Mechanism of Methanol Synthesis on
Cu(100) and Zn/Cu(100) Surfaces:
Comparative Dipped Adcluster
Model Study∗
HIROSHI NAKATSUJI,1,2 ZHEN-MING HU1,†
1

Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering,
Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
2
Institute for Fundamental Chemistry, 34-4 Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606, Japan
Received 28 July 1999; accepted 29 July 1999

ABSTRACT: The mechanism of methanol synthesis from CO2 and H2 on Cu(100) and
Zn/Cu(100) surfaces was studied using the dipped adcluster model (DAM) combinedwith ab initio Hartree–Fock (HF) and second-order Møller–Plesset (MP2) calculations. On
clean Cu(100) surface, our calculations show that five successive hydrogenations are
involved in the hydrogenation of adsorbed CO2 to methanol, and the intermediates areformate, dioxomethylene, formaldehyde, and methoxy. The rate-limiting step is thehydrogenation of formate to formaldehyde, and the Cu–Cu site is responsible for thereaction on Cu(100). The roles of Zn on Zn/Cu(100) catalyst are to modify the rate-limiting
step of the reaction: to lower the activation energies of this step and to stabilize thedioxomethylene intermediate at the Cu–Zn site. The present comparative results indicatethat the Cu–Zn site is the active site, which cooperates with the Cu–Cu site to catalyze
methanol synthesis on a Cu-based catalyst. Electron transfer from surface to adsorbates is
the most important factor in affecting the reactivity of these surface catalysts. c 2000 John
Wiley & Sons, Inc. Int J Quant Chem 77: 341–349, 2000

Key words: dipped adcluster model; cluster model; methanol synthesis; ab initio
quantum chemical methods and calculations; surface reaction; copper; zinc; carbon
dioxide; hydrogenation; formate∗ Dedicated to Professor Michael C. Zerner in celebration ofhis 60th birthday.
† Present address: Department of Chemistry, Dalhousie University, Halifax, Canada B3H 4J3.
Correspondence to: H. Nakatsuji.
Contract grant sponsors: Japanese Ministry of Education, Science, and Culture; Kyoto University VBL project.

International Journal of Quantum Chemistry, Vol. 77, 341–349 (2000)
c 2000 John Wiley & Sons, Inc.

CCC 0020-7608 / 00 / 010341-09

NAKATSUJI AND HUIntroductionT

he synthesis of methanol from syngas(CO2 /CO/H2 ) on a Cu-based (Cu/ZnO)
catalyst is one of the most extensively studied
industrial processes, since it is promising not onlywith regard to the use of CO2 [1, 2] but also because
methanol is a key material for the synthesis of otherorganic materials, such as formaldehyde, alkyl
halides, and acetic acids. Currently, considerable
attention has been given to clarify the reaction
mechanism and the nature of the active sites on thesurface catalysts [3 – 24], with the aim of identifying
a highly active and selective catalyst for methanol
synthesis.
Although a satisfactory mechanism has not yet
been worked out, it is now accepted that the carbon source for methanol synthesis is exclusively
CO2 [3 – 5], and the reaction occurs as
CO2 + 3H2 → CH3 OH + H2 O.
CO may follow the water–gas shift reaction to regenerate CO2 ,CO + H2 O = CO2 + H2 .
The mechanistic details of methanol formation from
CO2 and H2 are not well understood. It was shownthat the formate species, which is adsorbed at thebridge site with its molecular plane perpendicular
to the metal surface [6 – 9], is a precursor involved in
the methanol synthesis [5, 10]. Since several hydrogenation steps, such as the hydrogenation of CO2 ,formate, and other intermediates, are involved in
the actual reaction process, the identification of theintermediates and the rate-limiting step in this reaction route are the current challenging subjects. To
answer some of these questions, a series of investigations has been performed for methanol synthesis
using the model catalysts such as Cu(100) [11 – 15],
Cu foil [16], Cu(110) [17], and Zn vapor-deposited
copper surfaces [18 – 20]. The advantage of themodel system is that it can give fundamental insighton the mechanism of methanol synthesis in comparison with the real Cu/ZnO catalyst. Burch et al. [10]indicated that dioxomethylene is a possible intermediate, and the critical rate-limiting step in methanol
synthesis is the addition of the first hydrogen atom
to Cu formate. On the other hand, Chorkendorff andco-workers [12, 13] suggested that the hydrogenation of dioxomethylene may be the rate-limiting
step. The hydrogenation of formate and the hydro-

