富山大学水素同位体科学研究センター研究報告 23 : 29-41, 2003.

Study of Hydrogen Adsorption by V, V-Ti alloy and V-oxide throughab initio Calculations
L. Wang, R. Hayakawa, Y. Hatano and K. Watanabe
Hydrogen Isotope Research Center,Toyama University, Gofuku 3190, Toyama 930-8555, Japan(received March 25, 2004, accepted March 15, 2005)
ABSTRACTThe adsorption of hydrogen on surfaces of vanadium, vanadium-titatnium alloy and vanadium oxide was studied by ab initio calculations using Gaussian03 package. The activation
and adsorption energies for adsorption were evaluated by scanning potential energy surfacesof respective systems comprising a hydrogen molecule and small cluster consisting of several metal atoms for modelling an alloy surface to reduce computational cost. The surfaces
investigated were V(110), V-Ti(110), VO(111) and VO(110), diãerent cluster models being
adopted for some surfaces to examine their validities and to ånd an appropriate cluster modeland adsorption site.
By comparing the results obtained by using the alloy and/or compound in diãerent cases,
it was found that the activation energy for adsorption is larger for surfaces with an oxygen
adlayer than for clean and Ti-covered vanadium surfaces. These åndings are in good agreement with experimental observations. It was also demonstrated that diãerent cluster models
for a given alloy give similar activation and adsorption energies.

1. Introduction
Vanadium alloys are considered as one of the most promising structural materials forfusion reactors because of their high temperature strength, high thermal stress factor,
low activation property and so on [1]. An important concern for this application is theadsorption of hydrogen molecules. Hydrogen is adsorbed on clean vanadium surfaces
extremely fast, and then rapidly absorbed by the bulk because of the high diãusivity
and solubility of hydorogen atoms in this material[2]. But the environments assumed fortheir applications will contain some levels of oxygen that can aãect the hydrogen adsorption. Vanadium is one of the most sensitive materials to poisoning by impurity gases
containing oxygen, carbon and even nitrogen. Consequently the surface of vanadium iseasily contaminated by impurity gases even in high vacuum conditions. Surface oxides orcontamination layers thus formed act as barriers against the chemisorption of hydrogen291

王 利・早川 亮・波多野雄治・渡辺国昭

isotopes[3, 4, 5]. Therefore they provide eãective means to reduce tritium permeation
through the structural material as well as the tritium inventory in it. Furthermore, theycan enhance the super permeation of tritium atoms and ions generating in the edge plasma
region. From this view point, a number of investigations have been carried out to examine the eãectiveness of such kind of surface barriers on preventing hydrogen absorption
and/or accelating super permeation[6]. The results are, however, rather complicated andhence not well understood, because most of the experiments were done for poly crystlline
specimens with diãerent purities and pretreatments under various vacuum conditions.
To understand fundamental roles of these surface barriers on hydrogen absorption andsuper permeation, the adsorption of hydrogen molecules on the surfaces of V, V-Ti alloy
and V-oxide was studied from the årst principles in the present study. This is a formidable
task that has not been fully achieved in even the simplest case without making several
simplifying assumptions. The purpose of our present eãort is to undertake ab inito calculations for hydrogen adsorption for the above mentioned mateials by use of small clusters
consisting of several metal atoms as the models of crystal surfaces, to examine the validity of small cluster models, and to ånd eãects of such barriers on the adsorption. The
computations were performed on a PC workstation by using Gaussian 03[8].
2. Calculation details
2.1. Calculation of potential energy surfaces
For the dissociative adsorption of hydrogen via a bridge site on a metal surface, forexample, the following scheme is assumed to be validkÉ
É f
H2 + 2S ä S2H2 Ä!
^
KÉ

2SH(a);(1)

where H2 represents a hydrogen molecule, 2S adjacent metal atoms forming a bridgeÉsite, S2HÉ
2 the activated complex, SH(a) an adsorbed hydrogen atom, K the constant forpseudequilibrium between the reactants and acticated complex, k É
f the rate constant fordecompostion of the activated complex. The rate of adsorption is written as[7]kT
QÉ)() exp(ÄEact =k T )[H2][S] 2
h Q H2 Q S2kT
QÉkad = ()(
) exp(ÄEact =k T )h QH2 QS 2

É2
É É
2
vad = k É
f [S 2H2 ] = kf K [H2][S] = (= k ad [H2][S] 2;

