Shortest hydrogen hydrogen separation in metal hydrides
P.Vajeeston1, P.Ravindran1 , R.Vidya1, H.Fjellvag1 2, A.Kjekshus1 and A.Skjeltorp2.
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1 Department of Chemistry, University of Oslo, Box 1033, Blindern, N-0315, Oslo, Norway.
2 Institute of Energy Technology, P.O.Box 40, Kjeller, N-2007, Norway.
(October 4, 2001)
Abstract
First principle studies on total energy, electronic structure and bonding
nature of NiIn ( = La, Ce and Nd), and their saturated hydrides
( NiInH1 333) are performed using full-potential linear muÆn-tin orbital
method. All these series of compounds are formed in ZrNiAl-type structure.
When hydrogen is introduced in NiIn matrix, anisotropic lattice expansion
is observed along [001] and lattice contraction along [100]. In order to nd
the equilibrium structural parameters for these compounds we have performed
force minimization as well as volume and optimization. Our optimized
atomic positions, cell volume and - ratio are in very good agreement with
recent experimental ndings. From the electronic structure and charge density analysis we have identied the microscopic origin of anisotropic change
in lattice parameters by hydrogenation in NiIn. All these hydrides violate the well documented "2 A rule" for - separation in the whole metal
hydride family. The inter-nuclear separation between - is almost equal
to the sum of their covalent radii and the distance between - is 1.57
to 1.66 A which is very small compared to that in available metal hydrides.
is bonded with (2 ) in H-Ni-H dumb-bell shaped linear array, which
looks like 2 subunits. Our density of states study, valence charge density
and crystal orbital Hamiltonian population analyzes clearly indicate that the
bonding between the and (2 ) is covalent, the magnitude of this bond
being higher than other types of bonds present in these materials. Inspite of
shorter - distance, the interaction between them is not stronger owing to
the participation of valence electrons of in strong - covalent bond. As
there is not enough electrons for the repulsive interaction between in these
compounds, they posses unusually short - separation. Our calculation
shows that all these materials have metallic character.
PACS numbers: 71., 81.05.Je, 71.15.Nc, 71.20.-b
RE
RE
RE
:
RE
c=a
c=a
RE
H H
Ni H
H H
H
Ni
c
N iH
H
Ni
c
H H
H
Ni H
H
H H
Typeset using REVTEX
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I. INTRODUCTION
Hydrogen can be considered as an ideal fuel for many types of energy converters. Neither storage as a compressed gas nor as cryogenic liquid appear to be suitable for common
application. However, a major obstacle to its use is diÆculty in storing it economically.
Hydrogen storage as a metal hydride is the most promising alternative because of its unique
feature.1 2 For the past few decades lot of research is going on to identify the potential candidate for such type of application. The rare earth hydrogen storage alloys are used for
a wide range of applications owing to their high hydrogen density and ability to absorb
hydrogen under moderate conditions.1 3 The hydrogen absorption properties of these alloys
are very much dependent on the constituent metals. The metal-hydrogen bonding interactions play a major role in the stability of hydrides. In order to optimize the choice of
the intermetallic compound for a selected application, a better understanding of the role of
each alloy constituent on the electronic and structural properties of the material is crucial.
Several empirical models5 have been proposed for the heat of formation and heat of solution
of metal hydrides and attempt have been made for justifying the maximum hydrogen absorption capacity of the metallic matrices.4 6 7 These models show that the metal-hydrogen
interaction depend both on geometric and electronic factors.
Numerous compounds between transition metals and non-metals can accommodate hydrogen atoms in interstitial solid solutions or form hydride phases. The crystal structures of
these phases are often complex and there are several types of interstice that might conceivably accommodate hydrogen atoms. The distribution of hydrogen atoms on interstitial sites
in the structures appear to be mainly governed by the hole size, shape of the surrounding
metal atom polyhedron and distances to the nearest non-metal and hydrogen neighbors.8 9
Structural studies of intermetallic hydrides have revealed several empirical rules that can
be used to predict the hydrogen sub-lattice in a given metal lattice.10 11 One of the best
establisher, the so called "rule of 2 A " states that the distance between two hydrogen11
atoms in a metallic hydride must exceed 2 A and theoretical calculations12 also support this
rule. But Th2 AlH4 (metallic hydride)13 and K2 ReH9 (nonmetallic complex hydride)14 15 violate this rule, they have the H -H separation 1.79 and 1.87 A respectively. However, the
H -H separation in Th2 AlH4 is 1.97 and 1.95 A as found by high resolution powder neutron
diraction (PND) data16 and recent theoretical calculation17 respectively.
The recent experimental evidence of an ordered arrangement of deuterides with very
short H -H separation (around 1.5-1.6 A) in ZrNiAl-type intermetallic hydride RE NiInH
(RE = La, Ce and Nd, x = 1.19 to 1.24) has attracted much interest.18 The reason for this
unusually short H -H distance is not yet well known. Identication of the reason will give
more ideas about packing H in metal matrix in an eÆcient way. 1 H NMR of the RE NiInbased (RE = Ce and Pr) hydrides has given independent indications for the existence of
H::H pairs in CeNiIn hydride19 20 and PrNiIn hydride.21 On the basis of NMR study the
H -H separations have been estimated to be equal to 1.48 A in CeNiInH 19 and 1.5 to 1.8 A
21
in PrNiInH . Recent PND nding suggested that the H -H interaction is mediated via a
triangular RE3 cluster with probably strong RE -RE bonds, thus 'shielding' the direct H -H
interaction.18 It may be noted that in LaNiInH systems, a member of isomorphic group,
no evidence of the pairing of protons has been found.22 Therefore, any of the following type
of bonding may be expected: (a) two H atoms bonded to metal atom and (b) molecular
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bonding of two H atoms. In order to gain more knowledge about the nature of chemical
bonding and the microscopic origin of shortest H -H separation in these compounds detailed
electronic structure studies on these materials are needed and this is motivation for the
present study.
