First-Principle Studies on Adsorption of Cu + and Hydrated Cu + Cations on Clean Si(111) Surface

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1 CHEM. RES. CHINESE UNIVERSITIES 2010, 26(3), First-Principle Studies on Adsorption of Cu + and Hydrated Cu + Cations on Clean Si(111) Surface CHENG Feng-ming 1,2, SHENG Yong-li 1,3, LI Meng-hua 1, LIU Yong-jun 1*, YU Zhang-yu 1 and LIU Cheng-bu 1* 1. School of Chemistry and Chemical Engineering, 2. School of Environmental Science and Engineering, Shandong University, Jinan , P. R. China; 3. School of Chemistry and Chemical Engineering, University of Jinan, Jinan , P. R. China Abstract To study the adsorption behavior of Cu + in aqueous solution on semiconductor surface, the interactions of Cu + and hydrated Cu + cations with the clean Si(111) surface were investigated via hybrid density functional theory(b3lyp) and Møller-Plesset second-order perturbation(mp2) method. The clean Si(111) surface was described with cluster models(si 14 H 17, Si 16 H 20 and Si 22 H 21 ) and a four-silicon layer slab under periodic boundary conditions. Calculation results indicate that the bonding nature of adsorption of Cu + on Si surface can be viewed as partial covalent as well as ionic bonding. The binding energies between hydrated Cu + cations and Si(111) surface are large, suggesting a strong interaction between them. The coordination number of Cu + (H 2 O) n on Si(111) surface was found to be 4. As the number of water molecules is larger than 5, water molecules form a hydrogen bond network. In aqueous solution, Cu + cations will safely attach to the clean Si(111) surface. Keywords Silicon surface; Copper; Ion-solid interaction; Adsorption; Density functional calculation Article ID (2010) Introduction *Corresponding author. yongjunliu_1@sdu.edu.cn; cbliu@sdu.edu.cn Received June 8, 2009; accepted September 14, Supported by the National Natural Science Foundation of China(No ). The noble metal-patterned silicon surfaces have attracted much attention not only for their application in electronics and microelectronics industries but also for fundamental reasons. In the past decades, the chemical and physical properties of noble metal/si interfaces have been extensively studied by means of numerous experimental and theoretical methods. Owing to the chemical non-interactivity of Ag with Si, a well-defined Ag/Si interface can be formed. Cu, Ag and Au are in the same group in the Periodic Table. One might expect that Cu/Si interface should have similar properties of Ag/Si. In fact, the real situation is far from being expected. The reactivity of Cu is so high that Cu silicide can be formed even at room temperature [1,2]. Up to now, the initial stages of Cu/Si interface formation and the diffusion of Cu atom into the silicon bulk, in particular, the detailed understanding of the atomic geometry, electronic structure and chemical bonding of Si/Cu interface have still been to be gained [3 12]. Regarding the metallization of semiconductor surfaces, the mostly used approach is vacuum evaporation or sputtering. This process itself is of great technological importance for the formation of Schottky barrier and ohmic contact in electronic devices. As an alternative to the deposition from vapor phase, many metals can be electrodeposited onto semiconductors from solution. Recently, the electrochemical growth of metals is attracting an increasing interest because, different from other deposition technique, the adjustment of electrochemical potential via electrode potential offers a unique way of controlling the growth and structure of the