(2)
(3)

where [ ] represents the concentrations of respective species, and k and h are the Boltzmann and the Planck constants, respectively; Q's are partition functions of the activated302Study of Hydrogen Adsorption by V, V-Ti alloy and V-oxide through ab initio Calculations

complex, a hydrogen molecule and a metal atom on the surface, and Eact is the diãerencein the classical energy levels between the reactants and activated complex.
The rate constant kad is a function of quantum stats of reactants and activated complex.
By scanning the potential energy surface for a system consisting of H2 and metal surface,
the products and activated complex can be determined to evaluate the adsorption andactivation energies. If the partition functions could be calculated as well, the rate constantk ad is obtained through the ab initio calculations.
The key point for evaluating the rate constant is to ånd the reaction path connecting
the reactants and products through the activated complex in the potenrial energy surface(PES). In the present study, two dimensional PES's were calculated by adopting small
cluster models, where the energies were evaluated as funtions of the height of H2 moleculesfrom the surface and the distance between two H atoms, while the surface structure wasassumed to be invariant. Their details are described in section 2.2. Once the reaction
path could be evaluated, the adsorption energy of a hydrogen molecule on the metal
surface is calculated by
Eads = Etot (2SH ) Ä Etot (metal + H 2);(4)

where Etot(metal+H2) is the total energy of the unit cell with a H2 molecule in the vacuum
region, and Etot (2SH) is the total energy of the unit cell with two adsorbed H atoms on
the surface. Similarly, the activation energy of the adsorption is
Eact = Etot (S2H2É) Ä Etot (metal + H 2);(5)

where Etot(S2HÉ2) is the energy for forming the activated complex or transition state in
the adsorption process.
To evaluate PES for a system consisting of a metal surface and a hydrogen molecule, thepresent study used the density-functional method, where an extra quadratically convergent SCF (XQC) step was performed in case that the årst-order SCF was not converged[9].
For vanadium, oxygen and titanium atoms, the Eãective Core Potential (ECP) basis setsof Los Alamos ECP plus MBS atomic wavefunctions were applied[10], and a standard
6-31G basic set was used for hydrogen[11]. Then the Kohn-Sham equation was solved byusing B3LYP exchange-correlation functions. The B3LYP function is one of the hybrid
types. It consists of a careful mixing of Hatree-Fock exchange, Beche's B98 exchange
functions and the LYP correlation functions[12, 13].
An example of optional part in a routine input used in the calculation is shown below.
313

王 利・早川 亮・波多野雄治・渡辺国昭

Chk=scanV3H2
scan ub3lyp/lanL2dz nosymm guess=(tcheck,mix) iop(2/16=1) extrabasis
scf=(varacc,conver=6,xqc,Fermi,maxcycle=600) test
2D pes scanTo ånd the inçuence of oxygen and/or titanium atoms deposited on the vanadium surface on hydroge adsorption, clean vanadium surface V(110), vanadium surface covered byoxygen with vanadium structure V/O(110), VO(110,111) and vanadium surface coveredby titanium with vanadium structure V/Ti(110), where a hydrogen molecule is assumed
to be adsorbed via either a bridge site or on-top site of these surfaces.
2.2. Cluster Models
A given crystal was sliced to a slab comprising a set of given planes with several atomic
layers. Then the slab was cut by a plane perpendicular or with a given angle to theplane to make a cluster consisting of several atoms. The cluster was used as a modelof the crystal surface to evaluate the potential energy surface (PES) for evaluating theadsorption of a H2 molecule, where the distance between two hydrogen atoms and theheight of the center of H-H bond from the surface were varied for PES calculations. In
this case, the mutual distances and angles among the atoms forming the cluster were set
equal to those found in the crystal and kept constant; namely, no surface relaxation was
accounted for surface formation and also hydrogen adsorption.
2.2.1. Vandadium
Hydrogen adsorption on the clean surface of vanadium was followed for V(110) surface.
Vanadium has the body-centered cubic structure with a lattice constant of a=3.028ó
A, asshown by Fig.1, in which the V(110) lattice plane is drawn. Firstly, the V(110) surface
was modeled by clusters containing three or four atoms, which correspond to one- or twolayers thickness. Hereafter, the clusters containing three and four atoms are denoted as
V3 and V4 clusters, respectively, for convenience. When a hydrogen molecule is adsorbedon the V(110) surface, it would take place via an activated complex formed on the bridgeor on-top site with H-H bond oriented parallel to the surface; it should be noted here thatthe surface is represented by the bond connecting the two vanadium atoms in the årst or
second layer.
In the V3 models, triangular and linear geometries were adopted. The V3 triangularmodel is constructed by two vanadium atoms labeled by 1 and 2 and one vanadium atom

