Calculating water’s anomalous properties from first principles:
Mechanisms of ion transport in the bulk and at interfaces
Image: news.softpedia.com
Mark E. Tuckerman
Dept. of Chemistry
and Courant Institute of Mathematical Sciences
New York University, 100 Washington Sq. East
New York, NY 10003
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)
“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
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, JPCB 110 (2006)
Some of water’s anomalous properties
Density maximum at 4 oC
Many stable crystalline phases
High surface tension
Anomalously high transport of protons (H+)
and hydroxide (OH-) ions
PEM vs. AAEM fuel cells
(AAEM=Alkali-anion exchange membrane)
From Varcoe and Slade,
Fuel Cells 5, 198 (2005)
Anode: CH3OH  H 2O  6H   6e  CO2
3
O 2  6e   6H   3H 2 O
2
3
Overall: CH3OH  O2  2H 2 O  CO2
2
Cathode:
Anode:
Cathode:
Overall:
CH3OH  6OH   CO2  5H 2 O  6e
3
O2  3H 2O  6e   6OH 
2
3
CH3OH  O2  2H 2O  CO2
2
1806:
Structures of the excess proton in water
H3O+
H9O4+
H5O2+
Vehicle Mechanism
+
+
+
Grotthuss Mechanism (1806)
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
Hˆ  TˆN  Tˆe  Vˆee  VˆNN  VˆeN
F  ma
Ĥ   E 
The Algorithm
Electrons
Nuclei
Start with nuclei
Add electrons
Compute 
Add electrons
F
Propagate nuclei a
short time Δt with F
Ab initio molecular dynamics (AIMD)
Nuclei
Electrons
Kohn-Sham density functional theory:
E[{ },{R}]  
1
1
n(r )n(r)
2





d
r
d
r
 Exc [n]  Eext [n,{R}] Enn ( R )

i
i

2 i
2
r r'
n(r)    i (r)
2
 i  j   ij
i
Nuclear evolution
E0 ({R})  min E[{ },{R}]
{ }
E0
d 2R I
MI

2
dt
R I
Feynman
Feynman path
pathintegrals
integrals
MET, et al. JCP 99, 2796 (1993); Marx and Parrinello, JCP 104, 4077 (1996); MET, et al. JCP 104, 5579 (1996)
.
.
.. . . ..
.
.
.
..
P-1
  

 
 lim Z P

P
1


 

P 
Near perfect parallel scaling
with increasing P
3
2
Basis Sets
Y. Liu, D. Yarne and MET, PRB 68, 125110 (2003); H. –S. Lee and MET, JPCA 110, 5549 (2006)
Plane-waves (momentum eigenfunctions):
1
 i (r ) 
V
C
g ,i
e
2 n
g
L
ig r
g
1 2
g  Ecut
2
Discrete-variable representations [Light, et al. JCP 82, 1400 (1982)]:
Begin with a set of N square-integrable orthonormal functions φi(x)
N
ui ( x)  ai  l* ( xi )l ( x)
l 1
On an appropriately chosen quadrature grid {x1,…,xN}
ui ( x j ) 
 ij
ai
(position eigenfunctions!). Expand orbitals as:
i
 i (r)   Clmn
u l ( x)um ( y)un ( z )
lmn
Basis set size determined by # grid points. Core electrons replaced by atomic pseudopotentials
Radial distribution functions for BLYP Water
DVR
Neutron
X-ray
Grid = 753, t =60 ps
Ensemble: NVT, 300 K, μ = 500 au
3.5
3.0
DZVP
DZVP+BSSE-BLYP
SCP-BLYP
gOO(R)
2.5
2.0
1.5
1.0
0.5
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. JCP 106, 247 (1997)
X-ray: Hura, et. al. Chem. Phys. 113, 9140 (2000)
0.0
2
2.5
3
3.5
4
4.5
5
5.5
R [Å]
When basis sets are too small!
from C. J. Mundy (2008)
6
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)
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)
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
Quantum delocalization of structural defect
D. Marx, MET, J. Hutter and M. Parrinello Nature 397, 601 (1999)
Ultrafast pump-probe experiments
Woutersen and Bakker, Phys. Rev. Lett. 96, 138305 (2006)
Eigen/Zundel exchange time ≈ 100 fs
A Chemical Master Equation Theory of PT kinetics
A. Chandra, MET, D. Marx Phys. Rev. Lett. 99, 145901 (2007)
h(t )  0
h (t )  1
k1
A
B
h (t )  1
O*
h(t )  0
O*
k 1
B  C
k2
O*
Rate equations:
d [A]
 k1[A]  k1[B]
dt
d [B]
   k2  k1  [B]  k1[A]
dt
O*
g (t )  1 in all configurations above
Population correlation functions:
[A](t )  h(0)h(t )
[B](t )  h(0)[1  h(t )]g (t )
Chemical Master Equation Theory
1 
 k1  K   t / 2
 k1  K   t / 2

[A](t ) 


k

K
e



k

K
e




1
1


2

aslow e  t / slow
 afast e  t / fast

 k1  K   4k1k1
K  k2  k1
2
t=0
t
H
H
O*
Cc (t )  h(0) H (t )
H
O*
O
H
H

Exchange time:
H
 exch   dt Cc (t )
0
 fast  50 fs (Bakker: 100 fs)
 exch  1.52 ps (NMR: 1.3 ps)
O
Liquid/vapor interface of acidic solutions
Mucha, et al. JPCB 109, 7617 (2005)
Baldelli, et al. CPL 302, 157 (1999)
Tian, et al. JACS 130, 13033 (2008)
dangling
“acceptor only”
hydrogen bonded
Simulations of an HCl interface (96 waters + 1 HCl)
H. S. Lee and MET JPCA (submitted)
Petersen, et al. JPCB 108, 14804 (2004)
“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).
Spectra of 14 M KOH
IR
Raman
Librovich and Maiorov, Russian J. Phys. Chem. 56, 624 (1982)
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)
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)
Hydronium:
Water:
Hydroxide:
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.
Comparing IR spectra
Expt (KOH): Librovich and Maiorov, Russian J. Phys. Chem. 56, 624 (1982)
KOH solution
Pure water
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)
D’
Z. Zhu and MET, J. Phys.
O Chem. B 106, 8009 (2002)
Expt.: Librovich and Maiorov,
Russian J. Phys. Chem. 56, O*
624 (1982)
D*
D
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
•
•
•
•
•
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)
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
•
•
•
•
NSF
Alexander von Humboldt Foundation
Camille and Henry Dreyfus Foundation
ACS PRF