Theoretical studies of interstitial hydrogen in titanium

Surface Science 149 (1985) 273-284 North-Holland, Amsterdam

273

T H E O R E T I C A L S T U D I E S O F I N T E R S T I T I A L H Y D R O G E N IN TITANIUM Pietro C R E M A S C H I Centro CNR, c / o Istituto di Chimica Fisica, Via Golgi 19, 1-20133 Milano, Italy

and J e r r y L. W H I T T E N Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794, USA

Received 13 March 1984; accepted for publication 6 July 1984

Hydrogen atom absorption by hcp titanium is treated using an embedding theory (Whitten and Pakkanen, Phys. Rev. B21 (1980) 4357) to describe the electronic bonding. The very low concentration limit is modelled by treating a single H atom in a 43 atom titanium cluster to compute binding energies of different interstitial sites. An energy barrier to H penetration of the surface of 23 kcal/mol is found for the unrelaxed surface, and this result is attributed simply to short Ti-H distances in the surface plane. Hydrogen in an octahedral hole below the close packed titanium surface layer is 12 kcal/mol more stable than H in a tetrahedral hole for an unrelaxed lattice and this appears to be due to the better accommodation of the negatively charged H by the larger octahedral cavity. An energy barrier to the migration of H between interstitial sites is found.

1. Introduction T h e a b s o r p t i o n of h y d r o g e n b y metals has received a great deal of a t t e n t i o n b e c a u s e of the possibility of using metals for h y d r o g e n storage [1,2]. Elements to the left of the transition metal series l e a d to e x o t h e r m i c dissociative a d s o r p t i o n a n d reactions p r o c e e d to the f o r m a t i o n of metalfic hydrides, M H x, of n e a r l y s t o i c h i o m e t r i c c o m p o s i t i o n [3,4]. In s o m e transition metals the interstitial p o s i t i o n s o c c u p i e d b y h y d r o g e n are well established, b u t in others, i n c l u d i n g titanium, the evidence is inconclusive. It is often argued, however, that as a general trend, h y d r o g e n occupies t e t r a h e d r a l holes in transition m e t a l s to the left of the series, a n d o c t a h e d r a l holes in metals to the right [1]. M o s t work, b o t h theoretical [4,6] a n d e x p e r i m e n t a l [1,5], has dealt with rather high c o n c e n t r a t i o n s , or p e r i o d i c lattices of H in which H - H interactions can be i m p o r t a n t . Switendick [7] has carried out calculations on dilute H systems, 0 0 3 9 - 6 0 2 8 / 8 5 / $ 0 3 . 3 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)

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P. Cremaschi, J.L. lYhitten / Interstitial hydrogen in Ti

Ni32H and Pd32 H. In this work we consider a theoretical study of hydrogen in the low concentration limit in titanium employing an embedding theory previously applied successfully to the description of H 2 dissociation on the titanium surface [8,9]. 2. Theoretical model

2.1. Ti 4~H cluster The titanium atom cluster designed to study the energetically most favorable interstitial sites of the metal lattice for the hydrogen atoms is composed of three layers of 14, 15 and 14 metal atoms, respectively, corresponding to the geometry of the unreconstructed hcp lattice. In the first and third layers, the central ring of four titanium atoms is completely surrounded by the nearest neighbor metal atoms; the second layer is defined by the hexagonal symmetry of the (0001) plane including all nearest neighbor atoms of those in the first layer. In addition, the second and third layers are completely surrounded by additional titanium atom spherically symmetric potentials (a total of 49 atomic sites) representing the atoms of the bulk. The potentials stabilize the boundary of the cluster and are assumed to be unaffected by the local perturbations induced by the presence of the hydrogen (see ref. [9]). The cluster geometry is depicted in fig. 1.