324

Study of Hydrogen Adsorption by V, V-Ti alloy and V-oxide through ab initio Calculations

Fig. 1. The body-centered cubic structureof V with a Miller plane (110)Fig. 2. Arrangement of V-atoms in a twolayer slab of V(110)labeled by 3 in vanadium 110 substrate as shown in Fig.2, in which vanadium atoms 1,
2, 4, and 6 are in the top layer and the other atoms are in the second layer.
The adsorption of a hydrogen molecule through thebridge site of V3 triangular cluster with H-H bond oriented parallel to the surface are shown by Fig.3, in which
the distance between the two vanadium atoms in the top
layer is 3.028 ó
A, the third one is at 2.142 ó
A under the
Fig. 3. Adsorption of a hydrogen molecule on a bridge and ontop site on triangular V3 cluster

two atoms.
Three V3 linear clusters can be also possible for modeling V(110) surface. The årst one is the array of vana-dium atoms in the [0 1] direction (V3-linear 1), which is constructed by the vanadium
atoms 1, 2, and 3 in top layer of V(110) substrate shown by Fig.4, where the distance
between two adjacent atoms is 2.622 ó
A. The second one is the array in the [1 1] direction
and distance between two adjacent atoms is 3.028ó
A(V3-linear 2), which is constructedby the vanadium atoms 1, 4, and 5 shown by Fig.4. The third is the one in the [1 -1]
direction and the atomic distance is 4.283 óA, but the atoms are too far apart and thenthis cluster was excluded from inspection. Hereafter, the årst two types of linear clusters
are denoted as linear model 1 and 2, respectively.

335

王 利・早川 亮・波多野雄治・渡辺国昭

Fig. 4. Another view of the
two-layer slub of V(110)Fig. 5. Adsorption of a hydrogen molecule on on-top
sites of linear V3 cluster

It should be mentioned here that the two hydrogen atoms are in the same plane including the three vanadium atoms for all of V3 clusters mentioned above. The adsorption ofhydrogen molecule by the linear model-1 (a) and -2 (b) are decribed by Fig. 5.
In the V4 model as shown by Fig.2, there are
two vanadium atoms (1 and 4) in [1 0] direction
at the top-layer and two atoms (3 and 5) in [0 1]direction at the second layer, and the distance
between two vanadium atoms in the same layer
ó. The line connecting the center of theis 2.622 A
Fig. 6. Adsorption of a hydrogenmolecule on a bridge site of V4 cluster

former and the center of the latter is perpendicular to the (110) surface, and the angle between
the plane perpendicular to the surface decided

by the former and the plane perpendiculat to the V(110) surface decided by the latter is
70.53 degree. In this case, two hydrogen atoms and the two vanadium atoms at the top
layer were assumed to be in the same plane, as shown by Fig. 6.
2.2.2. V-Ti alloy
For the adsorption of hydrogen by V-Ti alloy, it was
assumed that a 50%V-50%Ti alloy has the same crystal structure and lattice constant as those of V. The
cluster models adopted here were V2Ti and VTi2. As
for the former (schematically drawn in Fig.7), a hyFig. 7. Adsorption of a hydrogen molecule on a bridge site ofV2 Ti or VTi2 cluster

drogen molecule was assumed to be adsorbed via thebrdige site consisting of two adjacent V atoms, and346

Study of Hydrogen Adsorption by V, V-Ti alloy and V-oxide through ab initio Calculations

for the latter via the brdige site comprising two adjacent Ti atoms. These clusters correspond to the model of V3 shown in Fig.3. In the present study, however, only theadsorption for the latter is reported.
2.2.3. Vandadium oxideFig. 9. Arrangement of V- and O-atoms
in a two-layer slab of VO(111)Fig. 8. The NaCl structure of VO with aMiller plane (111)The VO(111) surface was examined for the adsorption by VO of NaCl structure shownby Fig.8, for which the V2O and VO2 clusters were adopted as models. The former, whichis constructed by two vanadium atoms 1 and 2 in the årst layer and one oxgen atom labeled by 3 as shown by Fig.9, assuming that the adsorption takes place on vanadium sites.
In this case (V2O), hydrogen atoms are not in theplane decided by the two vanadium atoms and theone oxygen atom as seen in Figs.9 and 10. The angle
between the plane decided by V2-H-H and the plane
decided by V-V-O is 39.23 degree. The distance between two vanadium atoms is 2.894 óA, and the distance between the oxygen atoms and the center of two
Fig. 10. Adsorption of a hydrogen molecule on bridge sites oftriangular V2 O cluster

vanadium atoms is 1.447 ó
A. The VO 2 model has thesame geometric structure as V2O, as shown in Fig.9,
expect that two oxygen atoms come at the tope layer,
and a vanadium atom is at the second layer.