interface. It is well known that numerous electro and electroless deposition processes are carried out in aqueous solutions, therefore gaining the knowledge of interaction between metal cations and silicon surface at atomic level is vital to understanding the phenomena taking place at the solution/si interface during the deposition processes. However, to our knowledge, theoretical studies on the interaction between hydrated metal cations and dangling bonds of the clean silicon surface is very limited. Very recently, Pakkanen and coworkers [13,14] have studied the adsorption of hydrated Na +, Ag + and Cu + cations onto Cu(111) and Ag(111) surfaces. They found that water molecules play

2 No.3 CHENG Feng-ming et al. 473 different roles in the adsorption of Na +, Cu + and Ag + cations. In our previous papers [15,16], we have studied the adsorption of hydrated Au + and Na + on the clean Si(111) surface using hybrid density functional theory(b3lyp). The bonding nature of the chemical adsorption of Au + on Si surface can be classified as partial covalent as well as ionic bonding, while the interaction between Na + cation and the dangling bonds of Si(111) surface is primarily electrostatic. The covalent bonding nature of these noble monovalent cations can be attributed to their characteristic electronic properties with high electron affinity(ea). These noble metal monovalent cations have much smaller energy gaps(e gap ) between the highest occupied molecular orbital(homo) and the lowest unoccupied molecular orbital(lumo) in comparison with alkali metal monovalent cations. Their LUMOs are composed of s orbitals. The energies of occupied d orbitals are close to those of the s orbitals, while those of virtual p orbitals are high. Therefore the noble metal atoms show a strong orbital interaction between metal and silicon surface. As mentioned above, although Cu, Ag and Au are in the same group in the Periodic Table, they show different chemical reactivities with Si surface. We conjecture that the hydrated Cu + cation may display different behavior of adsorption on the clean Si(111) surface. For comparison, the present work gives a first-principle investigation of the interaction between hydrated Cu + and the clean Si(111) surface. 2 Computational Details The cluster model calculation was carried out via Gaussian 03 program package [17]. The hybrid density functional theory(b3lyp) method using Beck three-parameter nonlocal exchange functional with correction functional of Lee-Yang-Parr was used for geometry optimization [18,19]. It has been shown that B3LYP functional is very useful in studying hydrated Cu + cations [20] and adsorption behavior [21,22]. The Møller-Plesset second-order perturbation(mp2) method was employed for single-point calculation [23]. The effective-core-potential LANL2DZ [24] basis set was used for Si and Cu atoms, and 6-31+G(d) [25] basis set was used for H and O atoms. The effect of the basis set superposition error(bsse) was compensated with the use of counterpoise(cp) correction. Miyoshi et al. [26] have used Si 4 H 7 and Si 7 H 10 cluster models to study the adsorption of Na and Mg atoms on clean Si(111) surface. In our previous paper [15,16,27], we have employed Si 4 H 7 and Si 16 H 20 cluster models to study the adsorption of Au, Ag and Cu atoms on clean Si(111) surface, and used Si 14 H 17 and Si 22 H 21 to model the interaction between hydrated Au + and Na + cations with clean Si(111) surface. Therefore, we will take the similar approach and use Si 14 H 17, Si 16 H 20 and Si 22 H 21 clusters to investigate the adsorption of hydrated Cu + cation