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genation of methoxy are also possible candidates forthe rate-limiting step [13].
Regarding the active sites, early studies suggested that the copper ions (Cun+ ) induced by ZnO
were the active site for methanol synthesis [21]. Recent studies support a model which assumes thatthe active site on the Cu/ZnO catalyst is metallic
Cu, since the activity of the catalyst is directly proportional to the surface area of Cu [11 – 17]. Veryrecently, Nakamura and co-workers carried out aseries of important studies for methanol synthesis on the Zn-deposited copper single-crystal samples [18 – 20]. They found that, when Zn coverageis around 0.2, the Zn-deposited Cu(111) surface ishighly reactive and promotes methanol synthesisby an order of magnitude. The turnover frequencyof methanol with the model catalyst agreed withthat measured on real Cu/ZnO catalyst under thesame reaction conditions [19]. The Cu–Zn site isthen considered to be the active site, though they
once suggested that Cun+ species might be the active site [22 – 24].
Here, we give a comparative summary of our recent studies on the reaction mechanisms and theactive sites of methanol synthesis on both Cu(100)and Zn/Cu(100) catalysts [34 – 36]. The dipped adcluster model (DAM) [25] combined with the ab initio Hartree–Fock (HF) and second-order Møller–
Plesset (MP2) calculations are used. The DAM has
been proposed to study chemisorptions and surface reactions by involving the interactions between
bulk metal and admolecules with consideration of
the electron transfer between them and the image
force correction. It has been successfully applied tothe chemisorption of oxygen on Pd and Ag surfaces [26 – 28] and the mechanisms of the epoxidation and complete oxidation of ethylene [29, 30] andpropylene [31, 32] on a silver surface. A review of
DAM studies has been published recently [33].

Computational Details
A Cu8 (6,2) cluster, which contains six copper
atoms in the first layer and two copper atoms inthe second layer, as shown in Figure 1(a), wasused to model the Cu(100) surface. A Cu7 Zn cluster [Fig. 1(b)] was used to model the Zn/Cu(100)alloy surface. This cluster can model the Cu–Zn
bridge site reasonably and has almost the same sizeas the Cu8 (6,2) cluster: therefore, the results on a
Zn/Cu(100) surface can be compared reasonably
with those on a Cu(100) surface. The DAM [25] wasVOL. 77, NO. 1

MECHANISM OF METHANOL SYNTHESISThe Gaussian basis set for the Cu and Zn atoms
were the (3s2p5d)/[3s2p1d] set and the Ar core
was replaced by the effective core potential [38].
For oxygen and carbon, we used the (9s5p)/[4s2p]
set of Huzinaga–Dunning [39, 40]. For hydrogen,(4s)/[2s] [40] was adopted in HF optimization calculations. In MP2 calculations, the polarization dfunction of α = 1.154 and 0.60 [41] and the polarization p function of α = 1.1 [37] were added tooxygen, carbon, and hydrogen, respectively. Test energetic calculations with the present methodology
gave the results in reasonably good agreement withthe experimental values [34].

DAM vs. Cluster Model for the Study ofCoadsorption of CO2 and H2 and theFormate Formation on Cu(100)

FIGURE 1. Two-layer model clusters used in this study.
(a) Cu8 (6,2) cluster with atoms 1–6 in the first layer and 7
and 8 in the second layer. (b) Cu7 Zn1 (6,2) cluster with
Zn at the bridge position of the first layer.

used to include the effects of the bulk metal, suchas electron transfer between the admolecule andthe surface, and the image force. The calculations
were performed using the highest spin coupling
model [25] and so one-electron transfer from thebulk metal was assumed [28 – 32].
The Langmuir–Hinshelwood (LH) mode, whichcorresponds to the reaction between the coadsorbed
species on the surface, was assumed. The geometries of the reactants, products, and intermediates
were optimized at the HF level, except for the
metal–metal distances, which was fixed at its bulk
lattice values [34 – 36]. The detailed reaction mechanism in the hydrogenation of adsorbed CO2 tomethanol was studied by choosing the appropriate
bridge site reaction coordinates [34]. The electrostatic interaction energy between the adcluster and thebulk metal was estimated by the image force correction [26]. Electron correlations were included by
the MP2 method. The calculations were performed
using the Gaussian 94 software package [37].

