Hydrogen Bonds in Liquid Protonated Water

1
Hydrogen Bonds in Liquid Protonated Water
Markovitch Omer and Agmon Noam Department of
Physical Chemistry and the Fritz Haber Research
Center, The Hebrew University of Jerusalem,
Israel.
Corresponding author omerm_at_fh.huji.ac.il or
http//www.fh.huji.ac.il/omerm
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• Presentation outline
• 0) About this presentation
• MS-EVB (Multi State Empirical Valence Bond)
• Hydrogen bond (HBond) solvation shells
  terminology
• HBond population distribution
• Keq. for hydrogen bond cleavage
• A detailed view on the effect of R(OO) distance
  on HBond cleavage enthalpy.
• Results
• Discussion

3

• Second, a sample HBond population distribution
  is presented.
• Third, Keq. for HBond cleavage is taken to be
  consisted with Raman spectroscopy analysis.
• Last, we show the dependence of HBond cleavage
  enthalpy with the Roo distance.

• 0. About this presentation
• We have started working on HBond cleavage
  enthalpies some time ago in order to couple these
  results to proton hopping activation energy,
  calculated by the Voth Agmon groups before.
• This presentation tells the story of
  searching an optimal parameter to give reliable
  HBond cleavage enthalpy and is organized as
  follows
• We have simulated water with an excess of a
  single proton. First we will present our HBond
  terminology and check to what extent each
  hydronium solvation shell is different than the
  other and than regular water.

4

• 1. MS-EVB
• Underlying model TIP3P
• Empirical Valence Bond - resonance

q
R
-2q
q

• Simulation details
• 216 water molecules with an excess of a single
  proton.
• A box size of 18.64 ? with periodic boundary
  conditions.
• Integration step was 0.5 fs and coordinates were
  saved every 25 fs.

Schmitt et al, J. Phys. Chem. B 102, 5547 (1998)
5
2. Terminology of HBonds and solvation shells
Dotted lines represent HBond. Only a single
HBond type is plotted per oxygen, picture should
be completed by symmetry.
bulk/pure water far from the hydronium
1st shell
2nd shell
DW
D0
D1
D2
1
2
H3O
A2
A1
A0
Figure 2
6
Is our choice of looking only until the 2nd
solvation shell of the hydronium good? Radial
Distribution Function ( g(r) ) for oxygen-oxygen

• Water (blue)

g(r) for water (298 K), experiment - A. K. Soper
M. G. Phillips, Chem. Phys. 107, 47 (1986)
MS-EVB2 5 -
Figure 3a
7
Is our choice of looking only until the 2nd
solvation shell of the hydronium good? Radial
Distribution Function ( g(r) ) for oxygen-oxygen

• Hydronium (black)

g(r) for hydronium cation (298 K) experiment
Botti, A. et al, J. Chem. Phys. 121, 7840 (2004)
MS-EVB2 5 -
The repulsion from the H3O lone pair is too
high. Known bug for MSEVB2.
Figure 3b
Narrow peak due to high concentration of HCl,
causing a Cl- ion to replace an oxygen ligand in
first solvation shell of the hydronium.
8
Is our choice of looking only until the 2nd
solvation shell of the hydronium good? Radial
Distribution Function ( g(r) ) for oxygen-oxygen

• 1ST shell (red)

Figure 3c
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Is our choice of looking only until the 2nd
solvation shell of the hydronium good? Radial
Distribution Function ( g(r) ) for oxygen-oxygen

• 2ND shell (green)

Table 1
Yujie Wu et al, J. Chem. Phys. 124, 024503 (2006)
and references therein.
10
3. HBond population distribution For each
molecule we have measured the number of HBonds
(n) per type We mark n as the most
probable n
Figure 4
Back to systems color code
Table 2
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4. Keq. For HBond cleavage Monosmith and Walrafen
Keq. for water HBond is written as
eq. 1 The formation reaction
HBond broken HBond-intact eq. 2
Monosmith et al, J. Chem. Phys. 81, 669 (1984)
Walrafen et al, J. Chem. Phys. 85, 6970 (1986)
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Contd
For eq. 2 we define , n
being the most probable number of HBonds per
water molecule in figure 4 (table 2). Assuming
that the enthalpy does not change in a narrow
range of temperatures, plotting ln(Keq.) vs. 1/T
(vant Hoff) should give a straight line where
the slope is .
13