In this paper we present the results of accurate full-potential Linear MuÆn-tin Orbital
(FP-LMTO) calculations on series of RE NiIn (RE =La, Ce and Nd) and RE NiInH1 333
compounds. The main scope of this study is to reproduce the experimentally observed
shortest H -H separation and understand the reasons behind this unusual shorter separation.
Also it is interesting to identify the anisotropic lattice expansion during the hydrogenation
process of RE NiIn.
This paper is organized in the following sequence. The details about structural aspects
and computational method used in the present study are described in the Sec. II. In Sec. III
the results of our calculations are described and compared with experimental ndings. The
important conclusions drawn from our theoretical analysis are briey summarized in Sec. IV.
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II. STRUCTURAL ASPECTS AND COMPUTATIONAL DETAILS
A. Structural details
Most of the ABC intermetallic aluminides are formed in the ZrNiAl-type structure.23 24
By substituting Al atom by larger In atoms for RE -based compounds, the ab-plane of
the hexagonal structure expands. This makes hydrogen absorption more favorable owing to
enlarged interstitial sites. In RE NiIn compounds the 4h and 6i sites have been considered for
hydrogen absorption.19 20 But recent experimental ndings show that 4h site is fully occupied
by H at higher H concentration. In the saturated hydrides (RE3 Ni3In3 H4) H atoms are
located inside the RE3 Ni tetrahedra that share a common face, thereby forming a RE3 Ni2
trigonal bipyramid. In RE NiIn compounds the lattice expansion is highly anisotropic by
hydrogenation.
RE NiIn and RE NiInH1 333 crystallize in the hexagonal ZrNiAl-type structure with the
space group number 189 (P 62m). The structural details are given in Table I. As the unit
cell contains three formula units, 13 atoms involve in the calculation. It is important to
note that Ni atoms occupy two dierent crystallographic sites, one is at 1b position (we call
Ni(1b)) and the another is at 2c position (we call Ni(2c)) in the unit cell. Hence the nearest
neighbors of two Ni atoms are dierent from each other.
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B. Computational details
Our theoretical approach is based on generalized gradient approximation (GGA) with
the Perdew and Wang25 exchange correlation of density functional theory (DFT). The KohnSham equation was solved by means of a full-potential linear muÆn-tin orbital method.26
The calculations were relativistic including spin orbit coupling and employed no shape approximation to the charge density and potential. Spin-orbit terms are included directly
in the Hamiltonian matrix elements for the part inside the muÆn-tin spheres. The basis
functions, charge density and potential were expanded in spherical harmonic series inside
3
the muÆn-tins and in a Fourier series in the interstitial. In the present calculations the
spherical-harmonic expansion of the charge density, potential and basis functions were carried out up to ` = 6. The tails of the basis functions outside their parent spheres are linear
combinations of Hankel or Neumann functions depending on the sign of the kinetic energy of
the basis function in the interstitial regions. For the core-charge density, the Dirac equation
is solved self-consistently, i:e:, no frozen core approximation is used. The basis set contained
semicore 5p and valence 5d, 6s, 6p and 4f states for La (for Ce the 4f electrons are treated
as valence and localized core electrons, but Nd-4f electrons are treated as localized electrons using open core approximation), 4s, 4p and 3d for Ni, 5s, 5p and 5d for In and 1s,
2p and 3d states for H . All orbitals were contained in the same energy panel. Moreover,
the present calculations make use of a so-called multi basis, to ensure a well converged wave
function. This means that we use dierent Hankel or Neuman functions each attaching to
its own radial function. This is important to obtain a reliable description of the higher lying
unoccupied states and low lying semicore states. Integration over the Brillouin zone was
done using 'special-point' sampling,27 and self consistency was obtained with 105 k points
in the irreducible part of the Brillouin zone (IBZ) of the hexagonal Bravais lattice, which
corresponds to 768 k points in the whole Brillouin zone. We have made test calculations
by just double the k points to check for convergence. The optimized c=a ratio for 105 k
points and 210 k points for LaNiInH1 333 are essentially same. Hence 105 k points have been
used for the optimization of the c=a, cell volume and atomic position optimizations and the
calculation of electron density. For the DOS calculations, the Brillouin zone integration was
performed by means of tetrahedron method.28 To gauge the bond strength we have used
the crystal orbital Hamiltonian population (COHP29) analysis, which is implemented in the
TBLMTO-47 package.30 31 A measure of the magnitude of bonding was obtained by computing COHP which is the Hamiltonian population weighted density of states, identical to
well known crystal orbital overlap population. If COHP is negative, it indicates a bonding
character and if it is positive, indicates an antibonding character. The bulk moduli have
been obtained using the so called universal equation of state t for total energy as a function
of the volume.
