J. Phys. Chem. B 2000, 104, 11801-11804
11801
Hydrogen Elimination and Solid-State Reaction in Hydrogen-Bonded Systems under Pressure: The Case of HBr Takashi Ikeda,* Michiel Sprik,† Kiyoyuki Terakura,‡ and Michele Parrinello§ JRCAT, Angstrom Technology Partnership, 1-1-4, Higashi, Tsukuba, Ibaraki 305-0046, Japan, Department of Chemistry, UniVersity of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom, JRCAT, National Institute for AdVanced Interdisciplinary Research, 1-1-4, Higashi, Tsukuba, Ibaraki 305-8562, Japan, and Max-Planck-Institut fu¨ r Festko¨ rperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany ReceiVed: July 18, 2000; In Final Form: September 26, 2000
The ab initio constant-pressure molecular dynamics method was applied to investigate the high-pressure chemistry of hydrogen-bonded solid HBr. It is shown that the molecular solid becomes unstable against elimination of H2 at pressures beyond about 20 GPa. Our simulation suggests that the undercoordinated Br atoms in H-deficient HBr are not reactive under high pressure because of delocalization of the holes doped by H vacancies and the high diffusivity of H atoms. We also demonstrate that decompression process can reactivate undercoordinated Br atoms to form Br2. Mechanisms to explain these instabilities and solid-state reactions are discussed.
Introduction Pressure is a useful parameter for phase control in solids and often uncovers hidden competing factors in cohesive, transport, and magnetic properties. This was the motivation behind a number of recent high-pressure studies of hydrogen-bonded systems,1-3 which focused on proton hopping in double-well potentials, hydrogen-bond symmetrization, molecular rotation, related quantum effects, and structural phase transitions. A further important aspect of the use of pressure is the synthesis of materials. For example, polymerization of acetylene proceeds at room temperature without the help of catalysts once the pressure is raised above 3.5 GPa.4 Similarly, the multilayer highTc cuprate CuBa2Ca3Cu4O12-y can be synthesized under a pressure of 5 GPa at 1100 °C.5 As suggested by recent experiments,6,7 pressure can also have an effect on the chemistry of hydrogen-bonded systems, inducing decomposition followed by phase separation or hydrogen evaporation. Though critical pressures can vary significantly from system to system, these phenomena may be rather common features of hydrogen bonding in solids. In the present study of molecular solid HBr, we will encounter a typical example of this behavior. After discussing the stability of HBr against hydrogen elimination, we analyze the subsequent solid-state reaction of Br2 formation in a sample with hydrogen deficiencies. This simple example of solid-state chemistry under pressure contributes further to our understanding of hydrogen bonding. Let us first give a brief summary of the experimental information on HBr.6,8 Hydrogen bonding in HBr is comparatively weak, and 0.5 GPa of pressure is required to solidify HBr at room temperature. The molecules crystallize in an fcc structure (phase I) with full orientational disorder. Phase I extends at room temperature from the melting line to 13.6 GPa, where a transition to an ordered structure (phase III) is observed. * To whom correspondence should be addressed at JRCAT, Angstrom Technology Partnership. E-mail:
[email protected]. † University of Cambridge. ‡ JRCAT, National Institute for Advanced Interdisciplinary Research. § Max-Planck-Institute fu ¨ r Festko¨rperforschung.
At this elevated pressure, molar volume has been compressed to about 65% of the value in the low-pressure solid, corresponding to more than a 20% reduction in intermolecular hydrogen-bond distance. Further compression inevitably leads to symmetric hydrogen bonds, with the H atoms located midway between two neighboring anions. Hydrogen-bond symmetrization for HBr was detected recently by infrared absorption spectroscopy at around 40 GPa at 298 K.6 While hydrogen-bond symmetrization is expected to be a universal phenomenon and was actually also reported for ice,1 the occurrence of chemical transformations in the solid was a unique aspect of HBr when it was first observed by Katoh et al.6 One piece of evidence was the gradual change of the lattice vibrational spectrum while the sample was kept under 42.8 GPa of pressure for 24 h. Furthermore, on release of the pressure, their Raman measurements showed the appearance of lines characteristic of Br2. Very recently, the same group found signs of Br2 formation already at ∼20 GPa on pressure loading.9 Another recent experiment suggests that solid H2S may exhibit a similar high-pressure response.7 In a previous numerical study,3 we observed formation of H2 at 80 GPa. In view of the short duration of our molecular dynamics runs (picoseconds), this pressure must be considered an upper limit, and decomposition on longer time scales may begin in real samples at much lower pressures. Our result, however, provided a clear indication that H2 formation can create reactive Br atoms, and may, therefore, trigger formation of Br2. Furthermore, we speculate that under ambient temperature conditions, the produced H2 may escape from the sample. At this stage, we can also speculate that H2 may segregate in the sample, leading to phase separation. There is no qualitative difference between the two cases in the subsequent arguments on the reactivity of Br atoms once Br-rich regions are formed, anyway. However, the possibility of H2 segregation in the sample seems to be unlikely because no signals for H2 molecules were observed in Raman spectra.9 Therefore, we first make a thermodynamic estimate of the critical pressure Pc beyond which the molecular HBr crystal becomes unstable w.r.t H2 elimination,
10.1021/jp002534s CCC: $19.00 © 2000 American Chemical Society Published on Web 11/16/2000
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Ikeda et al.
