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Pressure-induced structural changes of HBr
Physica B 265 (1999) 101—104
Pressure-induced structural changes of HBr Takashi Ikeda *, Michiel Sprik , Kiyoyuki Terakura , Michele Parrinello CREST, Japan Science and Technology Corporation, Kawaguchi, Saitama 332-0012, Japan JRCAT, National Institute for Advanced Interdisciplinary Research, 1-1-4, Higashi, Tsukuba, Ibaraki 305-8562, Japan Max-Planck-Institut fu( r Festko( rperforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany
Abstract First-principles molecular dynamics simulation of solid HBr under pressure has been performed using the Car—Parrinello method. A detailed study of the pressure response of the vibrational and proton-transfer dynamics showed that the phase I can be described as a rotator phase with fluctuating hydrogen bonds up to &10 GPa. We reproduced the shoulder-like structure seen in the infrared spectra of the H—Br stretching mode in the disordered phase. 1999 Published by Elsevier Science B.V. All rights reserved. Keywords: Hydrogen bromide; Structural phase transition; Molecular dynamics
1. Introduction Hydrogen bromide (HBr) is a molecular solid with rather weak hydrogen bonding. Three solid phases have been reported at ambient pressure [1]. In the high-temperature phase I (118—186 K), the bromine atoms occupy the positions of an FCC lattice, while each hydrogen occupies 12 possible sites around a bromine atom randomly. In the ordered phase III ((90 K), the HBr molecules are arranged in parallel zigzag chains connected by * Correspondence address: JRCAT, National Institute for Advanced Interdisciplinary Research, 1-1-4 Higashi, Tsukuba, Ibaraki 305-8562, Japan. Fax:#81-298-54-2788; e-mail: [email protected]. Present address. Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK. The crystal structures at low temperature were determined for DBr by neutron diffraction. Those of HBr are assumed to be the same as DBr.
hydrogen bonding in an orthorhombic cell. In the intermediate phase II (90—118 K), the bromines are located at the same positions as in phase III with partial disorder of the hydrogen positions. Recently, high-pressure experiments of HBr have been performed at room temperature and pressures up to 40 GPa to investigate the crystal structure and vibrational modes [2,9]. At room temperature HBr crystallizes at 0.5 GPa into the same structure as in phase I. Increasing pressure, a structural phase transition was observed from phase I to phase III at 13.6 GPa; the H—Br stretching mode, consisting at low pressure of a single peak in the IR spectra, develops into two peaks with equal intensity at 13.6 GPa, signalling symmetry breaking due to the long-range order in phase III. It was also noticed that in phase I, the IR spectrum for the H—Br stretching vibration shows a shoulder on the low-frequency side of the peak above 8 GPa. On further compression this H—Br doublet is strongly
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red-shifted and broadened. This is followed by virtually complete loss of IR intensity around 30 GPa. This is interpreted as the consequence of progressive symmetrization of the hydrogen bond. In this contribution, we present the results of a constant pressure ab initio molecular dynamics (MD) simulation [3] of solid HBr. Electronic structure and atomic forces were determined using density-functional theory in the generalized gradient approximation [4,5]. We considered a system of 32 HBr molecules in a variable periodic box. The valence orbitals were expanded in plane waves with an energy cutoff of 70 Ry. The MD simulations were carried out using a time step of 6.5 a.u. (0.157 fs) and a fictitious electron mass of 1000 a.u. The time span of the MD simulation for a (P,T)state point is 3—4 ps in phase I samples, and 2 ps for the ordered state preceded by 1—2 ps of initial equilibration. The temperature of the ions was controlled by a Nose´—Hoover thermostat [6,10]. All nuclei were treated as classical particles.
2. Results and discussion We generated a set of MD trajectories at 300 K and pressures of 2, 10, 20, 30, and 40 GPa. For 2 GPa, even if the simulation was initiated from a phase III configuration, the molecular orientations became disordered within a picosecond. For the pressure of 10 GPa and higher, however, the phase III structure remained stable on the picosecond time scale of our runs. Similarly, the ordering of a phase I structure at higher pressure did not occur spontaneously. Therefore, the 10, 20, 30, and 40 GPa simulations were performed with two different initial configurations. One series of runs was a continuation of the 2 GPa phase I system at successively higher pressures while at each of these pressures we also started a simulation from a phase III structure.