Figure 2 shows a comparison between the DAM
and the neutral cluster model for the optimized
geometries and the energy diagrams of the coadsorption of CO2 and H2 and the formate formation on Cu(100). We see that the DAM can describe the coadsorption of CO2 and H2 and theformate formation on Cu(100). First, the DAM describes chemisorbed CO−
2 on a copper surface. In
the chemisorption state, about one (0.76) electron istransferred from the bulk metal into the π ∗ orbitalof CO2 , giving a bent anionic CO−
2 species on thesurface. The C—O and O—Cu bond distances arecalculated to be 1.25 and 2.15 Å, respectively. Mulliken population analysis shows that the net charge
on the adsorbed species is −0.76, and the charge
distribution of the metals is almost unchanged compared with that of the free cluster [34]. In the CO−2adsorbate, this electron transfer causes a large frontier density (spin population) on carbon, while thefrontier densities on other atoms are almost zero.
This large frontier density makes the carbon very
reactive in the adsorption state and lets this carbon
react with other coadsorbate, which is hydrogen.
On the other hand, the Cu8 cluster model cannot
describe the coadsorption of hydrogen and CO2 ona Cu(100) surface. It is 10.2 kcal/mol more unstable,
and the geometry of the CO2 adsorbate is almost
the same as that in the gas phase. If we suppose
the transfer of one electron from the cluster metals
to CO2 , the structure of this CO−
2 becomes similar
to that [Fig. 2(a)] calculated by the DAM, but it is33.8 kcal/mol less stable [34], and the Cu8 clusterside has unnaturally large net charges and frontierdensities. Then, the cluster is quite unstable, which

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NAKATSUJI AND HU

FIGURE 2. Optimized geometries and energy diagrams for the coadsorption of CO2 and H2 , and the formate
formation reaction on clean Cu(100) surface: comparison of the DAM and the neutral cluster model.

explains the large negative adsorption energy forthe chemisorbed CO−
2 on the neutral cluster.
For formate formation step, the DAM calculation
gives the activation energy of 12.3 kcal/mol, whichis in good agreement with the experimental value of
13.3 kcal/mol [14], and this reaction step is exothermic by 40.5 kcal/mol. This means that the reaction
leading to formate species is an easy reaction path,
which is again in agreement with the experimental finding that formate can be easily formed onclean Cu(100) surface [11 – 15]. In contrast, the cluster model gives the activation energy of 44 kcal/mol
and the exothermic energy of 28 kcal/mol, though
the geometries are almost the same for both models.
Thus, the cluster model cannot explain the formation of formate, while the DAM does it in a naturalway.
The above comparative calculations show thatthe electron transfer from the bulk metal to the adsorbates is a key factor for the coadsorption and thereaction of H2 and CO2 on a copper surface. The
transferred electron not only stabilize CO2 adsorbate, but also make the central carbon to be very
reactive, which initiates the series of reactions leading to methanol. Thus, the DAM is essential for

344

theoretical studies of surface reactions in which electron transfer from the bulk metal to adsorbates isimportant. A similar situation was also describedin the study of the roles of oxygen on a silver surface in the olefin partial oxidation reactions studied
previously [27 – 32]. We then use the DAM to study
the reaction mechanism of methanol synthesis on
Cu(100) and Zn/Cu(100) surfaces.

Overall Reaction Mechanism ofMethanol Synthesis on Cu(100)One key purpose of this series of studies is tounderstand the mechanistic details of the series of
the hydrogenation reactions on CO2 to methanol onclean Cu(100) surface. Since it is a very complicatedprocess, we focused on clarifying the reaction intermediates, the transition states, and the energetics of
the important hydrogenation reaction step. We thendetermined the overall reaction mechanism as wellas the rate-limiting step. The most important results
and discussions are summarized in this section, but
the detailed geometries and the energetics of eachelementary step are described elsewhere [34].

VOL. 77, NO. 1

MECHANISM OF METHANOL SYNTHESISFIGURE 3. Reaction energetics for the hydrogenations of CO2 to methanol on clean Cu(100) surface. Numbers inparentheses show the reaction steps given in the text, and the rate-limiting step is indicated by the column.

