Structures and optical properties of solid hydrogen at ultrahigh pressures
We have studied the electronic energy bands for the structures whose primitive cell contains up to four molecules, with full optimization of the structures, based on the GGA and LDA band calculations. Above 250 GPa, the eventual optimal structure obtained by the GGA or the LDA calculation is Cmca, w...
Gespeichert in:
| Datum: | 2003 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2003
|
| Schriftenreihe: | Физика низких температур |
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/128912 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Structures and optical properties of solid hydrogen at ultrahigh pressures / Hitose Nagara // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 947-950. — Бібліогр.: 12 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-128912 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-1289122025-02-23T17:22:59Z Structures and optical properties of solid hydrogen at ultrahigh pressures Hitose Nagara High-Pressure Studies We have studied the electronic energy bands for the structures whose primitive cell contains up to four molecules, with full optimization of the structures, based on the GGA and LDA band calculations. Above 250 GPa, the eventual optimal structure obtained by the GGA or the LDA calculation is Cmca, which is a layered structure with the molecular bonds lying in planes, and has a metallic band structure with no band gaps. The metallic property of the band structure still remains unchanged even if the molecular bonds in the plane of the Cmca were inclined such that the atoms in the molecule escape from the plane. The electronic bands of the Cmca and those of some other candidate structures are discussed in the light of recent experimental result. Effects of the occupation of electronic states on the predicted optimal structures are also studied. This work is supported by Grant-in-Aid for COE Research (10CE2004) of the Ministry of Education, Culture, Sports, Science and Technology of Japan. 2003 Article Structures and optical properties of solid hydrogen at ultrahigh pressures / Hitose Nagara // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 947-950. — Бібліогр.: 12 назв. — англ. 0132-6414 PACS: 62.50.+p, 61.50.Ah, 71.30.+h https://nasplib.isofts.kiev.ua/handle/123456789/128912 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
High-Pressure Studies High-Pressure Studies |
| spellingShingle |
High-Pressure Studies High-Pressure Studies Hitose Nagara Structures and optical properties of solid hydrogen at ultrahigh pressures Физика низких температур |
| description |
We have studied the electronic energy bands for the structures whose primitive cell contains up to four molecules, with full optimization of the structures, based on the GGA and LDA band calculations. Above 250 GPa, the eventual optimal structure obtained by the GGA or the LDA calculation is Cmca, which is a layered structure with the molecular bonds lying in planes, and has a metallic band structure with no band gaps. The metallic property of the band structure still remains unchanged even if the molecular bonds in the plane of the Cmca were inclined such that the atoms in the molecule escape from the plane. The electronic bands of the Cmca and those of some other candidate structures are discussed in the light of recent experimental result. Effects of the occupation of electronic states on the predicted optimal structures are also studied. |
| format |
Article |
| author |
Hitose Nagara |
| author_facet |
Hitose Nagara |
| author_sort |
Hitose Nagara |
| title |
Structures and optical properties of solid hydrogen at ultrahigh pressures |
| title_short |
Structures and optical properties of solid hydrogen at ultrahigh pressures |
| title_full |
Structures and optical properties of solid hydrogen at ultrahigh pressures |
| title_fullStr |
Structures and optical properties of solid hydrogen at ultrahigh pressures |
| title_full_unstemmed |
Structures and optical properties of solid hydrogen at ultrahigh pressures |
| title_sort |
structures and optical properties of solid hydrogen at ultrahigh pressures |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2003 |
| topic_facet |
High-Pressure Studies |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/128912 |
| citation_txt |
Structures and optical properties of solid hydrogen at ultrahigh pressures / Hitose Nagara // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 947-950. — Бібліогр.: 12 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT hitosenagara structuresandopticalpropertiesofsolidhydrogenatultrahighpressures |
| first_indexed |
2025-11-24T02:29:31Z |
| last_indexed |
2025-11-24T02:29:31Z |
| _version_ |
1849637072833347584 |
| fulltext |
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 947–950
Structures and optical properties of solid hydrogen at
ultrahigh pressures
Hitose Nagara
Division of Materials Physics, Graduate School of Engineering Science, Osaka University
Toyonaka, Osaka 560-8531, Japan
E-mail: nagara@mp.es.osaka-u.ac.jp
We have studied the electronic energy bands for the structures whose primitive cell contains up
to four molecules, with full optimization of the structures, based on the GGA and LDA band cal-
culations. Above 250 GPa, the eventual optimal structure obtained by the GGA or the LDA calcu-
lation is Cmca, which is a layered structure with the molecular bonds lying in planes, and has a
metallic band structure with no band gaps. The metallic property of the band structure still re-
mains unchanged even if the molecular bonds in the plane of the Cmca were inclined such that the
atoms in the molecule escape from the plane. The electronic bands of the Cmca and those of some
other candidate structures are discussed in the light of recent experimental result. Effects of the
occupation of electronic states on the predicted optimal structures are also studied.
