Bonding of H in O vacancies of ZnO
H. Takenaka and D.J. Singh
Materials Science and Technology Division and Center for Radiation Detection Materials and Systems,
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6032
(Dated: October 25, 2018)
We investigate the bonding of H in O vacancies in ZnO using density functional calculations. We
find that H is anionic and does not form multicenter bonds with Zn in this compound.
PACS numbers: 71.20.Ps,71.55.Gs
ZnO is of importance as an extremely fast inorganic
scintillator material when doped with Ga or In. It
is useful in alpha particle detection, e.g. for devices
such as deuterium-tritium neutron generators used in
radiography.1,2,3,4,5,6 In this application, H treatment has
been shown to improve properties. ZnO has also at-
tracted much recent attention motivated by potential
applications as an oxide electronic material,7,8,9,10 and
in optoelectronic and lighting applications.11,12,13,14,15 H
has been implicated as playing an important role in the
electronic properties for ZnO for those applications as
well.16,17,18 From a fundamental point of view, the be-
havior, and especially bonding of H, is of great inter-
est; H plays an exceptionally important role in chemistry,
and shows unique bonding characteristics. For example,
it readily forms compounds where it behaves as a halo-
gen ion and forms structures similar to fluorides, such as
rutile, perovskite, rocksalt, etc.,19,20,21 and at the same
time readily occurs a cation in other chemical environ-
ments. Polar covalent bonds involving H and hydrogen
bonds are central to much of organic chemistry as well
the properties of important substances such as water.22
Thus the recent report by Janotti and Van de Walle (JV)
that H forms a new type of strong multicenter bond in
O vacancies in ZnO is of wide ranging interest.23
In this paper, we present standard local density ap-
proximation (LDA) calculations of the electronic proper-
ties and structure of H containing O vacancies in ZnO.
We do not find the multicenter covalent bonds claimed by
JV, and instead characterize the behavior of H as quite
conventional in that it occurs as an anion on the anion
site in a polar crystalline environment.
Our calculations were done within the standard local
density approximation using the general potential lin-
earized augmented planewave (LAPW) method, includ-
ing local orbitals.24,25 Specifically, we constructed a 72
atom 3x3x2 wurtzite supercells of ZnO, with one O atom
removed and replaced by H. The calculations were done
using the bulk lattice parameters of ZnO, but the inter-
nal coordinates of all atoms in the supercell were fully
relaxed. No symmetry was assumed in the relaxations.
The LAPW method is an all electron method that makes
no shape approximations to either the potential or charge
density. It divides space into non-overlapping atom cen-
tered spheres and an interstitial region. The method then
employs accurate basis sets appropriate for each region.24
In the present calculations, LAPW sphere radii of 2.0 a0,
1.6 a0 and 1.2 a0 were used for Zn, O, and H respec-
tively, along with a basis set consisting of more than 8500
LAPW functions and local orbitals. Convergence tests
were done with a larger basis set of approximately 12000
functions, but no significant changes were found. The
relaxations were done without any imposed symmetry,
with a 2x2x2 special k-point zone sampling. A sampling
using only the Γ point was found to yield slightly different
quantitative results, due to the limited size of our super-
cell, but would lead to the same conclusions. The calcu-
lated value of the internal parameter is u=0.119, which
agrees almost exactly with the experimental value. The
densities of states used to analyze the electronic proper-
ties were obtained using the linear tetrahedron method
based on eigenvalues and wavefunctions at 36 k-points in
the half zone (k and -k are connected by time reversal).
In our relaxed structure for a neutral cell, we find that
H occurs in a slightly asymmetric position, with three Zn
neighbors at 2.03 Å, and one Zn neighbor (the one along
the c-axis direction) at 2.17 Å. For the singly charged
cell, we obtain a very similar result, specifically three Zn
neighbors at 2.02 Å, and the apical Zn at 2.21 Å. In the
following, we focus on the neutral cell except as noted.