2.2. General theory In this section the theoretical formulation is briefly reviewed; details of the theory are given ref. [8] and chemisorption applications to titanium and copper systems are reported in refs. [9-11]. The main premise of the theoretical approach is that a description of molecule-surface interactions and dissociative processes on surfaces may necessitate a reasonably sophisticated treatment of the surface region to account for changes in polarization and electron correlation accompanying reactions. For a metal this is not easily accomplished since electronic delocalization precludes a partitioning of the system into a small number of atoms proximate to the adsorbate independent of the remainder of the system. An alternative possibility adopted here is to define a local region not as a set of atoms but as an N-electron subspace extracted from the remainder of the system by a localization transformation. The adsorbate and local region are then treated at high accuracy (e.g. by configuration interaction at an ab initio level) as embedded in the fixed Coulomb and exchange field of the remainder of the electronic system. The use of electron exchange as the basis of a localization transformation, with reference to designated atoms on the surface, is discussed in refs. [8,9]. To summarize the argument, suppose that the binding of hydrogen to the lattice at several possible sites is of interest. Let u(1, 2) denote a density matrix

P. Cremaschi, J . L Whitten

03

275

•

~7

(~)6 O4

1

Interstitial hydrogen in Ti

•

O2

01

/

•

Oh

Td

i

I ~,

~3

I

6

H SITES Fig. 1. Three-layer cluster model of the Ti(0001) surface and interstitial sites. The surface layer contains 14 atoms, shown as (e); 15 atoms are in the second layer, shown as ( e ) ; the third layer contains 14 atoms in the,hcp continuation of the lattice. The inset depicts H adsorption sites calculated: above surface sites A and B; in plane sites C and D; interstitial sites E, F and G. Internuclear distances are those of bulk titanium.

P. Cremaschi, J.L. Whitten / Interstitial hydrogen in Ti

276

constructed by summing over the valence orbitals of atoms surrounding these sites. The single-particle states { @, } of the system are transformed, ~' = C. @, by maximization of the positive definite exchange integral, y = (u(1, 2)1r~11@'(1)~'(2)), with respect to coefficients C. This leads to an eigenvalue problem with solutions ordered in eigenvalues ]'1 > "t2 > " • • > YN, with corresponding eigenfunctions { ~, }. Transformation of the unoccupied (virtual) orbitals is carried out separately, and thus the total wavefunction of the system,

q' =~¢(q'i, ¢~,""" ,,I,N), t

¢

is invariant to the localization transformation. Only a relatively small number of orthogonal functions derived from the ( ~'k } set can be packed into the local region and these functions @'1,@~,"" ",@~, physically represent orbitals localized on the designated surface atoms, bonds between these atoms, bonds linking the surface atoms with the remainder of the lattice, and interior bonds of the lattice, with the overall order dictated by decreasing exchange eigenvalues. Following localization, the orbital basis is improved locally on the adsorbate and surface regions by adding atomic orbitals to provide radial and polarization flexibility. Also, in the case of transition metals any prior constraint used to determine s-band orbitals, such as the assignment of d electrons to an invariant atomic core, is removed on atoms directly bonded to the adsorbate. The final basis is fully orthogonal by construction. Configuration-interaction wave functions are then formulated as k

k

.

,

..

,

k

Here it is supposed that there are M electrons in the adsorbate-surface system, where the number of electrons contributed by the cluster itself is defined by the localizing transformation. The orbitals @~+1,"" ",@~ are associated with the interior of the lattice and are the eigenfunctions corresponding to the smaller exchange eigenvalues of the localizing transformation; they are taken as an invariant core in each configuration. Expansions, ~, are generated from an initial configuration, or' set of configurations, ~k0, by single and double excitations, to give excited configurations, ~k, k

where configurations are retained explicitly if the interaction threshold, (l(@,lnl@o>12/(Ek

- E0) } > 8,

is satisfied. The N dependency problem with CI expansions is greatly reduced

P. Cremaschi, J . L Whitten / Interstitial hydrogen in Ti

277

b y the fixed n u m b e r of electrons in the local s u b s p a c e a n d the m u l t i d e t e r m i n a n t n a t u r e of ~'0. T y p i c a l CI e x p a n s i o n s c o n t a i n - 500 configurations in the p r e s e n t work. Details of the theory are given in ref. [8]; see also ref. [13] for related m o l e c u l a r applications. In s u m m a r y , the p u r p o s e of the localization t r a n s f o r m a t i o n is twofold: (1) to i n t r o d u c e the delocalized c h a r a c t e r of the e x t e n d e d lattice into an electronic s u b s p a c e involving the a d s o r p t i o n site, a n d in the case of a cluster (2) to insulate the physically incorrect b o u n d a r y of the cluster a n d the roughly d e s c r i b e d interior region from o r b i t a l refinements in the local region. Overall, the t r a n s f o r m a t i o n scheme can be viewed as an alternative way of e n u m e r a t i n g the c o m p o n e n t orbitals to be included in the t r e a t m e n t of a d s o r p t i o n . I n s t e a d THEORETICAL