and then we study the process of Br2 formation in the residual dehydrogenated system. Such a solid-state reaction following hydrogen elimination under pressure, to the best of our knowledge, has not been investigated theoretically. Anticipating our results, we find an estimate for Pc of ∼20 GPa, which is consistent with the most recent experimental observation by Katoh et al.9 This suggests that in their previous experiment,6 conducted at a pressure of 42.8 GPa, that is, well over Pc, the loss of an amount of H2 molecules by evaporation must have been substantial, with nucleation of Br2 solid as a natural consequence. The new data on Pc can also be exploited to investigate the process of Br2 formation under more controlled circumstances. We set up our problem in the following way. A system at the critical pressure Pc will respond to a small increment in pressure by removal of H2, which will shift the equilibrium back below the threshold pressure, and we end up with a sample with a small amount of H deficiency. The question is, then, whether the nonbonded Br atoms are sufficiently reactive to form Br2 and, if possible, how the Br2 formation proceeds. An answer to this question might also explain why undercoordinated Br atoms are chemically inert at high pressure,3 and only become reactive on decompression, as we will demonstrate here. Moreover, the consideration of this issue may also give an interpretation of why the characteristic peaks of Br2 are clearly observed in Raman spectra on the unloading process. Our computational approach is based on the ab initio constantpressure molecular dynamics (MD) method,10 applied successfully in previous studies of structural transformation under pressure.11 In this method, pressure is applied using the ab initio MD implementation of the Parrinello-Rahman approach12 combined with a Nose´-Hoover thermostat.13 The electronic structure and atomic forces are obtained using the plane-wave pseudopotential approach to density functional theory (DFT) in the Becke-Lee-Yang-Parr approximation (without spin polarization).14 The hydrogen and bromine cores are described by norm-conserving pseudopotentials of the von Barth-Car15 for hydrogen and Troullier-Martins type16 for bromine. Brillouin zone sampling is restricted to the supercell Γ point. The accuracy of our employed exchange-correlation functional for predicting properties of HBr was discussed in detail in ref 3. Temperature is maintained at 300 K by a Nose´-Hoover thermostat13 unless mentioned otherwise. The simulations were performed using the CPMD package.17 Results and Discussion The defect H28Br32 system studied in the present work corresponds to a case where four hydrogen atoms have evaporated from a system originally containing 32 HBr molecules. This particular system is used in the analysis of the critical pressure simply because the same system is used in the subsequent simulations for Br2 formation.18 To examine the relative stability of the elimination product, we calculated the enthalpies H at 300 K for the perfect crystal under pressure (H32Br32), for the crystal with H vacancies (H28Br32) under the same pressure and for H2 molecules under ambient conditions (2H2). The solid line in Figure 1 shows the quantity defined by
∆H ) H[H32Br32] - H[H28Br32] - H[2H2]
(1)
The total energy is always lower for the perfect system compared to the H-deficient product plus free H2 molecules, whereas the volume is always larger at the same pressure. As a result, the Kohn-Sham energies and the pV terms give negative and
Figure 1. Comparison of enthalpies of solid HBr with and without hydrogen vacancies. Shown is the difference in enthalpy of the perfect HBr crystal under pressure (H32Br32) w.r.t the crystal with H vacancies under the same pressure (H28Br32) plus two H2 molecules under ambient conditions (2H2).