Fig. 1 shows the projection of the electronic density of
states onto the H LAPW sphere, of radius 1.2 a0. The
Fermi energy for our neutral cell lies at a position one
electron per cell into the conduction bands, correspond-
ing to the valence difference of one between O and H.
As may be seen, there are two prominent peaks in the
H component of the density of states, one, denoted “B”,
at ∼ -8 eV with respect to the Fermi level (-6 eV with
respect to the valence band maximum), and the other,
denoted “A”, high in the conduction bands at ∼ 6 eV. JV
identified these peaks, “B” and “A”, respectively, as the
bonding and antibonding combinations of metal and H
orbitals giving rise to the multicenter bond. In addition,
there is significant H s character distributed over the va-
lence bands, especially near the valence band maximum.
We note that the very large bonding-antibonding split-
ting of 14 eV implied by the assignment of JV indicates
extremely strong covalent bonds, which is somewhat sur-
prising considering the Zn-H distances. In any case, such
a large covalent gap would imply that the bonding and
antibonding states should have mixed character. In other
words, the bonding state should be of roughly half H s
character, while the remaining H 1s character should oc-
cur in the unoccupied antibonding level, so that the oc-
http://arxiv.org/abs/0704.0173v1
-8 -6 -4 -2  0  2  4  6  8
E(eV)
H pH in O vacancy
FIG. 1: Projection of the electronic density of states onto the
s and p components inside the H LAPW sphere, radius 1.2 a0,
for the 72 atom neutral cell. The two peaks identified by JV as
bonding and antibonding combinations are indicated by “B”
and “A”, respectively. The Fermi level lies in the conduction
bands. The position of the valence band maximum is denoted
by “VBM” (note that the LDA strongly underestimates the
3.3 eV band gap of ZnO).
cupancy of the H 1s orbital should be roughly 1 e, and
certainly significantly less than 2 e.
To analyze the bonding further it is convenient to com-
pare the charge density with an ionic model, as was done
for some alanates.30,31 As mentioned, H is known to en-
ter some solids as an anion, including tetragonal MgH2.
ZnH2 also exists though it is not as well characterized.
Furthermore, the simplest hydride, LiH, is of this ioni-
cally bonded type and includes H− anions coordinated
by six metal atoms.33,34 In these hydrogen anion based
materials, the negative H ion is stabilized by the Ewald
field. In fact, the importance of the Ewald field is one of
the essential differences between chemistry in solid state
and the chemistry of molecules. The long range Coulomb
interaction stabilizes ionic bonding for species that would
generally be largely covalent in small molecules, and in
particular stabilizes anions such as O2− and H−, which
are common in solid state chemistry but much less so
in gas phase molecules. This stabilization by the Ewald
field is reflected in the variability of the effective size of
H in crystal structure data for anionic hydrides.27,28,29 In
view of the common occurrence of H as an anion in many
metal hydrides, it would not be surprising if H− were sta-
bilized by the Ewald field of an anion vacancy in a polar
crystal such as ZnO. Thus we consider an ionic model,
based on the charge density of a H− ion stabilized by the
Ewald field, as simulated by a Watson sphere,35 as in Ref.
31. For such a H− ion, 0.525 e out of 2.0 e, i.e. ∼ 26% of
the charge, is inside a radius of 1.2 a0, so the majority of
the charge is outside. Because of the small sphere radius
used for H in our calculations the amount of charge in-
-8 -6 -4 -2  0  2  4  6  8
E(eV)
FIG. 2: Integration of the projection of the H s projected
density of states as in Fig. 1 normalized according to the
fraction of charge inside a 1.2 a0 sphere for a Watson sphere
stabilized H− anion (see text).
side the sphere is only weakly dependent on the Watson
sphere radius, which reflects the environment. For a non-
spin polarized neutral H in free space as described in the
LDA, 0.378 e (38%) would be inside a radius of 1.2 a0,
showing that there is a strong dependence on the charge
state, though not precise proportionality. Fig. 2 shows
the integral of the H s character as a function of energy
normalized by the fraction of the H− charge inside a 1.2
a0 sphere (0.525/2). Over the valence band region the
p contribution is less than 2%, and the d contribution is
less than 0.2%. The conduction bands, which are more
Zn sp derived, show a larger proportion of H p character,
as may be seen in Fig. 1. Thus the charge inside the
sphere, which comes from the occupied valence bands,
is mainly due to H s states, and not from orbitals on
neighboring atoms.
