Spontaneous Dissociation of Xenon Tetroxide: Phase and Structural

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Spontaneous Dissociation of Xenon Tetroxide: Phase and Structural Changes Vladimir Slepkov,* Svetlana Kozlova, and Svyatoslav Gabuda Nikolaev Institute of Inorganic Chemistry SB RAS, Lavrentieva Av., 3, Novosibirsk 630090, Russian Federation ABSTRACT: XeO4 is a noble gas compound remarkable for its high explosiveness in the crystalline state and spontaneous explosion at melting temperature. Both phenomena are studied by analyzing potential energy surfaces corresponding to elementary dissociation acts. It is shown that a spontaneous explosion of xenon tetroxide can be explained by a phase transition associated with structural Td f D2h change and be triggered by rearrangement of electron levels due to the Jahn Teller effect.

1. INTRODUCTION Xenon tetroxide XeO4 possesses a number of interesting properties. First, it is the highest possible oxidation state of xenon (+8) due to bonding with the oxygen that involves all eight valence electrons of xenon. Oxygen is the only element that can bring xenon up to its highest oxidation state since even fluorine can only form XeF6. Second, the substance easily explodes to form xenon and oxygen under external impacts such as stroke or heating. Third, and most incomprehensible, is that it explodes spontaneously in its liquid state when reaching melting temperature 35.9 °C without any apparent external stimuli. Gaseous xenon tetroxide XeO4 is a tetrahedral structure with Xe O distance 1.74 Å.1 The structure of solid xenon tetroxide has never been registered directly, but the comparison of the IR and Raman spectra measured for solid XeO4 with those of gaseous phase2,3 and theoretically calculated spectra for the tetrahedral symmetry shows it to be very close to the tetrahedron.4 As to liquid XeO4, neither its structure nor frequencies have ever been measured due to its utmost instability. Here we present a quantum chemical study to explain the spontaneous explosion of liquid XeO4, consider mechanisms of its crystal liquid phase transition, and discuss the role of the Jahn Teller effect in the spontaneous explosion of XeO4. 2. METHODS All DFT calculations were performed with the ADF 2008 package5 at BLYP,6 B3LYP,7 XLYP,8 OLYP,9 and OPBE10 levels of theory using all electron Slater valence triple-ζ + 2 polarization functions TZ2P11 as basis sets. Relativistic effects were taken into account with the ZORA formalism.12 Fundamental frequencies and displacement vectors were calculated according to the standard procedure realized within the DFT method.13 Bonding energy Eb was counted as the sum of the electronic bonding energy (i.e., the difference between the total electron energy of the system and electronic energies of all its atoms),14,15 vibrational r 2011 American Chemical Society

zero-point energy correction, and internal energy at 298 K; standard enthalpy of formation ΔHfθ was calculated as the 2Eb(O2); the activation energy ΔE difference Eb(XeO2) necessary to dissociate a molecule into xenon and two oxygen molecules was taken from potential energy surfaces built as functions of Xe O and O O distances from a series of singlepoint calculations with grid parameter 0.1 Å. The D2h isomer was additionally calculated at the CCSD/cc-pVDZ level of theory.16,17 The AIM topological analysis18 was carried out with the Xaim software developed by Jose Carlos Ortiz and Carles Bo, Universitat Rovira i Virgili, Tarragona, Spain. Electron localization function19,20 was visualized with the ADF-GUI module.

3. RESULTS AND DISCUSSION XeO4 Isomers. According to our calculations (Table 1), the XeO4 molecule optimized within Td symmetry is characterized by Xe O = 1.75 1.81 Å, O O = 2.86 2.95 Å distances, the standard enthalpy of formation at 298 K varies in the range of 7.09 7.38 eV, fundamental frequencies are close to those reported from spectroscopy data,2,3 and the calculated enthalpies of formation are compared with ΔHfθ298 measured for gaseous XeO4 in the reaction XeO4(g) f Xe(g) + 2O2(g)21 (Table 1). As can be seen, the OPBE level of theory gives generally best predictions about geometry of the system, its fundamental frequencies, and enthalpy of formation. We also discovered a planar D2h isomer XeO4 with Xe O and O O distances 2.08 and 1.41 Å, respectively, as suggested by OPBE calculations (Figure 1a). Calculations in Gaussian 03 according to a post-Hartree Fock ab initio method CCSD/ccpVDZ confirm the existence of energy minimum for the planar isomer with structural parameters and energy barrier close to our Received: April 6, 2011 Revised: June 4, 2011 Published: June 07, 2011 7811

