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

R OH = 0.9572Å.  HOH = 104.52º. 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. R OH = 0.9572.  HOH = 104.52

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

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  1. ROH = 0.9572Å HOH = 104.52º 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

  2. ROH = 0.9572 HOH = 104.52 = 1.86D ISIS Disordered Materials Group Neutron Database http://www.isis.rl.ac.uk/disordered/database/DBMain.htm

  3. ROH = 0.9572 HOH = 104.52 = 1.86D Umemoto, K.; Wentzcovich, R. M. Phys. Rev. B2004, 69, 180103.

  4. Uranus Neptune Triton Titan ROH = 0.9572 HOH = 104.52 = 1.86D Ganymede Callisto http://www.solarviews.com/eng/uranus.htm

  5. -1.04 ROH = 0.9572 Å 0.52 0.52 • HOH = 104.52° • = 2.18 D  = 0.6492 kJ/mol  = 3.153 Å 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.

  6. Quantum Mechanics Wave Function Theory: Density Functional Theory: Hohenberg, P.; Kohn, W. Phys. Rev.1964, 136, B864.

  7. Ice VIII (T=10K P=24GPa) 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. B2006, 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. A2006, 110, 640. Umemoto, K.; Wentzcovich, R. M. Phys. Rev. B2004, 69, 180103

  8. ‘Heaven’ Chemical Accuracy fully non-local hybrid meta GGA hybrid GGA Quantum Chemistry meta GGA GGA Materials Science LSDA ‘Earth’ Hartree Theory 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

  9. ‘Heaven’ Chemical Accuracy fully non-local High-level wave function theory hybrid meta GGA hybrid GGA meta GGA Density functional theory GGA LSDA ‘Earth’ Hartree Theory 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

  10. Literature clusters Liquid/vapor simulations Solid-phase simulations Coming up with a test set… Calculate Accurate Binding Energies Compare 25 DFT Methods to Accurate Energies

  11. light dimer medium trimer dark all hybrid meta GGA hybrid GGA meta GGA GGA LSDA All DFT calculations use the MG3S (6-311+G(2df,2p)) basis set. Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B2005, 109, 15677

  12. mPWLYP PBE PBELYP TPSSLYP mPWLYP1W PBE1W PBELYP1W TPSSLYP1W Optimize Y How should we parameterize our new method? The general form for a hybrid density functional method is: What if instead…

  13. light dimer medium trimer dark all hybrid meta GGA hybrid GGA meta GGA new methods GGA LSDA All DFT calculations use the MG3S (6-311+G(2df,2p)) basis set. Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B2005, 109, 15677

  14. ‘Heaven’ Chemical Accuracy fully non-local hybrid-meta GGA hybrid GGA meta GGA GGA LSDA ‘Earth’ Hartree Theory aMUEPM denotes mean unsigned error per molecule All DFT calculations use the MG3S (6-311+G(2df,2p)) basis set. Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B2005, 109, 15677

  15. Csonka, G. I.; Ruzsinsky, A.; Perdew, J. P. J. Phys. Chem. B, 2006, 109, 21475. Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B2005, 109, 15677 Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. BIn Press.

  16. light = AE6 dark = BH6

  17. ROH = 0.9572 HOH = 104.52 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. There’s no simple fix to this problem. Best geometry possible with this optimization procedure: R(O-H) = 0.9675 Å (H-O-H) = 104.5008

  18. 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.     

  19. Gas phase optimized Monte Carlo simulation of bulk water

  20. Gas phase optimized Monte Carlo simulation of bulk water MD simulation of ice VIII (g)

  21. 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.

  22. 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

  23. 2.74 2.01 1.18 0.31 0.14 0.07 New functional parameterized specifically for water PBE1W PBE BLYP B3LYP Most commonly used GGAs in simulation Most commonly used hybrid GGA in chemistry, recently used in water simulation Gas-phase versus simulation All structures Gas phase Simulation Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B in press

  24. 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

  25. Performance of density functionals for binding energies Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B in press

  26. Performance of density functionals for binding energies - large data set Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B in press

  27. 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

  28. Future Work Anderson, J. A.; Tchumper, G. S. J. Phys. Chem. A2006, published on the web 05/12/06

  29. Acknowledgments Don Truhlar Nate Schultz Yan Zhao Ilja Siepmann, Matt McGrath Renata Wentzcovitch, Koichiro Umemoto

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