Applications of SCC-DFTB method in important chemical systems

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Applications of SCC-DFTB method in important
chemical systems

• Hao Hu
• Dept. Chemistry
• Duke University

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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. 587260,
1998 Frauenheim Th. et al., Phys. Stat. Sol. B
217357, 2000
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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)

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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.
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pKa simulation

• Simulate relative pKa?
• Contribution of water is constant
• Contribution of proton solvation is constant
• Contribution of zero-point energy is constant

DG1
B1H x(H2O) ? B1- H(H2O)x
B1H
B1-
DDG?
B2H x(H2O) ? B2- H(H2O)x
B2H
B2-
DG2
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pKa simulation A two-step approach
1. Dual-topology/dual-coordinate QM/MM free
energy simulation with SCC-DFTB method
DG4 DG3 DG1 DG2 DDGsolv DG1
Hu Yang, J. Chem. Phys. 123041102,
2005 Similar work by Cui group
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pKa simulation A two-step approach
2. Recover ab initio free energetics from
SCC-DFTB simulations
DG8 DG7 DG4 DG6
Reference potential method, Warshel group
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pKa simulation
Correlation between SCCDFTB and DFT energies
Slope1.38
Slope0.94
Methanol
Methoxide
Sigma program interfaced with SCC-DFTB (2002),
Gaussian03 (2005), and NWChem (2006)
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pKa simulation
Correlation between SCCDFTB and DFT energies
Slope1.08
Slope0.95
Acetic acid
Acetic ion
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pKa simulation
Results
molecule pKa DDGexpr (kcal/mol) DDG4 (kcal/mol) DDG8 (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
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pKa simulation

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

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Simulating liquid water with the
Divide-and-Conquer method
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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.
MethodsYang, W. Phys. Rev. Lett. 661438,
1991 Application to a protein molecule Liu, H.
et al. Proteins 44484, 2001
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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
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Water simulation
O-O radial distribution function (RDF)
r 982 g/cm3 Evap 8.3 kcal/mol
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Water simulation
Re-examining the water clusters
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Water simulation
Re-examining the water clusters
http//www-wales.ch.cam.ac.uk/wales/CCD/anant-wat
cl.html Maheshwary, S., Patel, N., Sathyamurthy,
N., Kulkarni, A. D., Gadre, S. R., J. Phys.
Chem.-A 105, 10525-10537 (2001)
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Water simulation
Re-examining the water clusters
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Water simulation
Re-examining the water clusters
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Water simulation
Re-examining the water clusters
HF geometry
SCC-DFTB annealing
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Water simulation
O-O radial distribution function (RDF)
Too many first-shell neighbors
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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

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