As2O3 Polymorphs: Theoretical Insight into Their Stability and

Article pubs.acs.org/crystal

As2O3 Polymorphs: Theoretical Insight into Their Stability and Ammonia Templated Claudetite II Crystallization Piotr A. Guńka,*,† Maciej Dranka,† Jacek Piechota,‡ Grazẏ na Z. Ż ukowska,† Aldona Zalewska,† and Janusz Zachara*,† †

Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Pawínskiego 5a, 02-106 Warsaw, Poland

‡

S Supporting Information *

ABSTRACT: An original room-temperature and ambientpressure method of claudetite II crystallization consisting in ammonium arsenate(III) decomposition is presented. Claudetite II is characterized by single crystal and powder X-ray diffraction, Raman spectroscopy and differential scanning calorimetry. Claudetite I and II equations of state were obtained by DFT calculations of their energies incorporating dispersive contribution accounted for by the Grimme method. It has been shown that claudetite II is metastable in the investigated pressure range and a new high-pressure As2O3 polymorph has been predicted. Presented computational results indicate that the contribution of van der Waals interactions to the systems’ energy cannot be neglected.

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Claudetite II was obtained for the first time in the late 1940s by Kürbs and co-workers,5 and its structure was determined by Pertlik in 1970s.4 However, no method of obtaining pure samples of claudetite II has been described in the literature so far. Pertlik, for instance, obtained mixtures of claudetite I and II under hydrothermal conditions. As a result, there is no experimental powder diffractogram of claudetite II in databases and studies of claudetite II thermodynamic properties have been greatly hindered.6 Therefore, thermodynamic relations between As2O3 polymorphs remain obscure. There is a number of early papers dealing with thermal stability of arsenolite and claudetite I, summarized in an article by Becker et al. and references therein.7 The studies of arsenic trioxide polymorphs transitions are complicated because of high activation energy of the reaction and the fact that they are catalyzed by water. To our best knowledge, there is only one paper concerning the stability ranges of claudetite I and claudetite II.6 The researches described there indicate that claudetite II is metastable in the whole range of its existence, that is, the claudetite I/claudetite II system is monotropic. Besides, the chemistry of aqueous solutions of arsenic has attracted considerable interest recently. This is because uncovering the changes in As speciation as a function of concentration and temperature is crucial for understanding the hydrothermal processes involving As minerals dissolution and precipitation. Obtaining such information is also essential for studying complexation of elements like Au that form complex

INTRODUCTION Arsenic occurs both in the Earth's crust and in the biosphere. It participates in many geochemical and biological processes. The abundance of arsenic in crustal rocks equals 1.8 ppm which makes it the 51st element in terms of abundance in the Earth's crust. Arsenic, like antimony and bismuth, is a chalcophile, that is, it occurs in compounds together with S, Se, and Te rather than with oxide or silicate anions.1 Nonetheless, two minerals composed of arsenic(III) oxide do occur in nature, namely, arsenolite and claudetite. Arsenolite is a cubic polymorph of arsenic(III) oxide containing adamantane-like As4O6 molecules,2 whereas claudetite is a monoclinic modification built of infinite As2O3 layers.3 In addition to vitreous As2O3 there is one more crystalline polymorph of arsenic(III) oxide called claudetite II which crystallizes in monoclinic crystal system and is built of layers similar to those from claudetite I, mineral claudetite. The basic structural unit in all arsenious oxide polymorphs is a ψ-tetrahedron consisting of arsenic atomic core surrounded by three oxygen ligands and a lone electron pair (LEP). All of the oxygen atoms are shared between two ψtetrahedra to yield stoichiometry As2O3, which results in discrete As4O6 cages in arsenolite and infinite As2O3 layers in claudetites. The layers are built of fused 12-membered As6O12 rings. The most prominent structural difference between claudetite I and claudetite II layers lies in the way lone electron pairs on arsenic atomic cores are distributed above and below sheets formed by arsenic and oxygen atoms and in the degree of layers’ corrugation.4 The crystal structures of As2O3 polymorphs, together with a schematic representation of claudetites’ layers, are depicted in Figure 1. © 2012 American Chemical Society

