Platinum clusters on vacancy-type defects of nanometer-sized graphene patches.

Density functional theory calculations found that spin density distributions of platinum clusters adsorbed on nanometer-size defective graphene patches with zigzag edges deviate strongly from those in the corresponding bare clusters, due to strong Pt-C interactions. In contrast, platinum clusters on the pristine patch have spin density distributions similar to the bare cases. The different spin density distributions come from whether underlying carbon atoms have radical characters or not. In the pristine patch, center carbon atoms do not have spin densities, and they cannot influence radical characters of the absorbed cluster. In contrast, radical characters appear on the defective sites, and thus spin density distributions of the adsorbed clusters are modulated by the Pt-C interactions. Consequently, characters of platinum clusters adsorbed on the sp² surface can be changed by introducing vacancy-type defects.

1. Introduction

Graphitic carbon materials serve as a support material [1] for anode catalysts such as n class="Chemical">platinum clusters in proton exchange membrane (PEM) fuel cells [2,3,4,5,6,7,8,9]. The supported Pt clusters catalyze the activation of hydrogen molecules to form protons and electrons on the anode of fuel cells. Consequently, the size of Pt clusters is a crucial parameter in determining their catalytic activity. Actually, clusters of less than 3 nm are more effective for catalyzing the H2 dissociation [9]. During the catalytic reactions, adjacent clusters tend to coalescence, forming larger clusters. Accordingly, their catalytic activity decreases as the reaction proceeds. To retain the catalytic activity of supported Pt catalysts, a plausible approach is to strengthen interactions between Pt clusters and underlying carbon sp2 surface.

To come up with a strategy for constructing carbon supports suitable for n class="Chemical">Pt catalysts, computational simulations are becoming a powerful tool [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. Several computational studies suggest that disrupting the sp2 surface by introducing defects (vacancy-type and Stone-Wales type) [9,18,21,25,26,29,30,31], dopants (nitrogen or boron impurities) [14,15,16], and mechanical strain [25] can enhance the interactions with Pt clusters. With respect to the formation of the vacancy-type defects, recent high-resolution transmission electron microscopy (TEM) studies [32,33,34,35] show that electron irradiation of graphene creates vacancy-type defects by removing a few carbon atoms from the surface. After these events, unsaturated carbon atoms are generated. Some of the unsaturated atoms make a covalent bond with an adjacent atom to form a five-membered ring, whereas the others remain two-coordinated. These carbon atoms, which cannot be seen in pristine graphene, are more chemically reactive, and thus they serve as sites for strong adsorption of Pt clusters. Reactive carbon atoms can be also found on edges of zigzag-nanoribbons and zigzag-graphene patches, because their frontier orbital coefficients are located on edge carbon atoms [36,37,38,39,40,41,42]. Thus, one can utilize such reactive edge atoms to trap well Pt clusters [22,27]. Previously, we investigated by means of density functional theory (DFT) calculations how a Pt cluster is bound to the nanometer-size rhombic sp2 patch with zigzag-edges (C96H26) (Figure 1) [22]. Such H-terminated sp2 patches are contained in activated carbons as condensed-aromatic-ring fractions [43]. The DFT calculations found that a Pt6 cluster preferentially binds into edge atoms of C96H26 rather than into center atoms. In fact, the Pt6 additions to edge atoms were about 50 kcal/mol more stable than those to center atoms [22].

Figure 1

Optimized structure for C96H26graphene patch.

Another interesting feature of nanometer-size graphenes is that they have radical character in the ground state, depending on their shape and size [44,45,46,47,48,49,50,51]. Thus, we assume that interactions between a n class="Chemical">Pt cluster and a radical sp2 patch can modulate the catalytic activity of the supported cluster due to the onset of unpaired electrons on Pt atoms. Based on the assumption, the current study will focus on whether spin states of C96H26 support have a power to influence the properties of the adsorbed Pt clusters. Furthermore, we are interested in how introduction of vacancy-type defects on the radical C96H26 support changes the electronic properties of the surface. These changes would have an impact on determining the properties of Pt clusters adsorbed on the sp2 support. To increase our understanding of the interactions between a radical sp2 support and a Pt cluster, we performed density functional theory (DFT) calculations. The main aim in the current DFT study is to clarify how different electronic properties of C96H26 support with or without vacancy-type defects influence the interactions with Pt clusters, and concomitantly the properties of the absorbed clusters.

