1. science
2. physics

Physica B 292 (2000) 59}70
Excitons, electron center di!usion and adsorptivity of atomic
H on LiH (0 0 1) surface: Ab initio study
A.S. Shalabi *, A.M. El-Mahdy, M.A. Kamel, H.Y. Ammar
Chemistry Department, Faculty of Sciences, Benha University, Benha, Egypt
Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Received 23 November 1999; received in revised form 9 March 2000; accepted 9 March 2000
Abstract
An attempt has been made to examine the bulk and surface properties of exciton bands near F>, F and F\ centers (a,
b and c bands), di!usion of electron centers (F>, F and F\) and adsorptivity of atomic H over the undefected and
defected (F>, F and F\) surfaces of LiH using an ab initio embedded cluster method at the Hartree}Fock approximation
and Moller}Plesset second-order perturbation correction. The results con"rm the exclusive dependence of the exciton
bands on the type of the electron center. The activation energy for bulk di!usion increases monotonically in the series
F>PFPF\. Bulk and surface relaxation e!ects are more important for F> than for F and F\ centers. The
introduction of F or F\ center changes the nature of adsorption from physisorption to chemisorption. The introduction
of F\ center changes the nature of LiH surface from an insulating surface to a semiconducting surface. As F and
F\ centers are introduced, the HOMO and LUMO levels of the substrate shift to higher energies and the band gaps
become narrower. These changes in the electronic structure make charge transfer between adsorbate and substrate
energy levels and spin pairing with F center more facile in the course of adsorbate}substrate interactions. 2000
Elsevier Science B.V. All rights reserved.
Keywords: Excitons; F>, F and F\ di!usion; H/Li (0 0 1) adsorptivity; Ab initio calculations
1. Introduction
A non-traditional approach to understand the
host dependence of band gaps is to start with
a model for the host absorption. A complete treatment would involve the theories of excitons [1}3]
and defects [4}8] which take into account the band
structure of alkali halides. This would be a major
undertaking and well beyond our present goal. We
therefore use the simple electron-transfer model of
* Corresponding author. Tel.: #20-13-22578; fax: #20-24188738.
the fundamental optical absorption of ionic solids
developed by Hilsch and Pohl [9,10]. This model
treats ionic solids in the extreme tight-binding approximation and, in its simplest form, explains the
fundamental optical absorption as the transfer of
an electron from a negative ion to a neighboring
positive-ion. In more sophisticated treatments,
the "nal state is taken to be a symmetrized linear
combination of positive-ion states [11]. F and
F\ centers are well-de"ned defects in ionic crystal,
but F> could not have an absorption band in the
same way that we see absorption for the F and
F\ centers. However, it has been shown clearly that
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 4 8 7 - 7
60
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
an ultraviolet absorption band called a band arises
from the vacancy [12]. In KI, the band was found
at 2380 As , which is close to the "rst-exciton peak at
2130 As . This has led to the interpretation of the
band as arising from the formation of an exciton in
the vicinity of a vacancy. Bassani and Inchauspe
[13] were able to show a reasonable agreement
between calculations based on Hilsch and Pohl
model of exciton and experiment. If the exciton is
formed farther from the vacancy, it will be perturbed less and will therefore be closer to the fundamental exciton energy. The existence of the a band
is very useful in unraveling the motion and capture
of electrons in alkali halides as well as other processes involving impurities, di!usion of ions or electron transfer. An exciton formed near an F center
gives rise to an ultraviolet absorption called the
b band. The b band may be used to measure the
presence of F centers, but it is usually more convenient to measure the F band itself. It seems likely
that all centers have perturbed excitons formed
near them. In cases other than a and b bands, these
have not been extensively studied experimentally
since other properties of the centers are usually
easier to observe. However, theoretically, an exciton formed near an F\ center may give rise to an
ultraviolet absorption that we may call c band. One
aim of this paper is therefore to report, to our
knowledge, the "rst exciton band calculations near
F>, F and F\ centers in LiH.
Investigation of mass transport in alkali hydrides
are related to their functional properties and longterm stability [14]. Very often ion di!usion is associated with point defects. The di!usion of electron
centers F (one electron trapped by an anion vacancy) and F\ (two electrons trapped by an anion
vacancy) is practically not studied [15]. At the
same time, the extensive data on F center di!usion
in alkali halides is based on the mobility measurements under electrolytic coloration. The studies of
F> (anion vacancy) di!usion are based on the ionic
conductivity and radioactive-tracer di!usion
measurements. The signi"cant e!ect found is that
F> centers have activation enthalpies typically
about half of those of the F centers [16]. To our
knowledge theoretical and experimental information on electron center di!usion in alkali hydrides
are scarce, so that the second aim of this paper is to
examine the di!usion of the given hole centers in
the bulk and at the surface of LiH.