Using the ionic model for H−, i.e. incorporating the
factor of 0.525/2 as the fraction of charge inside the H
LAPW sphere, and integrating, one finds that the peak
“B” contains ∼ 0.8 H s electrons. Integrating over the
remaining valence bands brings the H s count to 2.0 elec-
trons, i.e. what is expected for H−. This leads to an
interpretation of the electronic structure, where the peak
“B” comes from the H 1s state. This hybridizes with
valence band states, which have mixed Zn d and O p
character. The second peak “A”, 14 eV higher, is then
the H s resonance. This is a very reasonable position for
the resonance of H−. In particular, the H−− resonance
of atomic H− is at ∼ 14.5 eV.36,37,38 JV emphasized the
shape of the charge density associated with the states in
the peak “B” and argued for bonding based partly on real
space images of this charge. As mentioned, in our pro-
jected density of states we find that this peak contains
0.8 s electrons (i.e. 40% H s character), which would
be consistent with a bonding orbital. However, the hy-
bridization is with other occupied states, and when the
integration is done over all the valence bands, we find 2
s electrons, consistent with H−. We emphasize that mix-
ing of occupied states does not contribute to the energy,
and that such hybridizations do not constitute bonds.
Our calculated binding energy relative H2 and a relaxed
neutral supercell with an O vacancy is 87 kJ/mol H.39
This may be an overestimate due to LDA errors,40 but
in any case is much smaller than the binding that would
be suggested by a 14 eV bonding-antibonding splitting.
We also calculated the positron wavefunction and life-
times for ZnO with an O vacancy and with the H contain-
ing O vacancy. This was done using the LAPW method
in the full inverted self-consistent Coulomb potential plus
the correlation and enhancement factors of Boronski and
Nieminen41 as calculated from the full charge density. We
obtain a bulk positron lifetime for ZnO of 144 ps, which
is at the lower end of the experimental range. Reported
experimental values are 151 ps (Ref. 42), 170 ps (Ref.
43), 141 ps - 155 ps (Ref. 44), and 182 ps (Ref. 45). Sig-
nificantly, positrons, which are positively charged, tend
to localize in voids and in sites that are favorable for
cations, and localize weakly if at all in anion sites, due
to the unfavorable Coulomb potential. We do not find
positron localization at the O vacancy in our ZnO super-
cell, indicating that the O is indeed an anion as expected,
nor do we find positron localization or a significant life-
time increase in the cell with a H containing O vacancy.
We also find no significant change in lifetime for H in an
O vacancy within a charged supercell with one electron
removed. In contrast, we obtain a bound positron state
for Zn vacancies, both with and without H, reflecting the
fact that Zn is on a cation site. The calculated lifetime
in a supercell with a Zn vacancy is 212 ps, while with a H
filled Zn vacancy we obtain 175 ps (in this case H bonds
to a single adjacent O to form a hydroxyl like unit with
H-O bond length of 1.01 Å).46
To summarize, we have performed density functional
calculations for ZnO supercells with both empty and H
filled O vacancies. Based on an analysis of the electronic
structure we do not find any evidence for hydrogen mul-
ticenter bonds, but rather find that H occurs as H−.
We are grateful for helpful discussions with L.A. Boat-
ner, J.S. Neal, and L.E. Halliburton. This work was sup-
ported by the Department of Energy, Office of Nonpro-
liferation Research and Development, NA22.
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40 The LDA generally overbinds solids, and this leads to over-
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46 The calculations for H in a Zn vacancy were done using a
different set of LAPW sphere radii, as was necessary due
to the short H-O bond length.