Received: August 10, 2012 Revised: October 12, 2012 Published: October 30, 2012 5663

dx.doi.org/10.1021/cg3011579 | Cryst. Growth Des. 2012, 12, 5663−5670

Crystal Growth & Design

Article

Figure 1. Arsenic(III) oxide polymorphs: arsenolite (a), claudetite I (b), and claudetite II (c). Schematic representation of claudetite I and II layers (d and e, respectively). Triangles represent ψ-tetrahedra and solid lines indicate LEP directed upward, whereas dashed ones indicate LEP aimed downward. parameters were optimized in a convergence study. The cutoff energy, limiting the number of plane waves used as basis functions, was set to 500 eV. The exchange-correlation energy was evaluated with the Perdew−Burke−Ernzerhof (PBE) functional based on the general gradient approximation (GGA),15,16 as well as with the local density approximation (LDA) functional for comparison.17 Integration in the reciprocal space was performed using a Monkhorst-Pack scheme.18 A Γ-centered Monkhorst-Pack grid with Ni k-points along the reciprocal → ⎯ lattice vector was used where number Ni equals max{1, l·| bi*| + 0.5} and the value of parameter l was set to 20. The calculations were stopped when the energy difference between consecutive cycles was less than 0.01 meV and maximum forces acting on atoms were smaller than 0.02 eV/Å. Initial structural parameters were taken from experimental X-ray diffraction data. In the first step, energy (Ei) of the structures was optimized with the positions of atoms and lattice constants allowed to change freely. These optimized structures were treated as starting points for subsequent calculations. Next, a series of constant cell volume (Vi) optimizations was carried out (i.e., all degrees of freedom except for volume were optimized). In the last step, the energy of As2O3 polymorphs was minimized with respect to atoms’ positions only and the unit cell shape was frozen. Integration in the first Brillouin zone was performed according to the tetrahedron method with Blöchl corrections in the final run.19 This procedure yielded a set of (Vi,Ei) points for both claudetites to which equations of state (EOS) were fitted. The QtiPlot program was used for the nonlinear least-squares fits and the applied method was scaled Levenberg−Marquardt algorithm without weighting. The results of all calculations including optimized energies and unit cell parameters are given in the Supporting Information (Tables S1−S6).

ions with As and for modeling the adsorption of elements onto the surfaces of As minerals.8−10 In this work, we present two original methods of obtaining pure batches of claudetite II single crystals free from other As2O3 polymorphs. We also show that by fine-tuning the reaction conditions one may obtain pure batches of arsenolite as well. Powder X-ray diffraction pattern, single crystal Raman spectrum and the results of claudetite II differential scanning calorimetry (DSC) studies are presented and commented. Last but not least, DFT calculations of claudetite I and II energies with their equations of state (EOS) are shown and critically evaluated.

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EXPERIMENTAL AND COMPUTATIONAL DETAILS