on the clean Si(111) surface [15,16]. Their structures are shown in Fig.1. Fig.1 Structures of the cluster models for Si(111) surface[(a) (C)] and slab model for periodic calculation(d) (A) Si 14 H 17 ; (B) Si 16 H 20 ; (C) Si 22 H 21. Si 14 H 17, Si 16 H 20 and Si 22 H 21 clusters were cut from a bulk Si(111) surface. Each surface Si atom has an unpaired electron(dangling bond), and all the other bonds of the Si cluster are terminated with hydrogen atoms. The structures of Si 14 H 17, Si 16 H 20 and Si 22 H 21 clusters were optimized with all the positions of silicon atoms fixed. In addition, the DFT calculation under a periodic boundary condition was performed with the DMol 3 program package. In the DMol 3 method [28 30], the physical wave functions were expanded in terms of accurate numerical basis sets. We used the doublenumeric quality basis set with polarization functions (DNP). The size of DNP basis set is comparable to Gaussian 6-31G**, but DNP is more accurate than Gaussian basis set of the same size. The generalized gradient approximation(gga) with Perdew and Wang (PW91) functional was employed as the exchangecorrelation functional. A periodic surface slab, shown in Fig.1(D), was used to model the clean Si(111) surface. The size

3 474 CHEM. RES. CHINESE UNIVERSITIES Vol.26 parameters of the cell were set to nm nm nm. The slab contains four silicon layers with the lowest layer terminated with hydrogen atoms. In the calculation, all Si atoms and saturating H atoms were fixed. 3 Results and Discussion 3.1 Cluster Model Adsorption of Cu and Cu + In the previous paper [27], we have studied the adsorption of Au, Ag and Cu atoms on the clean Si(111) surface using silicon clusters Si 4 H 7 and Si 16 H 20. Calculation results indicate that the most favorable adsorption site is on-top(t) site. In this work, for the sake of comparison, we examined the adsorption of a Cu atom and a Cu + cation at on-top(t), bridge(b) and hollow(h) adsorption sites, as shown in Fig.2. In the calculations, the adsorbate(cu atom or Cu + cation) was allowed to move only in the direction perpendicular to the Si(111) surface while the geometry parameters of Si(111) moiety were fixed. Since the size of our cluster models and the geometry optimization of the adsorbates is very time-consuming with MP2 method, we first optimized all the structures of Si 14 H 17 -M(M=Cu + or Cu) complexes with B3LYP method and then calculated MP2 energies at the optimal B3LYP geometries. The calculated structural parameters and binding energies(e b ) are shown in Table 1. Fig.2 Adsorption sites considered in this work (A) Bridge site; (B) on-top site; (C) hollow site. Table 1 Results for Si 14 H 17 -M(M=Cu + or Cu) complex by B3LYP and MP2 calculations * Species h e /nm E b /(kj mol 1 ) E cp b /(kj mol 1 ) BSSE ** /(kj mol 1 ) Si 14 H 17 -Cu(T) ( 221.0) 208.2( 177.0) 18.6(44.0) Si 14 H 17 -Cu + (T) ( 173.9) 233.8( 140.3) 7.9(33.6) Si 14 H 17 -Cu(B) ( 178.1) 163.5( 123.0) 19.5(55.1) Si 14 H 17 -Cu + (B) ( 209.0) 256.9( 162.4) 10.7(46.6) Si 16 H 20 -Cu(H) ( 125.5) 128.0( 68.5) 22.6(57.0) Si 16 H 20 -Cu + (H) ( 209.0) 253.1( 160.1) 10.5(48.9) * h e denotes the equilibrium distance between the adsorbate and Si(111) surface calculated by B3LYP method. E b =E tot [E M +E Si(111) ]. The energies include zero-point-energy(zpe) correction and are calculated by B3LYP method. The data in parenthesis are calculated by MP2 method. E cp cp b =E tot [E complex +E Si(111) ]. ** BSSE is the difference between E b and E cp b. As shown in Table 1, the adsorption energies(e b ) between adsorbates(cu and Cu + ) and Si(111) surface