Effects of the kinetic energy on the hydrogenabstraction dynamics on Cu(110)

Yoshio Miura a,b,*, Hideaki Kasai b,*, Wilson Agerico Di~nno b

a Japan Science and Technology Corporation, Kawaguchi, Saitama 332-0012, Japanb Department of Applied Physics, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan

Abstract

We investigate and discuss the effects of the kinetic energy (Et) of the incident hydrogen atom on the hydrogenabstraction dynamics on Cu(1 1 0) by performing quantum dynamics calculations on an ab initio potential energy

surface. Our calculation results show that the hydrogen abstraction probabilities on Cu(1 1 0) initially increase, then

decrease, with increasing Et, in the energy range Et ¼ 0:05–1.0 [eV]. Furthermore, we show that the mean vibrationalenergy of the product hydrogen molecules increases with increasing Et, while the mean surface parallel translationalenergy of the product hydrogen molecules decreases with increasing Et. From these results, we can conclude that in-creasing Et mainly enhances the excitation of the vibrational motion, rather than the surface parallel motion of producthydrogen molecules.

� 2003 Elsevier Science B.V. All rights reserved.

Keywords: Models of surface chemical reactions; Molecular dynamics; Chemisorption; Atom–solid interactions; Diffusion and

migration; Quantum effects; Copper; Hydrogen atom; Hydrogen molecule

1. Introduction

Investigations of hydrogen-surface reactions are

essential for obtaining a fundamental under-

standing of dynamical processes occurring on solid

surfaces, and performing efficient control of in-dustrially important gas-surface reactions. One of

the most challenging topics in the study of

hydrogen-surface reactions, both experimentally

[1–9] and theoretically [10–17], is hydrogen

abstraction on metal and semiconductor surfaces.

When a gas-phase hydrogen atom impinges a hy-

drogen pre-adsorbed surface, it abstracts an ad-

sorbed hydrogen atom in a single collision, then a

hydrogen molecule desorbs. This process corre-

sponds to �direct abstraction�. Otherwise, it isscattered back to the gas-phase, or trapped on the

surface. The trapped hydrogen atom diffuses along

the surface, and reacts with other adsorbed hy-

drogen atoms, then a hydrogen molecule desorbs.

This process corresponds to �indirect abstraction�.In a previous work [18], we investigated and

discussed the dynamics of hydrogen abstraction on

Cu(1 1 1) by performing quantum dynamics cal-culations. We introduced a new theoretical ap-

proach that quantum mechanically considers both

the direct abstraction and the indirect abstraction.

*Corresponding authors. Address: Department of Applied

Physics, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-

0871, Japan. Tel.: +81-6-6879-7857; fax: +81-6-6879-7859.

E-mail addresses: miura@dyn.ap.eng.osaka-u.ac.jp

(Y. Miura), kasai@dyn.ap.eng.osaka-u.ac.jp (H. Kasai).

0039-6028/03/$ - see front matter � 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0039-6028(03)00429-1

Surface Science 532–535 (2003) 148–153

www.elsevier.com/locate/susc

We discussed how the coverage of initially ad-

sorbed hydrogen atoms on Cu(1 1 1) affects the

vibrational and surface-parallel translational en-

ergy distributions of product hydrogen molecules.

Our results showed that the mean vibrational en-

ergy of product hydrogen molecules hEvibi de-creases with decreasing coverage, while the mean

surface parallel translation energy of product hy-

drogen molecules hEparai increases with decreasingcoverage. We concluded that for the low coverage

case, hydrogen abstraction occurs mainly through

the indirect process, where the vibrational excita-

tion of product hydrogen molecules is suppressed,

and the excitation of the surface parallel transla-tional motion is enhanced, as compared with those

for the high coverage case, where the hydrogen

abstraction occurs through both direct and indi-

rect processes.

Here, we report on the effects of the kinetic en-

ergy of the incident hydrogen atom on hydrogen

abstraction on Cu(1 1 0). Due to the attractive in-

teraction between a hydrogen atom and Cu(1 1 0),the incident hydrogen atoms have large kinetic

energies at the surfaces (�1.5 [eV]). This energy istransferred to the translational and other internal

degrees of freedom of the product hydrogen mol-

ecules. Therefore, to demonstrate energy flow and

energy disposal in the hydrogen abstraction on

Cu(1 1 0), it is essential to obtain a microscopic

understanding of the hydrogen abstraction mech-anisms. We perform quantum dynamics calcula-

tions on an ab initio potential energy surface

(PES), using the time-independent coupled-chan-

nel method. We calculate the hydrogen abstraction

probabilities, the mean vibrational energy hEvibi,and the mean surface parallel translational energy

hEparai, as a function of the kinetic energy of inci-dent hydrogen atoms.