  We investigate the bonding of H in O vacancies of ZnO using density
functional calculations. We find that H is anionic and does not form
multicenter bonds with Zn in this compound.

Bonding of H in O vacancies of ZnO
H. Takenaka and D.J. Singh
Materials Science and Technology Division and Center for Radiation Detection Materials and Systems,
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6032
(Dated: October 25, 2018)
We investigate the bonding of H in O vacancies in ZnO using density functional calculations. We
find that H is anionic and does not form multicenter bonds with Zn in this compound.
PACS numbers: 71.20.Ps,71.55.Gs
ZnO is of importance as an extremely fast inorganic
scintillator material when doped with Ga or In. It
is useful in alpha particle detection, e.g. for devices
such as deuterium-tritium neutron generators used in
radiography.1,2,3,4,5,6 In this application, H treatment has
been shown to improve properties. ZnO has also at-
tracted much recent attention motivated by potential
applications as an oxide electronic material,7,8,9,10 and
in optoelectronic and lighting applications.11,12,13,14,15 H
has been implicated as playing an important role in the
electronic properties for ZnO for those applications as
well.16,17,18 From a fundamental point of view, the be-
havior, and especially bonding of H, is of great inter-
est; H plays an exceptionally important role in chemistry,
and shows unique bonding characteristics. For example,
it readily forms compounds where it behaves as a halo-
gen ion and forms structures similar to fluorides, such as
rutile, perovskite, rocksalt, etc.,19,20,21 and at the same
time readily occurs a cation in other chemical environ-
ments. Polar covalent bonds involving H and hydrogen
bonds are central to much of organic chemistry as well
the properties of important substances such as water.22
Thus the recent report by Janotti and Van de Walle (JV)
that H forms a new type of strong multicenter bond in
O vacancies in ZnO is of wide ranging interest.23
In this paper, we present standard local density ap-
proximation (LDA) calculations of the electronic proper-
ties and structure of H containing O vacancies in ZnO.
We do not find the multicenter covalent bonds claimed by
JV, and instead characterize the behavior of H as quite
conventional in that it occurs as an anion on the anion
site in a polar crystalline environment.
Our calculations were done within the standard local
density approximation using the general potential lin-
earized augmented planewave (LAPW) method, includ-
ing local orbitals.24,25 Specifically, we constructed a 72
atom 3x3x2 wurtzite supercells of ZnO, with one O atom
removed and replaced by H. The calculations were done
using the bulk lattice parameters of ZnO, but the inter-
nal coordinates of all atoms in the supercell were fully
relaxed. No symmetry was assumed in the relaxations.
The LAPW method is an all electron method that makes
no shape approximations to either the potential or charge
density. It divides space into non-overlapping atom cen-
tered spheres and an interstitial region. The method then
employs accurate basis sets appropriate for each region.24
In the present calculations, LAPW sphere radii of 2.0 a0,
1.6 a0 and 1.2 a0 were used for Zn, O, and H respec-
tively, along with a basis set consisting of more than 8500
LAPW functions and local orbitals. Convergence tests
were done with a larger basis set of approximately 12000
functions, but no significant changes were found. The
relaxations were done without any imposed symmetry,
with a 2x2x2 special k-point zone sampling. A sampling
using only the Γ point was found to yield slightly different
quantitative results, due to the limited size of our super-
cell, but would lead to the same conclusions. The calcu-
lated value of the internal parameter is u=0.119, which
agrees almost exactly with the experimental value. The
densities of states used to analyze the electronic proper-
ties were obtained using the linear tetrahedron method
based on eigenvalues and wavefunctions at 36 k-points in
the half zone (k and -k are connected by time reversal).
In our relaxed structure for a neutral cell, we find that
H occurs in a slightly asymmetric position, with three Zn
neighbors at 2.03 Å, and one Zn neighbor (the one along
the c-axis direction) at 2.17 Å. For the singly charged
cell, we obtain a very similar result, specifically three Zn
neighbors at 2.02 Å, and the apical Zn at 2.21 Å. In the
following, we focus on the neutral cell except as noted.