positive contributions, respectively, to ∆H irrespective of the pressure. With increasing pressure, compression of the sample becomes harder, particularly for the perfect system in which the close-packed sublattice of Br atoms is maintained virtually to at least ∼40 GPa, leading to thermodynamic instability of HBr against H2 elimination. The critical pressure Pc estimated by ∆H is about 20 GPa.19 Entropy effects will favor the combination of the H-deficient solid and free hydrogen molecules, reducing Pc. The results of our previous paper3 indicate that the presence of H-atom vacancies is not sufficient to initiate Br2 formation, even at pressures as high as ∼40 GPa. To verify that this is not due to some energy barrier, we brought two selected pairs, a and b, of Br atoms closer together in the system with two H-atom vacancies, shown in Figure 2a, by using constraint techniques.20 We computed the free energy and found a monotonic increase up to as much as 40 kcal‚mol-1 at a typical Br2 bond distance of 2.3 Å for both the pairs, as shown in Figure 2b. Here, we propose the following rationalization for this remarkable stability. Under high pressure, the Br 4p states are extended and form a broad valence band, as shown in ref 3. The holes created in this band by H vacancies are also extended. Therefore, the weight of a hole on a a given 4p orbital is very small, even if the Br atom is unsaturated, making all Br atoms nonreactive. To activate a Br atom, the holes must be localized at definite Br sites at the expense of an amount of kinetic energy that can be roughly estimated by the 4p bandwidth. Lowering the pressure decreases the overlap and may therefore stimulate reactivity. We tested this hypothesis by carrying out a series of MD simulation with a variable supercell.21 Pressure was released from 40 GPa down to 6 GPa at the rate of -11 GPa‚ps-1. During decompression and for a short period afterward, velocity scaling was applied to reequilibrate the system at 300 K. An essential role of the decompression is the recovery of the molecular integrity of HBr. We quantified this process in Figure 3 by plotting the variation of the HBr bond length 〈rHBr〉 averaged over the 28 HBr molecules in each instantaneous configuration along with the magnitude of the corresponding fluctuations 〈∆rHBr〉. At high pressure, near the point of hydrogen-bond symmetrization, the equilibrium HBr bond length is elongated by as much as 0.1 Å, compared to 1.45 Å at low pressure. Also, the fluctuations are enhanced. This is consistent with a flatter H-Br potential and a minimum shifted toward larger bond distances. To expose Br2 formation, we show in Figure 3 the shortest (rBrBr1) and next shortest (rBrBr2) BrBr
Hydrogen-Bonded Systems under Pressure: HBr
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Figure 4. Schematic representation of the deactivation process in response to an attempt to form Br2 in the compressed HBr solid with H deficiencies.
Figure 2. (a) Selected pairs a and b of Br atoms in the system with two H-atom vacancies at 40 GPa used for estimating the difference of free energy using constraint techniques. Shown is the projection onto the bc plane. Filled and open circles indicate atoms located at different bc planes. The hydrogen-bond symmetrization occurs theoretically above ∼40 GPa. (b) The profile of free energy as a function of the distance between two Br atoms shown in (a). The free-energy curve for the pair a and b is represented by solid and dashed lines, respectively.
Figure 3. Time evolution of (a) pressure, (b) the shortest (rBrBr1) and next shortest (rBrBr2) BrBr distances, (c) the average HBr bond length evaluated over 28 HBr molecules for each configuration, and (d) the magnitude of the HBr bond length fluctuations w.r.t the average value.