2. Results and Discussion

2.1. Platinum Clusters on C96H26 in the Triplet State

To obtain a basic insight on how different spin states of n class="Chemical">C96H26 patch affect the interactions with Pt clusters, we investigated how Pt6 clusters bind into the sp2 surface. Following the previous study [22], two types of Pt6 cluster were considered, denoted by (i) and (ii) in Figure 2. The DFT calculations found that their triplet states are energetically stable relative to the corresponding singlet states. The stability of spin-polarized states in Pt clusters was also reported by other groups [52,53,54]. We obtained three optimized geometries for Pt6(i) or Pt6(ii) clusters adsorbed on C96H26 (Pt6-C96H26) in the singlet and triplet states. Within the three optimized geometries in Figure 3, one is that the Pt6(i) cluster makes four Pt-C bonds with the sp2 surface, and the other two are distinguished by whether the number of Pt-C bonds formed between the Pt6(ii) cluster and the surface is 2 or 4. In these geometries, optimized lengths of Pt-C bonds range from 2.288 to 2.334 Å.

Figure 2

Optimized structures for bare Pt6 cluster, and their spin density distributions. Isosurface α- and β-spins are given by pink and blue, respectively.

Figure 3

Spin density distributions of optimized C96H26 and Pt6-C96H26 configurations in the triplet state. Parts of the optimized geometries, corresponding to the region surrounded by pink hashed lines in Figure 1, are given. Isosurface α- and β-spins are given by pink and blue, respectively. Optimized bond lengths are in Å.

We estimated in Table 1 the energy difference between the triplet and singlet spin states in each configuration, ΔEstate(n class="Chemical">Pt6-C96H26), defined as [Etotal(triplet state) – E(singlet state)] where Etotal(triplet state) or Etotal(singlet state) is the total energy in each state. As shown in Table 1, the three configurations have negative ΔEstate(Pt6-C96H26) values. These negative ΔEstate(Pt6-C96H26) values indicate that the triplet state of a Pt6-C96H26 configuration is energetically favorable relative to the singlet state, irrespective of the cluster shapes. Furthermore, we see from Table 1 more significant ΔEstate values in the Pt6-C96H26 configurations than those in the bare Pt6 clusters. Thus, the Pt-C interactions influence relative stability of the triplet to singlet states of the Pt6 clusters.

Table 1

Energy difference between the singlet and triplet states in Pt6-C96H26 (ΔEstate in kcal/mol) a.

	Pt6(i)	Pt6(ii)-(1)	Pt6(ii)-(2)
Bare clusters	–14.5	–5.4	–5.4
Clusters on C96H26	–31.4	–23.6	–22.1

a ΔEstate(Pt6-C96H26) = Etotal(triplet state) – Etotal(singlet state). Negative ΔEstate values indicate that the triplet state of a Pt6-C96H26 configuration is energetically stable relative to the singlet state.

Spin density distributions in the triplet n class="Chemical">Pt6-C96H26 structures are also displayed in Figure 3, where isosurface α- and β-spins are given by pink and blue, respectively. As shown in Figure 3, the Pt-C interactions induce spin densities on C96H26, although the stable triplet state of pristine C96H26 has radical characters only on edge carbon atoms. Likewise, we see spin densities on the adsorbed Pt cluster in the configurations. Basically their spin density distributions are similar to those in the bare Pt6 clusters (Figure 2), but spin densities slightly decrease on Pt atoms that participates the Pt-C bond formation. The similarity between Pt clusters with and without the carbon support is understandable, because underlying carbon atoms do not have radical characters in pristine C96H26 in the stable triplet state, and thus they cannot perturb the spin density distributions of Pt clusters even though they interact substantially.