Fig. 1 shows the projection of the electronic density of
states onto the H LAPW sphere, of radius 1.2 a0. The
Fermi energy for our neutral cell lies at a position one
electron per cell into the conduction bands, correspond-
ing to the valence difference of one between O and H.
As may be seen, there are two prominent peaks in the
H component of the density of states, one, denoted “B”,
at ∼ -8 eV with respect to the Fermi level (-6 eV with
respect to the valence band maximum), and the other,
denoted “A”, high in the conduction bands at ∼ 6 eV. JV
identified these peaks, “B” and “A”, respectively, as the
bonding and antibonding combinations of metal and H
orbitals giving rise to the multicenter bond. In addition,
there is significant H s character distributed over the va-
lence bands, especially near the valence band maximum.
We note that the very large bonding-antibonding split-
ting of 14 eV implied by the assignment of JV indicates
extremely strong covalent bonds, which is somewhat sur-
prising considering the Zn-H distances. In any case, such
a large covalent gap would imply that the bonding and
antibonding states should have mixed character. In other
words, the bonding state should be of roughly half H s
character, while the remaining H 1s character should oc-
cur in the unoccupied antibonding level, so that the oc-
http://arxiv.org/abs/0704.0173v1
-8 -6 -4 -2  0  2  4  6  8
E(eV)
H pH in O vacancy
FIG. 1: Projection of the electronic density of states onto the
s and p components inside the H LAPW sphere, radius 1.2 a0,
for the 72 atom neutral cell. The two peaks identified by JV as
bonding and antibonding combinations are indicated by “B”
and “A”, respectively. The Fermi level lies in the conduction
bands. The position of the valence band maximum is denoted
by “VBM” (note that the LDA strongly underestimates the
3.3 eV band gap of ZnO).
cupancy of the H 1s orbital should be roughly 1 e, and
certainly significantly less than 2 e.
To analyze the bonding further it is convenient to com-
pare the charge density with an ionic model, as was done
for some alanates.30,31 As mentioned, H is known to en-
ter some solids as an anion, including tetragonal MgH2.
ZnH2 also exists though it is not as well characterized.
Furthermore, the simplest hydride, LiH, is of this ioni-
cally bonded type and includes H− anions coordinated
by six metal atoms.33,34 In these hydrogen anion based
materials, the negative H ion is stabilized by the Ewald
field. In fact, the importance of the Ewald field is one of
the essential differences between chemistry in solid state
and the chemistry of molecules. The long range Coulomb
interaction stabilizes ionic bonding for species that would
generally be largely covalent in small molecules, and in
particular stabilizes anions such as O2− and H−, which
are common in solid state chemistry but much less so
in gas phase molecules. This stabilization by the Ewald
field is reflected in the variability of the effective size of
H in crystal structure data for anionic hydrides.27,28,29 In
view of the common occurrence of H as an anion in many
metal hydrides, it would not be surprising if H− were sta-
bilized by the Ewald field of an anion vacancy in a polar
crystal such as ZnO. Thus we consider an ionic model,
based on the charge density of a H− ion stabilized by the
Ewald field, as simulated by a Watson sphere,35 as in Ref.
31. For such a H− ion, 0.525 e out of 2.0 e, i.e. ∼ 26% of
the charge, is inside a radius of 1.2 a0, so the majority of
the charge is outside. Because of the small sphere radius
used for H in our calculations the amount of charge in-
-8 -6 -4 -2  0  2  4  6  8
E(eV)
FIG. 2: Integration of the projection of the H s projected
density of states as in Fig. 1 normalized according to the
fraction of charge inside a 1.2 a0 sphere for a Watson sphere
stabilized H− anion (see text).