Theoretical and experimental studies of adsorbate}substrate interactions have become of increasing importance [17,18]. This is due to the fact that
they are related to a variety of technologically signi"cant processes, not least of which are catalysts,
corrosion and gas sensors. On the other hand,
smooth surfaces can have point defects or steps,
which can locally strongly modify the adsorbate}substrate interactions. The chief problem in
studying adsorbate}substrate interactions computationally is the treatment of the extended surface when examining a localized phenomenon like
chemisorption [19]. For simple systems such as
atoms or small molecules interacting on surfaces, it
can be feasible to use an extended two-dimensional
periodic systems, to study an ordered overlayer of
adsorbate on the surface. Such examinations have
sometimes used slab calculations [20], although
more recently surface embedding is providing
a promising route forward [21]. Several theoretical
studies have been done to simulate adsorption of
simple systems on ionic surface [22}24]. For oxide
surfaces, these studies highlight the formation of
metal}oxygen bonding and antibonding states, the
latter being either completely or partially "lled.
Thus the interactions are considered to be mainly
of a chemical nature. This is a reasonable assumption for relatively reactive surfaces such as those of
many metal oxides. However, other ionic surfaces
are known to be highly stable and the nature of the
metal-surface (1 0 0) bond is not so clear. The second aim of this paper is, therefore, to report results
of SCF and MP2 calculations on an electronically
inert (0 0 1) surface of an insulator LiH. The e!ects
of introducing the surface F>, F and F\ on modifying the nature of adsorbate}substrate interactions
were then examined. We have not been able to "nd
any experimental data on the characteristics of
hydrogen adatoms on lithium-hydride surface,
hence our results serve as theoretical predictions.
2. Methods and calculations
The optimal way to represent the extended
lattice appears to be to choose point ions which
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
correctly mimic the Madelung potential and its
gradient at the `active site(s)a for chemisorption
[25], or alternatively, for surfaces by a Parry summation [26,27], and the gradient can be determined
by its slope as a probe is removed away from the
`active site(s)a. This termination of the cluster by
point ions has signi"cant advantages in that it adds
little to the computational cost of the calculation;
only additional one-electron integrals need to be
calculated [19].
To represent the extended crystal properly, some
care needs to be taken in choosing the charges of
the point ions, according to the conditions outlined
by Harris [28]. For a bulk crystal, the criteria are
that there must be no net charge, no net dipole and
no net quadruple in the cluster. For a surface, there
is a small dipole which is induced by surface rumpling; so the criteria of no net dipole do not hold
rigorously [19]. The choice of the appropriate changes for the point ions has been discussed for an
FCC structure like MgO [29]. Early studies by
Kunz and co-workers [30] and by Clobourn and
Mackrodt [31] used clusters which were terminated by full ionic charges. One of the aspects of
these calculations (which is most surprising) is that
very small clusters * sometimes a single surface
ion * can be adequate to represent surface reactivity. This is a consequence of the high degree of
localisation of the electrons on the ions, and would
not hold for materials with any appreciable degree
of covalence.
To simulate the LiH crystal, we follow a procedure previously reported for MgO [32] and LiH
[33] crystals. A "nite crystal of 288 point charges
was constructed. The Coulomb potential along the
X- and >-axis of this crystal is zero by symmetry as
in the host crystal, Fig. 1. The charges on the outer
shells listed in Table 1 were modi"ed to make the
Coulomb potential at the four central sites equal to
the Madelung potential of the host crystal and to
make the eight points with coordinates (0, $R,
$R) and ($R, 0, $R), where R is half the lattice
distance, which for LiH is 2.04 As , equal to zero as it
should be in the host crystal. With these charges,
0.409283 and 0.800909, the Coulomb potential in
the region occupied by the central ions is very close
to that in the unit cell of the host crystal. All
charged centers with Cartesian coordinates $X,
61
Fig. 1. Representation of the Z"0 plane of the lattice used in
the calculations.