are dependent on the adsorption sites. For the adsorption of a Cu atom, the binding energy(e b ) at on-top(t) site( kj/mol for B3LYP result) is larger than those at bridge(b) and hollow(h) absorption sites ( and kj/mol, respectively). It agrees well with our previous calculated results [27]. But the adsorption of a Cu + cation is different from that of Cu atom, i.e., the binding energy(e b ) at on-top site( kj/mol for B3LYP result) is smaller than those at bridge(b) and hollow(h) sites( and kj/mol, respectively). The MP2 results show the same tendency. It is due to the different bonding natures between Cu atom and Cu + cation with the Si surface. The interaction between Cu atom and the dangling bond of surface is covalent [26] while that between Cu + cation with that of Si surface can be viewed as partial covalent as well as ionic bonding. For comparison, the Mulliken population analysis for Cu-Si 14 H 17 and Cu + -Si 14 H 17 at on-top(t) and bridge(b) adsorption sites are listed in Table 2. It is well known that overlap population is a measure of shared electronic density between the two atoms, where large positive value indicates that the atoms in question are bonded and large negative value indicates that the atoms are in an anti-bond state. For the adsorption of a Cu atom at on-top(t) site, the overlap population of Cu-Si 2 bond is as large as This value is even larger than that of the normal Si Si bonds in Si 14 H 17 cluster(0.292), displaying the characteristic of covalent bond between Cu atom and the dangling bond on clean Si(111) surface. But the overlap population of Cu + -Si 2 bond is for

4 No.3 CHENG Feng-ming et al. 475 Cu + -Si 14 H 17 (on-top site), suggesting a minor characteristic of covalent bond between Cu + cation and surface Si atom. We have also noted that the overlap populations for both Cu atom and Cu + cation adsorbed at bridge(b) sites are much smaller than that at on-top site, indicating a weak covalent bond at bridge site. Table 2 Mulliken population analysis of Cu-Si 14 H 17 and Cu + -Si 14 H 17 by B3LYP calculation Species Overlap population * On-top site Bridge site Cu-Si 14 H 17 Cu-Si 2 :0.381 Cu-Si 5 (Si 6 ):0.236 Cu + -Si 14 H 17 Cu + -Si 2 :0.290 Cu + -Si 5 (Si 6 ):0.208 * The overlap population of the normal Si Si bonds in Si 14 H 17 is To further explore the nature of bonding between Cu atom and Cu + cation with Si(111) surface, the frontal orbital interactions of Cu-Si 14 H 17 and Cu + -Si 14 H 17 (on top site) complexes were examined, which are shown in Fig.3. Fig.3(A) indicates that the SOMO(Single occupied molecular orbital) of Cu atom(s orbital) interacts with the SOMO of Si 14 H 17 (p orbital of Si 2 atom), resulting in the formation of a covalent bond between Cu atom and Si 2 atom, which agrees well with the above Mulliken population analysis(table 2). Fig.3(B) shows the orbital hybridization between the LUMO of Cu + cation(s orbital) and the SOMO of Si 14 H 17 (p orbital of Si 2 atom). Thus, Cu + cation has a strong tendency to attract electron clouds from surface Si atom and the interactions between Cu + cation and clean Si(111) surface can be viewed as partial covalent as well as ionic bonding. Fig.3 B3LYP frontier orbitals interaction diagram (A) Si 14 H 17 -Cu; (B) Si 14 H 17 -Cu +. Orbital energies are in ev. HOMO-n denotes the nth HOMO Adsorption of Cu + (H 2 O) n To model the adsorption of Cu + cation in aqueous solution on clean Si(111) surface, we used Si 14 H 17 and Si 22 H 21 cluster models and only considered the adsorption at on-top site to provide the simplest case. The hydrated copper monovalent