dx.doi.org/10.1021/jp2031658 | J. Phys. Chem. A 2011, 115, 7811–7814

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Table 1. Main Structural and Energy Parameters and Fundamental Frequencies Calculated for Td and D2h Isomers of XeO4a Xe O, Å Td

exp

O O, Å

ΔHfθ, eV

ΔE, eV

fundamental frequencies, cm

1.736 ( 0.002 2.832 ( 0.008 6.66 ( 0.03

1

879.2 ( 0.2 (t2), 305.9 ( 0.2 (t2) 775.7 ( 0.2 (a1), 267 ( 5 (e)

OPBE

1.76

2.87

7.13

5.22

910 (t2), 306 (t2), 771 (a1), 249 (e)

B3LYP

1.77

2.89

8.03

4.26

859 (t2), 304 (t2), 780 (a1), 253 (e)

OLYP

1.77

2.90

7.38

4.42

859(t2), 296 (t2), 777 (a1), 241 (e)

XLYP

1.78

2.90

7.12

3.18

848 (t2), 288 (t2), 765 (a1), 236 (e)

BLYP

1.81

2.95

7.09

3.73

790 (t2), 278 (t2), 711 (a1), 229 (e)

D2h OPBE

2.08

1.41

7.03

0.22

327 (b1u), 976 (b1u), 196 (b2u), 63 (b3u), 435 (b3u), 428 (ag), 1055 (ag), 529 (b2g), 210 (au)

B3LYP OLYP

2.12 2.12

1.44 1.44

7.50 7.03

0.4 0.11

203 (b1u), 899 (b1u), 194 (b2u), 78 (b3u), 377 (b3u), 403 (ag), 969 (ag), 500 (b2g), 233 (au) 263 (b1u), 903 (b1u), 186 (b2u), 70 (b3u), 378 (b3u), 389 (ag), 982 (ag), 482 (b2g), 209 (au)

XLYP

2.12

1.45

6.33

0.30


BLYP

2.17

1.48

6.27

0.24


Xe O stands for distances between xenon and oxygen atoms, ΔHfθ denotes standard enthalpy of formation, and ΔE is the activation energy necessary to dissociate a molecule. a

Table 2. Total Electron Energy and Density Characteristics for Xe O and O O Critical Points in D2h Isomer of XeO4 in Atomic Units E, ha

Figure 1. XeO4 isomer with D2h symmetry (a) and its electronic structure as imaged by ELF function and critical points of electron density (b). ELF isosurface is shown at ELF = 0.7, ELF cutting plane coincides with the plane of the molecule; bond and ring critical points are designated as bcp and rcp, respectively.

DFT calculations (Xe O = 2.20 Å, O O = 1.44 Å, ΔE = 0.084 eV). Table 1 shows fundamental frequencies and structural and energy parameters for the isomer calculated at various levels of theory. Bonding paths are present between Xe O and O O atoms (Figure 1b). Energy and density characteristics in corresponding critical points show a clear covalent interaction between O O atoms and a weaker covalent interaction between Xe O atoms (Table 2).18 The same conclusion is suggested by ELF basin present on the O O bond (Figure 1b).20 The calculated enthalpy of formation of the isomer is close to that of the tetrahedral isomer while the activation energy it needs to dissociate into xenon and two oxygen molecules is substantially smaller and lies between 0.11 and 0.30 eV. This fact can explain the phenomenon of spontaneous explosion of XeO4 at “crystal liquid” phase transition accompanied by structural Td f D2h change. Energy Balance in XeO4 Dissociation. Since both isomers have positive enthalpies of formation, there is an energy gain in XeO4 dissociation into xenon and two oxygen molecules.

