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(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
DG1
B1-
DDG=?
B2H + x(H2O)  B2- + H+(H2O)x
B2H
DG2
B2-
pKa simulation: A two-step approach
1. Dual-topology/dual-coordinate QM/MM free energy
simulation with SCC-DFTB method
BH(vac)
DG1
DG2
BH(aq)
B-(vac)
DG3
DG4
B-(aq)
DG4 = DG3 +DG1 – DG2 = DDGsolv +DG1
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,SCC-DFTB)
DG4
DG6
BH(aq, DFT)
B-(aq,SCC-DFTB)
DG7
DG8
B-(aq, DFT)
DG8 = DG7 +DG4 – DG6
DG6  kT ln exp    EDFT  ESCC  DFTB 
SCC  DFTB
Convergence of DG6 and DG7 can be verified from different
samples of the simulations.
Reference potential method, Warshel group
pKa simulation
Correlation between SCCDFTB and DFT energies
Slope=1.38
Methanol
Slope=0.94
Methoxide
Sigma program interfaced with SCC-DFTB (2002), Gaussian03 (2005),
and NWChem (2006)
pKa simulation
Correlation between SCCDFTB and DFT energies
Slope=1.08
Acetic acid
Slope=0.95
Acetic ion
pKa simulation
Results
DDGexpr
DDG4
DDG8
(kcal/mol) (kcal/mol) (kcal/mol)
molecule
pKa
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)
r = 982 g/cm3
VOO  1  exp  a0 r 6  a1 / r 6
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.html
Maheshwary, 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
HF geometry
SCC-DFTB
annealing
6
14
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.