All chemicals and solvents except for ammonium arsenate(III) were obtained from commercial sources and used as received. NH4AsO2 was synthesized according to the procedure reported earlier.11 Reactions were carried out in open glass vessels. The powder X-ray diffraction patterns were recorded on a Seifert HZG-4 automated diffractometer using Cu Kα radiation (λ = 1.5418 Å). All samples were measured at 295 K. The data were collected in the Brag-Brentano (θ/2θ) horizontal geometry (flat reflection mode) between 10 and 60° (2θ) in 0.04° steps. The optic of the HZG-4 diffractometer contains a system of primary Soller slits and a fixed aperture slit of 2.0 mm. One scattered-radiation slit of 2 mm was placed after the sample, followed by the detector slit of 0.2 mm. Raman spectra were recorded using Nicolet Almega Dispersive Raman spectrometer. Spectra of solid arsenolite, claudetite I and claudetite II samples were obtained using 780 nm excitation line and a 1200 lines/mm resolution grating. The exposition time was 120 s. DSC data were collected using a TA Instruments DSC Q200 scanning calorimeter. Samples were placed in aluminum Tzero hermetic pans. An empty pan served as a reference. Two cycles of heating and cooling at 5 °C/min in the temperature range of 20−300 °C were carried out in the flow of nitrogen. Density functional theory (DFT) energies of claudetite I and claudetite II were computed using the projector augmented-wave (PAW) method12 implemented in the VASP code (VASP 4.6.36 and VASP 5.2.12).13,14 The values of the computations-controlling

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RESULTS AND DISCUSSION Studies of Ammonium Arsenite Decomposition. Ammonium arsenite decomposition was studied in aqueous suspensions. A portion of NH4AsO2 crystals (0.4 g) was dissolved in a small amount (∼2 mL) of its aqueous solution, saturated at 7 °C. The resulting mixture was stirred and allowed to warm up to RT. During and after ammonium arsenite dissolution ammonia is evolved and well shaped claudetite II single crystals are formed. The faces of a representative single 5664



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concentrated As2O3 solutions as demonstrated by Tossell’s comparison of the calculated frequencies with experimental Raman spectra.8,22 All our considerations are naturally based on the assumption that claudetite II layers are formed from 12membered AsO rings and not from, for example, chains. On the other hand, claudetite I is formed upon slow decomposition of ammonium arsenite from less concentrated aqueous solutions (saturated at 7 °C) carried out at 10 °C. This suggests that, given enough time, oligomeric As(III) oxoanions present in the solution after dissolution of NH4AsO2 can rearrange to form precursors of claudetite I layers. Carrying out the process at lower concentrations of As slows down the decomposition leading to the formation of the thermodynamically more stable layered polymorph, claudetite I. Room-temperature decomposition of NH4AsO2 (0.2 g) dissolved in distilled water (∼5 mL), accompanied by the evolution of ammonia and evaporation of water, leads to goodquality single crystals of arsenolite. Another route to the crystallization of this polymorph is the decomposition of ammonium arsenite in absence of water, for example, by the decomposition of dry crystals or crystals suspended in methanol. As2O3 Crystallization in the Presence of an Amino Acid. To investigate the influence of amino acids on the templating effect of ammonia on the crystallization of As2O3, 0.5 g of arsenic trioxide was dissolved in water in the presence of an amino acid (glycine or alanine) and ammonia. The resulting solution was transferred into a Petri dish and left for crystallization via water evaporation. The obtained crude product was a mixture of claudetite II and amino acid crystals. Subsequently, amino acid was dissolved in water and claudetite II single crystals were separated from the resulting solution (see

crystal were indexed and the habit together with (hkl) indices is shown in Figure 2. The crystallization conditions suggest that

Figure 2. Claudetite II single crystals obtained via crystallization in the presence of glycine and the crystal habit of claudetite II with indexed faces.

claudetite II is formed under kinetic control. If one takes into account the Ostwald’s rule, they could say the dominant arsenic species in a concentrated NH4AsO2 solution must resemble quite closely the crystal structure of claudetite II. 20,21 Furthermore, taking advantage of Tossell’s results, one might conclude that the dominant species in concentrated ammonium arsenite solutions is As6O6(OH)6.8 This is contrary to the fact that As3O3(OH)3 seems to be the most abundant species in

Figure 3. Powder X-ray diffraction patterns of claudetite II: textured sample (a) and a sample without texture (b). 5665



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Figure 4. Raman spectra of As2O3 polymorphs.