MODEL

I. LATTICE (Cleon surface) - simple theory (SCF) to describe the s-bond

(~,J'

]I, LOCALIZATION OF S-BAND ORBITALS -exchange maximization with surface sites

~'=~k Uk~k max 7" =

- ~ . 7'2 •

}

+! Tp+!

_• ~

SURFACE(p electrons) REGION

INTERIOR

7"9 j REGION

"m'.CONFIGURATION INTERACTION(ADSORBATEa LOCALREGION) - variable d occupancy on surface sites -local improvement of basis(radial/polarization/correlation) - rigorous ontisymmetry - fixed coulomb and exchange field of the interior region k) (k) , ,

• =

!g

...×,.

variable occupancy

fixed field

Fig. 2. Schematic representation of the embedding theory. The terminology is that for the description of chemisorption on the surface. On application to an interstitial site the description interstitial region replaces surface region in the figure. The interior region refers to the electronic subspac¢ distant from the adsorbate. In the present work the first two steps are carried out with H present using a minimal basis (see text).

278

P. Cremaschi, J.L. Whitten / Interstitial hydrogen in Ti

of basing the treatment on delocalized orbitals, the argument is that adsorption breaks the symmetry so strongly that an effective enumeration can be made by taking the adsorption region as an origin and counting outward over the set of localized orbitals. Applications of the above procedure can be found in the following studies: hydrogen on copper where local improvement of the basis is important but 3d electrons can be assigned to an invariant core [10], the dissociation of H 2 on Ti(0001) where 3d interactions and configuration interaction significantly strengthen the bonding of hydrogen to the lattice and basis flexibility is necessary to describe the extensive electron transfer to the hydrogen [9]; and CO on Ti(0001) where exothermic adsorption requires a proper treatment of the d level splitting on surface Ti atoms neighboring the adsorbate [11]. Fig. 2 shows a schematic representation of the theoretical model.

2.3. Basis Set The functions ls, ls' of the hydrogen and those of titanium are taken from ref. [9]. While all core orbitals are left unchanged, the 3d and 4s orbitals are reduced to three components by combining the more diffuse components. Ti 4s' orbitals used to improve the flexibility of the valence region are more contracted spatially than the atomic 4s to better describe charge transfer from titanium to the hydrogen atom. The number of valence functions on a given Ti varies depending on its position in the cluster. A titanium in the exterior defined in fig. 1, is assumed to have an atomic configuration (3d) 3(4s)1; only one 4s orbital is included in the basis and the three d electrons are treated as a core pseudopotential. Ti atoms in the local region have a double zeta, 4s and 4s' basis. Each atom in the local region is improved by one singly occupied d orbital oriented symmetrically toward the center of symmetry of the tetrahedral and octahedral holes below the surface layer. Other d electrons of atoms in local region are treated by a core pseudopotential. Finally, the border atoms, shown in fig. 1 are present only as spherically symmetric potentials, the same as used in ref. [9].

2.4. Embedding theory and calculations Following the embedding model described in section 2.2, two regions of the cluster are defined. The four central atoms of the first layer and the three of the second form the local region defining two adjacent tetrahedral and octahedral holes, see fig. 1. All other active metal atoms of the cluster define the exterior region. Calculations are carried out in three stages. In the first stage only a minimal basis set of 4s and H l s functions is used to describe the Ti lattice and hydrogen; all d electrons are represented by a core potential. A localization transformation of the resulting s-band molecular orbitals about the