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III. RESULTS AND DISCUSSION
In order to understand the eect of H in the RE NiIn metal matrix and to verify the
experimentally observed unusually shorter H -H separation in RE NiInH1 333 we have carried
out the structural optimization study on these compounds. For this purpose, rst we have
taken the structural information from the experimental ndings (atomic position and lattice
parameter) for nonhydride materials. Feeding this as an input, we have relaxed the atomic
positions globally using force minimization technique, keeping the experimental c=a ratio
and cell volume (V0) xed. Then theoretical equilibrium volume is determined by xing
the optimized atomic positions and experimental c=a, and vary the cell volume 15 to 10
% of V0. Finally the optimized c=a is obtained by 2% variation of c=a ratio (in step of
0.02) while keeping the theoretical equilibrium volume xed. Theoretically obtained structural parameters are presented along with experimental one in Table I and lattice parameter
as well as inter-atomic distances are tabulated in Table II. Finally, xing the theoretically
achieved structural parameters for RE NiIn compounds, we introduce the H atom into the 4h
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site, and once again we have done the above mentioned structural optimization procedures.
Our optimized atomic positions (Table I) and lattice parameters (Table II) are in very good
agreement with high resolution powder neutron diraction (PND) data.18 It is interesting
to note that our calculation also conrms the unusual shortest H -H separation (around
1.57 A) present in RE NiInH1 333 hydrides, which is very closer to experimentally observed
value of 1.56 to 1.64 A.18 We also observed that the expansion of volume during hydrogenation process (in LaNiIn 2.54 A3 /H atom, in CeNiIn 4.45 A3 /H and in NdNiIn 3.93 A3 /H) is
highly anisotropic, which is exclusively along [001] (c=c = 12.7 to 16.7 %) and small lattice
contraction in [100] (a=a = 1.68 to 4 %). The results given in the rest of the paper are
based on the theoretical equilibrium lattice parameters.
CeNiIn is a valence-uctuating system with Kondo-like behavior.32 It is interesting
to note that hydrogenation of isoelectronic compound CeNiAl, which is considered as an
intermediate-valence compound,33 34 induces a localization of the (Ce)-4f electrons in the
hydride CeNiAlH2 04.35 In order to nd the valence of the Ce in CeNiIn and CeNiInH1 333,
we have made total energy calculations as a function of cell volume (see Fig. 4) for dierent
electronic congurations such as the trivalent state with the 4f electrons in the valence
(valence 4f 1 ), one 4f electrons as localized and put it in the core state (localized 4f 1 ) and
two 4f electrons as localized and put them in the core state (localized 4f 2 ). From the
minimum in the total energy curves in Fig. 4 we have obtained the equilibrium cell volumes
with Ce in dierent electronic congurations for CeNiIn and CeNiInH1 333 and are 238.48 A3
for localized 4f 2 , 215.89 A3 for localized 4f 1 and 194.02 A3 for 4f 1 as valence respectively.
The theoretically calculated cell volume 215.89 A ts very well with experimental volume
3
3+
of 212.93 A , indicating that Ce exists as Ce with 4f electrons well-localized and not
participate in both CeNiIn and CeNiInH1 333.
Using universal equation state t36 for the total energy as a function of the unit cell
volume, the bulk moduli (B0 ) and its pressure derivatives (B00 ) are obtained (Table II). Our
calculated B0 values for LaNiIn and CeNiIn are decreases by hydrogenation. This decrease
in bulk modulus can be explain by the volume expansion during hydrogenation. In the
case of NdNiIn the bulk modulus is increasing by the hydrogenation. This indicate that the
introduction of hydrogen in the NdNiIn lattice enhance the bond strength and this overcome
the volume expansion eect. The enhanced nature of bond strength by hydrogenation is
explained through COHP and the charge density analysis in the later section. There is no
experimental bulk modulus measurements on these materials are available to conrm our
results.
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A.
N i-H
and
H -H
separation
Compared to binary metal hydride structures which are characterized by a few, relatively
simple and usually highly symmetrical metal atom arrangement, ternary metal hydride
structures show a great variety of complex metal atom arrangements of various (usually
low) symmetries. In such type of hydrides, some of them have metal-hydrogen distance
almost closer to the sum of their covalent radius (for example in 0-MgNiH4, Ni-H distance
is 1.49 A, sum of the covalent radius of Ni-H is 1.47 A). Such short distances may not be
characteristic for all hydrogen atom sites belonging to a particular crystallographic location
because of possible local distortions in their metal atom environments. Metal-hydrogen
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distances correspond closely to those in the corresponding elemental hydrides, except that
they may be anomalously shortened due to partial occupancy of the hydrogen atom sites.
In all these metal hydrides considered here the 4h site occupancy is full and all H atoms
belonging to a same atomic environment in the crystal lattice. The distance between Ni(2c)H is 1.46 to 1.49 A (see Table III) which is almost equal to the sum of the covalent radius
of Ni and H . This may be due to the formation of H -Ni-H (NiH2 molecule) sub units in
these compounds.
The next interesting thing is the presence of shortest H -H separation in these compounds.
According to the available structural information on hydrides the H -H separation is never
less than 2 A which is so called "2 A rule" (Switendick criterion).11 This might occur when
the two H atoms in the metal hydride would come very closer to each other in a manner
in which the H -H bonding states were occupied and the anti-bonding states37 were empty
rise above the Fermi level (E ). The resulting structure containing H2 'dimers' which locate
inside a metallic matrix might appear to be highly unusual.38 This may happen in this series
of hydrides, because experimental as well as our structural optimization study show that
the H -H separation is around 1.56 to 1.60 A in the entire series. However our theoretical
analysis shows a quite dierent type of bonding present in between H atoms, which is
discussed below.
