Computational Challenges in the Simulation of Water

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Computational Challenges in the Simulation of
Water Ice the Motivation for an Improved
Description of Water-Water Interactions

• Erin E. Dahlke
• Department of Chemistry
• University of Minnesota
• VLab Tutorial
• May 25, 2006

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ISIS Disordered Materials Group Neutron Database
http//www.isis.rl.ac.uk/disordered/database/DBMai
n.htm
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Umemoto, K. Wentzcovich, R. M. Phys. Rev. B
2004, 69, 180103.
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http//www.solarviews.com/eng/uranus.htm
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Analytic potentials for water are generally
parameterized to get a specific physical property
right (i.e., vapor pressure, density, structural
properties)
TIP4P

• Variations of TIP4P
• TIP4P-FQ
• TIP4P-POL2
• TIP4P-EW
• TIP4P-ice
• TIP4P-m

Fast Accurate - Non-transferable
Jorgensen, W. L. Chandrasekhar, J. Madura, J.,
D. Impey, R. W. Klein, M. L. J. Chem.
Phys.1983, 79, 926.
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Quantum Mechanics
Wave Function Theory
Density Functional Theory
Hohenberg, P. Kohn, W. Phys. Rev. 1964, 136,
B864.
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Ice VIII (T10K P24GPa)
a (Å) c (Å) O-H (Å) OH (Å) O-O (Å) OO (Å) V (Å3)
Calc 4.727 6.817 0.986 1.929 2.914 2.77 76.16
Expt 4.656 6.775 0.968 1.911 2.879 2.743 73.43
Kuo, I.F. W. Mundy, C. J. Eggimann, B. L.
McGrath, M. J. Siepmann, J. I. Chen, B.
Vieceli, J. Tobias, D. J. J. Phys. Chem. B 2006,
110, 3738. McGrath, M. J. Siepmann, J. I. Kuo,
I.F. W. Mundy, C. J. VandeVondele, J. Hutter,
J. Mohamed, F. Krack, M. J. Phys. Chem. A 2006,
110, 640. Umemoto, K. Wentzcovich, R. M. Phys.
Rev. B 2004, 69, 180103
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Perdew, J. P. Schmidt, K. Density Functional
Theory and Its Application to Materials,
Doren,V., Alsenoy, C. V., Geerlings, P. Eds.
American Institute of Physics New York 2001
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Perdew, J. P. Schmidt, K. Density Functional
Theory and Its Application to Materials,
Doren,V., Alsenoy, C. V., Geerlings, P. Eds.
American Institute of Physics New York 2001
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Coming up with a test set
Calculate Accurate Binding Energies
Compare 25 DFT Methods to Accurate Energies
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light dimer medium trimer dark all
hybrid meta GGA
hybrid GGA
meta GGA
GGA
LSDA
All DFT calculations use the MG3S
(6-311G(2df,2p)) basis set.
Dahlke, E. E. Truhlar, D. G. J. Phys. Chem. B
2005, 109, 15677
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How should we parameterize our new method? The
general form for a hybrid density functional
method is
What if instead
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light dimer medium trimer dark all
hybrid meta GGA
hybrid GGA
meta GGA
new methods
GGA
LSDA
All DFT calculations use the MG3S
(6-311G(2df,2p)) basis set.
Dahlke, E. E. Truhlar, D. G. J. Phys. Chem. B
2005, 109, 15677
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aMUEPM denotes mean unsigned error per molecule
All DFT calculations use the MG3S
(6-311G(2df,2p)) basis set.
Dahlke, E. E. Truhlar, D. G. J. Phys. Chem. B
2005, 109, 15677
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Csonka, G. I. Ruzsinsky, A. Perdew, J. P. J.
Phys. Chem. B, 2006, 109, 21475. Dahlke, E. E.
Truhlar, D. G. J. Phys. Chem. B 2005, 109,
15677 Dahlke, E. E. Truhlar, D. G. J. Phys.
Chem. B In Press.
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MUEPM(kcal/mol) MUEPM(kcal/mol) MUEPM(kcal/mol)
Dimers Trimers All
PBE 0.22 0.27 0.23
BLYP 0.41 0.59 0.45
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light AE6 dark BH6
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Is getting the energies right enough?? What
about other things like geometries or
polarizabilities?
Fitting of the functional to get the best bond
length possible gives really bad energies for the
clusters. Theres no simple fix to this problem.
Best geometry possible with this optimization
procedure R(O-H) 0.9675 Å ?(H-O-H) 104.5008
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One way to get a feeling for whether a method is
getting the polarizability right is to look at
the many-body effects in the structure.
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Gas phase optimized
Monte Carlo simulation of bulk water
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Gas phase optimized
Monte Carlo simulation of bulk water
MD simulation of ice VIII
(g)
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• What do we hope to learn?
• Relative magnitudes of many-body terms in small
  clusters.
• Differences in many-body terms between gas-phase
  structures and those taken from simulation.
• Performance of common density functionals in the
  prediction of many-body effects.
• Performance of density functionals is the
  prediction of binding energies for larger water
  clusters.

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Relative magnitudes of many-body terms
5.86
Average absolute magnitude Max value Minimum value
2.01
0.53
0.14
-0.24
0.01
-0.46
Dahlke, E. E. Truhlar, D. G. J. Phys. Chem. B in
press
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Gas-phase versus simulation
All structures Gas phase Simulation
Dahlke, E. E. Truhlar, D. G. J. Phys. Chem. B in
press
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Performance of density functionals for many-body
terms
V2 (13.46) V3 (2.01) V4 V5 (0.12) All (6.13)
Dahlke, E. E. Truhlar, D. G. J. Phys. Chem. B in
press
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Performance of density functionals for binding
energies
Dahlke, E. E. Truhlar, D. G. J. Phys. Chem. B in
press
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Performance of density functionals for binding
energies - large data set
Dahlke, E. E. Truhlar, D. G. J. Phys. Chem. B in
press
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Conclusions

• Different density functional methods give vastly
  different results for different functionals.
• PBE1W shows improved performance over other GGA
  methods for small water clusters-and is
  competitive with hybrid and hybrid-meta methods.
• Selection of basis set is crucial to
  performance.
• All GGAs have shortcomings at predicting
  many-body effects.

Future Work

• Use PBE1W in the simulation of liquid water.
• Examine the use of PBE1W for structural
  properties and larger water clusters

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Future Work
Anderson, J. A. Tchumper, G. S. J. Phys. Chem. A
2006, published on the web 05/12/06
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Acknowledgments
Don Truhlar Nate Schultz Yan Zhao
Ilja Siepmann, Matt McGrath Renata
Wentzcovitch, Koichiro Umemoto