To answer the question whether phase I is a rotator phase or an orientational glass, we examined the time auto-correlation function of HBr bond vectors. For the phase I runs at 2, 10, 20, and 30 GPa the correlations indeed decay to zero according to an effectively exponential time dependence with time constants estimated as 0.4, 0.9, 1.6, and 3.8 ps, respectively. Except for the 30 GPa system, these relaxation times are well within the time window of our simulation. For these pressures the dynamical nature of the disorder is thus ensured. At 40 GPa the reorientational motion is essentially frozen and the system must be considered as an orientational glass. The distribution of molecular orientation in rotator phases is not fully isotropic but may show a modulation compatible with the crystal symmetry (cubic in our system). Analysis using cubic harmonics defined in terms of the unit vector directed along the covalent HBr bonds showed that the H atoms preferentially occupy the 12 11 1 02 pockets [7,11]. Molecules with this orientation point to nearest neighbors in the FCC lattice, as is necessary for the H atoms to form hydrogen bonds. When the Br atoms are pushed together, the hydrogen-bond distance approaches the covalentbond distance (&1.45 As ). The potential well for an H atom becomes shallower and the barrier between minima along a Br—Br axis tends to vanish. This makes it easier for the hydrogen to hop between the two sites. In order to expose this trend in our simulation, we have introduced a function d defined as d (t)"r(H Br )!r(H Br ), (1) L L L L K where H Br is the HBr molecule assigned at t"0 L L in the initial configuration. r(H Br ) is the distance L K between the nth hydrogen and the mth bromine atom. This atom Br is re-selected during the K course of time t according to the criterion r(H Br )"min r(H Br ). L K L I I$L
These calculations were carried out with the program CPMD, Version 3.0, written by J. Hutter, P. Ballone, M. Bernasconi, P. Focher, E. Fois, St. Goedecker, D. Marx, M. Parrinello, and M. Tuckerman at MPI fu¨r Festko¨rperforshung and IBM Zu¨rich Research Laboratory in 1995—1996.
(2)
If the H—Br covalent bond is not broken, d is L always negative. On the other hand, if the hydrogen is passed on to Br , d takes a positive value. K L Fig. 1 shows the distribution of d at 10, 20, 30, and
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difference in enthalpy *H shown in Fig. 3 together with the separate energy and volume contributions. These results may explain why the system is so reluctant to order. *H is essentially invariant under compression due to the anomalous pressure dependence of P*». To decide which of the two states is more stable, we should also consider the
Fig. 1. Pressure-induced hydrogen-bond symmetrization and proton hopping as measured by the parameter d defined in Eq. (1).
40 GPa in the disordered state. Hydrogen hopping begins at 20 GPa and stops again at 40 GPa where the hydrogen-bond symmetrization is almost completed. At 30 GPa, just before symmetrization, transfer rates have become fast enough for the onset of proton diffusion, even on the 2—3 ps time scale of the simulation, as can be seen from the tripling of the maximum of the d distribution. The process of bond symmetrization is also controlling the softening and broadening of the H—Br stretching mode. Fig. 2 shows the energy distribution for H—Br stretching vibrational modes in the disordered phase I to analyze the observed IR spectra. Here, we used the projection operators for symmetric and antisymmetric stretching vibrations of two HBr molecules connected by hydrogen bonding. We find that at 2 GPa the symmetric and antisymmetric modes have almost the same frequency while at 10 GPa the symmetric stretching mode has a frequency a little lower than the antisymmetric mode leading to the appearance of shoulder-like structure at 2000 cm\. We attribute the shoulder-like structure to formation of short zigzag chains similar to those in the phase III even in the disordered phase I rather than to a new phase I assumed in Ref. [8]. Finally, we examine the relative stability of the disordered and ordered systems. We computed the
Fig. 2. Density of states for stretching vibrational modes for HBr in the disordered phase I at 2 GPa (top) and 10 GPa (bottom). Dashed and dotted lines indicate, respectively, the symmetric and antisymmetric stretching modes for two HBr molecules connected by hydrogen bonding. The solid line shows the sum of the two modes.
Fig. 3. Enthalpy balance between the disordered (I) and ordered (III) states at high pressure. We show the relative enthalpy *H"H !H (solid) and the separate contributions due to ' ''' energy *º"º !º (dashed) and volume differences ' ''' P*»"P(» !» ) (dash dotted). The energies are averages ' ''' over constant pressure MD runs at 300 K.
