Supplementary Information
Freezing in resonance structures for better packing: XeF2 becomes
(XeF+)(F-) at large compression
Dominik Kurzydłowski, Patryk Zaleski-Ejgierd, Wojciech Grochala and Roald Hoffmann
CONTENTS:
1. Summary of XeF2 polymorphs studied
2. Relative enthalpy vs. pressure of all studied polymorphs of XeF2
3. Evolution of Xe∙∙∙F and F∙∙∙F contacts with pressure for XeF2 (I4/mmm and Pnma)
4. Histograms of Xe-F distances for I4/mmm, Pnma, Cmcm and Fmmm at 105 GPa and 200 GPa
5. Structure parameters for I4/mmm and Pnma at 105 GPa and movement of F atoms in the facecentered cell of I4/mmm leading to Pnma
6. Structure parameters (for conventional cells) and enthalpy of selected XeF2 polymorphs at
150 GPa
7. Electronic band structure for I4/mmm at 110 GPa as well as Pnma at 110 and 200 GPa
8. Full and partial electronic density of states for I4/mmm at 110 GPa as well as Pnma at 110
and 200 GPa calculated using the CASTEP code
9. Energy, enthalpy and pV term, all at 0 K, for the reaction: XeF2(solid) → Xe(solid) +
F2(solid)
10. Test calculations for XeF2 and F2 at 0 GPa
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1. Summary of XeF2 polymorphs studied
Name
Symmetry
Structure type
I4/mmm
I4/mmm
ambient pressure XeF2 polymorph [1]
Immm
Immm
XeF2 phase II [2] – converged to I4/mmm
Pnnm-1
Pnnm
XeF2 phase III [2] – converged to I4/mmm
Pnnm-2
Pnnm
XeF2 phase IV [2]
Fmmm
Fmmm
XeF2 phase V [2]
Fmm2
Fmm2
distortion of XeF2 phase V
Cmca
Cmca
CO2 phase III [3]
Pa-3
Pa-3
CO2 phase I [3]
Pbcn
Pbcn
N2O phase IV [4]
Pnma-2
Pnma
NO+NO3- [5]
P212121
P212121
HgClBr
P4/nmm
P4/nmm
BaFCl
Pmmn
Pmmn
FeOCl
Fddd
Fddd
InOF
Cmc21
Cmc21
P21/c
P21/c
P21/c-2
P21/c
Pnma
Pnma
C2
C2
P1
P1
P21
P21
Cmcm
Cmcm
USPEX calculations
2
2. Relative enthalpy vs. pressure plot of all studied polymorphs of XeF2
3
3. Evolution of Xe∙∙∙F and F∙∙∙F contacts with pressure for XeF2 (I4/mmm and Pnma)
There are a total of 9 and 8 F∙∙∙F contacts in I4/mmm and Pnma, respectively. Even at the highest
compression, 200 GPa, all of them are longer than 2 Å, while the second closest F∙∙∙F contacts in F2
at this pressure is around 1.8 Å (value calculated assuming that F2 is isostructural to Cl2 at this
pressure [6]). This indicates that no F–F bonding is observed for I4/mmm and Pnma up to 200 GPa.
4
4. Histograms of Xe–F distances for I4/mmm, Pnma, Cmcm and Fmmm at 105 GPa and 200
GPa
5
5. Structure parameters for I4/mmm and Pnma at 105 GPa, and movement of F atoms in the
face-centered cell of I4/mmm leading to Pnma. Cell vectors are in Å, angles in degrees,
volume in Å3.
Phase
I4/mmm
Pnma
a†
4.352
4.632
b†
4.352
3.850
c†
6.522
6.802
V/Z
30.89
30.32
(0, 0, 0)
(0, 0, 0)
Xe
position†
F
position†
†
(0, 0, 0.304)
F1: (0.009, 0, 0.292)
F2: (0.182, 0, –0.281)
Cell vectors and atomic positions are listed for the face-centered cell of the I4/mmm polymorph; for Pnma the
cell origin has been shifted by (0.261∙a, 0.25∙b, 0.030∙c).
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6. Structure parameters (for conventional cells) and enthalpy of selected XeF2 polymorphs at
150 GPa. Cell vectors are in Å, angles in degrees, volume in Å3. Enthalpy, referenced to that
of I4/mmm, is in eV per XeF2.