P. Cremaschi, J.L. l'Vhitten / Interstitial hydrogen in Ti

279

octahedral and tetrahedral holes is carried out by exchange maximization, thus defining a local region electronic subspace. For all sites investigated 8 occupied and 6 virtual localized orbitals were selected, leaving 14 orbitals in the exterior subspace. Localized occupied and virtual orbitals are then used together with the Ti 4s', 3d and H ls' functions in a second, improved basis, SCF calculation. CI calculations are then carried out after another localization transformation to enhance convergence. Included in the CI calculation are 14 exterior orbitals with fixed occupancy, singly occupied d orbitals and the 8 most localized doubly occupied orbitals with variable occupancy and a variable number of virtual orbitals. In the CI calculations, all configurations arising from single and double excitations with an interaction energy greater than 1.0 X 10 -5 a.u. with the SCF configuration of localized orbitals are used [9]. Test calculations with more than one parent configuration give only a scaling of the energies and the same relative stabilities. Similarly, different d electron multiplicities give rise to nearly degenerate (excited) states but the same relative stabilities of the different sites. Seven H sites are calculated on or inside the 43 Ti atom cluster: two sites above the surface with the H atom 1.32 ,~ above the Ti(0001) surface plane of nuclei, with and without a second layer Ti atom below, the hcp and fcc extension sites, respectively; two H sites in the surface plane; interstitial sites of tetrahedral and octahedral symmetry; and one underlayer site midway between the Td and O h holes. Sites are depicted in fig. 1 and binding energies are reported in table 1. Three stages of theoretical treatment are reported in table 1 for each hydrogen site calculated. Only the CI values are reliable for the present method of embedding calculation, but the other calculations reported are useful to show the development of qualitative differences between H binding sites. Hydrogen binding energies calculated using the simplest SCF model, that of a minimal s-basis and d-electron pseudo-potential are reported in the first column of energies in table 1. Compared to the final calculations, this simple treatment fails to describe the energetics properly except possibly for those interstitial sites where H is surrounded by many Ti neighbors. In other cases, particularly for H above the surface, the minimal basis does not allow the description of spatially expanded, H-like, orbitals required for significant electron transfer to hydrogen. The second SCF solution in which the s-basis is improved, (Ti 4s, 4s' and H ls, Is'), and one d orbital per titanium is allowed to mix with the s-band, shows a gain in stability of the surface sites relative to the interstitial sites. Hydrogen binding energies, shown in the second column of energies in table 1, are beginning to exhibit the trends found in the final treatment. Electron transfer to hydrogen is now adequately described by the basis and charges calculated by a Mulliken population analysis show net hydrogen charges

280

P. Cremaschi, J.L. Whitten / Interstitial hydrogen in Ti

ranging from -0.31el for interstitial sites to -0.51el for H above the Ti surface. This SCF treatment does not, however, provide a reliable description of d bonding, particularly for dissimilar sites, due to the fixed orientation of the singly occupied d basis orbitals. The most reliably calculated binding energies in the present work are shown in the last two columns of table 1. The first column contains values obtained directly from the embedding treatment described earlier, for which the s,d SCF solution is the preceding step. The last column contains values obtained by allowing d-orbital rotation on each of the seven atoms in the local region, while retaining the d 3 configuration found in the preceding CI treatment. This refinement is analogous to the inclusion of a crystal field effect in which the repulsive overlap of filled H orbitals with partially filled d-orbitals causes a rotation of the d-orbitals to reduce the repulsion. The effect would be accounted for automatically in a CI description if all five d orbitals were present on the

Table 1 Hydrogen atom in titanium (hcp) interstitial sites, surface sites and above the Ti(0001) surface; energies are reported for each H site at three different stages of treatment; only those energies in the final CI column are reliable for the present method of embedding calculation; values in parentheses include basis superposition effects; sites are designated in relation to the symmetry of the underlying hole between the first and second planes; the T d - O h midpoint site is midway between the centers of the interstitial T d and O h sites; sites are further described in fig. 1; energies are in eV and distances in ,~, z b) dist.

Ti-H dist.