2. Theory

We consider three coordinates (r; Z;X ) as dy-namical variables to describe the direct and in-

direct abstraction. r is the relative distance of thetwo hydrogen atoms, Z is the center-of-mass co-ordinate of the two hydrogen atoms normal to

the surface, and X is the center-of-mass coordi-

nate of the two hydrogen atoms parallel to the

surface, along the [1 �11 0] direction on Cu(1 1 0).X ¼ 0:0 [�AA] denotes the position of a gas-phasehydrogen atom when it is just above the adsorbed

hydrogen atom on Cu(1 1 0). We consider the

reaction between an incident H atom and a targetD atom initially adsorbed on a hollow short-

bridge (HL-SB) site of Cu(1 1 0) [19]. The incident

H either directly or indirectly abstracts the ad-

sorbed D, and the resulting HD desorbs from the

surface. In our calculations, the position of the

adsorbed D is fixed during the abstraction. This

means that the motion of the desorbing HD

parallel to the surface is suppressed in our cal-culations. The hydrogen abstraction on Cu(1 1 0)

is about 2.5 [eV] exothermic reaction, and most

of this energy is transferred to the translational

energy normal to the surface of the desorbing

HD. Therefore, the approximation that the center

of mass position of the desorbing HD parallel to

the surface hardly changes, is reasonable to de-

scribe the motion of desorbing HD in the ab-straction on Cu(1 1 0).

In order to include both the direct and indirect

processes in the quantum dynamics calculations, it

is advantageous to transform these Cartesian co-

ordinates ðr; ZÞ into reaction path coordinatesðs; vÞ [20,21]. s corresponds to the reaction pathcoordinate along the potential minimum on a PES,

and v corresponds to the vibrational coordinateperpendicular to the reaction path, respectively. In

this paper, we leave the details of the transfor-

mation to Ref. [18], and show only the final form

of the Hamiltonian, which is given by

H ¼ � �h2

2lg�1 o

osg�1 o

os

�þ g�1 o

ovgo

ov

�

� �h2

2Mo2

oX 2þ V ðs; v;X Þ: ð1Þ

Here, g is the Jacobian of the transformationgðs; vÞ ¼ 1� v CðsÞ. The reaction path curvatureCðsÞ ¼ Cmax= coshðs� s0Þ, where Cmax ¼ 5:3 [�AA�1]

and s0 ¼ 0:994 [�AA].V ðs; v;X Þ is the PES in the reaction path coor-

dinate system, and we can separate the v- andX -dependencies in the form

Y. Miura et al. / Surface Science 532–535 (2003) 148–153 149

V ðs; v;X Þ ¼ Vcorðs;X Þ þ Vvibðs; vÞ: ð2ÞTo evaluate the Vcorðs;X Þ, we perform total en-ergy calculations for various configurations of theincident atom H on the D adsorbed Cu(1 1 0)

based on the density functional theory and the

generalized gradient approximation (PW91) for

the exchange correlation energy [22]. The total

energies are computed in a supercell geometry,

using plane waves and pseudopotentials, with the

ab initio density functional code DACAPO [23].

We include three Cu(1 1 0) layers and three vac-uum layers in the supercell. Each layer includes a

(3 2) unit cell, where 3 and 2 Cu atoms areplaced along the [1 �11 0] and [0 0 1] directions, re-spectively. The plane-wave basis set cut off kinetic

energy is 350 [eV]. The surface Brillouin zone

integration is performed using the special point

sampling technique of Monkhorst and Pack [24].

In the V ðs;X Þ, s ¼ þ1 corresponds to the con-figuration of a gas-phase H and a D adsorbed on

a HL-SB site of Cu(1 1 0), s ¼ 0 corresponds tothe configuration of two hydrogen atoms (H and

D) on Cu(1 1 0), and s ¼ �1 corresponds to the

configuration of two hydrogen atoms (H and D)

in the gas-phase. Then, we fit the ab initio PES

results to an analytical functional form. We as-

sume a cosine function and a Gaussian functionfor describing the interaction between a gas-phase

H and a D adsorbed on Cu(1 1 0).

Vcorðs;X Þ ¼ V0ðsÞ þ V1ðsÞ cosð2pX=aÞþ ½V2ðsÞ þ V3ðsÞX 2 expð�X 2Þ; ð3Þ

where a ¼ 2:556 [�AA] is the lattice constant ofCu(1 1 0). The ViðsÞ ði ¼ 0–3Þ are determined sothat the difference to the ab initio PES results on

the average is smaller than 10 [meV]. Here, we giveViðsÞ ði ¼ 0–3Þ as follows:

V0ðsÞ¼a0=coshðb0ðs�c0ÞÞþd0 tanhðe0ðs�f0ÞÞþg0;

V1ðsÞ¼a1=coshðb1ðs�c1ÞÞþd1 coshðe1ðs�f1ÞÞþg1;

V2ðsÞ¼a2=coshðb2ðs�c2ÞÞþd2 tanhðe2ðs�f2ÞÞþg2;

V3ðsÞ¼a3=coshðb3ðs�c3ÞÞþd3 coshðe3ðs�f3ÞÞþg3:

ð4ÞThe fitting parameters ai to gi (i ¼ 0–3) are givenin Table 1.