Phase
H
I4/mmm
0.000
a
b
c
β
V/Z
Xe
F
2.957 2.957 4.516
90
28.2
(0, 0, 0)
(0, 0, 0.305)
Pnma
-0.167 4.516 3.614 6.759
90
27.6
(0.255, 0.25, 0.032)
Cmc21
-0.162 3.593 6.771 4.529
90
27.6
(0, -0.282, 0.152)
P21/c-2
-0.124 3.819 6.345 4.570 92.8 27.4
(-0.337, 0.107, 0.24)
P212121
-0.016 6.375 4.733 3.733
90
28.2
(0.357, 0.302, -0.18)
Cmcm
0.018
3.228 9.987 3.402
90
27.4
(0, -0.098, 0.25)
Cmca
0.216
4.216 3.683 7.237
90
28.1
(0.5, 0, 0)
(0, 0.096, -0.182)
Fmmm
2.458
4.048 4.048 6.991
90
28.6
(0, 0, 0)
(0.25, 0.25, 0.25)
7
F1: (0.265, 0.25, 0.319)
F2: (-0.025, 0.25, -0.252)
F1: (0, 0.433, 0.148)
F2: (0, -0.003, 0.397)
F1: (-0.108, 0.462, 0.230)
F2: (0.222, 0.256, -0.475)
F1: (-0.287, 0.317, -0.388)
F2: (-0.001, -0.485, -0.28)
F1: (0, 0.236, 0.25)
F2: (0, -0.236, 0.25)
7. Electronic band structure for I4/mmm at 110 GPa (left) as well as Pnma at 110 and 200 GPa
(center and left). The Fermi level (marked with a dashed vertical line) has been set as zero in
the energy scale. For the corresponding density of states see article.
8
8. Full and partial electronic density of states for I4/mmm at 110 GPa (left) as well as Pnma at
110 and 200 GPa (center and right) calculated using the CASTEP code [7] (ultra-soft
pseudpotentials [8]; Ecut-off = 600 eV; SCF convergence of 1∙10-7 eV/atom; k-point spacing of
0.25 Å-1). The Fermi level is set to 0 eV.
The VASP code does not enable reliable partitioning of the electronic density into s, p and atomic
contributions at elevated pressure. This can be done with another plane wave code, CASTEP [7],
which performs the population analysis by projecting the plane wave states onto a localized basis [9].
Using this technique. we obtain partial densities of states which confirm that for Pnma the lowest
lying s-type bands can be attributed to F1, while those lying higher originate predominantly from F2
states. Moreover, it can be seen that the centers of the fluorine p states are also shifted (the center of
F2 states lying higher than that of F1).
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9. Pressure dependence of the energy (dashed line), enthalpy (solid line) and pΔV term (dotted
line), all at 0 K, for the reaction: XeF2(solid) → Xe(solid) + F2(solid). The I4/mmm to Pnma
transition at 105 GPa is marked with a vertical dashed line
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10. Test calculations for XeF2 and F2 at 0 GPa. Errors between experimental and calculated
values are given in parentheses.
a
b
c
β
V/Z
4.315
4.315
6.99
90
65.07
R
Xe-F: 1.983
exp [1]
Xe∙∙∙F: 3.40
XeF2
calc
exp [10]
F2
calc
4.572
4.572
7.249
90
75.77
(6.0%) (6.0%)
(3.7%)
5.50
3.28
7.28
102.17 32.10
5.716
3.442
7.119
102.43 34.20
(-2.2%)
(0.3%) (6.6%)
(3.9%) (4.9%)
Xe-F: 2.078 (4.8%)
(16.4%) Xe∙∙∙F: 3.584 (5.4%)
F-F: 1.488
F-F: 1.426 (-4.2%)
The calculations give an ambient pressure enthalpy of formation of solid XeF2 from solid Xe and F2
of -144.1 kJ/mol compared with -151.4 kJ/mol from experiment (-4.8% difference). Experimentally,
the volume difference of this reaction is -30.1 Å3, while from calculations -39.2 Å3.
As XeF2 and F2 are molecular crystals, it is not surprising that the calculations overestimate the
volume of those structures. Geometry optimizations of a ‘molecule in a box’ (isolated molecular
units are placed in the center of a cell sufficiently large to ensure at least 10 Å space between
neighboring molecules) yield Xe-F / F-F bond lengths of 2.066 / 1.423 Å, while the experimental
values are 1.977 / 1.412 Å, respectively, which gives a 4.5% / 0.8% overestimation.
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