$> and Z"2R, 4R, 6R and 8R were then removed to generate a surface of 176-charged centers
occupying the three-dimensional space $X, $>
and !Z"0, 2R, 4R, 6R and 8R. The coordinates
of these charged centers are given in Table 1. Quantum clusters were then embedded within the central
region of the crystal bulk or surface. All the electrons of the embedded clusters were included in the
Hamiltonian of ab initio calculations. Other crystal
sites entered the Hamiltonian as point charges. The
adsorption energy E
of the adatom on the sub
strate surface was calculated from the relation
E
"E
!E
!E
.
The terms appearing on the right-hand side are the
total energies of the complex (adsorbate#substrate), the adsorbate (free hydrogen atom) and the
substrate (undefected or defected), obtained from
three independent calculations using the same
supercell. The negative adsorption energy E . in
dicates that the bound adsorbate is thermally
stable. The Hartree}Fock and electron correlation
calculations were carried out using the Gaussian
6}31##g(d, p) internal basis. This basis puts diffuse and polarization functions to both heavy
atoms and hydrogens. For an ionic cluster such as
62
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
Table 1
Speci"cation of the "nite lattice used for crystal bulk and surface calculations. R is half the lattice distance, which for LiH is 2.04 As and
r is the distance of the appropriate shell from the center of the lattice
R/r
Coordinates/R "X", ">", "Z"
No. of centers
Coordinates/R "X", ">", !Z
No. of centers
Charge "q"
2
6
10
14
18
22
26
26
30
34
34
38
38
42
46
50
50
50
54
54
58
66
54
62
66
82
86
110
112
310
312
114
332
510
314
512
334
530
532
116
514
316
550
534
710
552
336
730
554
712
732
118
910
912
4
8
8
16
8
8
8
16
16
8
8
16
8
16
16
4
16
8
8
8
8
8
16
16
8
8
16
110
112
310
312
114
332
510
314
512
334
530
532
116
514
316
550
534
710
552
336
730
554
712
732
118
910
912
4
4
8
8
4
4
8
8
8
4
8
8
4
8
8
4
8
8
4
4
8
4
8
8
4
8
8
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.409283
0.409283
0.800909
0.800909
0.800909
Crystal bulk.
Crystal surface.
Li H , with 40 interacting electrons, there are
250 basis functions and 400 primitive Gaussians. As
shown, the basis set is large enough so that the
basis set superposition error BSSE is minimized
even at the correlated level [33]. The present quantum mechanical calculations were carried out using
Gaussian 98 system [34].
3. Results and discussion
The host dependence of band gaps and exciton
bands on the type of the defect in the bulk and at
the surface of LiH is given in Table 2. The band gap
was calculated as the di!erence between the valence
and conduction bands, and the exciton band was
calculated as the di!erence in Coulomb potentials
attributed to the transfer of an electron from
a negative ion to a neighboring positive ion, both
placed in the deep Coulomb "eld of the simulated
crystal. The calculations were carried out for the
four central ions surrounded by the nearest-neighbors, Li H in the bulk and Li H at the surface.
All ion clusters were embedded in point charges as
de"ned in Table 1, and the ions as well as the point
charges were included in the Hamiltonian of the ab
initio calculations.
The results given in Table 2 emphasize the exclusive dependence of energies on the type of the
defect in a manner analogous to Glasner}Tompkins relation [35] in which the di!erence between
the "rst-exciton absorption energy and the F-band
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
63
Table 2
Bulk and surface band gaps E and exciton bands E in LiH
E /eV
Bulk
H\ Li H
F> Li H
F Li H
F\ Li H
Surface
H\ Li H
F> Li H
F Li H
F\ Li H
9.86
9.52
9.49
5.85
5.93
1.08
1.39
e-H\ Li H
e-F> Li H (a)
7.92
9.56
9.55
4.14
4.22
0.34
0.37
e-H\ Li H
e-F> Li H (a)
e-F Li H (b)
e-F\ Li H (c)
e-F Li H (b)
e-F\ Li H (c)
E /eV
E !E
17.32
17.97
15.5
16.89
17.16
15.78
17.35
7.46
8.45
6.01
11.04
11.23
14.70
15.96
17.42
18.06
15.64
16.89
16.96
16.02
16.53
9.50
8.50
6.09
12.75
12.74
15.68
16.16
Basis functions are added to the F>, F and F\ centers.