For Vvibðs; vÞ, we assume a harmonic type po-tential,

Vvibðs; vÞ ¼1

2lxðsÞ2v2; ð5Þ

xðsÞ is given byxðsÞ ¼ �hxgas � dxðtanhðs� s0Þ þ 1Þ; ð6Þwhere �hxgas ¼ 0:443 [eV], and dx ¼ 0:126 [eV].xðsÞ takes on the value of the vibrational fre-quency between an adsorbed D atom and Cu atomat s ¼ þ1, and the vibrational frequency of adesorbing HD at s ¼ �1.The basis set used in the coupled channel cal-

culations is determined by the incident energy

Et ¼ 0:050–1.0 [eV] and the exothermicity of thisreaction (2.5 [eV]). In this case, the calculation

results converge with maximum quantum numbers

m ¼ 75 and n ¼ 8, where m and n are the quantumnumbers for the surface parallel translational

motion and the vibrational motion of product

HD. We carefully checked the convergence for

calculations with maximum quantum number

m ¼ 80, n ¼ 9, respectively.

3. Results and discussion

We calculate the hydrogen abstraction proba-

bilities on Cu(1 1 0) as a function of the surface

normal kinetic energy Et of the incident H. As can

Table 1

The fitting parameters of the analytical functional V ðs;X Þ that represents the ab initio PES resultsai [eV] bi [�AA�1] ci [�AA] di [eV] ei [�AA�1] fi [�AA] gi [eV]

i ¼ 0 )3.82 1.08 1.12 )1.10 0.87 2.26 3.52

i ¼ 1 )1.41 )1.22 0.99 1.35 1.29 1.23 0.00

i ¼ 2 2.03 1.09 1.03 2.37 0.64 0.90 )2.40i ¼ 3 0.90 0.50 )0.30 0.50 3.00 1.80 0.00

150 Y. Miura et al. / Surface Science 532–535 (2003) 148–153

be seen in Fig. 1, the abstraction probabilities

initially increase, then decrease with increasing Et,taking a maximum at Et ¼ 0:20 [eV]. We can saythat increasing Et initially enhances the abstrac-tion. However, an additional increase in Et pre-vents the incident H from abstracting the adsorbed

D. The initial increase in Et < 0:20 [eV] can beattributed to the amplitude of the surface corru-

gation Ecor, which corresponds to the diffusionbarrier for the H trapped on Cu(1 1 0). From the

ab initio PES, Ecor � 0:20 [eV]. When an incidentH collides with the surface, it loses its normal ki-

netic energy (Elose) due to energy transfer fromsurface normal motion to surface parallel motion

as a result of the diffraction. Thus, the incident His trapped normal to the surface, but can move

parallel to the surface with an energy Eloss. (Here,we neglect the energy dissipation to surface pho-

nons.) If Eloss is smaller than Ecor, the incident H isalso trapped parallel to the surface. However, if

Eloss is larger than Ecor, it can move parallel to thesurface. After some time, it may bond with an-

other D adsorbed on the surface, and leave thesurface as a product HD. Therefore, the abstrac-

tion probabilities increase with increasing Et, untilthe incident H has a kinetic energy corresponding

to Ecor. On the other hand, we attribute the de-crease in the abstraction probabilities with in-

creasing Et for Et > 0:20 [eV] to the decrease of theindirect abstraction at high Et. Since the scattering

probabilities increase with increasing Et, the initialtrapping of the incident H on Cu(1 1 0) occurs less

frequently at high Et. This leads to a decrease inthe hydrogen abstraction through the indirect

process. Therefore, we see a decrease in the ab-

straction probabilities with increasing Et in Et >0:2 [eV]. Experiments [4] report that the scatteringprobabilities of the incident H on Cu(1 1 1) do not

increase with increasing Et in the energy range ofEt ¼ 0:07–0.3 [eV]. This means that the abstractionreaction probabilities increase with increasing Et inthis energy range. This kinetic energy dependence

in the experimental results [4] agrees with the ini-

tial increase we observe in Fig. 1 (in the energyrange Et ¼ 0:05–0.2 [eV]).We show the mean vibrational energy hEvibi and

the mean surface parallel translational energy

hEparai as a function of Et in Fig. 2. As can be seenin Fig. 2, for Et > 0:20 [eV], hEvibi and hEparai haveopposite Et dependence, i.e., hEvibi increases withincreasing Et, while hEparai decreases with increas-ing Et. When the hydrogen abstraction occurspredominantly through the indirect process, most

of the energy (large momentum parallel to the

surface) of the diffusing H will eventually be

transferred to the product HD. Therefore, the

decrease of hEparai with increasing Et indicates adecrease in hydrogen abstraction through the

Incident Energy Et [eV]

Abs

trac

tion

Pro

babi

litie

s

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.00.0 0.20.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fig. 1. The hydrogen abstraction probabilities on Cu(1 1 0) as a

function of the surface normal kinetic energies Et of the incidentH.