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difference in entropy. This quantity can be estimated very roughly by setting the entropy of the disordered phase to ln 12, the number of approximately discrete orientations of a molecule, and the entropy of the ordered phase to zero. This gives ¹*S"6.2 kJ/mol. Comparing with the values of *H in Fig. 3, we see that disorder will prevail for all pressures in the interval 2—30 GPa. Although the directional correlations of HBr bond vectors are limited to the nearest neighbors below 10 GPa, these are extended over the next nearest neighbors above 20 GPa. Corrections for these effects, which become more significant at high pressure, will favor ordering. The absence of a spontaneous transition to an ordered state means that the duration of the MD run is not long enough to reach equilibrium. Recall that the disordered sample at the highest pressure can be considered an orientational glass. This suggests that the amorphous state can exist as a meta-stable state in the pressure region we investigate. 3. Conclusions We have performed a series of Car—Parrinello MD simulations of solid HBr at 300 K and high
pressures. The simulation confirms that the range of the disordered phase I observed at ambient pressure extends up to &10 GPa. We reproduce the shoulder-like structure seen in the infrared spectra of HBr stretching modes in the disordered phase. Our results also suggest that the amorphous state can compete with the ordered phase III under high pressure.
References [1] A. Ikram, B.H. Torrie, B.M. Powell, Mol. Phys. 79 (1993) 1037. [2] E. Katoh, Y. Matsushita, M. Sakashita, K. Aoki, in preparation. [3] P. Focher, G.L. Chiarotti, M. Bernasconi, E. Tosatti, M. Parrinello, Europhys. Lett. 26 (1994) 345. [4] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [5] C. Lee, W. Yang, R.C. Parr, Phys. Rev. B 37 (1988) 785. [6] S. Nose´, J. Chem. Phys. 81 (1984) 511. [7] M.L. Klein, in: Proc. XCVII Int. School of Physics Enrico Fermi, North-Holland, Amsterdam, 1986. [8] T. Kume, T. Tsuji, S. Sasaki, H. Shimizu, Phys. Rev. B 58 (1998) 8149. [9] Y. Matsushita et al., private communication. [10] W.G. Hoover, Phys. Rev. A 31 (1985) 1695. [11] S. Nose´, M.L. Klein, Mol. Phys. 46 (1982) 1063.
Pressure-induced structural changes of HBr Takashi Ikeda *, Michiel Sprik , Kiyoyuki Terakura , Michele Parrinello CREST, Japan Science and Technology Corporation, Kawaguchi, Saitama 332-0012, Japan JRCAT, National Institute for Advanced Interdisciplinary Research, 1-1-4, Higashi, Tsukuba, Ibaraki 305-8562, Japan Max-Planck-Institut fu( r Festko( rperforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany
Abstract First-principles molecular dynamics simulation of solid HBr under pressure has been performed using the Car—Parrinello method. A detailed study of the pressure response of the vibrational and proton-transfer dynamics showed that the phase I can be described as a rotator phase with fluctuating hydrogen bonds up to &10 GPa. We reproduced the shoulder-like structure seen in the infrared spectra of the H—Br stretching mode in the disordered phase. 1999 Published by Elsevier Science B.V. All rights reserved. Keywords: Hydrogen bromide; Structural phase transition; Molecular dynamics
1. Introduction Hydrogen bromide (HBr) is a molecular solid with rather weak hydrogen bonding. Three solid phases have been reported at ambient pressure [1]. In the high-temperature phase I (118—186 K), the bromine atoms occupy the positions of an FCC lattice, while each hydrogen occupies 12 possible sites around a bromine atom randomly. In the ordered phase III ((90 K), the HBr molecules are arranged in parallel zigzag chains connected by * Correspondence address: JRCAT, National Institute for Advanced Interdisciplinary Research, 1-1-4 Higashi, Tsukuba, Ibaraki 305-8562, Japan. Fax:#81-298-54-2788; e-mail: [email protected]. Present address. Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK. The crystal structures at low temperature were determined for DBr by neutron diffraction. Those of HBr are assumed to be the same as DBr.
