Computational Challenges in the Simulation of Water & Ice: the Motivation for an Improved Description of Water-Water Interactions R OH = Å  HOH = º Erin E. Dahlke Department of Chemistry University of Minnesota VLab Tutorial May 25, 2006

R OH =  HOH =  = 1.86D ISIS Disordered Materials Group Neutron Database

R OH =  HOH =  = 1.86D Umemoto, K.; Wentzcovich, R. M. Phys. Rev. B 2004, 69,

R OH =  HOH =  = 1.86D UranusNeptune Triton Titan GanymedeCallisto

 HOH = °  = 2.18 D  = kJ/mol  = Å R OH = Å TIP4P Jorgensen, W. L.; Chandrasekhar, J.; Madura, J., D.; Impey, R. W.; Klein, M. L. J. Chem. Phys.1983, 79, 926. Analytic potentials for water are generally parameterized to get a specific physical property right (i.e., vapor pressure, density, structural properties) + Fast + Accurate* - Non-transferable Variations of TIP4P 1.TIP4P-FQ 2.TIP4P-POL2 3.TIP4P-EW 4.TIP4P-ice 5.TIP4P-m

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

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, 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, a (Å) c (Å) O-H (Å) O … H (Å) O-O (Å) O … O (Å) V (Å 3 ) Calc Expt Ice VIII (T=10K P=24GPa)

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

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

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

LSDA GGA meta GGA hybrid GGA hybrid meta GGA lightdimer mediumtrimer darkall Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B 2005, 109, All DFT calculations use the MG3S (6-311+G(2df,2p)) basis set.

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

LSDA GGA meta GGA hybrid GGA hybrid meta GGA new methods lightdimer mediumtrimer darkall Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B 2005, 109, All DFT calculations use the MG3S (6-311+G(2df,2p)) basis set.

Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B 2005, 109, All DFT calculations use the MG3S (6-311+G(2df,2p)) basis set. LSDA GGA meta GGA hybrid-meta GGA hybrid GGA fully non-local ‘Earth’ Hartree Theory ‘Heaven’ Chemical Accuracy a MUEPM denotes mean unsigned error per molecule

Csonka, G. I.; Ruzsinsky, A.; Perdew, J. P. J. Phys. Chem. B, 2006, 109, Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B 2005, 109, Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B In Press.

MUEPM(kcal/mol) DimersTrimersAll PBE BLYP

light = AE6 dark = BH6

Is getting the energies right enough?? What about other things like geometries or polarizabilities? R OH =  HOH = 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) = Å  (H-O-H) =

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.    

Gas phase optimized Monte Carlo simulation of bulk water

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

What do we hope to learn? 1.Relative magnitudes of many-body terms in small clusters. 2.Differences in many-body terms between gas-phase structures and those taken from simulation. 3.Performance of common density functionals in the prediction of many-body effects. 4.Performance of density functionals is the prediction of binding energies for larger water clusters.

Average absolute magnitude Max value Minimum value Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B in press Relative magnitudes of many-body terms

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

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 Performance of density functionals for many-body terms

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

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

C onclusions 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. F uture W ork Use PBE1W in the simulation of liquid water. Examine the use of PBE1W for structural properties and larger water clusters

Anderson, J. A.; Tchumper, G. S. J. Phys. Chem. A 2006, published on the web 05/12/06 F uture W ork

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