The ground state geometries of the pure Sc_n (n = 2–8, 13) clusters, which are in good consistence with other theoretical calculations,^[8] are first optimized as shown in Fig. 1. On the basis of the optimized Sc_n geometries, different adsorption sites of CO molecule for determining the different-sized COSc_n isomers, i.e., top site, bridge site, and face site, are taken into account. For all isomers of each cluster, the local minima of the potential energy surface are guaranteed by the harmonic vibrational frequencies without imaginary mode. In addition, the initial structures in different spin states are optimized. Among all of the calculated results, the lowest energy structures of COSc_n isomers (n = 2–8, 13) are chosen and regarded as the ground state structures, which are also plotted in Fig. 1.

Fig. 1.

	Figure Option ViewDownloadNew Window
	Fig. 1. Ground state structures of pure Scn and COScn clusters. The red and gray balls represent O and C atoms, respectively.

All of the ground state structures of COSc_n (n = 2, 3, 4, 6, 8, and 13) complexes are viewed as C atom adsorbed on face position of corresponding Sc_n cluster (except for n = 2). Meanwhile, the O atom prefers to bond with neighboring Sc atoms, covering another face laterally. An important feature of this evolution is that the basic framework of corresponding Sc_n cluster, within the range of n = 2, 3, 4, 6, 8, and 13, is not modified even though CO is adsorbed on the face position. However, essentially structural change occurs at n = 5, 7. One can see that the triangular bipyramid structure of Sc₅ transforms into a square pyramid with C atom nearly in the center of the bottom. Meanwhile, O atom still shows the tendency to unite with other two Sc atoms by occupying the bridge site. Similarly, the adsorption of CO leads to the fundamental alteration of the host Sc₇ cluster, accompanied by the alike adsorption model as n = 5.

Such evolution behaviors are basically similar to those of COY_n complexes,^[16] but different from those of CO on Ni, Pd, Au, and Mn clusters where the C atom of CO tends to occupy the bridge site (Mn, Ni), or top position (Mn, Au, Pd) of corresponding cluster.^[12–15] Apparently, the adsorption model of face site easily makes more Sc atoms bond with C atom, giving rise to the enhancement of adsorption strength.

The adsorption strength between cluster and small molecule can generally be reflected by the adsorption energy which is defined as

Figure 2 shows the plot of the calculated adsorption energy versus cluster size. It is seen that the adsorption energy follows the tendency of oscillational increase in the size range of n = 2–5, exhibiting the largest value of 4.43 eV at n = 5. Then, the variation of this value basically is in the range from 3.8 eV to 3.9 eV at n = 6, 7, 8, and 13. Obviously, the adsorption energies calculated here are significantly larger than those of X_nCO series (X = Mn, Au, Ni, and Pd), in which the values are not beyond 2 eV in most cases.^[12–14] Even though Y_n exhibits favorable performance in the sense of adsorbing CO molecule, the value of adsorption energy is still less than those of COSc_n complexes in most sizes as shown above. Namely, our calculated results suggest that Sc exhibits a bigger value of adsorption energy in regard to adsorbing CO molecule in most sizes than those of other TM clusters.

Fig. 2.

	Figure Option ViewDownloadNew Window
	Fig. 2. Adsorption energies of COScn (n = 2–8, 13) clusters.

A necessary step of analyzing the catalytic ability is to explore the variation of bond length and vibrational frequency of small molecule adsorbed on cluster. Hence, we present the calculated C–O bond lengths and vibrational frequencies of CO for corresponding COSc_n (n = 2–8) clusters in Fig. 3. In comparison with the bond length of 1.142 Å of free CO molecule, the bond length of C–O, when CO is adsorbed on Sc_n cluster, becomes longer in all of the sizes, and the value of elongation are beyond 20% except for n = 2. Specially, the outstanding peak of 1.529 Å at n = 5 indicates that the interaction between C and O is so weak that the C–O bond appears to be faint.

Fig. 3.

	Figure Option ViewDownloadNew Window
	Fig. 3. CO bond lengths (above) and vibrational frequencies (below) of COScn (n = 2–8, 13) clusters.

Such an extension amount is far more than those in CO adsorbed on Mn, Ni, Pd, and Au clusters, in which the C–O bond length is roughly 1.1 Å.^[12–15] It is noted that the variation tendency of bond length of C–O in COY_n complexes is coincident with COSc_n clusters in the same size with the exception of n = 8.^[16] In contrast to the molecular adsorptions of COX_n (X = Mn, Ni, Pd, and Au) complexes, which correspond to a really small elongation of C–O bond length, the adsorption of CO on Sc_n cluster could be regarded as dissociated adsorption according to the size of C–O bond length.