energy in alkali halides depends almost exclusively
on the negative ion species. The validity of the
present calculations of band gaps and exciton
bands has been veri"ed with the Mollwo}Ivey relation [36,37] for the F center, and Hilsch}Pohl
model [9,10] for the exciton band of the undefected
crystal as well as with experiment [38]. For
F center, the Mollwo}Ivey value is 4.76 eV and the
experimental value is 5.0 eV. For exciton band, the
Hilsch}Pohl model value is 17.17 eV. While the
present exciton band of 17.32 eV in e}H\ Li H
compares well with the empirical value 17.17 eV of
Hilsch and Pohl model, the present band gap of
5.85 eV in F-Li H does not compare well with
the experimental value 5.0 eV. We may note that
a band gap of 4.82 eV was calculated for F-Li
cluster with vacancy centered functions [39]. We
therefore added basis functions to the defect centers
and recalculated the corresponding band gaps and
exciton bands. As shown in Table 2, while the
addition of basis functions to the F center of the
bulk FLi H cluster did not enhance the band
gap value (5.93 eV) relative to the experimental
value (5.0 eV), the addition of basis functions to the
F center of the surface Fli H cluster slightly en hanced the band gap value (4.22 eV) relative to the
experimental value. Moreover, the addition of basis
functions reversed the trends of E values, but did
not change the trends of E or E }E values (Fig. 2).
However, the present values of F band gaps are
more consistent with the fact that the gap between
occupied and unoccupied states in the Hartree}
Fock scheme overestimates the transition energy.
Moreover, the shown di!erence between bulk and
surface band gaps and exciton bands must be attributed to the di!erence in crystalline potentials.
Since an electron center appears as a charged
defect of quantum mechanical nature, it is very
likely to be associated with local distortions in the
lattice. We have "rst determined the optimal-relaxation modes corresponding to simultaneous
inward}outward displacements of the nearestneighbor cations to the defect center. Bulk and
surface optimal-relaxation modes were found to be
represented by simultaneous outward displacements of the nearest-neighbor cations to the defect
and are given schematically in Fig. 3. Secondly, the
nearest-neighbor cations to an electron center
namely F>Li , FLi and F\Li in the bulk and
F>Li , FLi and F\Li at the surface were simul
taneously displaced outwards by 10% of the lattice
interionic distance to estimate its contribution to
energy lowering. Since the ion cluster model represented by an electron center surrounded by only
64
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
Fig. 2. A model of creation of an exciton in which the arrow
represents the transfer of an electron. eH\ Li H and
eH\Li H represent exciton in the bulk and the surface of the
perfect crystal. e-F> Li H (a) and e-F> Li H (a) represent
excitons near F> centers in the bulk and the surface (a-bands).
e-FLi H (b) and e-FLi H (b) represent exitons near
F centers in the bulk and the surface (b-bands). e F\ Li H (c)
and e-F\Li H (c) represent excitons near F\ centers in the
bulk and the surface (c-bands).
nearest-neighbor cations sees only point charges at
the cluster boundaries, the calculations were repeated taking into account the nearest neighbor
cations to defect sites in F>Li H , FLi H ,
F\Li H , F>Li H , FLi H and F\Li H to
determine the e!ects of replacing the next nearestneighbor point charges by real ions. Energy changes attributed to simultaneous outward displacements of nearest-neighbor cations to a defect site by
10% of the lattice-interionic distance in the bulk
and at the surface of LiH and the e!ects of replacing the next nearest-neighbor point charges by real
ions are given in Table 3. The calculated energy
changes show that the bulk and surface relaxation
e!ects are more important for F> than for F and
F\, the e!ects of replacing the next nearest-neighbor point charges by real ions are more important
in the bulk than on the surface. On the other hand,
Fig. 3. Z"0 plane representation of the optimal relaxation
mode.
Table 3
Energy changes attributed to simultaneous outward displacments of nearest-neighbor cations to a defect site by 10% and
the e!ects of replacing the next nearest-neighbor point charges
by real ions. Energies are given in eV
Bulk
F> Li
F Li
F\ Li
F> Li H
F Li H
F\ Li H
3.40
1.02
2.00
3.21
1.90
1.57
Surface
F> Li
F Li
F\ Li
F> Li H
F Li H
F\ Li H
3.01
1.14
2.24
2.83
0.80
2.12
the energy changes are heavily dependent on the
defect type and crystalline environment and are
mainly attributed to the signi"cant changes in
Coulombic interactions between a defect center
and its surrounding crystalline potential.