Figure 3 shows the overall reaction energetics
of methanol synthesis from CO2 and H2 on clean
Cu(100) studied by the DAM combined with theMP2 calculations. The elementary reaction steps on
the surface can be summarized as follows where (g)indicates gas phase and (a) indicates adsorbed state.
H2 (g) → 2H(a),(1)

CO2 (g) → CO2 (a),(2)

CO2 (a) + H(a) → HCOO(a),(3)

HCOO(a) + H(a) → H2 COO(a),(4)

H2 COO(a) + H(a) → H2 CO(a) + OH(a),(5)

H2 CO(a) + H(a) → H3 CO(a),(6)

H3 CO(a) + H(a) → CH3 OH,(7)OH(a) + H(a) → H2 O.

(8)Among these elementary reactions, (3)–(7) constitute the core steps in methanol synthesis as shownin Figure 3. The energy diagram shown in Figure 3
is composed of the energetics of the elementary
reaction steps [34] and gives an intuitive understanding of the reaction pathway. It is noted thatsince the composition of hydrogen varies in thereaction steps, an energy comparison among the different steps may have little meaning, except for theactivation energy. Figure 3 is to provide an overview
of the reaction mechanism in methanol synthesis
based on our theoretical studies [34].
Among the hydrogenation steps, the hydrogenation of adsorbed formate giving adsorbed dioxomethylene, i.e., step (4), is the rate-limiting step,
as shown in Figure 3. The activation energy ofthis step is calculated to be 23.0 kcal/mol, which
is higher than that in other hydrogenation steps.
This step is also endothermic by 17.1 kcal/mol. This
result is consistent with the suggestion based on
experimental findings that the critical rate-limiting
step in methanol synthesis is the addition of thefirst hydrogen atom to adsorbed formate [5, 10,16]. The high-energy barrier and an unstable dioxomethylene intermediate account for the lower activity of a clean copper surface as compared witha Cu-based catalyst in practical methanol synthesis. Dioxomethylene has been suggested to be anintermediate in methanol synthesis [10, 13], butthere is no direct experimental evidence to confirm
this point. Our optimization calculations show that
dioxomethylene is adsorbed on a Cu(100) surface atthe bridge site with its molecular plane perpendicular to the metal surface; i.e., an adsorption geometry
similar to that of formate adsorbed on the surface.

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NAKATSUJI AND HU
Another high-energy barrier (17 kcal/mol) is calculated for step (5), the hydrogenation of adsorbed
dioxomethylene to give formaldehyde, while thisstep is exothermic by 35.7 kcal/mol. Therefore,
step (5) may cooperate with step (4) to be ratelimiting, though the former seems be easier thanthe latter. Experimentally, Chorkendorff and coworkers [12, 13] suggested that step (5) may berate-limiting. On the other hand, the decomposition of dioxomethylene into formate, i.e., the backward reaction, is also favorable: The energy barrieris 5.9 kcal/mol and the reaction is exothermic by
17.1 kcal/mol. One can expect that dioxomethylene
will decompose into formate in the absence of coadsorbed hydrogen. Thus, step (5) is important forachieving a high selectivity in methanol synthesis:
It is more reasonable to say that the formate toformaldehyde reactions [steps (4) and (5)] are therate-limiting steps. Compared with steps (4) and (5),steps (6) and (7) are both easy and rapid, leading toan overall exothermic methanol synthesis.
Our calculations show that chemisorbed CO−
2,formate, dioxomethylene, formaldehyde, andmethoxy are the main intermediates in methanol
synthesis, and Eqs. (3)–(7) provide a reasonable
reaction route leading to methanol formation on a
Cu(100) surface. Surface formate is readily formedby the reaction of adsorbed atomic hydrogen withcoadsorbed CO2 , which exists as a bent anionicCO−
2 species. About one electron is transferredfrom the metal surface to the π ∗ orbital of CO2 ,making the carbon very reactive. Adsorbed formate
is easily synthesized from CO2 and H2 on a Cu(100)surface [10, 14], as has been shown experimentally.
Adsorbed formate has been confirmed to be areaction intermediate by infrared [5, 42] andtemperature programmed desorption (TPD) [43]experiments.