intense one, are split. Namely, the Ag As−O−As deformation mode, which gives a single band, centered at 459 cm−1 in spectrum of claudetite I, is split into two contributions with maxima at 451 and 473 cm−1 in the spectrum of claudetite II. The most striking difference between the spectra of these forms is the presence of a strong band at 530 cm−1 for claudetite II. This band can correspond to one of the AsO3 symmetric stretching vibrations. Weak bands at 561 and 588 cm−1 can also be ascribed to AsO3 symmetric stretch, while peak at 737 cm−1 should be assigned to one of the AsO3 asymmetric stretching vibrations. The tentative assignment of other bands is given in Table 1. The spectrum of cubic crystalline As2O3, arsenolite, is in excellent agreement with literature data.24,25 According to the assignment of Jensen et al., the most intense band in the spectrum, at 370 cm−1, corresponds to As−O−As bending vibrations. Third, DSC curves of claudetite II recorded within the 20− 300 °C temperature range are presented (Figure 5). The As2O3 samples were subjected to two cycles of heating and cooling, all of them at a 5 °C/min rate. The endothermic transitions during heating and exothermic transitions during cooling are attributed to melting and crystallization, respectively. Our hypothesis is based on the fact that Becker and co-workers report the melting point of claudetite II to be 310.5 °C.6 Analysis of powder diffractograms of the samples after DSC measurements has indicated that they contain claudetite II only (see Figure S1 in Supporting Information). This observation remains in agreement with the statement of Becker et al. that claudetite I/ claudetite II is a monotropic system.6 The endothermic peak that appears around 270 °C is attributed to liberation of gaseous As4O6. It was shown by a few DSC and TG-MS experiments that it appears only during the

Figure 2.). The identification and determination of the As2O3 polymorph purity was accomplished via powder diffraction experiments on Agilent Gemini A Ultra diffractometer (see Figure S1 in Supporting Information). Characterization of claudetite II. First of all, we present here the first experimental powder diffractogram of claudetite II (Figure 3). Interestingly, reflections intensities in the experimental diffractogram deviate significantly from the intensities in the calculated diffractogram when claudetite II sample is ground in a mortar (Figure 3a). This is attributed to a substantial preferred orientation in the sample in the direction of (001) crystallographic planes. Claudetite II contains (001) cleavage planes due to weak interactions between layers containing strong covalent bonds. As a result thin plates are formed upon grinding which orient themselves in such a way that texture is observed. Although the crystal structure of claudetite II was determined by Pertlik in 1975,4 we redetermined it at room temperature and at 100 K by single crystal X-ray diffraction experiments. The crystal data which are much more precise than the previous ones are available in the Supporting Information. There are no significant differences between our RT crystal data and Pertlik’s data as exemplified by the As−O bond lengths which vary from 1.765(3) to 1.800(3) Å (our data) and from 1.771(15) to 1.821(17) Å (ref 4.). Second, we present the Raman spectrum of a claudetite II single crystal and compare it with spectra of other arsenic trioxide polymorphs. Raman spectrum of claudetite II has not been described so far, and literature data for the other monoclinic form, claudetite I, are rather scarce. The most complete assignment was given by Mercier and Sourisseau.23 As shown in Figure 4, the spectrum of claudetite II resembles that of claudetite I, but several bands, including the most 5666



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I and II energy as a function of unit cell volume in order to theoretically determine their equations of state and find out which polymorph is predicted to be more stable from the theoretical point of view. Both LDA and GGA approximations were applied. The Birch−Murnaghan EOS, having the following form, was used in this study.26

Table 1. Assignment of Claudetite I and Claudetite II Raman Bands (cm−1) claudetite Ia

claudetite II

assignmentb

123 172 190 Ag 216 Bg 236 Bg 247 Bg (dp) 257 Ag 283 (p) 328 Bg

198 220 232 262 270 280 (p) 331

δsAsO3

355 Ag (p)

348

δsAsO3

459 Ag (p)

451 (p)

δsAsO3

E (V ) = E 0 +

473 (p)