We have considered the di!usion of F>, F and
F\ centers along the 11 1 02 axis to the next nearest-neighbor anions. The di!usion path D has been
divided into six steps, D"0.0}0.5. D"0.0 represents the original defect con"guration and D"0.5
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
represents the next nearest-neighbor anion displaced midway along the di!usion path, Fig. 4. The
total energies of defect con"guration are given as
a function of the di!usion path D in Fig. 5. As
shown in Fig. 5, both of the equilibrium and
saddle-point con"gurations are sensitive to the defect type (F>, F and F\), crystalline "eld (bulk or
surface), the level of calculations (SCF or MP2) and
the outward relaxation of the nearest-neighbor ions
(to the two anion sites at the 11 1 02 direction) by
5% of the internuclear separation. The activation
energy of the defect-di!usion hops was calculated
as the di!erence in the total energies of these two
con"gurations (equilibrium and saddle point).
Within the bulk crystalline "eld, these were calculated to be 0.47, 2.35 and 1.68 eV at the SCF
level, and 0.46, 2.24 and 2.31 eV at the MP2 level
for F>, F and F\, respectively. Within the surface
crystalline potential, activation energies were calculated to be 0.38, 1.37 and 0.38 eV at the SCF
level, and 0.36, 1.41 and 0.36 eV at the MP2 level
for F>, F and F\, respectively, as shown. While the
activation energy for bulk di!usion increases
monotonically in the series F>PFPF\, the activation energies for surface di!usion of F> and F
are close and increase in the direction F>"
F\PF. The contribution of MP2 correction to the
activation energy was marginal and did not alter
the predicted orders. On the other hand, while the
migration energies for the positively and negatively
charged defects, F> and F\, are small (0.36 eV) and
Fig. 4. Z"0 plane representation of electron center di!usion
hops.
65
close and that for the neutral F center is much
larger (1.41 eV) for the unrelaxed surface, the migration energies for the F>, F and F\ defects are
quite close (0.442, 0.441 and 0.397 eV) for the relaxed surface. The importance of surface relaxation
is therefore con"rmed and the disturbed trends of
F>, F and F\ surface migration energies relative to
the bulk could be attributed to the non-homogeneous surface potentials where each ion is a!ected by
the potentials of only "ve nearest-neighbors. Moreover, the nature of interaction between an anion
vacancy or its trapped electron(s) and the surrounding crystalline "eld is expected to control the
order of defect migration energy.
The interaction of hydrogen with solid surface
underpins a number of catalytic processes. It is
important in its own right as well as being exemplar
of a simple model system. Kunz and co-workers
used a small point ion block with fully ionic charges
to represent the environment, treating H chemisorption at defects like anion vacancies [40] and
cation vacancies [41]. Pople et al. [42] have investigated the chemisorption of H on the V center,
assuming a symmetric reaction path in which the
hydrogen approaches parallel to the surface. More
recently, Kobayashi et al. [43] carried out ab initio
calculations on the adsorption of hydrogen molecule onto MgO (1 0 0) surface. Guo and Bruch
[44] examined the electrostatic energy in the adsorption of monatomic H and He on MgO (0 0 1)
and LiF (0 0 1). Kobayashi et al. [45] carried out
density functional calculations on the dissociative
adsorption of hydrogen molecule on MgO surfaces.
In general, adsorbate}substrate interactions result
from the tendency of the adsorbate valence electrons to hybridize with the available substrate electronic states. This hybridization can be expected to
have a major role if there exists a small energy gap
between the adsorbate and substrate electronic
states, or if the adsorbate has an open-shell electronic structure.
We discuss our results of adsorbate}substrate
interactions by studying the di!usion characteristics of a single H atom on the undefected and
defected (F>, F and F\) surfaces of LiH. The ion
clusters, H\Li H , F>Li H , FLi H
and
F\Li H were embedded in three dimensional
array of point charges ($X, $> and !Z) as
66
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
Fig. 5. Total energies of F>, F and F\con"gurations as a function in the di!usion path D.
described in the methods sections and the point
charges as well as the real ions were then included
in the Hamiltonian of ab intio calculations.