Roles of the Zn–Cu Site in theRate-Limiting Step: Comparison
with Cu(100)As shown above, the rate-limiting step inmethanol synthesis is clarified to be the steps (4)and (5). Figure 4 shows the energy diagrams ofthese steps on a Zn/Cu(100) alloy surface in comparison with those on a clean Cu(100) surface: thehydrogenation of formate to dioxomethylene involving transition state 2 (TS2) and the hydrogenation of dioxomethylene to formaldehyde involving
TS3. The Cu–Cu site of the Cu(100) catalyst and the346

Cu–Zn site of the Zn/Cu(100) catalyst are both responsible for these reaction steps, and the reaction
mechanisms are essentially the same and comparative between the two catalyst surfaces [35].
The differences between the two energy diagrams are evident. On a Cu(100) catalyst, the activation energy of step (4) was calculated to be
23 kcal/mol, and the dioxomethylene is endothermic by 17.1 kcal/mol. The next step [step (5)]has an activation energy of 17 kcal/mol. The experimental activation energy for the hydrogenation of formate on a Cu(100) surface was reported
to be 19.6 kcal/mol [15]. The relatively large energy barriers in steps (4) and (5) and an unstable dioxomethylene intermediate at the Cu–Cu site
indicate a slow reaction rate and explain low activity of the clean Cu(100) catalyst. On the other
hand, on the Zn/Cu(100) catalyst, the activation energy of step (4) was calculated to be 8.5 kcal/mol,and it is exothermic by 2.7 kcal/mol. The dioxomethylene intermediate formed at the Cu–Zn site
is 7.4 kcal/mol more stable than that at the Cu–
Cu site. Formate on the Cu–Cu site migrates onto
the Cu–Zn site to pass through the lower activation
barrier leading to dioxomethylene. The activationenergy of step (5) at the Cu–Zn site is 11.5 kcal/mol,which is again lower than 17 kcal/mol for thesame reaction at the Cu–Cu site. All these results
indicate that the Cu–Zn site on a Zn/Cu(100) catalyst cooperates with the Cu–Cu site to make thereaction easier and works as the active site forthe hydrogenation of formate to formaldehyde, therate-limiting step in methanol synthesis.
Another interesting feature of the results is thatthe formate and the formaldehyde species adsorbed
at the Cu–Zn site are calculated to be less stable thanthat at the Cu–Cu site. Since the adsorbates prefer tooccupy the most stable site on the surface, most ofthem will be adsorbed at the Cu–Cu site. The Cu–Cu
site should play an important role in formate formation and in the reaction process of formaldehyde tomethanol product. Indeed, these reaction steps arepreviously calculated to proceed much easier than
the rate-limiting step on clean Cu(100) surface [34].
The above results provide a clear understandable
reaction mechanism for methanol synthesis on the
Zn-deposited copper catalysts. CO2 reacts with hydrogen on the catalysts to produce the adsorbed formate intermediate. Formate adsorbed at the Cu–Cu
site can be hydrogenated into dioxomethylene witha relatively higher activation energy. On the Zndeposited copper catalyst, the Cu–Zn alloy sites areformed by substitution of Zn atoms with the Cu

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MECHANISM OF METHANOL SYNTHESISFIGURE 4. Energy diagram for the rate-limiting hydrogenation steps (4) and (5) on the model Zn/Cu(100) alloy
catalyst (solid line) and on the model Cu(100) clean catalyst (dashed line).

