H bond network in water

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H bond network in water
Roberto Car, Princeton University
Croucher ASI, Hong Kong, Dec. 7 2005
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H-bond network
Many special properties of water are associated
to its H-bond network The H-bond network imposes
characteristic correlations on the positions and
relative orientations of neighboring
molecules Here we focus on the effect of these
correlations on the static and dynamic dielectric
properties of water within ab-initio Molecular
Dynamics
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Water molecules
Maximally Localized Wannier (Boys) Orbitals in
H2O a polar molecule bond (green) and lone
(pink) pairs
A water dimer two water molecules form a H-bond
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Hydrogen Bonds
water dimer
Local tetrahedral H-bond order Donors (D) and
Acceptors (A) Pauling ice rule 2D 2A Proton
disorder
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The static dielectric constant of water is
unusually large why?
Reproduced from L. Pauling, General Chemistry
(1970)
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In condensed phases the effective dipole moment
of a water molecule is enhanced (from 1.8D to
3D) but this is not sufficient. Alignment
of independent dipoles
In water and/or ice
this gives
To explain the large dielectric constant one
needs a more refined model including the effect
of the H-bonds
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Short-range dipole-dipole correlations are
consequence of the Pauling ice rules
Anti-parallel correlations between neighboring
dipoles would necessitate H-bond breaking and are
suppressed. Thus the local dipole is enhanced
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First-principles Molecular Dynamics
from electronic ground-state within DFT
In presence of en electric field electric
enthalpy functional
Use Maximally Localized Wannier Functions (MLWF
defined according to Marzari and Vanderbilt) at
each time step P is calculated from the
displacements of the ions and the MLWF centers
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Distribution of dipoles in liquid water
from Silvestrelli and Parrinello, PRL (1999)
molecular dipoles are defined using MLWFs
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First-principles water has a large dielectric
constant
At the temperature of the simulation (T325K) the
experimental dielectric constant is ? 70 , the
calculated value is ? 79 ? 5
Dipole-dipole correlations
Short range correlations are present even in
absence of electric field
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A simple lattice model to model H-bonds
correlations

• We take a cubic (diamond) model of ice (standard
  structure of ice is hexagonal)
• We assume that Pauling ice rules are exactly
  satisfied configurations in absence of an
  applied field are only distinguished by entropy
  not by energy
• We apply a finite electric field and include the
  dipolar coupling to the field for each molecule
  characterized by an average dipole moment (a
  parameter of the model)

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Bernal-Fowler-Pauling (BFP) model of ice in
electric field
Dipole configurations satisfying the Pauling ice
rules in presence of an external electric field
can be generated by a Monte Carlo (MC) procedure
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The polarization in the lattice model has values
close to those of first-principles water, if the
molecular dipoles in the lattice model are equal
to the average dipole of first-principles water
(? 3D)
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Dipole-dipole correlations in ab-initio water and
in the BFP model of ice show strikingly similar
behavior
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(No Transcript)
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Fitting the BFP model to experiment at one
temperature reproduces well the observed
temperature behavior
The best fit corresponds to ? 2.64
D Interestingly this is very close to the value
(? 2.60 D) predicted for ice by Coulson and
Eisenberg (Proc. Roy. Soc. 1966)
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Some historical perspective Onsager and
Kirkwood applied the concept of Lorentz field
(local field) to understand the dielectric
properties of polar liquids
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All these treatments describe a polar liquid as a
collection of dipolar molecules Onsager treats a
molecule as a cavity in a statistical continuum
of uniform dielectric constant equal to that of
the liquid in the bulk. In this treatment
environmental effects are only due to long range
Coulomb effects, the effect of the H-bonds enters
at most as an enhancement of the dipole moment of
a molecule in the liquid phase compared to the
gas phase In Kirkwoods treatment the cavity
includes a molecule and its shell of neighbors.
In this way he models the effect of hindered
relative rotations of neighboring molecules due
to H-bonds. This is a different kind of
environmental effect directly related to the
chemistry of the bonds
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Kirkwoods theory is a phenomenological model
that depends on 2 parameters the bond angle
among water molecules and the dipole moment of a
molecule in the liquid phase. Using a tetrahedral
bond angle and a reasonable estimate for the
enhanced dipole he gets a value of 55 for the
dielectric constant of water (experiment 79).
The unmodified Onsager theory leads to a value of
31. Applications to lattice models of liquid
water by Pople (in the 1950s) led him to
conclude that the dielectric constant of water is
a strong indication for the existence of an
H-bond network in the liquid There is no way of
estimating the 2 parameters in the context of the
theory. Besides, the concept of a molecular
dipole is ill-defined in condensed phase.
Furthermore the precise value of the local field
acting on the molecules is difficult to estimate.
These difficulties are solved in our
first-principle treatment which models water as a
collection of nuclei and electrons
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Issues of interest

• dielectric response in supercritical water
• proton disordered and proton ordered forms of ice