cations, Cu + (H 2 O) n (n=1 6), have been studied theoretically by Lee and co-workers at B3LYP/6-31+G(d) and MP2/6-31+G(d) levels [31]. The coordination number of Cu + (H 2 O) n was found to be 2. We have taken similar approach and used B3LYP/6-31+G(d) method to optimize the geometries of Cu + (H 2 O) n (n=1 4) complexes. The lowest-energy structures of Cu + (H 2 O) n are in excellent agreement with Kim s results [31]. To obtain the equilibrium geometries of hydrated Cu + cation on the clean Si(111) surface, one to four water molecules were placed around the Cu + cation. Cu + cation was allowed to move only in the direction perpendicular to the Si(111) surface, where no restrictions were placed onto water molecules. For the Si 14 H 17 -Cu + -H 2 O system, we found that the initial position of water molecule had no effect on the final structures since the optimization algorithm derives the same optimal structure even with different initial geometries. The final geometries of Si 14 H 17 - Cu + (H 2 O) n are shown in Fig.4. However, for the systems of Si 14 H 17 -Cu + (H 2 O) n (n=2 4), different initial positions of water molecules resulted in different final structures. For example, Si 14 H 17 -Cu + (H 2 O) 2 has two types of

5 476 CHEM. RES. CHINESE UNIVERSITIES Vol.26 lowerenergy configurations, which are named 1+1 and 2+0(see Fig.4). 1+1 corresponds to one water-water H-bond interaction, while 2+0 corresponds to no H-bond interaction. The latter is 17.6 kj/mol more stable than the former at MP2 level. Similarly, Si 14 H 17 -Cu + (H 2 O) 3 has two types of lower-energy configurations, i.e. 3+0 and 2+1(the case of 1+2 is not shown). Configuration 3+0 is 10.7 kj/mol more stable than configuration 2+1 at MP2 level. For Si 14 H 17 -Cu + (H 2 O) 4, configuration 4+0 is only 2.1 kj/mol(mp2 result) more stable than configuration 3+1. These results imply that the fourth water molecule can either bind directly to Cu + cation or form hydrogen bond with one of water molecules that have already cooperated with Cu + cation. The binding energies of Si 14 H 17 -Cu + (H 2 O) n (n=1 4) are listed in Table 3. Fig.4 Optimized structures of Cu + (H 2 O) n (n=0 4) adsorbed on the Si(111) surface of Si 14 H 17 Cu + -surface lengths are in nm. Table 3 Results for Si 14 H 17 -Cu + (H 2 O) n (n=1 4) (on-top site) by B3LYP and MP2 calculations * Species h e /nm E b /(kj mol 1 ) E b cp /(kj mol 1 ) BSSE ** /(kj mol 1 ) Si 14 H 17 -Cu + (H 2 O) ( 183.6) 182.8( 156.6) 6.3(27.0) Si 14 H 17 -Cu + (H 2 O) 2 (2+0) ( 134.2) 105.8( 130.2) 13.5(4.0) Si 14 H 17 -Cu + (H 2 O) 2 (1+1) ( 175.9) 168.8( 149.2) 1.6(26.7) Si 14 H 17 -Cu + (H 2 O) 3 (3+0) ( 155.1) 102.8( 155.2) 18.6( 0.1) Si 14 H 17 -Cu + (H 2 O) 3 (2+1) ( 131.4) 97.1( 128.6) 11.4(2.8) Si 14 H 17 -Cu + (H 2 O) 4 (4+0) ( 165.4) 94.4( 175.5) 23.2( 10.1) Si 14 H 17 -Cu + (H 2 O) 4 (3+1) ( 142.4) 97.0( 206.2) 27.4( 63.8) * h e denotes the equilibrium distance between the adsorbate and the Si(111) surface calculated by B3LYP method. E b =E tot [E complex +E Si(111) ], where E complex represents the energies of the separately optimized Cu + (H 2 O) n. The energies including zero-point-energy(zpe) correction are calculated by B3LYP method. The data in parentheses are calculated by MP2 method. E cp b =E cp tot [E cp complex +E cp Si(111) ]. ** BSSE is the difference between E b and E cp b. Table 3 shows that MP2 binding energies are larger than B3LYP results. But both of them show the same tendency. Because the binding energies E b and E b cp were calculated by subtracting the energies of Si 14 H 17 and separately optimized Cu + (H 2 O) n