3

F, ea

Xe O

0.04

0.11

O O

0.22

0.31

3

For Td isomer the reproduction factor k = (ΔHfθ + ΔE)/ΔE, which is the ratio of the energy released in a single elementary dissociation act to the activation energy needed to trigger the next dissociation act, varies between 2.37 and 3.24 which means that the released energy is enough to start a chain reaction.22 For the planar isomer the reproduction factor k varies from ∼20 to ∼60. Since the threshold is very shallow, it can be overcome by small thermal fluctuations which induce a fast escalating explosive reaction. Potential Energy Surfaces. Consider potential energy surfaces for both isomers as functions of Xe O and O O distances. Since XeO2 is a highly unstable molecule,4 we will assume that the dissociation implies simultaneous formation of two oxygen molecules. In fact, the two-stage process is also spin-forbidden since, as far as ground states are considered, both XeO4 and XeO2 are singlets while the O2 molecule is triplet. Therefore, in this model we consider each elementary dissociation act as a onestage process XeO4 f Xe + 2O2 rather than a two-stage process XeO4 f XeO2 + O2 f Xe + 2O2. Figure 2 shows potential energy surfaces for D2d (green) and D2h (semitransparent blue) symmetries of XeO4 corresponding to its Td and D2h isomers, respectively. Both surfaces have two distinct minima: the first is associated with the equilibrium state of each isomer, the second images the dissociation products Xe + 2O2 with Xe O distances infinitely increasing and O O distances approaching the interatomic distance in the O2 molecule. The minimum of the tetrahedral isomer has an elongated shape so that the surface is extended along the O O axis and steeply rises along the Xe O axis. This means that Xe O distances are rather rigid in contrast to O O distances which can vary widely without substantial energy change. The minimum of the planar isomer is elongated along the Xe O axis and steeply rises along the O O axis to signify rigid O O distances and loose Xe O bonding. In both cases the system starts from the minimum, passes a transition state, and falls into the dissociation valley. Physically, 7812

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The Journal of Physical Chemistry A the system undergoes phase transitions “crystal-gas” in the first case and “liquid-gas” in the second case. Since the surfaces have a common intersection line, there is a possibility for the system, on its way from a Td minimum, to jump from the D2d surface to D2h surface and go down to its minimum after crossing an effective barrier ∼2 eV rather than trying to overcome the “crystal-gas” barrier ∼5 eV. In this case the crystal phase first transforms into the intermediate liquid phase “crystal liquid” and then dissociates to produce gas phase. The probability of a “crystal liquid” jump is also supported by the fact that the only imaginary frequency 141 cm 1 (b1) in the common point of the reaction path and the intersection line between the surfaces corresponds to the oscillation that twists the molecule by placing the opposite oxygen pairs in the same plane (Figure 2, inset). The Jahn Teller Effects in Xenon Tetroxide. Consider the role of the Jahn Teller effect23,24 in XeO4 dissociation. Tetrahedral Isomer. The Td isomer has a triply degenerate HOMO level with HOMO LUMO gap of 2.38 eV (Figure 3a).

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When thermal or mechanical impacts are applied to the substance, oscillations are excited. As mentioned above, highest amplitudes are associated with the oscillations that change O O distances rather than Xe O distances. There are three such fundamental frequencies 278 cm 1 (T2) which bring together oxygen atoms without changing Xe O. If the tetrahedral structure is distorted along and by the length of the corresponding displacement vectors to obtain O O distances equal to 2.06, 2.95, 2.52, 2.56, 3.56, and 3.74 Å, the degeneracy disappears and the HOMO LUMO gap shrinks down to 0.20 eV (Figure 3a) to create favorable conditions for the pseudo-Jahn Teller effect. Therefore, the pseudo-Jahn Teller effect can further enforce the molecular deformation by bringing together the oxygen atoms. Planar Isomer. The D2h isomer has a nondegenerate HOMO level with HOMO LUMO gap of 0.38 eV. In the structure distorted in the direction of the largest oscillation amplitude corresponding to frequency 358 cm 1 (ag) (Xe O = 2.27 Å, O O = 1.48 Å, symmetry D2h) the gap shrinks down to 0.05 eV (Figure 3b). Since the gap is small, the pseudo-Jahn Teller effect alone can cause spontaneous dissociation of liquid xenon tetroxide.