Fig. 6 shows schematically the 3-D unit cells and
the path along which we have optimized the
adatom}surface distance at selected substrate locations D. Optimal adsorption energies E /E and
heights R /As for the di!usion of atomic H over the
undefected and defected (F>, F and F\) surfaces of
LiH from the top of H\ (D"0.0) to the top of the
nearest neighbors H, F>, F or F\ (D"1.0) are
represented graphically in Fig. 7. De"ning the optimal adsorption site as the substrate location D at
which the strongest adsorbate}substrate interaction occurs, the optimal adsorption site of the undefected surface was found to be on the top of the
substrate H\ ion, 3.5 As above the substrate plane
in the SCF calculations and 3.3 As in the MP2
calculations. The optimal adsorption sites of the
F> surface were found to be on the top of a substrate location D"0.5, 1.02 As above the substrate
plane in the SCF calculations and D"0.3, 0.51 As
Fig. 6. 3-D representation of atomic hydrogen di!usion over the
undefected H\ Li H and defected F> Li H , F Li H and
F\ Li H surfaces of LiH.
above the substrate plane in the MP2 calculations.
An optimal adsorption site for both of F and
F\ surfaces was observed in the substrate plane at
location D"1.0, in the SCF and MP2 calculations.
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
The contribution of electron-correlation correction
to adsorbate}substrate interactions decreases
monotonically in the series F>PFPF\. The near
67
coincidence of SCF and MP2 curves for F\ surface
may imply that repulsive interactions play a dominant role. The results show that the optimal
Fig. 7. The adsorptivity of atomic H over the undefected H\ Li H and defected F> Li H , F Li H and F\ Li H surfaces of LiH as
a function in the di!usion path D.
68
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
adsorption energies have been enhanced by 0.138,
3.29 and 5.11 eV at the SCF level and by 0.44, 3.86
and 5.1 eV at the MP2 level under the e!ect of
introducing F>, F and F\ centers respectively.
A strong sign for hybridization or chemical bond
formation between adsorbate and substrate electronic states of F and F\ surfaces is therefore
expected, mainly because of spin pairing (for F surface) and because of the small energy gap between
adsorbate and substrate electronic states (for
F\ surface).
Vidali et al. [46] reported 17.8 meV and 2.7 As for
adsorption energy and height in H/LiF(0 0 1) system. This result may be compared with the present
8.5 meV and 3.3 As for adsorption energy and
height calculated for the adsorption of H at the
undefected surface in the MP2 calculations at the
optimal substrate location D"0.0. The basic difference between adsorption energies and heights in
the two systems is attributed to the very di!used
nature of surface hydrides due to the large fractional excess of the negative charge. We may note
that the electrostatic "elds near the surface of an
ionic crystal are large enough [47}52] that the
polarization energy is a major component of the
adsorption energy for many physisorbed species.
However, the "elds are so nonuniform [53,54] that
the dipole polarizability gives an inaccurate account of the polarization energy. Guo and Bruch
[44] calculated the electrostatic polarization energy for H and He on LiF and MgO surfaces and
reported that it contributes at the 10% level for
atomic hydrogen. They also reported: The trend is
that the electrostatic terms will be signi"cant for
more polarizable inert gases such as Kr and Xe.
Calculating the polarization energy to within 25%
for such adsorbates will require inclusion of many
multipole con"gurations.
Binding of atomic H at H\ is favored over binding at the substrate location D"0.5 of the undefected surface, and binding at the substrate location
D"0.3 or 0.5 is strongly favored over binding at
the other substrate locations of F> surface. For
F and F\ surfaces, binding at the anion vacancy is
also favored over binding at the other substrate
locations. These preferential bindings suggest the
possibility of atomic H di!usion over the surface.
To examine this probability, we have calculated the
Table 4
HOMO, LUMO and HOMO}LUMO energies of F>, F and
F\ surfaces of LiH. Energies are given in Hartrees
F> Li H
F Li H
F\ Li H
HOMO
LUMO
HOMO}LUMO
!0.45623
!0.45669
!0.19055
!0.19269
!0.04952
!0.18675
!0.16367
!0.16504
!0.06548
!0.06478
!0.03366
0.00779
!0.29256
!0.29165
!0.12507
!0.12791
!0.01586
!0.19454
Basis functions are added to the F>, F and F\ centers
largest variations in the correlated adsorption energies in Fig. 7. These were calculated to be 1.8 meV
for the undefected surface and 51.7 meV, 2.94 and
4.5 eV for the F>, F and F\ defected surfaces
respectively. These results show that the activation
barriers for the mobility of atomic H over the
defected surfaces increase nearly exponentially in
the series F>PFPF\. However, in reality, the
adatom di!usion on these surfaces may include
more complicated mechanisms, such as atomic exchange mechanisms, which we have not attempted
to examine here.
To investigate the di!erences in adsorption
among F>, F and F\ surfaces, the local densities
of state (LDOS) have been evaluated. The band
gap as the di!erence between HOMO and LUMO
of F>, F and F\ surfaces are given in Table 4.