δsAsO3

503 Bg (dp)

506

υsAsO3

541 Bg (dp)

530 (p)

υsAsO3

561

υsAsO3

588

υsAsO3

628 Bg (dp) 817

630

where B0 is the bulk modulus, B′0 is the bulk modulus derivative with respect to pressure, E0 is the energy (per unit cell, Z = 4) and V0 is the volume of ground state. The parameters resulting from a least-squares fit are summarized in Table 2 and the EOS curves with calculated points are depicted in Figure 6. Table 2. Parameters of Birch−Murnaghan EOS for Claudetite I and II within the GGA and LDA Approximations GGA approximation

υasAsO3

737

υasAsO3

801

υasAsO3

835

υasAsO3

⎞ B0 V ⎛ (V0/V )B0′ B0 V0 ⎜⎜ − 1⎟⎟ − B0′ ⎝ B0′ − 1 B0′ − 1 ⎠

E0 (eV) V0 (Å3) B0 (GPa) B′0

LDA approximation

claudetite I

claudetite II

claudetite I

claudetite II

−120.7707(11) 384.9(6) 2.9(1) 10.0(2)

−120.8817(15) 399.1(5) 3.1(1) 9.9(2)

−135.419(3) 285.5(3) 22.2(2) 8.4(3)

−135.338(2) 299.1(3) 18.6(1) 8.0(2)

a

Ag, Bg = symmetry class of the vibration. p and dp stand for polarized and depolarized bands, respectively bBand attribution after Mercier and Sourisseau.23

The results of our calculations are inconclusive. EOS obtained within the GGA approximation (PBE functional) indicates that claudetite II is more stable than claudetite I, whereas according to the EOS fitted to the LDA energies claudetite I is a more stable polymorph. The differences between theoretical ground state volumes and experimental results (308.3 Å3 and 327.6 Å3 for claudetite I and II, respectively) are of the order of −10% and +20% for LDA and PBE, respectively, which is, in our opinion, unacceptable even though DFT calculations yield results for T = 0 K. The results confirm the fact that LDA and PBE exchange-correlation functionals are not suitable for describing periodic systems where both strong covalent bonds and weak van der Waals interactions play significant roles.27,28 This is the case in claudetites I and II where infinite As2O3 layers containing

first heating and is accompanied by a weight loss of ∼5% (see Figure S2 in Supporting Information). No peaks up to 300 m/z on the mass spectrum of gases leaving thermobalance were observed. In order to prove our hypothesis that the weight loss corresponds to the evolution of arsenic trioxide vapors, we heated carefully a portion of claudetite II crystals in a sealed capillary placed in a melting point apparatus up to 280 °C and recorded Raman spectrum of the substance that condensed on the walls of capillary that were sticking out of the heating chamber. The substance was arsenolite. DFT Study of Relative Claudetite I and II Thermodynamic Stability. We performed DFT calculations of claudetite

Figure 5. DSC curves of two cycles of claudetite II heating and cooling. 5667



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tional Kohn−Sham DFT energy.32,33 Bučko and co-workers have implemented this method in VASP and have shown that, although it is computationally inexpensive, it produces results which are in reasonably good agreement with experiment. It has also been found that the scheme overestimates vdW interactions and, consequently, resulting lattice parameters are underestimated.34 Thus, we performed our calculations with the PBE functional only. Recently, Allen and co-workers have studied tin monoxide, a system which is similar to claudetites in that it is built of layers and that there is a LEP on the tin atomic core.35 Two approaches have been successfully utilized and compared: one which the authors referred to as DFT-vdW and DFTD2. We have decided to apply the Grimme’s approach only as it introduces fewer empirical parameters and has been tested on a wider range of systems than the DFT-vdW approach outlined in the article. The parameters of the obtained Birch−Murnaghan EOS are given in Table 3 and the EOS curves are depicted in Figure 7. Table 3. Parameters of Birch−Murnaghan EOS for Claudetite I and II within the DFTD2 Approximation DFTD2 E0 (eV) V0 (Å3) B0 (GPa) B′0

claudetite I

claudetite II

−126.724(3) 300.2(2) 30.0(2) 4.72(8)