But the calculation for the latter, which has two oxgen atoms in the årst layer and one
vanadium atom in the second layer of VO surface, did not converge well, and then the357

王 利・早川 亮・波多野雄治・渡辺国昭

result is not described here.

Fig. 11. The NaCl structure of VO with aMiller plane (110)Fig. 12. Adsorption of a hydrogen molecule
on a bridge site of triangular V2 O cluster formodeling VO(110)

In addition to VO(111), the adsorption of hydrogen on VO(110) was also studied byscanning the PES of the systems consisting V2O and two hydrogen atoms. The VO(110)
surface is shown by Fig.11, in which vanadium atoms 1, 2 in the årst layer and oxygen
atom 3 in the second layer is modelled to V2O model(VO-V2O(110)). In this system,
all atoms are in a plane, i.e. the plane containing two vanadium and one oxygen atoms,
and two hydrogen atoms is perpendicular to the surface. Figure 12 shows the parallel
approach of a hydrogen molecule to the bridige sites of V2O cluster for VO(110).
3. Results and discussion
As mentioned above, for all of the models two dimensional PESs were calculated by
Gaussian 03; namely, the energy was evaluated as a function of the distance between twohydrogen atoms and the height of the center of two hydrogen atoms from the surface,where the geometry of the substrate was set invariable throughout the PES calculation.
Some of them are presented in this section as examples. Figure 13 represents the 3D- (a)and contour (b) mapping of the PES for V(110) by Model 1, the parallel approach of H2
on the trianglular V3 cluster shown in Fig.3, where Half rHHx is the half of the distance
betweem two H-atoms, Height indicates the distance between the center of the H-H bondand the surface, both in ó
Aunit, and E is the energy in the Hartree unit. It was found thatthe activation and adsorption energies were 0.106 eV and -0.454 eV, respectively. Figures
14 shows the PES of the adsorption of hydrogen molecule via the on-top site of V3 linear
model 1 with H2 oriented parallel to the V(111) surface, for which the resulted activation
368

Study of Hydrogen Adsorption by V, V-Ti alloy and V-oxide through ab initio Calculations

3

2.5

Height/ A

Half rHH/ A

2

E /hartree

1.5

1Height/ A

0

0.5

1

1.5

2

2.5

Half rHH/ A

Fig. 13. 3D- and contour-mapping of the PES for triangular V3 clluster shown by Fig.3

and adsorption energies are 0.083 eV and -1.288 eV, respectively. Fig.15 shows the PES
for the hydrogen adsorption via the bridege site of V2 O clulster modeling with H2 oriented
parallel to the VO(111) surface, in which the resulted activation and adsorption energies
are 0.638 and -0.407 eV, respectively.

3

2.2
2

Height/ A

Height/ A

2.5
1.8
1.6
1.4

2

1.5

1.2
1

1
0.8
0

0.5

1

1.5

2

0

Half rHH/ A

Fig. 14. Contour map of the PES for V3 linear 1 shown by Fig.5 (a)

0.5

1

1.5

2

2.5

Half rHH/ A
Fig. 15. Contour map of the PES for V2 O
cluster shown by Fig.10

Although other PES's for other cluster models will not be shown here, calculated activation and adsorption energies are summarized in Table 1 along with their structures.
As seen in the table, the hydrogen adsorption on the V(110) surface requres relatively379