complex from the total energy of Si 14 H 17 -Cu + (H 2 O) n system, the binding energy includes the (de)stabilization energy, which results from the change in the optimal geometry of the separately optimized Cu + (H 2 O) n complex when they were brought from infinite separation to the vicinity of the surface. Table 1 and Table 3 show that the adsorption of bare Cu + cation on clean Si(111) surface corresponds to the largest binding energy. The binding energies decrease with increasing the number of water molecules. It implies that the presence of water molecules weakens the interaction between Cu + cation and clean Si(111) surface. To investigate the effect of cluster size on the adsorption of hydrated Cu + on clean Si(111) surface, we used the larger cluster model Si 22 H 21 to describe the Si(111) surface. The optimized structures of Cu + (H 2 O) n (n=0 4) adsorbed on the surface of

6 No.3 CHENG Feng-ming et al. 477 Si 22 H 21 cluster are shown in Fig.5. The binding energies calculated by B3LYP method are listed in Table 4. From Table 4, one can see that the binding energies of Si 22 H 21 -Cu + (H 2 O) n are slightly larger than those of Si 14 H 17 -Cu + (H 2 O) n, suggesting the binding energies are weakly dependent on the size of the clusters. Fig.5 Optimized structures of Cu + (H 2 O) n (n=0 4) adsorbed on the Si(111) surface of Si 22 H 21 Cu + -surface lengths are in nm. Table 4 B3LYP results for Si 22 H 21 -Cu + (H 2 O) n (n=1 4) (on-top site) * Species h e /nm E tot /a.u. E tot CP /a.u. E b /(kj mol 1 ) E b cp /(kj mol 1 ) BSSE ** /(kj mol 1 ) Si 22 H 21 -Cu Si 22 H 21 -Cu + -(H 2 O) Si 22 H 21 -Cu + -(H 2 O) 2 (2+0) Si 22 H 21 -Cu + -(H 2 O) 2 (1+1) Si 22 H 21 -Cu + -(H 2 O) 3 (3+0) Si 22 H 21 -Cu + -(H 2 O) 3 (2+1) Si 22 H 21 -Cu + -(H 2 O) 4 (4+0) Si 22 H 21 -Cu + -(H 2 O) 4 (3+1) * h e denotes the equilibrium distance between the adsorbate and the Si(111) surface. The total energies included zero-point-energy(zpe) correction. Counterpoise(CP) corrected energies. E b = E tot [E complex +E Si(111) ]. E cp b = E cp tot [E cp complex +E cp Si(111) ]. ** BSSE is the difference between E b and E cp b. Fig.5 shows that the adsorbed Cu + (H 2 O) n (n=0 4) ions on the surface of Si 22 H 21 cluster have similar geometries as those on Si 14 H 17 cluster. In particular, they have very similar Cu + -surface distances. It implies that the interaction between Cu + and the dangling bond of surface Si atom plays an important role in the adsorption of Cu + (H 2 O) n on Si(111) surface. Although the magnitude of the binding energies is different in these two cluster models, both the results show the same tendency that the binding energies(e b cp ) become to saturate as the number of water molecules increases. 3.2 Slab Model The adsorption of hydrated Cu + cations on Si(111) surface was also studied via slab model. The optimized structures, total energies and binding energies of Cu + (H 2 O) n (n=1 6) on the clean Si(111) surface are shown in Fig.6, in which the periodic(dmol 3 ) calculation gives the very similar results as those calculated via cluster models: (1) the Cu + (H 2 O) n complexes have the very similar geometries as those on cluster model; (2) the coordination number of Cu + (H 2 O) n was found to be 4, which is in accord with cluster model result(the configurations of 2+0, 3+0, and 4+0 are more stable than those of configurations 1+1, 2+1 and 3+1 respectively); (3) all the binding energies calculated with slab model are larger than those calculated with cluster model, but both of them show the same tendency. We also put five and six water molecules around a Cu + cation. Calculations indicate that the lowest-energy configurations correspond to four water molecules binding directly to the Cu + cation with the Cu + -O(in water) distances