PACS: 62.50.+p, 61.50.Ah, 71.30.+h
1. Introduction
Recent experimental study of the compressed hy-
drogen revealed nonmetallic behavior at pressures
higher than � 300 GPa [1,2]. They report a possibility
of the metallization by the closure of the direct elec-
tronic band gaps at even higher pressures. The result
contradicts many theoretical studies based on the first
principles band calculations which predict the closure
of indirect band gaps at lower pressures in energeti-
cally favorable structures [3–5], and caused a ques-
tion about an ability of the band calculations to pre-
dict the structures of compressed hydrogen.
In spite of the well-known shortcoming of the band
calculation based on the local density approximation
(LDA) or its modification with the gradient correc-
tion (GGA), that is, underestimation of the electronic
band gaps, recent first principles band calculations
have achieved much success in predicting structures
and properties of solids at ambient as well as at high
pressures. In the study of compressed hydrogen,
whether this shortcoming might hamper the prediction
of the structures and mislead us into false structures or
not is still unclear because of lacking available experi-
mental data of the structure above 100 GPa.
In order to check this point at some levels, we have
carried out some preliminary calculations and re-ex-
amined the structures which have been predicted to be
most probable at high pressures, paying attention to
the occupation of the electronic bands by the elec-
trons. We perform full optimization of the structures
above 250 GPa in the GGA and the LDA and study
the changes of the electronic bands for structures
which appear in the course of the optimization. We
compare the results with new type of the calculation
[6] which is expected to overcome the shortcoming
and discuss the band structures in the light of very re-
cent optical measurements [1].
2. New restrictions imposed on the structures
The results of the optical experiment [1] impose
new restrictions on the structures from 150 GPa to at
least 320 GPa. The first important point to be men-
tioned is that the softening of the vibron frequency
seems to occur continuously with increasing pressure.
No jump of the frequency nor the change of the slope
have been observed, which means no drastic changes
of the structure. If the structure changes at all, it
should be accompanied by a very small change of the
vibron frequency. The second point is that the experi-
ment reports the features characteristic of a direct
band gap, which means the top of the valence band
and the bottom of the conduction band are located at
the same place in the Brillouin zone.
© Hitose Nagara, 2003
In earlier experiments, the vibron frequencies and
the optical properties at pressures over 250 GPa were
reported and the pressure of direct-gap closure has
also been estimated from the optical data [7,8]. The
recent optical measurements show the pressures and
the character of the optical absorption more clearly.
These new results impose important restrictions on the
structures of solid hydrogen above the well-known
150 GPa transition. Bearing these points in mind, we
examine again some of the structures which have been
theoretically studied so far.
3. Calculations and results
The structures which can be transformed continu-
ously among them are Pca21, Cmc21, Cmca, and Pbca
family, which are shown in Fig. 1. Starting from one
of those structures, the others are obtained by chang-
ing the molecular centers and the molecular orienta-
tion continuously.
At pressures lower than 200 GPa, the candidates of
the most probable structure are Cmc21, Pca21 with
hcp molecular centers or its slight modifications [3,4].
The structure, however, becomes unstable at pressures
higher than about 200 GPa according to theoretical
calculations [3–5]. In those calculations, they used
the methods based on the LDA or the GGA which has
a shortcoming of underestimating band gaps, resulting
in the closure of indirect band gaps at around
200 GPa. Optimization of the structure is a delicate
problem and the shortcoming might mislead us into
the false optimal structures because of the false occu-
pation of the states by the electrons whose energy is in
the vicinity of the Fermi level. To investigate the
effect of the electron occupation, we performed the
calculations restricting the electron occupation.
We carried out band calculations using the
plane-wave basis functions with energy cut-off of 40
hartree and a pseudo-potential for the ionic potential.
Throughout our calculations, we used the packaged
codes ABINIT [9] and PHI98PP [10].
3.1. Preliminary calculations under restricted and
unrestricted electronic occupation
To study the effect of the false occupation on the
optimal structures, we performed following prelimi-
nary calculations. First we show an example in which
the restricted electron occupation and the unrestricted
one give different conclusions in the comparison of to-
tal energies.
