1. Calculating water’s anomalous properties from first principles: Mechanisms of ion transport in the bulk and at interfaces Mark E. Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Sciences New York University, 100 Washington Sq. East New York, NY 10003 Image: news.softpedia.com

2. 1808: “We are perhaps not far removed from the time when we shall be able to submit the bulk of chemical phenomena to calculation.” Joseph Louis Gay-Lussac (1778-1850)

3. “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact solution of these laws leads to equations much to complicated to be soluble.” Paul Dirac on Quantum Mechanics (1929). BG/L@RPI

4. Why study water? Most important liquid on Earth One of the most mysterious substances known “Science Journal: The structure of water isn’t certain after all” -- from the Wall Street Journal March 10, 2006 BiologyAtmospheric Chemistry Image source: www.cbs.cnrs.fr Energy Technology From Petersen and Voth, JPCB 110 (2006) Wernet, et al. Science (2004)

5. Some of water’s anomalous properties Density maximum at 4 o C Many stable crystalline phases High surface tension Anomalously high transport of protons (H+) and hydroxide (OH-) ions

6. PEM vs. AAEM fuel cells (AAEM=Alkali-anion exchange membrane) From Varcoe and Slade, Fuel Cells 5, 198 (2005)

7. 1806:

8. Structures of the excess proton in water H9O4+H9O4+ H5O2+H5O2+ H3O+H3O+

9. +++ Grotthuss Mechanism (1806) Vehicle Mechanism

11. Chemistry in the “Virtual Laboratory” On the “shelf”: Nuclei of the chemical elements Unlimited supply of electrons Instrumentation: Fundamental laws of physics: Nuclei: Newton’s second law Electrons: Schrödinger equation

12. Nuclei Electrons Start with nucleiCompute Propagate nuclei a short time Δt with F Add electrons The Algorithm

13. Nuclei Electrons Ab initio molecular dynamics (AIMD) Kohn-Sham density functional theory: Nuclear evolution

15. Feynman path integrals............. 1 2 3 P-1 P MET, et al. JCP 99, 2796 (1993); Marx and Parrinello, JCP 104, 4077 (1996); MET, et al. JCP 104, 5579 (1996) Feynman path integrals Near perfect parallel scaling with increasing P

16. Basis Sets Plane-waves (momentum eigenfunctions): Discrete-variable representations [Light, et al. JCP 82, 1400 (1982)]: Begin with a set of N square-integrable orthonormal functions φ i (x) On an appropriately chosen quadrature grid {x 1,…,x N } (position eigenfunctions!). Expand orbitals as: Y. Liu, D. Yarne and MET, PRB 68, 125110 (2003); H. –S. Lee and MET, JPCA 110, 5549 (2006) Basis set size determined by # grid points. Core electrons replaced by atomic pseudopotentials

17. Radial distribution functions for BLYP Water DVR Neutron X-ray H. –S. Lee and MET, JPCA 110, 549 (2006) H. –S. Lee and MET JCP 125, 154507 (2006). H. –S. Lee and MET JCP 126, 164501 (2007). Neutron: Soper, et. al. JCP 106, 247 (1997) X-ray: Hura, et. al. Chem. Phys. 113, 9140 (2000) Grid = 75 3, t =60 ps Ensemble: NVT, 300 K, μ = 500 au r(Å) When basis sets are too small! from C. J. Mundy (2008)

20. The Grotthuss mechanism in water MET, et al,JPC, 99, 5749 (1995); JCP 103, 150 (1995) D. Marx, MET, J. Hutter, M. Parrinello, Nature 397, 601 (1999). N. Agmon, Chem. Phys. Lett. 244, 456 (1995) T. J. F. Day, et al. J. Am. Chem. Soc. 122, 12027 (2000) Solvent coordinate view: P. M. Kiefer, J. T. Hynes J. Phys. Chem. A 108, 11793 (2004)

21. The Grotthuss mechanism in water Second solvation shell H-bond breaking followed by formation of intermediate Zundel complex: P Presolvation Concept: Proton-receiving species must be “pre-solvated” like the species into which it will be transformed in the proton-transfer reaction. MET, et al,Nature 417, 925 (2002)

22. The Grotthuss mechanism in water Computed transfer time τ = 1.5 ps NMR: 1.3 ps Transfer of proton resulting in “diffusion’’ of solvation structure: A. Chandra, MET, D. Marx Phys. Rev. Lett. 99, 145901 (2007)