7 478 CHEM. RES. CHINESE UNIVERSITIES Vol.26 smaller than 0.25 nm. The fifth and sixth water molecules are far from the Cu + cation and form hydrogen bonds with one of the four water molecules bound to Cu + cation. Fig.6 Optimized structures of Cu + (H 2 O) n (n=0 6) adsorbed on Si(111) slab surface Total energies(e tot ) are in a.u. and the binding energies(e b ) are in kj/mol. All the energies are zero-point energy(zpe) uncorrected. E b =E tot [E complex +E Si(111) ]. 4 Conclusions The interaction of Cu + and hydrated Cu + with clean Si(111) surfaces were studied via cluster and slab models. Calculation results indicate that the bonding nature of Cu + to Si surface can be viewed as partial covalent as well as ionic bonding. The binding energies between hydrated Cu + cations and clean Si(111) surface are large, suggesting a strong interaction between hydrated Cu + cations and clean Si(111) surface. The coordination number of Cu + (H 2 O) n on the clean Si(111) surface was found to be 4. As the number of water molecules is larger than 5, the water molecules form a hydrogen bond network. In aqueous solution, Cu + cations will safely attach to the clean Si(111) surface. References [1] Daugy E., Mathiez P., Salvan F., et al., Surf. Sci., 1985, 154, 267 [2] Kemmann H., Müller F., Neddermeyer H., Surf. Sci., 1987, 192, 11 [3] Vaz C. A. F., Steinmuller S. J., Moutafis C., et al., Surf. Sci., 2007, 601, 1377 [4] Reitzle A., Renner F. U., Lee T. L., et al., Surf. Sci., 2005, 576, 19 [5] Mutombo P., Cháb V., Surf. Sci., 2003, , 645 [6] Zhang Y. P., Yang L., Lai Y. H., et al., Surf. Sci., 2003, 531, L378 [7] Savchenkov A., Shukrinov P., Mutombo P., et al., Surf. Sci., 2002, , 889 [8] Shukrinov P., Savchenkov A., Mutombo P., et al., Surf. Sci., 2002, 506, 223 [9] Yasue T., Koshikawa T., Jalochowski M., Bauer E., Surf. Sci., 2001, 480, 118 [10] Koshikawa T., Yasue T., Tanaka H., et al., Surf. Sci., 1995, , 506 [11] Yasue T., Koshikawa T., Tanaka H., et al., Surf. Sci., 1993, 287, 1025 [12] Tosch S., Neddermeyer H., Surf. Sci., 1989, 211/212, 133 [13] Karttunen A. J., Rowley R. L., Pakkanen T. A., J. Phys. Chem. B, 2005, 109, [14] Karttunen A. J., Pakkanen T. A., J. Phys. Chem. B, 2006, 110, [15] Liu Y. J., Liu Y., Wang H. L., Surf. Sci., 2007, 601, 1265 [16] Liu Y. J., Wang Z. G., Suo Y. R., J. Phys. Chem. C, 2007, 111, 3427 [17] Frisch M. J., Trucks G. W., Schlegel H. B., et al., Gaussian 03, Revision B.03, Gaussian Inc., Pittsburgh PA, 2003 [18] Becke A. D., J. Chem. Phys., 1993, 98, 5648 [19] Lee C., Yang W., Parr R. G., Phys. Rev. B 1989, 37, 785 [20] Burda J. V., Pavelka M., Šimánek M., J. Mol. Struct.(Theochem.), 2004, 683, 183 [21] Qin W., Li X., Meng X. L., et al., Chem. J. Chinese Universities, 2009, 30(1), 164 [22] Xue Y. B., Tang Z. A., Chem. J. Chinese Universities, 2009, 30(3), 583 [23] Moller C., Plesset M. S., Phys. Rev., 1934, 46, 618 [24] Hay P. J., Wadt W. R., J. Chem. Phys., 1985, 82, 270 [25] Foresman J. B., Frisch A. E., Exploring Chemistry with Electronic Structure Methods, 2nd Ed., Gaussian Inc., Pittsburgh PA, 1995 [26] Miyoshi E., Mori H., Tanaka S., et al., Surf. Sci., 2002, 514, 383 [27] Liu Y. J., Li M. H., Suo Y. R., Surf. Sci., 2006, 600, 5117 [28] Delley B., J. Chem. Phys., 1990, 92, 508 [29] Delley B., J. Phys. Chem., 1996, 100, 6107 [30] Delley B., J. Chem. Phys., 2000, 113, 7756 [31] Lee H. M., Min S. K., Lee E. C., et al., J. Chem. Phys., 2005, 122,