As far as the vibrational frequency is concerned, the calculated results show a trend opposite to the variation of bond length. As displayed in Fig. 3, COSc₂ has the largest value of 1254.51 cm⁻¹ whereas smallest dip is found at n = 5 (717.8 cm⁻¹). In addition to these, an invariable trend of vibrational frequency can be observed in other range, in which the value is almost aconstant of about 1050 cm⁻¹. In fact, all of the C–O vibrational frequencies are evidently smaller than 2096.29 cm⁻¹ of the free CO molecule. Such behaviors imply that a large red shift occurs under the interaction of Sc atoms, and the red shift reaches 50% at least.

According to the discussion above, we easily learn that COSc₅ is in possession of the large adsorption energy and weakened interaction between C and O atom in comparison to the structures of other sizes. This could be attributed to the unusual structure as discussed in Section 1, in which the C atom contributes to bond with four Sc atoms instead of adopting the pattern as done by the structures with other sizes. As is well known, the electronic configuration of an isolated C atom is 2s²2p², which will redistribute to sp³ hybridization to form four equivalent C–Sc bonds as C approaches four Sc atoms. This behavior is actually in favour of the stability of the corresponding cluster. In this case, the O atom has more chances to bond with near Sc atoms to form stronger Sc–O bonds which can be mirrored by the shortest Sc–O bong length as displayed in Table 1, leading to the improvement of the stability of COSc₅ cluster.

The energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) is a commonly used measure of the ability for cluster to undergo activated chemical reactions with small molecule, so we analyze the variation tendencies of the HOMO–LUMO gaps for Sc_n and COSc_n clusters.

Fig. 4.

	Figure Option ViewDownloadNew Window
	Fig. 4. HOMO–LUMO gaps of Scn (small figure) and COScn (n = 2–8, 13) clusters.

First, the change trends of the HOMO–LUMO gaps of Sc_n (n = 2–8, 13) calculated here are in consistence with the outcomes presented in Ref. [8]. It is found that within the calculated range, the HOMO–LUMO gaps for Sc_n maintain the values in a range of about 0.28 eV–0.4 eV in most sizes, with a sharp drop from n = 3 (0.50 eV) to n = 6 (0.21 eV). However, dramatic changes occur due to the adsorbing CO molecule. One can see that the energy gap has a relatively large value (about 1.0276 eV) at n = 2, then it rapidly decreases as the size increases from n = 3. Also, all of the values are less than 0.1 eV in a range of n = 6, 7, 8, and 13, in which a value of local minimum (about 0.0073 eV) is found at n = 7. Smaller energy gap usually means high chemical activity for corresponding cluster, so it is possible for COSc_n clusters to interact with more CO molecules in the relatively larger size.

For exploring the essence of interaction between CO and Sc_n cluster, the partial densities of states (PDOSs) for different size clusters are calculated. Here, the PDOS for COSc_n (n = 3, 5, and 7) are selectedas displayed in Figs. 5–7, respectively.

Fig. 5.

	Figure Option ViewDownloadNew Window
	Fig. 5. Partial densities of states (PDOSs) of COSc3 clusters.

Fig. 6.

	Figure Option ViewDownloadNew Window
	Fig. 6. Partial densities of states (PDOSs) of COSc5 clusters.

Fig. 7.

	Figure Option ViewDownloadNew Window
	Fig. 7. Partial densities of states (PDOSs) of COSc7 clusters.

It is seen that both COSc₃ and COSc₇ have similar features at the lower energy states. Namely, two sharp peaks at the Fermi level can be clearly observed which means that the strong s–p–d overlaps. Besides, the contribution from d state seems to be large near the Fermi level (about −0.01 eV), whereas weak s–p–d overlaps, which is the same characteristic at the higher energy level (about 0.03 eV) for both COSc₃ and COSc₇.

However, distingushing features of three prominent peaks for COSc₅ at the energy levels from −0.15 eV to 0 are observed, showing strong localization of bonding electrons. Generally, more peaks of s–p–d overlaps near the Fermi level always mean the intense interactions between CO and Sc₅ cluster. This resultaccords well with the description of adsorption energy, as well as the exhibition of C–O bond length and vibrational frequency.

The variation of magnetism of Sc_n cluster, derived from the adsorption of CO molecule, is also the interesting topic to be discussed. As we know, Sc_n (n = 2–13) complexes always possess relatively large magnetic moments in certain cluster sizes as shown in Table 1. However, adsorbing CO results in the dramatic decreases in these sizes, even the quenching for n = 2, 4, and 6. This result is adverse to Mn cluster, in which the adsorbed CO molecule enhances the magnetism of pure Mn_n cluster at n = 4, 6–8.^[12] Even though the magnetism of Y_n cluster is weakened due to the adsorption of CO, the COY_n complexes still maitain certain magnetic moments in a few sizes such as n = 3, 6.^[16]

Given this, the analysis of charge transfer, as well as the magnetic ordering of COSc_n complexes is necessary, which is calculated as displayed in Table 1.