side the sphere is only weakly dependent on the Watson
sphere radius, which reflects the environment. For a non-
spin polarized neutral H in free space as described in the
LDA, 0.378 e (38%) would be inside a radius of 1.2 a0,
showing that there is a strong dependence on the charge
state, though not precise proportionality. Fig. 2 shows
the integral of the H s character as a function of energy
normalized by the fraction of the H− charge inside a 1.2
a0 sphere (0.525/2). Over the valence band region the
p contribution is less than 2%, and the d contribution is
less than 0.2%. The conduction bands, which are more
Zn sp derived, show a larger proportion of H p character,
as may be seen in Fig. 1. Thus the charge inside the
sphere, which comes from the occupied valence bands,
is mainly due to H s states, and not from orbitals on
neighboring atoms.
Using the ionic model for H−, i.e. incorporating the
factor of 0.525/2 as the fraction of charge inside the H
LAPW sphere, and integrating, one finds that the peak
“B” contains ∼ 0.8 H s electrons. Integrating over the
remaining valence bands brings the H s count to 2.0 elec-
trons, i.e. what is expected for H−. This leads to an
interpretation of the electronic structure, where the peak
“B” comes from the H 1s state. This hybridizes with
valence band states, which have mixed Zn d and O p
character. The second peak “A”, 14 eV higher, is then
the H s resonance. This is a very reasonable position for
the resonance of H−. In particular, the H−− resonance
of atomic H− is at ∼ 14.5 eV.36,37,38 JV emphasized the
shape of the charge density associated with the states in
the peak “B” and argued for bonding based partly on real
space images of this charge. As mentioned, in our pro-
jected density of states we find that this peak contains
0.8 s electrons (i.e. 40% H s character), which would
be consistent with a bonding orbital. However, the hy-
bridization is with other occupied states, and when the
integration is done over all the valence bands, we find 2
s electrons, consistent with H−. We emphasize that mix-
ing of occupied states does not contribute to the energy,
and that such hybridizations do not constitute bonds.
Our calculated binding energy relative H2 and a relaxed
neutral supercell with an O vacancy is 87 kJ/mol H.39
This may be an overestimate due to LDA errors,40 but
in any case is much smaller than the binding that would
be suggested by a 14 eV bonding-antibonding splitting.
We also calculated the positron wavefunction and life-
times for ZnO with an O vacancy and with the H contain-
ing O vacancy. This was done using the LAPW method
in the full inverted self-consistent Coulomb potential plus
the correlation and enhancement factors of Boronski and
Nieminen41 as calculated from the full charge density. We
obtain a bulk positron lifetime for ZnO of 144 ps, which
is at the lower end of the experimental range. Reported
experimental values are 151 ps (Ref. 42), 170 ps (Ref.
43), 141 ps - 155 ps (Ref. 44), and 182 ps (Ref. 45). Sig-
nificantly, positrons, which are positively charged, tend
to localize in voids and in sites that are favorable for
cations, and localize weakly if at all in anion sites, due
to the unfavorable Coulomb potential. We do not find
positron localization at the O vacancy in our ZnO super-
cell, indicating that the O is indeed an anion as expected,
nor do we find positron localization or a significant life-
time increase in the cell with a H containing O vacancy.
We also find no significant change in lifetime for H in an
O vacancy within a charged supercell with one electron
removed. In contrast, we obtain a bound positron state
for Zn vacancies, both with and without H, reflecting the
fact that Zn is on a cation site. The calculated lifetime
in a supercell with a Zn vacancy is 212 ps, while with a H
filled Zn vacancy we obtain 175 ps (in this case H bonds
to a single adjacent O to form a hydroxyl like unit with
H-O bond length of 1.01 Å).46
To summarize, we have performed density functional
calculations for ZnO supercells with both empty and H
filled O vacancies. Based on an analysis of the electronic
structure we do not find any evidence for hydrogen mul-
ticenter bonds, but rather find that H occurs as H−.
We are grateful for helpful discussions with L.A. Boat-
ner, J.S. Neal, and L.E. Halliburton. This work was sup-
ported by the Department of Energy, Office of Nonpro-
liferation Research and Development, NA22.
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