distance as functions of time. The curves show clear correlations. For the first 3 ps, rBrBr1 and rBrBr2 increase following the isotropic dilation of the cell. This is accompanied by a gradual reduction of 〈rHBr〉, which reaches its usual length of 1.45 Å at 3.0 ps. At this point, rBrBr1 suddenly drops to ∼2.5 Å, which is still about 0.2 Å longer than the gas-phase value. Between 3.0 and 6.0 ps,
rBrBr2 starts deceasing as well and finally merges with rBrBr1. At 6.0 ps, rBrBr1 undergoes a second discontinuity, shrinking to about 2.3 Å. After that, the oscillations in rBrBr1 and rBrBr2 are rapid but stationary, while, also, the fluctuations in HBr bond length are less pronounced. We can therefore safely assume that at around 6.0 ps, the mixed system of HBr and Br2 reaches thermal equilibrium. In the dynamical simulation just described, we found a further important aspect of the reassembling of HBr molecules during Br2 formation that is related to the mobility of protons in the sample. The situation is qualitatively explained by the simplified two-dimensional model in Figure 4. In this model, two bare Br atoms happen to be at neighboring sites and are ready to join up in a Br2 pair (Figure 4a). However, in the compressed solid, H atoms located between surrounding Br atoms may use the opportunity to make more room for themselves and can do so quickly because of the shallower confining potential at high pressure. Therefore, as soon as the two bare Br atoms come closer, the H atoms near them can jump into the extra space that has been freed up by the movement of these Br atoms (Figure 4b). As a result, these Br atoms are no longer bare, and they return back to their original positions. If the pressure is released, locking the H atoms in HBr molecules, such movement of H atoms will not occur, and the process of Br2 formation can be completed.22 Indeed, whereas the initial configuration for the decompression run was prepared so as to satisfy the condition of Figure 4a, Br2 formation that appeared to happen just at the beginning of the run was inhibited by the movement of neighboring H atoms. The actual probe of dynamics and crystal symmetry under high pressure is spectroscopy, such as infrared absorption or Raman scattering measurements. Figure 5 shows the vibrational density of states in the low-wavenumber region between 0 and 600 cm-1. The spectrum is calculated from the velocity autocorrelation of all atoms, that is, 32 Br and 28 H atoms (solid), using the configurations after 6.0 ps when the pressure has settled at 6.0 GPa. The vibrational modes for the perfect HBr crystal in this wavenumber region can be categorized into two groups: translational modes between 0 and 200 cm-1 and librational modes between 300 and 600 cm-1. The librational modes of the system with the H-atom vacancies are responsible for the broad spectrum between 200 and 600 cm-1. A clear structure is missing due to the disorder in the molecular orientations. The rather sharp peak located at around 230 cm-1 can be attributed convincingly to stretching mode of Br2.
11804 J. Phys. Chem. B, Vol. 104, No. 49, 2000
Figure 5. Vibrational density of states calculated from the velocities of all atoms (solid), 32 bromine atoms (dashed), and 28 bromine atoms that do not form Br2 (dot-dashed).
Conclusion We have computed the reaction enthalpy for H2 elimination from a HBr molecular crystal and showed that the system becomes thermodynamically unstable when pressure increases above ∼20 GPa. We then studied the process of Br2 formation in the H-deficient HBr solid. Our simulations demonstrate that decompression is needed for the reaction to occur. Our interpretation is that the holes doped by the H vacancies are not sufficiently localized at undercoordinated Br sites as a consequence of broadening of the Br 4p bands at high pressure, making the Br atoms less reactive. A further factor is the high diffusivity of the H atoms, which frustrates incipient Br2 bond formation by passivating active Br atoms. Decompression restores the molecular integrity of HBr, which enhances localization of holes at the bare Br atoms and suppresses H atom migration. Thus, our calculations clarified that at high pressure the two collective aspects, hole delocalization and concerted H motion, inhibit Br2 formation, whereas at low pressure Br2 formation is realized as a usual reaction between two reactive Br atoms. Acknowledgment. We thank Dr. K. Aoki and his group for their valuable discussion and useful experimental information prior to publication. The present work was partly supported by NEDO (New Energy and Industrial Technology Development Organization) and CREST (Core Research for Evolutional Science and Technology) of the Japan Science and Technology Corporation. References and Notes (1) Goncharov, A. F.; Struzhkin, V. V.; Somayazulu, M. S.; Hemley, R. J.; Mao, H. K. Science 1996, 273, 218. Aoki, K.; Yamawaki, H.; Sakashita, M.; Fujihisa, H. Phys. ReV. B 1996, 54, 15673. Struzhkin, V.