hydrogen bonding in an orthorhombic cell. In the intermediate phase II (90—118 K), the bromines are located at the same positions as in phase III with partial disorder of the hydrogen positions. Recently, high-pressure experiments of HBr have been performed at room temperature and pressures up to 40 GPa to investigate the crystal structure and vibrational modes [2,9]. At room temperature HBr crystallizes at 0.5 GPa into the same structure as in phase I. Increasing pressure, a structural phase transition was observed from phase I to phase III at 13.6 GPa; the H—Br stretching mode, consisting at low pressure of a single peak in the IR spectra, develops into two peaks with equal intensity at 13.6 GPa, signalling symmetry breaking due to the long-range order in phase III. It was also noticed that in phase I, the IR spectrum for the H—Br stretching vibration shows a shoulder on the low-frequency side of the peak above 8 GPa. On further compression this H—Br doublet is strongly
0921-4526/99/$ — see front matter 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 3 3 3 - 7
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T. Ikeda et al. / Physica B 265 (1999) 101—104
red-shifted and broadened. This is followed by virtually complete loss of IR intensity around 30 GPa. This is interpreted as the consequence of progressive symmetrization of the hydrogen bond. In this contribution, we present the results of a constant pressure ab initio molecular dynamics (MD) simulation [3] of solid HBr. Electronic structure and atomic forces were determined using density-functional theory in the generalized gradient approximation [4,5]. We considered a system of 32 HBr molecules in a variable periodic box. The valence orbitals were expanded in plane waves with an energy cutoff of 70 Ry. The MD simulations were carried out using a time step of 6.5 a.u. (0.157 fs) and a fictitious electron mass of 1000 a.u. The time span of the MD simulation for a (P,T)state point is 3—4 ps in phase I samples, and 2 ps for the ordered state preceded by 1—2 ps of initial equilibration. The temperature of the ions was controlled by a Nose´—Hoover thermostat [6,10]. All nuclei were treated as classical particles.
2. Results and discussion We generated a set of MD trajectories at 300 K and pressures of 2, 10, 20, 30, and 40 GPa. For 2 GPa, even if the simulation was initiated from a phase III configuration, the molecular orientations became disordered within a picosecond. For the pressure of 10 GPa and higher, however, the phase III structure remained stable on the picosecond time scale of our runs. Similarly, the ordering of a phase I structure at higher pressure did not occur spontaneously. Therefore, the 10, 20, 30, and 40 GPa simulations were performed with two different initial configurations. One series of runs was a continuation of the 2 GPa phase I system at successively higher pressures while at each of these pressures we also started a simulation from a phase III structure.
To answer the question whether phase I is a rotator phase or an orientational glass, we examined the time auto-correlation function of HBr bond vectors. For the phase I runs at 2, 10, 20, and 30 GPa the correlations indeed decay to zero according to an effectively exponential time dependence with time constants estimated as 0.4, 0.9, 1.6, and 3.8 ps, respectively. Except for the 30 GPa system, these relaxation times are well within the time window of our simulation. For these pressures the dynamical nature of the disorder is thus ensured. At 40 GPa the reorientational motion is essentially frozen and the system must be considered as an orientational glass. The distribution of molecular orientation in rotator phases is not fully isotropic but may show a modulation compatible with the crystal symmetry (cubic in our system). Analysis using cubic harmonics defined in terms of the unit vector directed along the covalent HBr bonds showed that the H atoms preferentially occupy the 12 11 1 02 pockets [7,11]. Molecules with this orientation point to nearest neighbors in the FCC lattice, as is necessary for the H atoms to form hydrogen bonds. When the Br atoms are pushed together, the hydrogen-bond distance approaches the covalentbond distance (&1.45 As ). The potential well for an H atom becomes shallower and the barrier between minima along a Br—Br axis tends to vanish. This makes it easier for the hydrogen to hop between the two sites. In order to expose this trend in our simulation, we have introduced a function d defined as d (t)"r(H Br )!r(H Br ), (1) L L L L K where H Br is the HBr molecule assigned at t"0 L L in the initial configuration. r(H Br ) is the distance L K between the nth hydrogen and the mth bromine atom. This atom Br is re-selected during the K course of time t according to the criterion r(H Br )"min r(H Br ). L K L I I$L
These calculations were carried out with the program CPMD, Version 3.0, written by J. Hutter, P. Ballone, M. Bernasconi, P. Focher, E. Fois, St. Goedecker, D. Marx, M. Parrinello, and M. Tuckerman at MPI fu¨r Festko¨rperforshung and IBM Zu¨rich Research Laboratory in 1995—1996.
