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Mark E. Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Sciences

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.

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Mark E. Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Sciences

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  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 Wernet, et al. Science (2004) Biology Atmospheric Chemistry Energy Technology Image source: www.cbs.cnrs.fr From Petersen and Voth, JPCB110 (2006)

  5. Some of water’s anomalous properties Density maximum at 4oC 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 Cells5, 198 (2005)

  7. 1806:

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

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

  10. 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

  11. The Algorithm Electrons Nuclei Start with nuclei Add electrons Compute Propagate nuclei a short time Δtwith F Add electrons

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

  13. Feynman path integrals Feynman path integrals . MET, et al. JCP99, 2796 (1993); Marx and Parrinello, JCP104, 4077 (1996); MET, et al. JCP104, 5579 (1996) . . . . . . . P-1 1 P . . . . . 2 3 Near perfect parallel scaling with increasing P

  14. Basis Sets Y. Liu, D. Yarne and MET, PRB68, 125110 (2003); H. –S. Lee and MET, JPCA110, 5549 (2006) Plane-waves (momentum eigenfunctions): Discrete-variable representations [Light, et al. JCP82, 1400 (1982)]: Begin with a set of N square-integrable orthonormal functions φi(x) On an appropriately chosen quadrature grid {x1,…,xN} (position eigenfunctions!). Expand orbitals as: Basis set size determined by # grid points. Core electrons replaced by atomic pseudopotentials

  15. Radial distribution functions for BLYP Water DVR Grid = 753,t =60 ps Ensemble: NVT, 300 K, μ= 500 au Neutron X-ray r(Å) 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. JCP106, 247 (1997) X-ray: Hura, et. al. Chem. Phys. 113, 9140 (2000) When basis sets are too small! from C. J. Mundy (2008)

  16. The Grotthuss mechanism in water MET, et al,JPC, 99, 5749 (1995); JCP 103, 150 (1995) D. Marx, MET, J. Hutter, M. Parrinello, Nature397, 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. A108, 11793 (2004)

  17. 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)

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

  19. Quantum delocalization of structural defect D. Marx, MET, J. Hutter and M. Parrinello Nature397, 601 (1999)

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

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

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

  23. Liquid/vapor interface of acidic solutions Mucha, et al. JPCB109, 7617 (2005) Baldelli, et al.CPL302, 157 (1999) Tian, et al.JACS130, 13033 (2008) dangling “acceptor only” hydrogen bonded

  24. Simulations of an HCl interface (96 waters + 1 HCl) H. S. Lee and MET JPCA (submitted) Petersen, et al. JPCB108, 14804 (2004)

  25. “Proton hole” or mirror image mechanism of hydroxide mobility H+ OH- 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).

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

  27. 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)

  28. 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)

  29. Hydronium:

  30. Water:

  31. Hydroxide:

  32. 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.

  33. Comparing IR spectra Expt (KOH): Librovich and Maiorov, Russian J. Phys. Chem. 56, 624 (1982) KOH solution Pure water D’ 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) O Expt.: Librovich and Maiorov, Russian J. Phys. Chem. 56, 624 (1982) O* D* D

  34. NSF Alexander von Humboldt Foundation Camille and Henry Dreyfus Foundation ACS PRF Acknowledgments Students Postdocs • 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 • 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 External Funding • 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)

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