Ikeda et al. V.; Goncharov, A. F.; Hemley, R. J.; Mao, H. K. Phys. ReV. Lett. 1997, 78, 4446. (2) Benoit, M.; Marx, D.; Parrinello, M. Nature 1998, 392, 258. (3) Ikeda, T.; Sprik, M.; Terakura, K.; Parrinello, M. J. Chem. Phys. 1999, 111, 1595. (4) Aoki, K.; Usuda, S.; Yoshida, M.; Kakudate, Y.; Tanaka, K.; Fujiwara, S. J. Chem. Phys. 1988, 89, 529. (5) Ihara, H.; Tokiwa, K.; Ozawa, H.; Hirabayashi, M.; Negishi, A.; Matuhata, H.; Song, Y. S. Jpn. J. Appl. Phys. 1994, 33, L503. (6) Katoh, E.; Yamawaki, H.; Fujihisa, H.; Sakashita, M.; Aoki, K. Phys. ReV. B 1999, 59, 11244. (7) X-ray patterns of solid H2S above ∼30 GPa and at room temperature agree well with those for phase II of solid S [Fujihisa, H.; Sakashita, M.; Yamawaki, H.; Aoki, K. Meeting Abstracts Physical Society of Japan, 1999; Vol. 54 [4], p 768 (in Japanese)]. (8) Kume, T.; Tsuji, T.; Sasaki, S.; Shimizu, H. Phys. ReV. B 1998, 58, 8149. (9) E. Katoh et al. Private communication. (10) Car, R.; Parrinello, M. Phys. ReV. Lett. 1985, 55, 2471. Focher, P.; Chiarotti, G. L.; Bernasconi, M.; Tosatti, E.; Parrinello, M. Europhys. Lett. 1994, 26, 345. (11) Benoit, M.; Bernasconi, M.; Focher, P.; Parrinello, M. Phys. ReV. Lett. 1996, 76, 2934. Scandalo, S.; Bernasconi, M.; Chiarotti, G. L.; Focher, P.; Tosatti, E. Phys. ReV. Lett. 1995, 74, 4015. M. Bernasconi, Parrinello, M.; Chiarotti, G. L.; Focher, P.; Tosatti, E. Phys. ReV. Lett. 1996, 76, 2081. (12) Parrinello, M.; Rahman, A. Phys. ReV. Lett. 1980, 45, 1196. (13) Nose´, S. J. Chem. Phys. 1984, 81, 511. Hoover, W. G. Phys. ReV. A 1985, 31, 1695. (14) Becke, A. D. Phys. ReV. A 1988, 38, 3098. Lee, C.; Yang, W.; Parr, R. C. Phys. ReV. B 1988, 37, 785. (15) Laasonen, K.; Sprik, M.; Parrinello, M.; Car, R. J. Chem. Phys. 1993, 99, 9080. (16) Troullier, N.; Martins, J. L. Phys. ReV. B 1991, 43, 1993. (17) These calculations were carried out with the program CPMD (Hutter, J.; Ballone, P.; Bernasconi, M.; Focher, P.; Fois, E.; Goedecker, St.; Marx, D.; Parrinello, M.; Tuckerman. CPMD, Version 3.0; MPI fu¨r Festko¨rperforshung and IBM Zurich Research Laboratory, 1995-1996. (18) The reason for adopting the system with four H-atom deficiencies for the simulations of decompression process is that at least four H atoms should be removed to create two bare Br atoms at high pressures, where each hydrogen atom is shared with two neighboring Br atoms. (19) The pV term does not include a contribution from escaped hydrogens because we assume that eliminated hydrogens are evaporated from the sample. However, if hydrogens do not escape from the sample, hydrogen molecules are likely to react to form hydrides with just gasket metal, as is known to occur in high-pressure experiments of solid hydrogen unless a proper gasket metal is used [Mao, H. K.; Hemley, R. J. ReV. Mod. Phys. 1994, 66, 671]. In this case, the critical pressure may be more or less increased from our estimation. (20) Carter, E. A.; Ciccotti, G.; Hynes, J. T.; Kapral, R. Chem. Phys. Lett. 1989, 156, 472. Boero, M.; Parrinello, M.; Terakura, K. J. Am. Chem. Soc. 1998, 120, 2746. (21) The slow convergence of the stress tensor with the number of plane waves forced us to use a high-energy cutoff of 70 Ry. The time step of the MD simulations is 6.5 au (0.157 fs) with a fictitious electron mass of 1000 au. (22) In our calculations, quantum effects of protons were neglected. However, the quantum effects do not alter the point of our discussions, because hydrogen distribution becomes more delocalized by the quantum effects, which inhibit Br2 formation more efficiently at high pressure. At low pressure, the quantum effects are known to be minor [Vesel, J. E.; Torrie, B. H. Can. J. Phys. 1977, 55, 592]. Anyway, our calculations were done at room temperature, where shallow potentials are, in fact, least affected by zero-point motion.