Mea

n K

inet

ic E

nerg

y of

Pro

duct

HD

[eV

]

Incident Energy Et [eV]

Mean vibrational energyMean surface parallel translational energy

0.8 0.9 1.0

0.5

0.6

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.10.0

0.0 0.70.6

Fig. 2. The mean vibrational energy hEvibi (open-square lines-points) and the mean parallel translational energy hEparai (solid-triangle lines-points) of product HD as a function of the

incident energy Et.

Y. Miura et al. / Surface Science 532–535 (2003) 148–153 151

indirect process. On the other hand, when hydro-

gen abstraction occurs predominantly through the

direct process, the product HD will only have a

small momentum parallel to the surface. The ex-

cess energy coming from the exothermicity (2.5

[eV]) of the reaction is mainly used for the exci-

tation of the vibrational motion of product HD.

Therefore, the increase of hEvibi with increasing Etindicates that hydrogen abstraction preferentially

occurs through the direct process rather than the

indirect process at high Et.We show the vibrational distributions of prod-

uct HD desorbing from Cu(1 1 0) as a function of

Et in Fig. 3. We observe a strong Et dependence ofvibrational distributions. As can be seen in Fig. 3,

hydrogen abstraction probabilities for productHD in the vibrational ground state decrease with

increasing Et. However, hydrogen abstractionprobabilities for product HD in the vibrationally

excited states increase with increasing Et. Thismeans that in hydrogen abstraction, large amounts

of kinetic energies are transferred to the vibra-

tional motion of the product HD, thus exciting the

vibrational state.

4. Summary

In this paper, we investigate the effects of the

kinetic energy of the incident hydrogen atom on

the hydrogen abstraction dynamics on Cu(1 1 0) by

performing quantum dynamics calculations on the

ab initio PES. Our results show that increasing the

kinetic energy of the incident H initially enhances

the abstraction. However, additional increases in

the kinetic energy prevents the incident H from

abstracting the adsorbed D. Furthermore, themean vibrational energy of the product HD hEvibiincreases with increasing Et, while the mean sur-face parallel translational energy of the product

HD hEparai decreases with increasing Et. Theseresults indicate that additional increase in the ki-

netic energy of the incident H enhances the exci-

tation of the vibrational motion, rather than the

surface parallel motion of product HD. We alsoconclude that the hydrogen abstraction preferen-

tially occurs through the direct process, rather

than the indirect process, at high Et.In the present study, we employed an approxi-

mate treatment for the surface-parallel motion

and rotational motion of a hydrogen molecule.

For our future work, we will go beyond this and

also investigate the hydrogen abstraction dynam-ics on more industrially significant metal and

semiconductor surfaces, to obtain a more detailed

understanding for the selectivity of DIRECT/IN-

DIRECT reaction and the energy distribution of

product hydrogen molecules.

Acknowledgements

We thank Dr. Hiroshi Nakanishi for discussions

and comments on this work. This work is partly

supported by the Ministry of Education, Science,

Sports and Culture of Japan through their Grant-

in-Aid for COE Research (10CE2004), Scientific

Research(C) (11640375, 13650026) programs, the

New Energy and Industrial Technology Develop-ment Organisation (NEDO) through the Materials

and Nanotechnology program, the Japan Science

and Technology Corporation (JST) through their

Research and Development Applying Advanced

Computational Science and Technology program,

and the Toyota Motor Corporation through their

Cooperative Research in Advanced Science and

Technology program. Some of the calculationspresented here were done using the computer fa-

cilities of the JST, and the ISSP Supercomputer

Et=0.10 [eV]Et=0.25 [eV]Et=0.50 [eV]Et=0.75 [eV]Et=1.00 [eV]

Vibrational state of product HD

Abs

trac

tion

prob

abili

ties

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0.00 1 2 3 4 5 6

Fig. 3. The vibrational distributions of product HD in the

hydrogen abstraction on Cu(1 1 0) as a function of the incident

energy Et.

152 Y. Miura et al. / Surface Science 532–535 (2003) 148–153

Center (University of Tokyo). Y.M. gratefully

acknowledges Fellowship grant from the JST

through their Research and Development Apply-

ing Advanced Computational Science and Tech-

nology program. W.A.D. acknowledges support

from the Marubun Research Promotion Founda-tion.

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