The band gaps were reduced by 4.56 eV for F and
by 2.97 eV for F\ surface as a consequence of
the HOMO and LUMO shifting to higher energies.
The energy levels of the atomic hydrogen occupied
and unoccupied AO's were calculated to be
!13.57 and 2.63 eV respectively. Since charge
transfer occurs from the hydrogen occupied AO
to the surface unoccupied or singly occupied
MO's (donation) and from the surface occupied
or singly occupied MO's to the hydrogen unoccupied AO (back-donation), the reported change in
the electronic structure makes charge transfer and
spin pairing (with F surface) more facile in the
course of adsorbate}substrate interactions. This is
supported by our previous observation that adsorptivity was drastically increased over F and F\ surfaces.
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
4. Conclusions
Some important properties of LiH-ionic crystal
such as excitons, band gaps, activation energies of
defect di!usion and adsorbate}substrate interactions can be adequately described using ab initio
methods of molecular electronic structure calculations. In the present study, while band gaps and
exciton bands were found to decrease monotonically in the series F>PFPF\, the corresponding
di!erences were found to decrease in the same
series, suggesting the possible existence of c exciton
bands. Lattice relaxation is important, particularly
at crystal surface where non-homogeneous crystalline potentials are dominant. Anion vacancy
centers with one or two trapped electrons can reduce the valence}conduction band gaps and improve the electrical properties of ionic materials.
Spin pairing between an open shell adsorbate and
a single electron center such as F center is probable
with signi"cant increase of adsorbate}substrate interaction (chemical adsorption) relative to defect
free surfaces. Extension of this study to include
higher cation or anion hydrides may be suggested
for future investigations.
References
[1] R.S. Knox, Theory of Excitons, Academic Press, New
York, 1963.
[2] V.G. Plekhanov, Phys. Rev. B 54 (1996) 3869.
[3] A.A.OE Connel-Bronin, Phy. Stat. Sol 38 (1996) 1489.
[4] G.F. Koster, J.C. Slater, Phys. Rev. 95 (1954) 1167.
[5] G.F. Koster, J.C. Slater, Phys. Rev. 96 (1954) 1208.
[6] J.H. Crawford, L.M. Slifkin (Eds.), Point Defects in Solids,
Plenum, New York, 1972.
[7] W. Hayes, A.M. Stoenham, Defects and Defect Processes
in Non-Metallic Solids, Wiley, New York, 1985.
[8] E. Kotomin, A. Popov, Nucl. Instr. and Meth. B 141 (1998)
1 and references therein.
[9] R. Hilsch, R.W. Pohl, Z. Phys. 57 (1929) 145.
[10] R. Hilsch, R.W. Pohl, Z. Phys. 59 (1930) 812.
[11] A.W. Overhouser, Phys. Rev. 101 (1956) 702.
[12] C.J. Delbecq, P. Pringsheim, P.H. Yuster, J. Chem. Phys.
19 (1951) 574.
[13] F. Bassani, N. Inchauspe, Phys. Rev. 105 (1957) 819.
[14] A.S. Shalabi, A.M. El-Mahdy, Kh.M. Eid, M.A. Kamel,
Model. Simul. Mater. Sci. Eng. 7 (1999) 1.
[15] A.I. Popov, E.A. Kotomin, M.M. Kuklja, Phys. Stat. Sol.
195 (1996) 61.
69
[16] F.W. Clinaro, L.W. Hobbs, in: R.S. Johnson, A.N. Orolov
(Eds.), Physics of Radiation E!ects in Crystals, Series in
Modern Problems in Condensed Matter Sciences, NorthHolland, Amsterdam, 1986.
[17] H.J. Freund, E. Umbach, Adsorption on Ordered Surfaces
of Ionic Solids and Thin Films, Springer, Berlin, 1993.
[18] H. Hakkinen, M. Manninen, J. Chem. Phys. 105 (1996)
10565.
[19] E.A. Colbourn, Rev. Solid State Sci. 5 (2&3) (1991) 91.
[20] E. Wimmer, C.L. Fu, A.J. Freeman, Phys. Rev. Lett. 55
(1985) 2618.
[21] C.R.A. Catlow, W.C. Mackrodt, in: C.R.A. Catlow, W.C.
Mackrodt (Eds.) Computer simulation of solids, Lecture
Notes in Physics, Vol. 166, Springer, Berlin, 1982.