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B. Electronic structure
In general hydrogen absorption modies the electronic structure of the host compound by
creation of new metal-hydrogen bonding states, by shift of the Fermi level, by modication
of the symmetry and by the width of the bands. The calculated band structure for LaNiIn
and LaNiInH1 3333 are shown in Fig. 5a and b respectively. These illustrations clearly indicate
that inclusion of H in the LaNiIn matrix has a noticeable impact on the band structure,
mainly in the valence band (VB). Three low lying (Fig. 5a at the point a single s band
and doubly degenerated p-band) bands are originating mainly from In-s and La-p electrons.
In 3 to 1 eV energy range hybridized In-p, Ni-d and La-d bands are present and the
electrons corresponding to these bands are mainly participating the chemical bonding. A
similar type of band structures are obtained for CeNiIn, NdNiIn and its hydrides but not
shown here. The unoccupied La-f electrons are present in the conduction band region
around 2.5 eV above E . As the unit cell contains three formula units, four electrons are
additionally introduced when LaNiInH1 3333 is formed from LaNiIn. Therefore two additional
s-bands are present in the lowest portion of VB (from 10.85 to 4eV) in LaNiInH1 3333.
In Fig. 5b lowest energy band (almost like free electron band around point) corresponds
to one of the H -s band. The other H -s band well dispersed and hybridized with the rest
of the valence bands in the region around 8 eV to 3 eV. A cluster of well localized bands
in the VB around 2 eV are originating from Ni-3d electrons. Due to the addition of extra
electrons in the lowest portion of VB, the hybridized bands are moved towards E . From
Fig. 5a and b, it is clear that several bands cross the Fermi level hence these compounds
have metallic behavior. This is further conrmed by total DOS, showing a nite number of
electrons at the Fermi level.
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C. Nature of Chemical Bonding
The nature of bonding of the system will give clear picture about the reasons behind
the shortest Ni-H and H -H separation in these compounds. Hence we have analyzed the
chemical bonding via density of states (DOS), charge density and crystal orbital Hamiltonian
population analysis.
1. DOS
All the DOS curves for RE NiIn and RE NiInH1 333 are having close similarity (Fig.6).
The interesting feature of this gure is that the hydride systems there is a pseudogap (deep
valley closer to E ) and this is well pronounced in the case of CeNiInH1 333. The strong
covalent interaction between N (2b)-H is mainly responsible for the creation of pseudogap.
In general one can gain in total energy for stability when the E lye in the vicinity of
pseudogap.39 This may be one of the reason for the stabilization of these metal hydrides
with shorter H -H distance. When we move from La to Nd the additional f -electrons are
treated as a localized electrons, hence they are not participating the chemical bonding.
However, due to the variation in the interatomic distance between the constituent atoms
there is small dierence (viz: narrowing or broadening of the DOS). The metallic character
of all these compounds are mainly originated from the nite DOS contribution at E of
RE -d, Ni-d and In-p states. It is well established that the bonding nature of solids can
be analyzed from the calculated partial density of states (PDOS).40 In order to analyze
the bonding nature and the changes in electronic structure by hydrogenation we display
in Fig.7 the calculated PDOS of the LaNiIn and LaNiInH1 333. In the lowest portion of
the DOS curve of LaNiIn in the 5 to 4.2 eV energy range a nite band gap with the
width of 1.2 eV is present, below this energy range In-s and Ni-s states are present. In
the energy range 4.2 eV to E large amount of electrons are present which are contributed
by La-d, Ni-d and In-p states. These states are energetically degenerate, which implies
the possibility of covalent bonding between RE -Ni(1b), RE -Ni(2c), RE -In, Ni(1b)-In and
Ni(2c)-In. The interatomic distance between Ni2-In (2.76 to 2.9 A) and Ni(1b)-In (2.73
to 2.9 A) is much closer than RE -Ni(2c) (3.02 A) and RE -In (3.39 to 3.41 A). Hence there
is a covalent bond formation between Ni(1b)=Ni(2c)-In favorable both energetically as well
as spatially in the RE NiIn matrix. The unoccupied electron energy states are present above
E and in particular the La-f states are present around 2.5 eV.
Once we introduce H into the RE NiIn matrix the atoms are rearranged in order to
accommodate H . Hence, the energy levels are also modied depending upon the atomic
environment. One of the common features of the electronic structure of metal hydrides is
the formation of H -induced states in the bottom of the VB. Inclusion of additional H -s
energy levels in the 8.2 to 3.4 eV energy range changes the lowest portion of DOS, with
systematic shift in E towards unoccupied side. Moreover the energy gap between 5 to
4.2 eV disappear when we move from non-hydride to hydride. Another interesting feature
in DOS of hydrides is that In-s states get broadened ( 8.25 to 3.75 eV) due to reduction
of interatomic distance between Ni(2b) and In resulting from the lattice contraction along
a. In LaNiInH1 333 the In-s, H -s, Ni-d and La-p states are energetically degenerate in the
8.2 to 3.4 eV energy range, implying a possible formation of covalent bonding between
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In-H , Ni-H , La-H and H -H . But Ni(2c)-H separation is very smaller (1.45 to 1.49 A),
hence presence of Ni(2c)-H covalent bonding is more favorable than the other possibilities.
Both Ni(1b) and Ni(2c) DOS are broadened considerably in the 8 to 4 eV energy range.
This is mainly due to the interaction between Ni(2c)-H in the latter case and the reduction
in the Ni(1b)-La distance in the former case. However, the changes in Ni(2c) DOS is more
than that in Ni(1b) DOS, which is mainly due to strong Ni(2b)-H covalent bond formation
and reduction in Ni(2b)-In distance.