H binding energies a) SCF-A

SCF-B

CI

s-basis d pseudopot,

s,d basis d constraint

d

Incl. d

constraint

rotation 3.2 (3.2) 2.2 (2.1) 2.8 (2.7) 2.3 (2,3) 1.7 (1.8) 3.3 (3.1) 1.6 (1.6)

T0-above-surface

1.32

2.15

1.16

1.94

2.66

T0-surface-plane

0.00

1.70

1.57

0.84

1.24

--0.60

1.81

2.59

1.18

1.62

Oh-above-surface

1.32

2.15

0.36

0.98

1.84

Oh-surface-plane

0.00

1.70

1.04

0.24

0.72

Oh-interstitial

-- 1.20

2.09

3.54

1.85

2.52

T d - O h midpoint

-0.90

1.73

1.72

0.03

0.65

Td-interstitial

a) Energies are per H atom, A E + 2.36eV, where A E is calculated from the reaction ~2H 2 + metal = metal. H to minimize correlation energy errors. b) The z coordinate of H where z = 0 for the surface plane of nuclei.

P. Cremaschi, J.L. Whitten / Interstitial hydrogen in Ti

281

titanium atoms, but since only one d-orbital is explicitly included in the full calculation, the maximum possible response on configuration interaction would be a depopulation of the d shell, from d 3 to d 2. The calculations show that this does not occur for any of the sites investigated, however. The energy changes on d rotation are calculated by taking the electron density from the full calculation and using it to generate an effective field, including both the electrostatic and Pauli principle (orthogonality) contributions, which acts on the d electrons of the individual Ti atoms in the local region. The importance of the energy adjustment is seen in the increase in binding energies in the final column in table 1. The relative energies of the interstitial sites are not changed significantly by the d-rotation adjustment, but the above surface sites are stabilized only half as much as the interstitial sites due to the longer T i - H distances and the presence of only three nearest neighbor Ti atoms to H. Values in parentheses in the table are binding energies calculated including basis set superposition effects obtained by recalculating the clean surface energy in the presence of the hydrogen basis functions. Superposition corrections are relative to the Td-above-surface H site of table 1. It is not certain that the superposition correction, calculated in the usual way as described here, is justifiable because of the partial occupancy of the basis by the hydrogen electrons. Adopting the nomenclature defined in fig. 1 where H sites are referred to in relation to their underlying interstitial hole, viz., Td-above-surface (hcp extension), Td-surface-plane, Td-interstitial, Oh-above-surface (fcc extension), O hsurface-plane, Oh-interstitial, and the interstitial Td-O h midpoint sites, H atom binding energies can be grouped in magnitude as follows: 3.2-3.3 eV Td-above-sur face Oh-interstitial

2.8 eV Td-interstitial

2.2-2.3 eV Td-surface-plane Oh-above-surface

1.7-1.6 eV O h-surface-plane Td-O h midpoint

Binding energies of 3.2 and 3.3 eV are comparable to the binding energy per H atom obtained in an earlier study of the dissociation of H 2 on Ti(0001), for the same vertical distance of 1.32 A of H above the surface plane of nuclei. It is surprising that the different 3-fold symmetry surface sites above the surface differ so much in H binding, with the Td-above-surface site the more stable. The Td-surface-plane H site is also more stable than the Oh-surface-plane site. Comparing the charge distributions in table 2 suggests that these differences in H stability may not be simply a numerical detail since the source of H charge transfer differs greatly in the two cases, particularly for Td-surface-plane and O h-surface-plane sites where the calculated layer charges are different although the total electron population on hydrogen is about the same. It should be emphasized that the H-surface distance is not optimized and that it is possible that the Td-above-surface (hcp extension) and the Oh-above-surface (fcc extension) H equilibrium distances are different. For H 2 on Ti(0001) there is no evidence to suggest that this is the case but in that study two H atoms were