4. CONCLUSIONS According to quantum chemical calculations xenon tetroxide can exist as both Td and D2h isomers. Dissociation of XeO4 molecule is exothermal due to positive enthalpy of formation of both isomers. The Td isomer dissociates with activation energy ∼3 5 eV and reproduction factor n ∼ 2 3 and, therefore, can start an exothermal chain reaction under the impact of some external factor. The D2h isomer dissociates with activation energy ∼0.11 0.30 eV and reproduction factor ∼20 60 and is capable of initiating spontaneous chain reaction. A spontaneous explosion of xenon tetroxide can be explained by phase transition associated with structural Td f D2h change and be triggered by rearrangement of electron levels due to the Jahn Teller effect. Figure 2. Potential energy surfaces for D2d (green) and D2h (semitransparent blue) symmetries of XeO4 corresponding to its Td and D2h isomers, respectively.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

Figure 3. Energy levels and HOMO LUMO gaps in the tetrahedral (a) and the planar (b) XeO4 isomers in their equilibrium and distorted states. 7813


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’ ACKNOWLEDGMENT The authors thank Anton Nizovtsev for his help with the CCSD calculations. ’ REFERENCES (1) Gundersen, G.; Hedberg, K.; Huston, J. L. J. Chem. Phys. 1970, 52, 812–815. (2) Huston, J.; Claassen, H. J. Chem. Phys. 1970, 52 (11), 5646– 5648. (3) McDoWell, R.; Asprey, L. J. Chem. Phys. 1972, 57 (8), 3062– 3068. (4) Pyykk€o, P.; Tamm, T. J. Phys. Chem. A 2000, 104 (16), 3826–3828. (5) te Velde, G.; Bickelhaupt, F. M.; van Gisbergen, S. J. A.; Fonseca Guerra, C.; Baerends, E. J.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931. (6) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (7) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (8) Xu, X.; Goddard, W. A., III Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 2673. (9) Handy, N. C.; Cohen, A. J. Mol. Phys. 2001, 99, 403. (10) Swart, M.; Ehlers. A.W., A. W.; Lammertsma, K. Mol. Phys. 2004, 102, 2467. (11) van Lenthe, E.; Baerends, E. J. J. Comput. Chem. 2003, 24, 1142. (12) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597. (13) Fan, L.; Ziegler, T. J. Chem. Phys. 1992, 96, 9005. (14) Baerends, E. J.; Branchadell, V.; Sodupe, M. Chem. Phys. Lett. 1997, 265, 481. (15) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, 1. (16) Bartlett, R. J.; Purvis, G. D. Int. J. Quantum Chem. 1978, 14, 561. (17) Cizek, J. Adv. Chem. Phys. 1969, 14, 35. (18) Bader, R. F. Atoms in Molecules: A Quantum Theory; Clarendon: New York, 1990. (19) Becke, A. D.; Edgecombe, K. E. J. Chem. Phys. 1990, 92, 5397. (20) Silvi, B.; Savin, A. Nature 1994, 371, 683. (21) Gunn, S. R. J. Am. Chem. Soc. 1965, 87 (10), 2290–2291. (22) Hinshelwood, C. N. The kinetics of chemical change; Clarendon Press: Oxford, 1942. (23) Knox, R. S.; Gold, A. Symmetry in the Solid State; W.A. Benjamin, Inc., New York and Amsterdam, 1964. (24) Bersuker, I. The Jahn Teller Effect; Cambridge University Press: Cambridge, 2006.

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Spontaneous Dissociation of Xenon Tetroxide: Phase and Structural

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