Spin density distributions of on class="Chemical">ptimized C96H26 and Pt6-C96H26 configurations in the triplet state. Parts of the optimized geometries, corresponding to the region surrounded by pink hashed lines in Figure 1, are given. Isosurface α- and β-spins are given by pink and blue, respectively. Optimized bond lengths are in Å.

2.2. Vacancy-Type Defects Formed by Removing Carbon Atoms from C96H26

Prior to discussing Pt clusters adsorbed on the n class="Gene">sp2 surface with vacancy-type defects, we look at how introduction of a vacancy-type defect on C96H26 changes its electronic structures. In this study, we considered the number (n) of carbon atoms removed from C96H26, ranging from 1 to 3. Removed carbon atoms are colored in Figure 4. First, we constructed mono-, di-, and tri-vacancy defects by removing the green atom, the green and blue atoms, and the three colored atoms, respectively. The vacancy-type defects will be denoted by C96–H26. Using the initial geometries, we obtained optimized structures for the vacancy-type defects in the triple and singlet states. Then, the energy difference between the two spin states was evaluated in each vacancy-type defect, given as ΔEstate(C96–H26) in Table 2. We can see from Table 2 negative ΔEstate(C96–H26) values irrespective of the number of carbon atoms removed from C96H26. The negative ΔEstate(C96–H26) values indicate that each C96–H26 has energetically stable triplet state.

Figure 4

Vacancy type defects (C96–H26), constructed by removing a few carbon atoms from C96H26 where n ranges from 1 to 3. Parts of the optimized geometries, corresponding to the region surrounded by pink hashed lines in Figure 1, are given. Optimized bond lengths are given in Å. Their spin density distributions in the triplet state are also given. Isosurface α- and β-spins are given by pink and blue, respectively.

Table 2

Energy difference between the singlet and triplet states in C96-H26 (ΔEstate in kcal/mol) a.

	N
	0	1	2	3
ΔEstate	-12.8	–14.0	–14.8	–31.4

a ΔEstate(C96–H26) = Etotal(triplet state) – Etotal(singlet state). Negative ΔEstate values indicate that the triplet state of a C96–H26 configuration is energetically stable relative to the singlet state.

Vacancy type defects (C96–n class="Chemical">H26), constructed by removing a few carbon atoms from C96H26 where n ranges from 1 to 3. Parts of the optimized geometries, corresponding to the region surrounded by pink hashed lines in Figure 1, are given. Optimized bond lengths are given in Å. Their spin density distributions in the triplet state are also given. Isosurface α- and β-spins are given by pink and blue, respectively.

Figure 4 also displays their optimized structures in the triplet state as well as corresponding n class="Gene">spin density distributions. As shown in Figure 4, all optimized structures for the vacancy-type defects have some five-membered rings formed by connecting two orange atoms. There is one five-member ring in the mono-vacancy defect (C95H26), while there are two five-member rings in the other vacancy-defects (C94H26 and C93H26). Besides, removing odd-numbered carbon atoms from C96H26 generates one coordinatively unsaturated carbon atom, given by red in Figure 4. In fact, they are bound to only two neighboring atoms. The presence of vacancy-type defects perturbs significantly spin density distributions of pristine C96H26. As displayed in Figure 4, we can see radical carbon atoms around defective sites. In particular, significant spin densities were found in the tri-vacancy defect site. More interestingly, we found that the structural features of the defects have a correlation with how spin densities are distributed. On the unsaturated (red) atoms in the mono- and tri-vacancy-defects, spin densities are distributed on the carbon plane, which come from non-bonding orbitals. In contrast, spin densities on the orange atoms, which are a part of five-membered rings, are found perpendicular to the plane. The onset of radical carbon atoms at the center of the patch differentiates the defective surfaces from the pristine in terms of the interactions with Pt clusters, as will be mentioned below.