(2)
If the H—Br covalent bond is not broken, d is L always negative. On the other hand, if the hydrogen is passed on to Br , d takes a positive value. K L Fig. 1 shows the distribution of d at 10, 20, 30, and
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difference in enthalpy *H shown in Fig. 3 together with the separate energy and volume contributions. These results may explain why the system is so reluctant to order. *H is essentially invariant under compression due to the anomalous pressure dependence of P*». To decide which of the two states is more stable, we should also consider the
Fig. 1. Pressure-induced hydrogen-bond symmetrization and proton hopping as measured by the parameter d defined in Eq. (1).
40 GPa in the disordered state. Hydrogen hopping begins at 20 GPa and stops again at 40 GPa where the hydrogen-bond symmetrization is almost completed. At 30 GPa, just before symmetrization, transfer rates have become fast enough for the onset of proton diffusion, even on the 2—3 ps time scale of the simulation, as can be seen from the tripling of the maximum of the d distribution. The process of bond symmetrization is also controlling the softening and broadening of the H—Br stretching mode. Fig. 2 shows the energy distribution for H—Br stretching vibrational modes in the disordered phase I to analyze the observed IR spectra. Here, we used the projection operators for symmetric and antisymmetric stretching vibrations of two HBr molecules connected by hydrogen bonding. We find that at 2 GPa the symmetric and antisymmetric modes have almost the same frequency while at 10 GPa the symmetric stretching mode has a frequency a little lower than the antisymmetric mode leading to the appearance of shoulder-like structure at 2000 cm\. We attribute the shoulder-like structure to formation of short zigzag chains similar to those in the phase III even in the disordered phase I rather than to a new phase I assumed in Ref. [8]. Finally, we examine the relative stability of the disordered and ordered systems. We computed the
Fig. 2. Density of states for stretching vibrational modes for HBr in the disordered phase I at 2 GPa (top) and 10 GPa (bottom). Dashed and dotted lines indicate, respectively, the symmetric and antisymmetric stretching modes for two HBr molecules connected by hydrogen bonding. The solid line shows the sum of the two modes.
Fig. 3. Enthalpy balance between the disordered (I) and ordered (III) states at high pressure. We show the relative enthalpy *H"H !H (solid) and the separate contributions due to ' ''' energy *º"º !º (dashed) and volume differences ' ''' P*»"P(» !» ) (dash dotted). The energies are averages ' ''' over constant pressure MD runs at 300 K.
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difference in entropy. This quantity can be estimated very roughly by setting the entropy of the disordered phase to ln 12, the number of approximately discrete orientations of a molecule, and the entropy of the ordered phase to zero. This gives ¹*S"6.2 kJ/mol. Comparing with the values of *H in Fig. 3, we see that disorder will prevail for all pressures in the interval 2—30 GPa. Although the directional correlations of HBr bond vectors are limited to the nearest neighbors below 10 GPa, these are extended over the next nearest neighbors above 20 GPa. Corrections for these effects, which become more significant at high pressure, will favor ordering. The absence of a spontaneous transition to an ordered state means that the duration of the MD run is not long enough to reach equilibrium. Recall that the disordered sample at the highest pressure can be considered an orientational glass. This suggests that the amorphous state can exist as a meta-stable state in the pressure region we investigate. 3. Conclusions We have performed a series of Car—Parrinello MD simulations of solid HBr at 300 K and high
pressures. The simulation confirms that the range of the disordered phase I observed at ambient pressure extends up to &10 GPa. We reproduce the shoulder-like structure seen in the infrared spectra of HBr stretching modes in the disordered phase. Our results also suggest that the amorphous state can compete with the ordered phase III under high pressure.
References [1] A. Ikram, B.H. Torrie, B.M. Powell, Mol. Phys. 79 (1993) 1037. [2] E. Katoh, Y. Matsushita, M. Sakashita, K. Aoki, in preparation. [3] P. Focher, G.L. Chiarotti, M. Bernasconi, E. Tosatti, M. Parrinello, Europhys. Lett. 26 (1994) 345. [4] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [5] C. Lee, W. Yang, R.C. Parr, Phys. Rev. B 37 (1988) 785. [6] S. Nose´, J. Chem. Phys. 81 (1984) 511. [7] M.L. Klein, in: Proc. XCVII Int. School of Physics Enrico Fermi, North-Holland, Amsterdam, 1986. [8] T. Kume, T. Tsuji, S. Sasaki, H. Shimizu, Phys. Rev. B 58 (1998) 8149. [9] Y. Matsushita et al., private communication. [10] W.G. Hoover, Phys. Rev. A 31 (1985) 1695. [11] S. Nose´, M.L. Klein, Mol. Phys. 46 (1982) 1063.