• HBond definition Both distance oxygen-oxygen
  angle must be below cutoff criteria for a HBond
  to be considered intact.
• Maximum allowed angle was always kept at 30 deg.
• Maximum allowed Roo was NOT picked at the first
  minimum
• of g(r), instead we have tested a range of
  cutoff distances

Angle(OOH)
R(OO)
Rcov.
Figure 5
14
Contd

• Only Di HBonds were tested because they are most
  likely to allow the path to distribute/solvate
  the proton excess charge.
• Analysis was performed for a reduced set of
  trajectories and temperatures.
• Near the red points the cleavage enthalpy is
  less sensitive to Roo distance and so these
  distances were selected for the full analysis.
• For water we picked the very popular value of
  Roo lt 3.5 ?.
• Interesting! Roo cutoffs are at the same
  distance from the first maximum of g(r).

Table 2
15

• 5) Results
• Figure 5 is with reduced sampling space.
• Vant Hoff plot for each HBond (maximum Roo that
  define a HBond are in table 2, maximum OO-H
  angle was always 30 degrees)

Figure 6
Back to systems color code
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H-Bond cleavage enthalpies
DW
D0
D1
D2
1
2
H3O
A2
A1
Figure 7
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• 6. Discussion
• There are two types of HBonds
• Di- donor type HBond strengths increase upon
  approaching the core shell.
• Ai- acceptor type HBond weakens upon approaching
  the core shell.
• The donor HBonds might be viewed as the
  Transport path for the hydronium excess
  positive charge.
• Recent study by Smiechowski and Stangret 1
  suggested up to four solvation shells of acids
  but with no acceptor HBonds (table I of ref. 1).
• We argue that the IR peaks of figure 9 (see next
  page) could be assigned to the D0, D1, A2 and A1
  HBonds. In this case we find here ??H is 9.2
  kJ/mol for D0 minus D1 and 3.7 kJ/mol for D1
  minus A2, very similar to the energetic
  difference of the IR peaks (after dividing by
  1.41 to correct the isotop effect). The
  difference between A1 and A2 is 4.8 kJ/mol while
  the experimental difference is only 1.8 kJ/mol.
  This might suggest that our A1 HBond strength is
  underestimated.

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Contd III) The D0 HBond (from the hydronium
to its first solvation shell water ligands) is
more than two times stronger than that of bulk
water. This, together with Omtas et al
observation that first shell water ligands
exhibits longer orientation correlation time 2
suggests that the hydronium is better described
as a larger cation, H9O4.

• This would decrease the non-Grotthuss component
  of proton mobility self diffusion 3 and could
  also enhance the viscosity of concentrated acids
  according to the Einstein model 3, 4.

1 Smiechowski et al, J. Chem. Phys. 125, 204508
(2006) 2 Omta et al, Science 301, 347
(2003) 3 Agmon, J. Chim. Phys. Phys.-Chem.
Biol. 93, 1714 (1996) 4 Einstein A., Furth R.
and Cowper D., Investigations on the Theory of
Brownian Movement, Dover (1926)
19
Acknowledgements Gregory A. Voth Matt K.
Peterson for discussions and instructions in
using MS-EVB2 5. This work is supported by the
Israel Science Foundation, grant 191/03.
5 Day et al, J. Chem. Phys. 117, 5839 (2002).
How to quote this work further information
Markovitch Agmon Structure and Energetics of
the Hydronium Hydration Shells, J. Phys. Chem. A
111 (12), 2253-2256 (2007), supporting
information available on-line.