[22] K.H. Jhonson, S.V. Pepper, J. Appl. Phys. 53 (1982) 6634.
[23] A.B. Anderson, C. Ravimohan, S.P. Mehandru, Surf. Sci.
183 (1987) 438.
[24] J.A. Horsley, J. Am. Cerm. Soc. 101 (1979) 2870.
[25] R.P. Ewald, Z. Phys. 64 (1921) 253.
[26] D.E. Parry, Surf. Sci. 49 (1975) 33.
[27] D.E. Parry, Surf. Sci. 54 (1976) 195.
[28] F.E. Harris, in: H. Eyring and D. Henderson (Eds.), Theoretical Chemistry: Advances and Perspectives, Vol. I,
Academic Press, New York, 1975.
[29] E.A. Colbourn, in: C.R.A. Catlow (Ed.), Advances in Solid
State Chemistry, Vol. I, JAI Press, London, 1989.
[30] G.T. Surrat, A.B. Kunz, Phys. Rev. Lett. 40 (1978) 347.
[31] E.A. Colbourn, W.C. Mackrodt, Surf. Sci. 117 (1982) 571.
[32] A.S. Shalabi, A.M. El-Mahdy, J. Phys. Chem. Solids 60
(1999) 305.
[33] A.S. Shalabi, M.M. Assem, S. Abd El-Aal, M.A. Kamel,
M.M. Abd El-Rahman, Solid State Commun. 111 (1999)
735.
[34] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria,
M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, Jr., R.E. Stratmann, J.C. Burant, S. Dapprich,
J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O.
Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B.
Mennucci, C. Pomelli, C. Adamo, S. Cli!ord, J. Ochterski,
G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K.
Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.
Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A.
Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L.
Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A.
Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W.
Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C.
Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople,
Gaussian 98, Revision A.6, Gaussian, Inc., Pittsburgh, PA,
1998.
[35] A. Glasner, F.C. Tompkins, J. Chem. Phys. 21 (1953) 1817.
[36] E. Mollwo, Nachr. Ges. Wiss. Gottingen 1 (1931) 97.
[37] H.F. Ivey, Phys. Rev. 72 (1947) 341.
[38] A.A.OE . Connel-Bronin, V.G. Plekhanov, U.A. Pustovarov,
F.F. Gavrilov, S.O. Cholakh, Opt. Spectrosc. (USA) 51 (2)
(1981) 204.
[39] A.S. Shalabi, A.M. El-Mahdy, Kh.M. Eid, M.A. Kamel,
A.A. El-Barbary, Phys. Rev. B 60 (1999) 9377.
70
A.S. Shalabi et al. / Physica B 292 (2000) 59}70
[40] G.G. Wepfer, G.T. Surrat, R.S. Weidman, A.B. Kunz,
Phys. Rev. B1 (1980) 2596.
[41] G.T. Surrat, A.B. Kunz, Phys. Rev. B 19 (1979) 2352.
[42] S.A. Pople, M.F. Guest, I.H. Hillier, E.A. Colbourn, W.C.
Mackrodt, J. Kendrick, Phys. Rev. B28 (1983) 2191.
[43] H. Kobayashi, M. Yamaguchi, T. Ito, J. Phys. Chem. 94
(1990) 7206.
[44] Z.C. Guo, L.W. Bruch, J. Phys. Chem. 97 (1992) 7748.
[45] H. Kobayashi, D.R. Salahub, T. Ito, J. Phys. Chem. 98
(1994) 5487.
[46] G. Vidali, G. Ihim, H.-Y. Kim, M.W. Cole, Surf. Sci. Rep.
12 (1991) 133.
[47] J.E. Gready, G.B. Bacskay, N.S. Hush, J. Chem. Soc.
Faraday Trans. II 74 (1978) 1430.
[48] R. Dovesi, R. Orlando, F. Ricca, C. Roetti, Surf. Sci. 186
(1987) 267.
[49] B. Deprick, A. Julg, Nouv. J. Chem. 11 (1987) 299.
[50] B. Deprick, A. Julg, Chem. Phys. Lett. 110 (1984)
150.
[51] A. Lakhli", C. Girardet, J. Chem. Phys. 94 (1991) 688.
[52] A. Lakhli", C. Girardet, Surf. Sci. 241 (1991) 400.
[53] J.E. Lennard-Jones, B. Dent, Trans. Faraday Soc. 24
(1928) 92.
[54] B.R.A. Nijboer, Physica A 125 (1984) 275.