Pressure-induced localisation of the
hydrogen-bond network in KOH-VI
Supplementary Information
Andreas Hermann, Malcolm Guthrie,
Richard J. Nelmes, and John S. Loveday
November 25, 2015
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Simple ionic structures in potassium hydroxide phases
At ambient conditions, potassium hydroxide takes up the monoclinic P 21 /mKOH-II phase.[1] In this structure, the oxygen-potassium sub-lattice resembles a sodium chloride lattice, an archetypal ionic structure type. In Figure 1,
we superimpose the appropriate ”unit cell” on the actual P 21 /m unit cell.
The orientations of the OH groups lead to monoclinic distortions and, ultimately, to the bilayer arrangement suggested in the main manuscript and
the literature.
At P = 0.7 GPa and room temperature, the P 21 /m-KOH-II phase transforms to the P 21 /n-KOH-IVa phase, which is also found below T = 233 K
(T = 251 K for KOD) at ambient pressure. The KOH-IVa phase is also
ionic, with a sodium chloride sub-lattice of oxygen and potassium, and the
appropriate ionic ”unit cell” is also shown in Figure 1.
At high pressures (above P ∼ 6.5 GPa in experiment, and above P =
9 GPa in ground state DFT calculations), KOH takes up a different structure, KOH-VI, identified in the main manuscript as a tetragonal phase with
localised (OH)4 units. In this phase, the oxygen-potassium sub-lattice resembles a cesium chloride lattice, arguably the second best known ionic structure
type. In Figure 1, we superimpose the CsCl ”unit cell” on the actual I4/m
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unit cell as obtained in our calculations. The pseudo-cubic arrangement of
the potassium atoms is quite significantly distorted, owing to the presence of
the protons (and hence elongated OH groups) as well as the hydrogen bond
network.
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Crystallographic information of KOH candidate phases
Additional crystallographic information of structural candidates from our
crystal structure prediction that were considered in the main manuscript,
mostly in the ground state enthalpy plot, is given in Table 1. Note that
the I4/mmm phase included there is not to be confused with the protondisordered phase discussed in the main manuscript. Here, it represents a
proton-ordered phase with all protons positioned at the mid-points between
oxygen atoms within the (OH)4 units. Such a symmetric hydrogen bond is
similar to the proton arrangement in the high-pressure phase ice X, and only
stable at very high pressures (around P = 160 GPa in our calculations).
In the ground state, the high-pressure phases I4/m and P 4/mnc are
metastable at P = 1 atm with respect to the P 21 /n-KOH-IVa phase by
about 125 meV per formula unit.
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Analysis of potential KOH-VI phases
In Figure 2, we compare the volumes per formula unit of various candidate
structures for the high-pressure phase of potassium hydroxide. The enthalpically most favored structures, of I4/m and P 4/mnc symmetry, are also the
most compact structures across the entire pressure range, which hints at their
stability under compression.
We also show in Figure 2 the partial charges on both potassium and
hydrogen, as obtained from a Bader analysis, up to P=30 GPa, and for
the P 21 /n-KOH-IVa and I4/m-KOH-VI phases. The charges on potassium
indicate a loss of ionicity under pressure; as K+ and OH− come closer, charge
transfer between them reduces. The evolution of the partial hydrogen charges
(an indicator for the strength of the covalent O-H bond) is less clear, but
ultimately the hydrogen partial charge reduces at high pressures. The trend
is less distinct than the strong decrease in the O-H stretch frequencies (see
2
Figure 1: Structures of KOH/KOD, with underlying ionic sub-lattices. Top
left: P 21 /m-KOD-II; top right: P 21 /n-KOD-IVa; bottom: I4/m-KOH-VI.
Purple (red, light blue/white) spheres denote potassium, oxygen, and deuterium/hydrogen atoms. The NaCl and CsCl ”unit cells” are sketched with
thick black lines, while thin black lines outline the actual unit cells. Note
half-occupancy of deuterium sites in P 21 /m-KOD-II.
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Table 1: Crystal structures of high-pressure phases of KOH from our ground
state calculations (pressures and origins indicated).
Phase
Lattice parameters [Å,◦ ]
Atomic positions
P 21 /n
a=5.848, b=4.023, c=8.107 K(-0.283, 0.254, 0.066)
(1atm, KOH-IVa)
β=67.2
O(0.210, 0.276, 0.212)
H(0.071, 0.121, 0.234)
P 21 21 21
a=7.839, b=4.013, c=5.633 K(-0.171, 0.255, 0.102)
O(0.078, -0.277, -0.073)
(1atm, LiOH)
H(0.480, 0.126, 0.315)
P 4/nmm
a=b=5.183, c=3.642
K(3/4, 1/4, 0)
(1atm, LiOH-II)
O(1/4, 1/4, -0.263)
H(1/4, 1/4, 0.470)
I41 /acd
a=b=7.652, c=14.77
K1 (0, 1/4, 3/8)
K2 (0, 1/4, 1/8)
(1atm, LiOH-III)
O(0.090, 0, 1/4)
H(-0.282, 0, 1/4)
P bcm
a=3.607, b=6.886, c=7.129 K(-0.350, 1/4, 0)
O(-0.193, -0.069, 1/4)
(1GPa, NaOD-V)
H(0.030, 0.011, 1/4)
Ima2
a=6.986, b=6.204, c=6.097 K(0.470, 0.231, 0.181)
O1 (1/4, -0.486, -0.036)
(20GPa)
O2 (1/4, -0.461, 0.423)
H1 (1/4, -0.034, -0.239)
H2 (1/4, -0.328, -0.058)
I4/mmm
a=b=5.617, c=6.818
K1 (0, 1/2, 1/4)
(30GPa)
K2 (0, 0, 0.305)
O(0.215, 0.215, 0)
H(-0.221, 0, 0)
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Figure 2: Left: Pressure-volume relations for relevant KOH phases. Right:
partial K and H charges, from Bader analysis, for P 21 /n and I4/m phases
as function of pressure.
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main manuscript), which indicates substantial reduction of covalent bond
strength, possibly due to enhanced hydrogen bonding. The differences in
partial charges between the KOH-IVa and KOH-VI phases are small; both
ionic and covalent bonding contribution are very similar in both phases, while
they differ substantially in the hydrogen bond network structure and overall
packing of the constituents.
References
[1] Bettina
Mach,
Herbert
Jacobs,
and
Wolfgang
Schäfer.
Bindungsverhältnisse in kristallinen Phasen von Kaliumdeuterohydroxid, KOD.
Z. Anorg. Allg. Chem., 553(10):187–195, October
1987.
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