282

P. Cremaschi, J.L 14"hitten / Interstitial hydrogen in 77

always present in adjoining 3-fold sites on the surface. If the titanium lattice is not allowed to relax during its interaction with hydrogen, which is not likely physically in view of the high exothermicity of the reaction, the present results would imply that H would enter the Td hole more easily, because of the smaller surface-plane energy barrier, but would encounter a barrier to migration to the O h hole. The octahedral interstitial H site is calculated to be 0.5 eV (12 kcal/mol) more stable than the tetrahedral site for the unrelaxed Ti lattice. In the case of the tetrahedral interstitial site the H charge transfer of -0.291e J is the smallest value found for any of the sites suggesting a possible inhibition of the charge transfer by the small tetrahedral cavity where the T i - H distance is 1.81 ,~. The octahedral site, with a T i - H distance of 2.09 ,~, shows greater charge transfer to H and a larger H binding energy. The in-plane sites show lateral confinement of H and decreased binding compared to H either above or below the surface. An energy barrier of 23 kcal/mol is found for passage through the surface layer (Td-surface-plane site) from the T0-above-surface H site, while the barrier to escape from the Td-interstitial site through the surface plane is 14 kcal/mol. Short T i - H distances also occur for the Td-O h midpoint site, as shown in table 2, and the calculated binding energy is comparable to that of the Oh-surface-plane site. For hydrogen below the surface, the calculations have consistently shown the octahedral site as energetically more favorable for hydrogen atom absorption than the tetrahedral site. A smaller cluster study of the other type of tetrahedral site below the surface layer, defined by one surface layer Ti atoms, showed H stability comparable to the less deep tetrahedral site examined in this work. Experimentally, there is some evidence that the tetrahedral site is Table 2 Charge distribution and principal H peaks in the local density of states for a H atom in titanium interstitial, surface plane and above surface sites; the titanium hcp lattice is modelled as a 43 atom cluster, shown in fig. 1; charges are calculated from Mulliken populations (see text for uncertainties in interpretation), titanium charges, reported per layer of atoms, show major differences for the tetrahedral and octahedral series of sites; energies are in a.u. (1 a.u. = 27.21 eV); net H or layer charges are in units of the electronic charge for Ti 4s and 3d and H orbital populations H energy levels

Td-above-surface Td-surface-plane Td-interstitial Oh-above-surface O h-surface-plane Oh-interstitial T d - O h midpoint

-0.42, -0.51, -0.54 -0.40, -0.51, -0.56, -0.56,

-0.30 -0.41, -0.37 -0.27 -0.41 -0.41, -0.27 -0.41, -0.28

Net charge distribution Surface layer

Layer 2

s

d

s

d

s

Layer 3

0.19 0.46 0.46 0.51 0.15 0.05 -0.15

-0.09 -0.04 -0.09 -0.12 -0.06 -0.10 -0.08

1.01 -0.07 -0.14 0.57 0.82 1.05 1.05

-0.03 -0.04 -0.05 -0.07 -0.07 -0.13 -0.06

-0.61 0.03 0.11 -0.37 -0.45 -0.46 -0.46

-0.48 -0.33 -0.29 -0.51 -0.39 -0.41 -0.30

P. Cremaschi, J.L. Whitten / Interstitial hydrogen in Ti

283

favored in titanium, the octahedral hole becoming occupied at high temperature. The experiments are carried out at higher H concentration, however. Since the diffusion of hydrogen into titanium is known to change the structure from hcp to tetragonal, the present theoretical results for the unreconstructed lattice may not be applicable to the experimental conditions. The only other known theoretical calculation reporting the relative stability of the two interstitial sites finds a 0.3 eV preference for the octahedral site for a 1 x 1 H underlayer [6]. This corresponds to the 0.5 eV difference between the octahedral and tetrahedral underlayer sites found in the present work, an agreement remarkably close in view of the technical differences between the density functional and ab initio treatments and the differences in interactions that would be expected for a 1 x 1 underlayer compared to the low H concentration limit. The 2.9 to 3.1 eV binding energies per H found for the 1 x 1 H overlayer are comparable to the 3.2 eV value found for the H in above surface fcc extension site. There appear to be differences between the two calculations in the details of the electronic structure. Feibelman et al. [6] have photoemission evidence to support the interpretation of T i - H bonding as directly involving Ti 3d and H ls electrons, and have interpreted the bonding as involving the formation of T i - H molecular orbitals. Our calculations show some of the same characteristics, viz., a deeply bound H surface state and higher levels involving H in the vicinity of the Ti 3d levels which could affect the 3d level photoionization. The 3d orbital participation occurs however in two distinct ways: the usual mixing with s orbitals to form a local molecular orbital, and for 3d orbitals already occupied a rotation to avoid the H adsorbate. Although not directly calculated, the charge transfer to H would be expected to deepen core levels of neighboring Ti atoms.