2. Charge Density analysis
In order to understand the microscopic origin of the shortest Ni(2c)-H and H -H separation we have made the valence charge density analysis for non-hydrides as well as hydrides
in dierent planes and that for (100) plane is given in Fig. 8 and Fig. 9 for LaNiIn and
LaNiInH1 333 respectively. The rest of the compounds are also having the same kind of
charge density distribution hence we have not presented them in this paper.
In the electronegativity point of view, electronegativity dierence between Ni and In is
0.1, this indicates that the possibility of covalent interactions between them is more probable
than ionic bonding, which is conrmed from our charge density analysis. In Fig. 8, nite
charge present between the nearest neighbors Ni(2c) and In, hence sharing of electrons
takes place resulting in covalent bonding. The Ni(2b)-In bond strength is stronger than
other bonds present in RE NiIn and this is quantitatively analyzed latter. RE -Ni(1b) and
RE -In have mixed bonding nature (partial covalent and partial ionic character) which may
be due to the electronegativity dierence of 0.5 between RE and Ni as well as RE and
In. Alternative Ni(2c)-In layers (see Fig. 8) have no charges between them indicating the
presence of a void which is the room for accommodating H .
When non-hydride is hydrogenated, the hole is occupied by H and shifted towards Ni(2c),
forming new Ni(2c)-H bond, due to which small lattice contraction occurs along a. Ni(2c)
and H form dumb-bell like linear arrangement along [001] resulting in lattice expansion
exclusively along c-axis. Hence anisotropic change in the lattice occurs. Another important thing is that, the interatomic distance between Ni(2c) and H is almost equal to the
covalent radius of Ni(2c)-H , therefore Ni(2c)-H bond results in linear NiH2 molecule- like
feature (see Fig. 9). The same type of bonding is present in Na2 PdH2.41 The Pd-H separation in Na2 PdH2 (1.68 A) is closer to Ni(2b)-H (1.46 to 1.49 A) separation present in these
series, but the H -H separation (3.35 A) in the former is more than that in the present cases.
The covalent bond strength of Ni(2c)-In is reduced, in-spite of reduction in their interatomic distance from 2.89 to 2.79 A upon hydrogenation and this is evidently seen from the
charge density analysis of the hydride and the nonhydride (more quantitative discussion see
Sec. III C 3). This is because Ni(2c)-d electrons form NiH2 molecule like feature and hence
smaller amount of Ni(2c)-d electrons participate the covalent bonding between Ni(2c) and
In. Even though, H -H separation is very less (1.57 A), the interaction between them is
very weak since no considerable electronic charge is present between them (see Fig. 9b). The
main reason behind this extraordinary behavior is that, H -1s electron is strongly bonded
with Ni(2b)-3d electrons, hence not enough electrons are left in H atoms to repel each other.
This could explain the presence of H in very shortest distance in these compounds.
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3. COHP
The simplest way to investigate the bond strength between two interacting atoms in a
solid would be to look at the complete COHP between them, taking all valence orbitals into
account. To understand the bonding pattern further, we have undertaken a COHP study of
these materials. The results of the COHP analysis for LaNiIn and LaNiInH1 333 are shown
in Fig. 10 for each possible interaction (within 3.5 A range) present in these systems. An
interesting aspect of this illustration is that valence band is lled up with bonding orbitals
(negative value of COHP) and the antibonding orbitals are some 3 eV above E . Integrated
COHP (ICOHP) values at the E are tabulated in Table III. From this table we have found
that the interaction between Ni(2c)-H is quite strong (ICOHP value is 3.32 to 3.44 eV)
compared with all the other bonding present in this series of compounds.
The magnitude of bonding interaction between Ni(2c)-In is 1.19 to 1.25 eV up-to E
in this series, which is reduced during hydrogenation process (ICOHP is 0.84 to 0.87 eV
in the hydrides) This indicates that the Ni(2c)-In bond strength decreases by hydrogenation
in RE NiIn. The reduction in bond strength between Ni(2c)-In by hydrogenation may be
understand as follows. When the H atoms are introduced in to the 4c position in RE NiIn
the Ni(2c) 3d electrons are moving towards the H atoms and forming strong Ni(2c)-H
covalent bond. As a result, there is not enough Ni(2c)-3d electrons available to participate
the covalent bonding between Ni and In and hence the Ni-In bond weaken. Even though the
H -H separation is very shorter, ICOHP value is very small 0.04 to 0.045 eV indicating
that there is no dominant covalent bonding interaction between H atoms in these hydrides.
The smaller value of ICOHP is due to both bonding and antibonding states are present
below E . But ICOHP value of bonding state is 0.14 to 0.23 eV, which is much smaller
than ICOHP of Ni(2c)-H . This indicates that the interaction between H -H is considerably
weaker than Ni(2c)-H interaction. Our charge density analysis also yields the same result,
which disagrees with NMR studies on CeNiInH and PrNiInH hydrides19{21 that presence of
H-H pairing is the main reason for the unusual shortest separation. Recent PND experiment
speculated that H -H interaction is shielded by RE -RE interaction. But our COHP study
shows that the interaction between RE -RE is not strong enough, (ICOHP value is 0.61
to 0.62 eV, COHP was not shown in Fig. 10) which is approximately 5 to 6 times smaller
than Ni(2c)-H interaction.