−126.212(3) 302.9(3) 22.7(2) 7.5(2)

Figure 6. Curves of Birch−Murnaghan EOS for claudetite I and II within the GGA (a) and LDA (b) approximations. Only filled points were used for fitting. Dashed vertical lines (Iexp and IIexp) indicate experimental unit cell volumes of claudetite I and II (308.3 and 327.6 Å3, respectively).

covalently bonded As and O atoms interact with each other via weak interactions.29 Matsumoto et al. have performed DFT calculations with the PBE exchange-correlation functional and have found that arsenolite is predicted to be slightly less stable at low temperatures than claudetite II.30 There is, however, an experimental report on the relative stability of claudetite I and arsenolite where it was shown that arsenolite is more stable at low temperatures, below 13 °C.31 Taking all of our results into account, including ones with dispersion correction (see below), it is highly questionable to rank As2O3, Sb2O3, and Bi2O3 polymorphs in energetic hierarchies, as the authors proposed, because the energy differences between polymorphs quoted in the article are of the order of 0.1 eV/formula unit or even less and van der Waals interactions are not taken into account in their calculations.30 We cannot fail to note that the authors mention only two polymorphs of As2O3 (one cubic and one monoclinic) while there are three crystalline and one glassy indeed. Therefore, to account for van der Waals interactions present in the claudetites structures, we performed DFT calculations with the Grimme correction (DFTD2). This approach consists in adding a semiempirical dispersion potential to the conven-

Figure 7. EOS curves of claudetite I and II within the DFTD2 approximation. Only filled points were used for fitting. The inset shows the region, indicated by a dashed rectangle, where polymorphic transition of claudetite II takes place. Dashed vertical lines (Iexp and IIexp) indicate experimental unit cell volumes of claudetite I and II (308.3 and 327.6 Å3, respectively).

The results are completely different from the ones without van der Waals interactions taken into account. Claudetite I is predicted to be more stable than claudetite II and the EOS curves do not intersect with each other which implies that claudetite II is metastable in the whole pressure range studied. The ground state volumes are in much better agreement with experiment than before (contractions of 2% and 8% for claudetite I and II, respectively). Last but not least, DFTD2 calculations predict that claudetite II should undergo a 5668



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Figure 8. Polymorphic transition of claudetite II predicted by DFTD2 calculations taking place at around 150 kbar. Views along crystallographic X axes.

determined at 100 K and at room temperature). This material is available free of charge via the Internet at http://pubs.acs. org/.

structural transformation into a new polymorph when subjected to pressures higher than 150 kbar (note the discontinuity at around 230 Å3 in Figure 7). The low- and high-pressure structures of claudetite II are shown in Figure 8. For lattice constants and fractional coordinates of atoms in the structure of high-pressure As2O3 polymorph see Table S7 in the Supporting Information.

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Corresponding Author

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*E-mail: [email protected] (P.A.G.); [email protected] (J.Z.).