We compare the energies of the Cmc21 and the
Pca21 structures with molecular centers fixed at the
hcp sites and with c/a fixed at the ideal hcp value
(see Fig. 1). We used the unit cell containing 4 mole-
cules for both structures. In the first calculation, we
performed the usual calculations in which the elec-
trons occupy the states with energies lower than the
Fermi energy. And in the second one, we restricted the
occupation of the electronic states to the lowest 4
branches at each k-point, which simulates the insula-
tor type of the electronic occupation of the bands. Up
to rs = 1.25, which corresponds to a pressure around
430 GPa, the lowest 4 branches of the electronic en-
ergy states in the Cmc21 and the Pca21 seem to be well
separated from the 5th branch. Here the rs is the den-
sity parameter which is defined by the radius of the
sphere, in units of Bohr radius, whose volume is equal
to the volume per electron.
Comparing the energies of these two structure, we
find that the Cmc21 is of lower energy than the Pca21
in the case of the first calculation. On the other hand,
in the case of the second calculation, the Pca21 be-
comes lower.
3.2. Full optimization of the structures
Above example shows the possibility that the false
occupation of the electronic states might affect the op-
timal structures at each pressure. The change of the
occupation occurs when the indirect band gaps disap-
pear. Starting from some arrangements of the atomic
positions, we then performed full optimization of the
structures.
As a starting arrangement, we take the Pca21 struc-
ture with orthorhombic unit cell containing 4 mole-
cules. We have set the molecular centers at ideal hcp
lattice sites and at several points between that of the
ideal hcp site and the molecular center of the Pbca
948 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
Hitose Nagara
Pca21
Pbca
Cmc21
Cmca
�
Fig. 1. The structures Pca21, Cmc21, Pbca, and Cmca.
Arrows show the directions of molecular axes whose direc-
tion consigns with the z axes are positive. These structure
can be mutually transformed by continuously changing
the molecular centers and orientations.
structure (see Fig. 1). The optimization has been done
at constant volumes, at rs = 1.40, 1.35, 1.30, and 1.25,
which correspond to the pressures around 200, 270,
330, and 430 GPa, respectively. The pressures are esti-
mated from the volume dependence of the total energy
obtained in our calculations. The LDA calculations
show smoother convergence than the GGA ones which
contain the calculation of the density gradient. In the
optimization of the structures, some runs did not con-
verge to any meaningful structures. This is probably
due to some problems in the optimization codes.
All structures converged and obtained as optimal
ones in our runs are of Cmca for rs � 1.35. We note
here that the compression seems to be nearly isotropic
above 200 GPa (rs � 1.40). Although the molecular
centers move from the ideal hcp sites to that of the
Cmca, the orthorhombic unit cell is compressed
isotropically. At highest density rs = 1.25, the c/a of
the orthorhombic lattice decreased about 3 % and the
b/a (distance between the layers) increased about
3 %, with molecular bonds tilted about 76� from the z
axes and the bond length 1.41a0. They did not show
any molecular dissociation at all densities studied.
These results are same as those obtained from the
usual calculations with no restriction of the band oc-
cupation for both GGA and the LDA.
4. Changes of the electronic band structure
We study then the changes in the electronic band
structures for those structures studied in the optimiza-
tion process. The Cmc21 structure is also a layered
structure with molecular bonds lying in the planes.
The Cmc21 space group holds for any position of the
molecular center between the hcp site and the molecu-
lar center of the Cmca. When the molecular bond is
inclined in a certain way in the Cmc21 and two atoms
of the molecule are off the plane, the structure be-
comes Pca21. For the extreme case of the Pca21 in
which the molecular center is moved to that of the
Cmca, the space group becomes Pbca.
To compare the band structures we take the
nonprimitive unit cell containing 4 molecules for all
structures studied. All structures, except for the
Cmca, have the band structure in which the lowest 4
branches are well separated from higher ones up to the
highest densities rs = 1.25. The indirect band gaps,
however, closes at much lower densities. The gaps be-
comes wider when the molecules in the Cmc21 are
tilted toward the Pca21 structure.
The Cmca has the band structure completely differ-
ent from the others, where the band structure has no
band gaps. The lowest 4 branch touches the higher
ones at some points on the �-, �- and c-lines. The na-
ture of the touching is line-type [3]. We show in
Fig. 2 the band structure of the Cmca taking the
nonprimitive unit cell. Even when the molecular
bonds are tilted towards the Pbca structure, the me-
tallic band character still remains unchanged, though
the changes of the distances between the branches are
observed at several points in the Brillouin zone. In
Fig. 2, we compare the band structure of the Cmca
with that of the Pbca at rs = 1.25.