23. Quantum delocalization of structural defect D. Marx, MET, J. Hutter and M. Parrinello Nature 397, 601 (1999)

24. Ultrafast pump-probe experiments Woutersen and Bakker, Phys. Rev. Lett. 96, 138305 (2006) Eigen/Zundel exchange time ≈ 100 fs

25. A Chemical Master Equation Theory of PT kinetics O* A. Chandra, MET, D. Marx Phys. Rev. Lett. 99, 145901 (2007) Population correlation functions: Rate equations:

26. Chemical Master Equation Theory Exchange time: O*O* H H HOO*O* H H H O t = 0t

27. Liquid/vapor interface of acidic solutions “acceptor only” hydrogen bonded dangling Mucha, et al. JPCB 109, 7617 (2005)Baldelli, et al. CPL 302, 157 (1999) Tian, et al. JACS 130, 13033 (2008)

28. Simulations of an HCl interface (96 waters + 1 HCl) Petersen, et al. JPCB 108, 14804 (2004) H. S. Lee and MET JPCA (submitted)

29. “Proton hole” or mirror image mechanism of hydroxide mobility H. Daneel, Z. Elektrochem. 16, 249 (1905) E. Hückel, Z. Elektrochem. 34, 546 (1928) N. Agmon, Chem. Phys. Lett. 319, 247 (2000); Asthagiri, et al. PNAS (2004) M. L. Huggins, J. Phys. Chem. 40, 723 (1936). OH - H+

30. Spectra of 14 M KOH IR Raman Librovich and Maiorov, Russian J. Phys. Chem. 56, 624 (1982)

31. Identified in neutron scattering of concentrated NaOH and KOH solutions: A. K. Soper and coworkers, JCP 120, 10154 (2004); JCP122, 194509 (2005). Also in other CPMD studies: B. Chen, et al. JPCB 106, 8009 (2002); JACS 124, 8534 (2002). And in X-ray absorption spectroscopy: C. D. Cappa, et al. J. Phys. Chem. A 111, 4776 (2007)

32. Weak H-bond donated by hydroxide also identified in neutron scattering of concentrated NaOH and KOH solutions: A. K. Soper and coworkers, JCP 120, 10154 (2004); JCP122, 194509 (2005). M. Smiechowski and J. Stangret, JPCA 111, 2889 (2007). T. Megyes, et al. JCP 128, 044501 (2008). B. Winter, et al. Nature (2008)

34. Hydronium :

35. Water:

36. Hydroxide:

37. MET, et al. Nature, 417 (2002) Follows “presolvation” picture: Proton-receiving species must be coordinated like the species into which it will be transformed before the proton can transfer.

38. Comparing IR spectra Expt.: Bertie, et al. J. Phys. Chem. 93, 2210 (1989) ( ν >700 cm -1 ) Zelsmann, J. Mol. Spect. 350, 95 (1995). ( ν < 600 cm -1 ) Z. Zhu and MET, J. Phys. Chem. B 106, 8009 (2002) Expt.: Librovich and Maiorov, Russian J. Phys. Chem. 56, 624 (1982) Pure water KOH solution O D* D D’D’ O* Expt (KOH): Librovich and Maiorov, Russian J. Phys. Chem. 56, 624 (1982)

39. Acknowledgments NSF Alexander von Humboldt Foundation Camille and Henry Dreyfus Foundation ACS PRF Postdocs Yi Liu (Merrill-Lynch) Hee-Seung Lee (UNC, Wilmington) Dawn A. Yarne (Goldman-Sachs) Radu Iftimie (U. de Montréal) Anatole von Lilienfeld (Sandia) Robin L. Hayes Funding Students Yi Liu (Merrill-Lynch) Tim Berkelbach Zhongwei Zhu (Goldman-Sachs) Joseph A. Morrone (Princeton) Lula Rosso (Imperial College, London) Peter Minary (Stanford University) Rachel Chasin David Krisiloff External Dominik Marx (Ruhr-Universität Bochum) Amalendu Chandra (IIT Kampur) Alan Soper (Rutherford Appleton Lab) Teresa Head-Gordon (UCB, LBL) Feng Wang (BU) Chris Mundy (PNNL) Doug Tobias (UCI)