMaheshwary, S., Patel, N., Sathyamurthy, N., Kulkarni, A. D., & Gadre, S. R., J. Phys. Chem.-A 105, 10525-10537 (2001)

Water simulation

Re-examining the water clusters

Water simulation

Re-examining the water clusters

Water simulation

Re-examining the water clusters

6 14

HF geometry

SCC-DFTBannealing

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 McKelveyDr. Thomas FrauenheimDr. 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.