In CO–X (X = Ni, Au, Mn, Pd) series, much attention has been paid to the variation of C–O bond which provides sufficient information about the electronic properties of corresponding cluster.^[12–15] However, the interaction between O and X atom (X = Ni, Au, Mn) is regarded as being weak due to the indirect bond between O and X atoms, so the authors insist that O–X (X = Ni, Au, Mn) bond makes almost no contribution to the stability of corresponding cluster. By contrast, Y–O bond has important effects on the stability, electronic properties and magnetism of COY_n clusters. Nevertheless, no comparison can be found between Y–C and Y–O bond.^[16] As is well known, the adsorption behavior of CO on Sc_n cluster is similar to those of COY_n complexes. Then, it is significant to study the interplay between Sc–C and Sc–O, as well as the charge transfer between CO and Sc_n clusters. Here, both the average bond lengths of Sc–C and Sc–O are simultaneously calculated to compare these differences.

Table 1.

Table 1.

Table 1. Values of average bond length of Sc–C and Sc–O (L), Mulliken charge transfer distribution (Q) of the C and O atoms, magnetic moments (M) of Scn, COScn, C, and O atoms. . n L/Å Q/e M/μB Sc–C Sc–O C O Scn COScn C O 2 1.961 2.000 −0.018 −0.482 4 0 0 0 3 2.094 2.088 −0.191 −0.569 1 1 −0.028 −0.015 4 2.009 2.094 −0.149 −0.572 2 0 0 0 5 2.187 2.004 −0.220 −0.607 1 1 −0.028 −0.003 6 2.118 2.114 −0.150 −0.576 2 0 0 0 7 2.119 2.104 −0.141 −0.572 1 1 0 −0.001 8 2.124 2.113 −0.125 −0.576 4 2 −0.006 −0.004 13 2.135 2.113 −0.120 −0.570 19 5 −0.026 −0.006

Table 1. Values of average bond length of Sc–C and Sc–O (L), Mulliken charge transfer distribution (Q) of the C and O atoms, magnetic moments (M) of Scn, COScn, C, and O atoms. .

It could be readily seen that the change of average bond length of Sc–C is closely related to the cluster size, from 1.961 Å at n = 2 to 2.135 Å as n = 13. By contrast, the Sc–O bond in corresponding size seems to be shorter, indicating that the interaction between Sc and O is stronger than that of Sc–C. Specially, the local minimum (2.003 Å), except for n = 2, is observed with n = 5, implying comparatively strengthened interplay occurs between CO and Sc₅ cluster. This is coincident with the exhibition of stability discussed above. In comparison with COY_n clusters, the values of Sc–O are apparently smaller than those of Y–O bonds (2.147 Å–2.169 Å),^[16] which illustrates that the action force between CO and Sc_n clusters is greater than that between the COY_n complexes.

In regard to the charge transfer of COSc_n clusters, we find that both C and O atoms gain electrons in all of the calculated sizes, and the electrons accepted by O atom are more than those by C atom, and the difference between the numbers of accepted electrons is about 0.45e. Obviously, the fact that more electrons are accepted by O atom means the strengthened interaction between O and Sc atoms as comparedwith that between C–Sc bonds. Moreover, the number of electrons accepted by O atom (0.607e) for COSc₅ is the biggest in all of the calculated range, which is in accord with the exhibition of the shortest bond length of Sc–O at n = 5. Such a result is fundamentally different form those from COMn_n, COAu_n series, in which C atom prefers to lose electrons whereas O atom prefers to accept electrons.^[12,13] Although similar charge distributions of C and O atoms in COY_n clusters is also observed,^[16] the accepted electrons of them are less than those of COSc_n series calculated here.

Besides, we perform a detailed investigation of the magnetism of COSc_n series so as to analyze the influence of adsorbing CO on the Sc_n clusters. First, the magnetic moment of pure Sc_n clusteris calculated as shown in Table 1, and the outcomes accord well with the results reported earlier.^[8]

As is well known, the free CO molecule has no magnetic moment. However, adsorbing CO has an effect on the magnetic moments of the Sc_n clusters. One can see that the magnetic moments of bare Sc_n clusters decrease as a whole, along with the exhibition of antidirection magnetic ordering of C and O atoms in certain sizes. For example, the antiferromagnetic moments of C and O atoms (−0.028 μ_B for C, and −0.003 μ_B for O) are found in COSc₅ cluster. It is clear that adsorbing CO tends to weaken the magnetic moments of pure Sc_n clusters, even the quenching for n = 2, 4, and 6.

In general, the magnetic moments of clusters are closely related to the overlap of the orbitals and geometrical symmetry. This is the fact in the COSc_n complexes. One can see that the adsorption of CO molecule lowers the symmetry of corresponding structure of the host Sc_n cluster. Meanwhile, severe interaction between CO and Sc_n cluster contributes to the improvement in the orbital hybridization between them. All of these make Sc atom of corresponding cluster not keep the 3d state localized, which naturally gives rise to the reduction of the magnetic moment in corresponding cluster size.