From the analysis of electronic structure, it is found that the Ni(2c)-3d and H -1s hybridization results in strong attractive interatomic forces between Ni(2c) and H . In order
to understand the H -H interaction and to nd the possibility of H2 sub unit formation in
this metal matrix we have made the following model calculation. We have xed the theoretically obtained cell volume, atomic position (except H position) and c=a, only changed
the H -H separation towards and away from each other and calculated total energies as a
function of H separation. This H displacement is equivalent to the reduction or enlargement
of Ni(2c)-H distance depending upon H movement from the Ni(2c). If H -H distance is
reduced, it is corresponding to decrease the covalent interaction between Ni(2c)-H and increase the overlap interaction between H atoms. The calculated total energy as a function
of H displacement curve shows (see Fig. 11) two minimas, one (denoted by a) corresponds
to the equilibrium H -H separation obtained from our structural optimization and the other
minima (denoted by b in Fig. 11) corresponding to the formation of NiH2-like molecule. The
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sudden increase in total energy when the H -H separation is reduced below 1.325 A owing to
repulsive Coulomb interaction of electrons between the H atoms. The drastic enhancement
in total energy when the H -H separation is higher than 1.775 A is owing to the increase in
the repulsive Coulomb interaction of electrons between H and Ni(2c). However, the energy
dierence between these two minima are very small (0.122 mRy/f.u.) indicate the H atoms
are interact with the Ni atoms and formed almost like a NiH2 molecule. Another important
point to note that when we reduce the H -H separation further and further the calculated
energy increases enormously and this indicating that formation of H -H molecule is almost
improbable.
From the COHP analysis along with our charge density analysis we have identied the
reason behind the shortest H -H separation present in this series of compounds as follows.
When H is introduced to the lattice, the H atoms are forming strong covalent bonding
with the neighboring Ni(2c) atoms resulting the formation of dumb-bell shaped like NiH2
molecules. As a result, not enough electrons are present in between the H atoms to contribute
the repulsive interaction when the H atoms are brought together. Hence, we have the H -H
separation is extraordinarily smaller than the metal hydrides reported in the literature.
From the above analysis we found that the Ni(2c)-H interaction plays a major role
to keep the H -H in such short distance in this particular crystal structure. It would be
interesting to study whether the short H -H is due to special type of crystal structure or
due to the strong Ni(2c)-H covalent interaction. In order to verify this and also identify
potential hydrides with shortest H -H separation one have to study the role of Ni site alloying
on the changes in the H -H separation. We are currently working on this aspect and the
results will be published in forthcoming paper.
IV. CONCLUSION
We have carried out detailed investigation on electronic structure and bonding nature of
RE NiIn and RE NiInH1 333 (RE = La, Ce and Nd) using the generalized gradient corrected
:
full-potential density functional calculations and we have arrived at the following conclusions.
RE NiIn and RE NiInH1 333 are formed in the ZrNiAl-type structure. Our optimized struc:
tural parameters exhibit highly anisotropic lattice expansion 13 to 17 % along the [001]
direction and small (1.68 to 4 %) contraction along [100] direction. This is in very good
agreement with experimental ndings. Our optimized atomic position, unit cell volume and
c/a ratios are in very good agreement with experimental ndings.
This series of compounds are having shortest H -H separation, among the available metal as
well as complex metal hydrides. They violate the well known 2 A rule for H -H separation in
hydrides. Our DOS, charge density analysis and COHP studies show that strong Ni(2c)-H
bonding is the main reason for the violation of 2 A rule.
Our model calculation predicts that the interaction between H -H is strong repulsive and
hence the possibility to form H in the molecular form in metal hydrides is less probable. We
have not observed any H ..H pairing mechanism in these compounds as was suggested by
NMR study and the RE -RE interaction is quite small compared to Ni(2c)-H and RE -In
bonding, hence the probability for shielding the H -H interaction via RE -RE is question10
able.
These compounds are having nite number of electrons at the E resulting in metallic
feature.
F
ACKNOWLEDGMENTS
PR and PV gratefully acknowledges Prof. John Wills and Prof. O.K. Andersen for
supplying their computer codes used in this study. The authors also acknowledge Dr. Florent
Boucher for useful communications on COHP and Prof. Yartys and Prof. Hauback for
useful discussions as well as providing the structural information to do this calculation.
This work has received support from The Research Council of Norway (Programme for
Supercomputing) through a grant of computing time. PR wish to thank Prof. Olle Eriksson,
Dr. Per Andersen and Dr. Hakan Hugosson for useful communication and The Research
Council of Norway for the nancial support.
11
TABLES
TABLE I. The optimized atomic positions of
Theory
x
y
z
RE
NiIn and
x
NiInH1 3333.
Experiment18
y
RE
:
z
LaNiIn
La
0.5866
0.0
1/2
0.594
0.0
1/2
In
0.2475
0.0
0.0
0.256
0.0
0.0
LaNiInH1 3333
La
0.6036
0.0
1/2
0.6035
0.0
1/2
In
0.2444
0.0
0.0
0.2437
0.0
0.0
H
1/3
2/3
0.6728
1/3
2/3
0.6759
CeNiIn
Ce
0.588
0.0
1/2
0.594
0.0
1/2
In
0.248
0.0
0.0
0.256
0.0
0.0
CeNiInH1 3333
Ce
0.6077
0.0
1/2
0.6013
0.0
1/2
In
0.2507
0.0
0.0
0.2462
0.0
0.0
H
1/3
2/3
0.6752
1/3
2/3
0.6737
NdNiIn
Nd
0.5886
0.0
1/2
0.594
0.0
1/2
In
0.2496
0.0
0.0
0.256
0.0
0.0
NdNiInH1 3333
Nd
0.6013
0.0
1/2
0.6013
0.0
1/2
In
0.2483
0.0
0.0
0.2462
0.0
0.0
H
1/3
2/3
0.6723
1/3
2/3
0.6737
Ni atoms are in two dierent atomic positions Ni(1b) is at (0,0,0.5) and Ni(2c) is at (1 3 2 3 0).