CONCLUSIONS Summing up, the results of our research indicate that the decomposition of ammonium arsenite is a convenient method of obtaining various polymorphs of arsenic(III) oxide. This is an original synthetic route toward pure batches of claudetite II single crystals at ambient conditions. Another convenient way to obtain claudetite II is to recrystallize As2O3 in the presence of ammonia and glycine or alanine. It must be stressed that, to our best knowledge, these are the only methods of crystallizing pure claudetite II. The reactions may be carried out at ambient conditions which is also significant, given that the methods exploited so far require hydrothermal conditions. The fact that claudetite II is formed under kinetic control suggests that concentrated ammonium arsenite solutions contain among others 12-membered As6O6(OH)6 rings. The results of DFT computations of layered arsenic(III) oxide polymorphs are strongly dependent on the choice of the exchange-correlation functional, when PBE functional is used, claudetite II seems to be more stable than claudetite I, whereas LDA calculations suggest otherwise. However, when a correction involving the effects of van der Waals interactions is included into the DFT framework, the results change qualitatively and indicate that claudetite II is less stable than claudetite I in the whole range of pressures. To verify the existence of the predicted polymorph high-pressure diffraction experiments of As2O3 polymorphs are planned. Finally, the results of DSC measurements show that claudetite II does not undergo any irreversible transition to another arsenic(III) oxide polymorph within the temperature range from 20 to 300 °C and they are in agreement with the commonly accepted opinion claudetite I/claudetite II is a monotropic system.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the Warsaw University of Technology. Calculations were carried out in the Interdisciplinary Centre for Mathematical and Computational Modelling (computational grant No. G28-3). Preparation and interpretation of X-ray powder diffraction patterns of claudetite II by A. Ostrowski is gratefully acknowledged.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Powder diffraction patterns of claudetite II samples before and after DSC measurements, TG curve of claudetite II, results of DFT calculations together with structural parameters for the high-pressure As2O3 polymorph and crystallographic information in CIF format (crystal structures of claudetite II 5669



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(19) Blöchl, P. E.; Jepsen, O.; Andersen, O. K. Phys. Rev. B 1994, 49, 16223−16233. (20) Ostwald, W. Z. Phys. Chem. 1897, 22, 289−330. (21) Threlfall, T. Org. Process Res. Dev. 2003, 7, 1017−1027. (22) Pokrovski, G.; Gout, R.; Schott, J.; Zotov, A.; Harrichoury, J. Geochim. Cosmochim. Acta 1996, 60, 737−749. (23) Mercier, R.; Sourisseau, C. Spectrochim. Acta, Part A 1978, 34, 337−342. (24) Gilliam, S. J.; Merrow, C. N.; Kirkby, S. J.; Jensen, J. O.; Zeroka, D.; Banerjee, A. J. Solid State Chem. 2003, 173, 54−58. (25) Jensen, J. O.; Gilliam, S. J.; Banerjee, A.; Zeroka, D.; Kirkby, S. J.; Merrow, C. N. J. Mol. Struct.: THEOCHEM 2003, 664−665, 145− 156. (26) Murnaghan, F. D. Proc. Natl. Acad. Sci. 1944, 30, 244−247. (27) Dobson, J. F.; McLennan, K.; Rubio, A.; Wang, J.; Gould, T.; Le, H. M.; Dinte, B. P. Aust. J. Chem. 2001, 54, 513−527. (28) Li, Y.; Lu, D.; Nguyen, H.; Galli, G. J. Phys. Chem. A 2009, 114, 1944−1952. (29) Gibbs, G. V.; Wallace, A. F.; Cox, D. F.; Dove, P. M.; Downs, R. T.; Ross, N. L.; Rosso, K. M. J. Phys. Chem. A 2009, 113, 736−749. (30) Matsumoto, A.; Koyama, Y.; Togo, A.; Choi, M.; Tanaka, I. Phys. Rev. B 2011, 83, 214110. (31) Schulman, J. H.; Schumb, W. C. J. Am. Chem. Soc. 1943, 65, 878−883. (32) Grimme, S. J. Comput. Chem. 2006, 27, 1787−1799. (33) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys. 2010, 132, 154104. (34) Bučko, T.; Hafner, J.; Lebègue, S.; Á ngyán, J. G. J. Phys. Chem. A 2010, 114, 11814−11824. (35) Allen, J. P.; Scanlon, D. O.; Parker, S. C.; Watson, G. W. J. Phys. Chem. C 2011, 115, 19916−19924.

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As2O3 Polymorphs: Theoretical Insight into Their Stability and

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