It should be noted that the touching of the
branches are due to the symmetry properties of the
structure, independent of the approximation GGA or
LDA used in the calculations. The distance among the
branches depends on the approximation.
5. Discussion and summary
We discuss these results in the light of the recent
optical measurements. Although the Cmca is energeti-
cally most favorable, it may be excluded because of
the metallic character of band structure. The large
fluctuation of the molecular orientation remaining in
the Cmca structure [11] might change the electronic
Structures and optical properties of solid hydrogen at ultrahigh pressures
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 949
E
n
e
rg
y
,
e
V
30
25
20
15
10
5
0
–5
–10
–15
–20
Y X ���
a
E
n
e
rg
y
,
e
V
30
25
20
15
10
5
0
–5
–10
–15
–20
Y X ���
b
Fig. 2. The electronic band structures for the Cmca (a)
and the Pbca (b) at rs = 1.25. To compare the changes in
the energy bands, we used the nonprimitive unit cell con-
taining 4 molecules for the Cmca structure whose primi-
tive cell contains 2 molecules.
bands. The metallic character of the electronic bands
of the Pbca, however, may offer some negative insight
into the changes of the band structure due to the fluc-
tuation, although the movement from the Cmca to the
Pbca is coherent. The possible fluctuation of the mo-
lecular center leaving the positions of the Cmca to-
ward those of the Cmc21, however, might lift the me-
tallic character of the electronic bands. If the
energetically favorable Cmca structure is denied,
there will remain two possibilities. One is that there
are some other structures which we have overlooked in
our study. An example is a structure of larger unit cell
[4]. The second possibility is the case that all of the
present GGA and LDA based calculations fail to pre-
dict energetically favorable structures of compressed
hydrogen. In that case, the structure might remain
those which is close to the Cmc21 or Pca21 up to at
least 320 GPa. The possibility of the second case has
been reported recently in the new type of calculation
[6] which is designed to overcome the shortcoming of
the GGA and the LDA, though the optimization of the
structures has not been carried out by that type of cal-
culations owing mainly to machine resources.
We mention here the low lying librational and
phonon modes observed in Raman experiments [12].
The Pca21 has 9 optical phonons and 8 librational
modes which are Raman active, and the Cmc21 has 3
optical phonons and 4 librational such modes, while
the Cmca has only 4 librational modes with no Raman
active optical phonons.
Finally we mention that the metallization, which is
predicted to occur at � 450 GPa by the extrapolation
of the absorption edge to higher pressure, might hap-
pen at some lower pressures when the metallization is
due to the closure of the indirect band gaps [8].
We have studied the optimal structures and the
electronic bands in those energetically favorable struc-
tures. The new results of the optical measurements
brought about new problems into the theoretical stud-
ies of compressed hydrogen.
Acknowledgments
This work is supported by Grant-in-Aid for COE
Research (10CE2004) of the Ministry of Education,
Culture, Sports, Science and Technology of Japan.
1. P. Loubeyre, F. Occelli, and R. LeToullec, Nature
416, 613 (2002).
2. C. Narayana, H. Luo, J. Orloff, and A.L. Ruoff,
Nature 393, 46 (1998).
3. K. Nagao, T. Takezawa, and H. Nagara, Phys. Rev.
B59, 13741 (1999).
4. J. Kohanoff, S. Scandolo, S. Gironcoli, and E. To-
satti, Phys. Rev. Lett. 83, 4097 (1999).
5. K.A. Jonson and N.W. Ashkroft, Nature 403, 632
(2000).
6. M. Stadele and R.M. Martin, Phys. Rev. Lett. 84,
6070 (2000).
7. H.K. Mao and R.J. Hemly, Science 244, 1462 (1989).
8. M. Hanfland, R.J. Hemly, and H.K. Mao, Phys. Rev.
B43, 8767 (1991).
9. The ABINIT code is a common project of the Université
Catholique de Louvain, Corning Incorporated, and other
contributors, URL http://www.abinit.org.
10. M. Fuchs and M. Scheffler, Comput. Phys.
Commun. 119, 67 (1999), URL http://
www.fhi-berlin.mpg.de/th/fhi98vd/fhi98PP/index.
html.
11. H. Kitamura, S. Tsuneyuki, T. Ogitsu, and T. Miyake,
Nature 404, 259 (2000).
12. A.F. Goncharov, R.J. Hemly, H.K. Mao, and J. Shu,
Phys. Rev. Lett. 80, 101 (1998).
950 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
Hitose Nagara
|