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Do H-bonds play a role also in the dynamical
response of water?
We focus here on the Infrared Response (IR) of
water From M. Sharma, R. Resta, and R.C., PRL
2005
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Dynamic response of water to an electric field
IR spectroscopy
Within linear response theory the infrared
absorption coefficient derives from the
fluctuations of the cell dipole moment M ?i ?i
We focus on the modes at 185 cm-1 which are
associated to hindered translations of the water
molecules
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Rigid translations of the central molecule are
hindered by the H-bonds that a molecule forms
with its neighbors, which define a (distorted)
local tetrahedral cage
Translations of a rigid dipole do not couple to
uniform electric fields. Hence the origin of the
IR feature at 185 cm-1 must be electronic. It
has been attributed (Madden and Impey, CPL 1986)
to an induced molecular dipole, a consequence of
the dynamic polarizability of the water molecule
(induced intramolecular dipole)
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Ab-initio MD simulations do not support this
interpretation
Spectrum including intramolecular (ij)
correlations only
The origin of the 185 cm-1 feature must be
intermolecular!
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Pasquarello and Resta (PRB 2003) suggested that
the IR activity of the translational modes in
water originates from dynamic charge transfer
between neighboring H-bonded molecules, i.e. the
analogue, for rigid molecular translations in a
condensed environment, of dynamical Born
effective charges in ionic crystals (induced
intermolecular dipole)
Correlations of the distances from the center of
mass of the central molecule of the centers of
the 4 neighboring MLWF that are bonded to the
central molecule
Our analysis is fully consistent with the
intermolecular dipole model The strongest
coupling is in the plane perpendicular to the z
axis
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Strong environmental effects due to H-bonds
(local chemistry)
This should be contrasted with the classical
treatment of Madden and Impey in which the effect
of the environment only enters through the value
of the local field (long range Coulomb
correlations) at the molecular dipole.
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Covalent charge fluctuations in water?
Intermolecular induced dipoles are a
manifestation of electron charge fluctuations
between neighboring molecules (a quantum
effect) This should be contrasted with the
standard interpretation of the translational IR
activity as due to intramolecular charge
fluctuations (a classical effect) In principle
the issue could be resolved experimentally
because the two effects have different selection
rules
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Modes at 60 cm-1 why are they absent or very
weak in the experimental spectra?
These are bending modes of the H-bond network for
which intermolecular dipole fluctuations are
absent to a first approximation
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Conclusions
Classical simulations consider water as a
collection of dipolar molecules Ab-initio
simulations consider water as an assembly of
classical nuclei and quantum electrons this
allows us to determine from first principles the
response of water to both static and dynamic
fields The resulting picture agrees with
earlier models for the static dielectric constant
and leads to an entirely new picture for the
dynamic response, showing that even in the latter
case the environmental effect of the H bonds
plays a crucial role.
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Hydrophobic interactions another H-bond effect

• Non-polar solutes like hydrocarbons in water
  experience a solvent mediated attractive
  interaction the hydrophobic interaction
• Thermodynamic properties (e.g. T dependence)
  suggest that the effect (for small hydrophobic
  solutes) is controlled by entropy, i.e. few or
  none H-bonds are broken but the network
  rearranges around the solute in a way that
  reduces the entropy (more order)

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Two methane (CH4) molecules in water solution
attract each other by solvent mediated forces (J.
Luen Li et al. 2005)
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hydrocarbon-water accessible area and transfer
energy

• Experimentally, the
• hydrocarbon-water transfer
• energy is proportional to the
• accessible surface area
• ?G ? ?A
• The same surface tension
• parameter ?47 cal mol-1 Å-2 1
• is valid for all paraffin series
• (methane, ethane, , decane)

1 Sharp et. al. Science, 252, 106 (1991)
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Association of two methanes in water (surface
tension model)

• free energy per accessible surface area ?E
  ?? ?A
• water radius 1.4 Å
• methane radius 1.95 Å
• ? ?03.35 Å
• methane contact distance d 3.9 Å
• ?47 cal mol-1 Å-2 1

W
?
0
r
CH4
The free energy change from two well-separated
methanes to two methanes in contact is ?E
??2??0? ?r
kcal mol-1
1 Sharp et. al., Science, 252, 106 (1991)
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Ab-initio MD calculation of the Potential of Mean
Force between a methane pair
The strength of the hydrophobic interaction is in
rough agreement with the surface tension
model There is only a shallow solvent-separated
minimum
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Diffusion of H2O near methane is substantially
reduced
H2O
H2O near the methane pair average over all 63 H2O
in a unit cell center of the methane pair
H2O near the methane pair
displacement2 Å2
H2O
CH4-CH4
time ps
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Number of waters in the first solvation shell
plateau indicates a more stable local structure
Clathrate structures?
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Conclusions

• Ab-initio simulations reveal features of the
  H-bond network
• Two crucial aspects of H-bonds that emerge from
  the studies presented here are
• their directional character
• the possibility of many nearly degenerate
  configurations leading to important entropic
  effects

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Acknowledgement
Collaborators Manu Sharma and Raffaele Resta
(Trieste) dielectric properties Je-Luen Li,
Chao Tang (NEC), Ned Wingreen hydrophobic
effect Support from NSF and from ONR is
gratefully acknowledged