:
:
:
= ;
12
= ;
TABLE II. Calculated lattice parameters ( and in A), ratio, variation in ( ),
axis ( ) and volume ( ) during hydrogenation process (all are in %), density of state at
Fermi level [N(E ) in states Ry. 1f.u 1], bulk modulus ( 0 in GPa) and its pressure derivative( 00 )
for NiIn and NiInH1 333 compounds.
LaNiIn LaNiInH1 333 CeNiIn CeNiInH1 333 NdNiIn NdNiInH1 333
The. Exp.18 The. Exp.18 The. Exp.18 The. Exp.18 The. Exp.18 The. Exp.18
7.5604 7.5906 7.2603 7.3810 7.5807 7.5340 7.4536 7.2921 7.5207 7.5202 7.2408 7.2255
3.9924 4.050 4.5522 4.6489 3.9806 3.9750 4.4871 4.6238 3.9023 3.9278 4.5560 4.5752
0.5281 0.5336 0.6270 0.6399 0.5251 0.5276 0.6020 0.6341 0.5189 0.5223 0.6292 0.6332
| | -3.969 -2.76 | | -1.68 -3.21 | | -3.72 -3.92
| | 14.02 14.8 | | 12.72 16.3 | | 16.75 16.50
| | 5.15 8.54 | | 8.97 8.98 | | 7.60 7.53
N(E ) 38.22 | 35.30 | 38.90 | 38.10 | 43.74 | 28.13 |
70.38 | 69.45 | 86.24 | 81.67 | 76.20 | 86.03 |
0
0
4.12 | 4.08 | 2.88 | 3.48 | 4.35 | 4.12 |
0
a
c=c
c=a
a
a=a
v=v
B
F
RE
c
RE
B
:
:
:
a
c
c=a
a=a
c=c
v=v
F
B
B
13
:
c
TABLE III. Interatomic distances (in A) and integrated COHP (in eV) value of NiIn and
NiInH1 333
NiIn
NiInH1 333
The.
Exp.18
ICOHP
The.
Exp.18
ICOHP
LaNiInH1 333
Ni2-H
|
|
|
1.4891
1.5065
-3.44
H-H
|
|
|
1.5734
1.6350
-0.14
La-H
|
|
|
2.3609
2.4064
-0.72
Ni2-In
2.8993
2.8688
-1.26
2.7990
2.8490
-0.85
La-Ni1
3.1251
3.0359
-0.67
2.8791
2.9262
-0.86
Ni1-In
2.7358
2.8062
-1.24
2.8857
2.9390
-1.21
Ni2-La
3.0290
3.0783
-0.66
3.1835
3.2441
-0.61
CeNiInH1 333
Ni2-H
|
|
|
1.4573
1.5086
-3.32
H-H
|
|
|
1.5721
1.6061
-0.22
Ce-H
|
|
|
2.4271
2.3708
-0.79
Ni2-In
2.9045
2.8474
-1.22
2.8427
2.8026
-0.87
Ce-Ni1
3.1229
3.0133
-0.54
2.9237
2.9070
-0.88
Ni1-In
2.7375
2.7692
-1.19
2.9192
2.9268
-1.33
Ni2-Ce
3.0320
3.0407
-0.57
3.2102
3.2124
-0.63
NdNiInH1 333
Ni2-H
|
|
|
1.4928
1.5064
-3.34
H-H
|
|
|
1.5699
1.5618
-0.23
Nd-H
|
|
|
2.3499
2.3421
-0.69
Ni2-In
2.7667
2.7308
-1.14
2.7731
2.7704
-0.84
Nd-Ni1
2.9785
2.9331
-0.25
2.8866
2.8870
-0.65
Ni1-In
2.9075
2.9415
-1.21
2.9015
2.9038
-1.35
Ni2-Nd
3.1572
3.1690
-0.39
3.1771
3.1793
-0.64
RE
RE
:
RE
RE
:
:
:
14
:
FIGURES
FIG. 1. The crystal structure of NiInH1 333( =La,Ce and Nd). Legends to the dierent
kinds of atoms are given on the illustration. The dark lines connecting the atoms represents the
presence of H-Ni(2c)-H linear array in the crystal structure.
RE
RE
:
FIG. 2. Total-energy curves for NiIn and NiInH1 333 as functions of V/V0. LaNiIn (E=
31803+ ), LaNiInH1.333(E= 31805+ ),CeNiIn (E= 32539+ ) CeNiInH1.333 (E =
32540+ ) NdNiIn(E= 34068+ ), NdNiInH1.333(E= 34069+ )
RE
E
RE
:
E
E
E
E
E
FIG. 3. Total-energy curves for NiIn and
energy scale are as similar to that in Figure 2
RE
RE
NiInH1 333 as functions of
:
c=a
ratio. The
FIG. 4. Total energy
0 for CeNiInH1 333 with Ce in dierent valence state. The equilibrium volume 0=212.93 A3 is taken from experiment lattice parameters given in Ref. 18.
vs: V =V
:
V
FIG. 5. The energy bands E(k) of (a) LaNiIn and (b) LaNiInH1 333 along the high symmetry
directions of the hexagonal BZ. The Fermi energy is set to zero.
:
FIG. 6. Total DOS for
RE
NiIn and
RE
NiInH1 333.