王 利・早川 亮・波多野雄治・渡辺国昭

small activation energies about 0.1 eV or below as seen for triangular V3 and V3-linear 1
models, but the adsorption via the on-top site of V3 -linear 2 does not likely occur becauseof a noticeably higher activation energy. It should be mentioned here that the adsorption
via the bridge site of V4 gave very similar activation energy with that for the triangular
V3 cluster along with the similarity of adsorption energy, although the structures of activated and adsorbed states diãer a little from those for triangule V3 cluster. As for thealloying with Ti, the activation enery for Ti2 V cluster seems a little higher than that fortriangular V3 , although the structure of activated complex is very similar to that of triangular V3 . These results suggest that hydrogen adsorption on V(110) surface takes placemost likely via the bridge site or the on-top site of the atomic array in [01] direction, andthe alloying with Ti does not change signiåcantly the activation energy. Further details
in the activation energy as well as heat of adsorption, however, should be compared by
calculations applying much larger clusters.
Table 1. Energies and structures of activated and adsorbed states for diãerent clusters;
calculated with scf=(Vshift=200,conver=8,xqc,Fermi,maxcycle=600)

Cluster

Activated state

Adsorbed state

Energy(eV) Half-rHH(óA)a Height(óA)b Energy(eV) Half-rHH(óA)a Height(óA)bV3-triangle

0.11

0.60

1.60

-0.45

2.05

1.60

V3-linear 1

0.08

0.42

1.95

-1.29

1.31

1.31

V3-linear 2

0.29

0.42

1.86

-1.22

1.53

0.76

V3-Ti2 V

0.16

0.60

1.65

-0.41

2.12

1.70

V4

0.07

0.44

1.65

-0.41

1.90

1.60

V3-V2 Oc

0.66

0.53

1.55

-0.23

2.21

1.53

VO-V2O(110)

0.78

0.53

1.75

-0.24

1.73

1.72

VO-V2O(111)

0.64

0.40

1.95

-0.41

1.76

1.65

a

: half-length of H-H distanceb: height of the center of the H-H bond from the surfacec: pseud-oxide, where the bottom V was replaced by O of the triangular V3 cluseterOn the contracy, considerably larger activation energies were obtained for the adsorption
via the bridge sites of VO(111) and VO(110); they are 0.64 and 0.78 eV for V2O(111) andV2O(110) clusters, respectively. But as for the heat of adsorption, two cluster models of
VO gave rather small values; they are comparative or even smaller in comparison with
10
38

Study of Hydrogen Adsorption by V, V-Ti alloy and V-oxide through ab initio Calculations

those observed for triangular V3 and Ti2V clusters, and apparently smaller than thosefor linear V3 clusters. This is because the site for adsorption in this case is similarly avanadium atom on the surface. Larger heat of adsorption can be expected for oxygensites.
All of the above mentioned results indicate that the features of hydrogen adsorption
on vadadium and vanadium covered by oxygen obtained by cluster models are in good
agreement with experimental observations that the rate of hydrogen ab/adsorption by
vanadium is drastically decreased with the presence of adsorbed oxygen or oxide ålmon the surface[2]. In addtion, it is shown that there is no signiåcant diãerence among
the activation energies of hydrogen adsorption on the diãerent models, as seen for the
triangular V3 and V4 as well as other combinations not described here. It is noted here,
however, that the exact values of activation energy and the heat of adsorption along withthe structures of activated complex and adsorbed speceis should be discussed by more
precise calculations with periodic boundary conditions.
4. Conclusions
The adsorption of hydrogen on the surfaces of vanadium, vanadium-titatnium alloys
and vanadium oxides was modeled by simple clusters comprising three or four atoms andthe potential energy surfaces were calculated by ab initio calculations using Gaussian03
package. The surfaces investigated were V(110), V-Ti(110), VO(111) and VO(110), wherediãerent cluster models were adopted for some of the surfaces to examine their validities
and to ånd an appropriate cluster model. The calculation indicated that hydrogen adsorption takes place most easily via the on-top site of the atomic array in [1 0] direction on
V(110) surface, and a hydrogen atom is stably adsorbed at the midpoint between the two
vanadium atoms in the array. On the other hand, the presence of oxygen on the surface
will signiåcantly hinder the adsorption owing to the notable increase in the activationenergy. These features are in good agreement with experimental observations that therate of hydrogen ab/adsorption by vanadium is drastically decreased with the presence ofadsorbed oxygen or oxide ålm on the surface.
The present calculations also showed that simple cluster models consisting of a few
atoms can give usefull information of the inçuence of crystal faces exposed to hydrogen,eãect of alloying, and consequence of surface poisoning by oxygen, sulfer and others onhydrogen adsorption by metals. However, more accurate geometric models are necessary1139王 利・早川 亮・波多野雄治・渡辺国昭

to obtain precise values of activation and adsorption energeis as well as structure of activation and adsorption species.

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Study of Hydrogen Adsorption by V, V-Ti alloy and V-oxide through ab initio Calculations

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