surface atoms as confirmed by the experimental
scanning tunneling microscopy (STM) images [44].
Since dioxomethylene intermediate at the Cu–Znsite is more stable and reactive than that on theCu–Cu site, formate on the Cu–Cu site will migrate onto the Cu–Zn site and is hydrogenated into
dioxomethylene via a lower transition state. The
hydrogenation of dioxomethylene to formaldehyde
will proceed mainly at the Cu–Zn site because of
the existence of a low-energy path. The formaldehyde product at the Cu–Zn site will then migrateback to the Cu–Cu site due to a larger stability. As aresult, both the Cu–Zn and Cu–Cu sites are important, and they cooperate with each other to realize
high reactivity in methanol synthesis. The Cu–Znsite provides an active site for the rate-limiting stepand hence enhance the activity of the catalysts.
As pointed out in a previous study [34], a key toenhance the overall reactivity in methanol synthesis is to design the catalyst which stabilizes thedioxomethylene intermediate and works to lower
the energy barrier in the hydrogenation of formate.
The Cu–Zn site on the Zn-deposited copper catalyst
plays just such a role and explains the high reactivity reported experimentally [18 – 20].
The electronic origin of the higher reactivity of
Zn/Cu(100) catalyst as compared with Cu(100) catalyst is explained from the difference in the electronic properties of Zn and Cu. Since all the ad-sorbates are the electron-withdrawing species, thecharge-transfer ability of the catalyst appears to be
the main factor in affecting the reactivity. The Zn
atom of the Zn/Cu(100) catalyst shows different
electronic state from the Cu atoms: Though Cu isin a neutral metallic state, the Zn atom is almostin the ionic Zn+ state. Therefore, Zn acts as an electron source and modifies the electronic properties of
the catalyst to realize a larger charge-transfer ability. Our calculation shows that in the rate-limiting
step, the adsorbates have larger negative charges on
the Zn–Cu site than on the Cu–Cu site [35]. Thisconfirms that the Zn-deposited copper catalyst haslarger charge-transfer ability and affects the reactivity of the catalysts toward methanol synthesis byaffecting the most significant rate-limiting reaction
steps (4) and (5). The facts that the promoter modifies the electronic properties of the metal surface
and hence affect the reactivity have been reported
for the reactions of S2 and O2 with metallic Cu
and Cu/ZnO by Rodriguez et al. [45, 46]. It is also
noteworthy that, in the rate-limiting reaction step,
the O—Zn bond distance is calculated to be shorter
than the O—Cu bond distance. The O–Zn interaction is then stronger than the O–Cu interaction,
another difference of the Zn/Cu(100) catalyst incomparison with the Cu(100) catalyst. More details
about the geometries and the electronic properties

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NAKATSUJI AND HU
of the reaction species on the Zn/Cu(100) catalyst
will be described elsewhere [36].

Conclusions
The reaction mechanism and the active sites formethanol synthesis from CO2 and H2 on Cu(100)and Zn/Cu(100) surfaces are clarified by using
the dipped adcluster model (DAM) combined withab initio HF and MP2 calculations.
On clean Cu(100) surface, our calculations showthat five successive hydrogenations are involved in
the course of the methanol synthesis from CO2 andH2 : The intermediates are formate, dioxomethylene,
formaldehyde, and methoxy. The rate-limiting stepis the hydrogenation of adsorbed formate leading toformaldehyde with dioxomethylene intermediate,
and the Cu–Cu site is responsible for the reaction
on Cu(100).
The effects of Zn on a Zn/Cu(100) catalyst are tomodify the rate-limiting step of the reaction, and theroles are twofold: One is to lower the activation energies of the hydrogenation reactions of formate anddioxomethylene, and another is to stabilize the dioxomethylene intermediate at the Cu–Zn site. The roleof the Cu–Zn site is then to enhance the reactivity of
the adsorbed formate and dioxomethylene species,
and then acts as an active site in methanol synthesis.
The formate and formaldehyde species at the Cu–
Cu site are more stable than that at the Cu–Zn site.
Except for the rate-limiting step, other reaction stepsof methanol synthesis would proceed on the Cu–Cu
site. Therefore, for overall methanol synthesis both
Cu–Zn and Cu–Cu sites are important and cooperate for smooth overall progress of the series of thereactions.
Electron transfer is an important key feature inthis catalytic reaction processes. The DAM is thenan appropriate model. All the adsorbates are anionic on the surface, and the role of Zn is to modify
the electronic properties of the Zn/Cu(100) catalyst
so as to realize larger electron transfers. This is themain factor which is responsible for the high reactivity of the formate and dioxomethylene on a
Zn/Cu(100) catalyst.
ACKNOWLEDGMENTS
We celebrate the 60th birthday of Professor
Michael C. Zerner who has made pioneering studies
in many different fields of chemistry, in particular,
excited-state chemistry, biological chemistry, and348

catalytic chemistry which are the fields in which wehave long shared common interests and exchanged
our sciences. Some of the calculations of this study
were performed using the computers at the Institute for Molecular Science. Part of this study was
supported by a Grant-in-Aid for Scientific Researchfrom the Japanese Ministry of Education, Science,and Culture and by a grant from the Kyoto University VBL project.

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