3. Conclusions Hydrogen atom absorption by hcp titanium is treated by a n embedding theory based on SCF and local CI descriptions of the electronic bonding. The very low concentration limit is modelled by treating a single H atom in a 43 atom titanium cluster to compute binding energies of different interstitial sites. An energy barrier to H penetration of the surface of 23 kcal/mol is found for the unrelaxed surface, and this result is attributed simply to short T i - H distances in the surface plane. Hydrogen in an octahedral hole below the close packed titanium surface layer is 12 kcal/mol more stable than H in a tetrahedral hole for an unrelaxed lattice and this appears to be due to the better accommodation of the negatively charged H by the larger octahedral cavity. The lower energy for H in the octahedral hole is in accord with previous calculations on titanium for a 1 × 1 H underlayer. An energy barrier to the

284

P. Cremaschi, J.L. Whitten / Interstitial hydrogen in Ti

migration of H between interstitial sites is f o u n d ; for the site midway between the octahedral a n d tetrahedral holes, the T i - H distances are short, c o m p a r a b l e to the T i - H distance for H in the surface plane. The electronic description that emerges from the calculation is one involving considerable electron transfer to H with the a d d i t i o n a l charge a c c o m m o d a t e d in a more diffuse H l s orbital strongly mixed with Ti 4s orbitals [12]. The charge transfer is almost entirely from the metal 4s b a n d . I n a d d i t i o n to the f o r m a t i o n of molecular orbitals, some of the occupied 3d orbitals u n d e r g o an energy lowering rotation to avoid the hydrogen. Finally, the present work is clearly limited in scope since only symmetric sites are e x a m i n e d a n d lattice relaxation is n o t considered.

Acknowledgments Support of this research by the U S D e p a r t m e n t of Energy, C o n t r a c t No. DE-AC02-77ER04387, a n d by a travel grant (RG-246.81) from N A T O , is gratefully acknowledged.

References [1] [2] [3] [4]

J. Ward, J. Less-Common Metals 73 (1980) 183, and references therein. M.A. Pick, J.W. Davenport, M. Strongin and G.J. Dienes, Phys. Rev. Letters 43 (1979) 286. G.F. Wedler and H. Strothenk, Z. Physik. Chem. (Frankfurt) 48 (1966) 86. W.D. Wilson and S.C. Keeton, Sandia Report, SAND81-8676 (1982); W.D. Wilson and S.C. Keeton, in: Proc. Symp. on Advances Tech. Chart. Hydrogen Met., 1981, Eds. N.F. Fiore and B.J. Berkowitz (Met. Soc. AIME, Warrendale, PA). [5] H. Pinto, C. Korn, S. Goren and H. Shaked, Solid State Commun. 32 (1979) 397. [6] P.J. Feibelman, D.R. Hamann and F.J. Himpsel, Phys. Rev. B22 (1980) 1734. [7] A.C. Switendick, Bull. Am. Phys. Soc. 26 (1981) 376; A.C. Switendick, Electronic Structure of Transition Metal Hydrides, in: Transition Metal Hydrides, Ed. R. Ban (Am. Chem. SOc., Washington, DC, 1978). [8] J.L. Whitten and T.A. Pakkanen, Plays, Rev. B21 (1980) 4357. J.L. Whitten, Phys, Rev. B24 (1981) 1810. [9] P. Cremaschi and J.L. Whitten, Surface Sci. 112 (1981) 343; Phys. Rev. Letters 46 (1981) 1242. [10] P. Madhavan and J.L. Whitten, J. Chem. Phys. 77 (1982) 2673. [11] C.R. Fischer, L.A. Burke and J.L. Whitten, Phys. Rev. Letters 49 (1982) 344. [12] The description is similar to that found for Ni-H interactions in ref. [7]. [13] J.L. Whitten and M. Hackmeyer, J. Chem. Phys. 51 (1969) 5584.