:
FIG. 7. Site and orbital projected DOS for LaNiIn (left) and LaNiInH1 333(right)
:
FIG. 8. Valence electron density plot for LaNiIn in the (100) [the origin is shifted to (0.333,0,0)]
plane with 25 contours are drawn between 0 to 0.75 electrons/a.u3.
FIG. 9. Valence electron density plot for LaNiInH1 333 in the (100) [the origin is shifted to
(0.333,0,0)] plane with 25 contours are drawn between 0 to 0.75 electrons/a.u3.
:
FIG. 10. COHP for LaNiIn and LaNiInH1 333, describing the contributions from Ni-H, H-H,
La-H, Ni-In, LaNi1, Ni1-In, In-H and Ni-La atoms.
:
FIG. 11. Total energy
vs:
variation of H-H displacement in LaNiInH1 333. E= 31805+
:
15
E
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Electronic address: ponniah.vajeeston@kjemi.uio.no
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17
H
RE
In
Ni(2c)
Ni (1b)
H
RE
In
−0.16
LaNiIn
LaNiInH1.333
−0.115
−0.125
−0.18
−0.135
−0.2
−0.145
−0.22
−0.155
−0.24
∆Ε (Ry/f.u.)
0.05
CeNiIn
CeNiInH1.333
−0.775
0
−0.825
−0.05
−0.875
−0.1
−0.668
NdNiIn
NdNiInH1.333
−0.56
−0.688
−0.708
−0.58
−0.728
−0.6
−0.748
−0.62
−0.768
0.85 0.9 0.95
1
1.05 1.1
0.85 0.9 0.95
V/V0
1
1.05 1.1
LaNiIn
−0.7415
LaNiInH1.333
−0.381
−0.383
−0.7425
−0.385
−0.7435
−0.387
CeNiIn
∆Ε (Ry/f.u.)
−0.075
CeNiInH1.333
−0.953
−0.955
−0.077
−0.957
−0.079
−0.959
−0.081
−0.961
NdNiIn
−0.766
NdNiInH1.333
−0.871
−0.873
−0.767
−0.875
−0.768
−0.877
0.49
0.51
0.53
0.55
0.57
0.55 0.57 0.59 0.61 0.63 0.65 0.67
c/a ratio
−0.725
1
Ce−4f localized
−0.775
−0.825
−0.875
0.85
0.9
0.95
1
1.05
1.1
−1
∆E(Ry.f.u. )
2
Ce−4f localized
−0.05
−0.1
−0.15
0.9 0.95
1
1.05 1.1 1.15 1.2 1.25
−0.27
1
Ce−4f valence
−0.29
−0.31
−0.33
−0.35
0.8
0.85
0.9
V/V0
0.95
1
1.05
Energy(eV)
−11
−9
−7
−5
−3
−1
1
3
Γ
K M
Γ
(a)
A
L H
A
EF
Γ
K M
Γ
(b)
A
L
H
A
LaNiInH1.333
LaNiIn
4
3
2
−1
−1
DOS (states eV f.u. )
1
4
CeNiIn
CeNiInH1.333
NdNiIn
NdNiInH1.333
3
2
1
4
3
2
1
−7.5 −5 −2.5 0 2.5
5 7.5
−7.5 −5 −2.5 0 2.5
Energy (eV)
5 7.5
0.375
H−s
0.125
In−s
In−p
0.75
In−s
In−p
Ni(1b)−s (X 2)
Ni(1b)−p (X 2)
Ni(1b)−d
Ni(1b)−s (X 2)
Ni(1b)−p (X 2)
Ni(1b)−d
0.375
−1
−1
DOS (states eV f.u. )
0.25
0.125
Ni(2c)−s (X 2)
Ni(2c)−p (X 2)
Ni(2c)−d
0.75
Ni(2c)−s (X 2)
Ni(2c)−p (X 2)
Ni(2c)−d
0.25
1.5
La−s (X 4)
La−d
La−f
La−s (X 4)
La−d
La−f
1
0.5
−7.5 −5 −2.5 0
2.5
5
7.5
−7.5 −5 −2.5 0
Energy (eV)
2.5
5
7.5
11
00
00
11
In
00
11
00
11
In
00
11
Ni
Ni
111
000
000
111
111
000
La
111
000
111
000
111
000
La
111
000
11
00
00
11
In
00
11
111
000
000
111
In
000
111
Ni
Ni
11
00
00
11
00
11
La
00
11
In
Ni
000
111
000
111
La
000
111
In
Ni
11
00
00
11
00
11
La
00
11
Ni
H
111
000
000
111
000
111
La
000
111
H Ni H
11
00
00
11
00
11
In
00
11
In
11
00
00
11
La
11
00
Ni
In
H
H
111111
000000
000000
111111
0.09
000000
111111
Ni
In
11
00
00
11
La
00
11
H Ni H
000
111
In
000
111
(a)
H
Ni
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
000
111
11
000
000
111
000
111
In
(b)
1
0.25
0
0
−1
−0.25
Ni−H
La−Ni1
0.5
0.25
0
0
−0.5
−0.25
Ni1−In
COHP
H−H
0.25
0.05
0
0
La−H
−0.25
0.25
0.25
0
0
−0.25
−10
0
5
Ni−La
−0.25
Ni−In
−5
In−H
−0.05
10
−10
Energy(Ry.)
−5
0
5
10
−0.376
b
a
−1
∆E (Ry f.u. )
−0.3735
1.55
−0.3785
1.65
1.75
−0.381
−0.3835
1.35
1.45
1.55
1.65
H−H distance (Å)
1.75