2.3. Platinum Clusters on Vacancy-Type Defects (C96H26) Depending on Spin States

2.3.1. Singlet State

Despite the preferences of the triplet state of C96–H26 over the singlet state, let us first use the singlet state to increase our understanding of how a n class="Chemical">Pt cluster interacts with a defective site on the sp2 surface. Following the previous study on interactions between a Pt6 cluster and pristine C96H26, we have a special interest on how the presence of a vacancy-type defect of the patch affects the interactions with a Pt6 cluster. In addition, we will discuss dependences of the interaction energies on size of clusters whose number of contained Pt atoms (k) being smaller than 6. Figure 5–Figure 7 show optimized structures for a Pt6 cluster adsorbed on the mono-, di-, and tri-vacancy-type defects, respectively.

Figure 5

Optimized geometries for Pt6 cluster on the mono-vacancy-type defect in the singlet state (Pt6-C95H26). Optimized bond lengths are given in Table 3.

Figure 7

Optimized geometries for Pt6 cluster on the tri-vacancy-type defect in the triplet state (Pt6-C93H26). Optimized bond lengths are given in Table 5.

Several modes for the cluster bindings were considered. For example, we obtained six optimized geometries for a n class="Chemical">Pt6 cluster binding into the mono-vacancy-type defect in Figure 5. The four Pt6-C95H26 structures displayed in Figure 5 are relatively stable in energy. In general, stable Pt-C95H26 structures have a Pt-1 moiety contained in stable Pt-1-C95H26 structures. Of course, there are other possibilities for Pt binding modes. However, our computational resource is limited, reluctantly we did not obtain other optimized geometries. We evaluated the binding energy in each configuration defined as [Ebind = Etotal(Pt-C96–H26) – Etotal(C96–H26) – Etotal(Pt)], where k ranges from 1 to 6 (Table 3–Table 8).

Table 3

Key parameters of Pt on mono-vacancy defect (C95H26) (k is 1 or 6) in Figure 5. Separations of a Pt atom from orange atoms (Pt-C(orange)) and those from the red atom (Pt-C(red)). Separations of carbon atoms from a Pt atom except for the nearest Pt atom (other Pt-C), and those between the two orange atoms (C-C). Bond lengths are in Å. The Ebind and ΔE(Pt) values are given in kcal/mol. Their definition was given in the text.

	E bind	Pt-C(orange)	Pt-C(red)	other Pt-C	C-C Bond	ΔE(Ptk)
Pt1	–145.7	1.953, 1.954	1.942	––	2.764	––
Pt6(i)-(A)	–152.0	1.986, 1.988	1.968	––	2.745	4.2
Pt6(i)-(B)	–146.6	1.947, 1.968	1.958	2.215	2.768	16.8
Pt6(ii)-(C)	–151.6	1.980, 1.981	1.991	2.074	2.728	17.4
Pt6(ii)-(D)	–157.1	1.983, 1.983	2.010	2.114	2.729	8.1
Pt6(ii)-(E)	–136.7	1.978, 1.976	1.991	2.200, 2.083, 2.252	2.803	15.3
Pt6(ii)-(F)	–143.4	1.986, 1.977	1.982	2.113	2.740	6.3

Table 8

Key parameters of Pt on tri-vacancy defect (C93H26) (k = 2 ~ 5) in Figure 10. Separations of a Pt atom from orange atoms (Pt-C(orange)) and those from the red atom (Pt-C(red)). Separations of carbon atoms from a Pt atom except for the nearest Pt atom (other Pt-C), and those between the two orange atoms (C-C). Bond lengths are in Å. The Ebind and ΔE(Pt) values are given in kcal/mol. Their definition was given in the text.

	E bind	Pt-C(orange)	Pt-C(red)	other Pt-C	C--C Bond	ΔE(Ptk)
Pt2-(A)	–172.3	1.944, 1.968, 1.988, 1.950	2.038	––	2.839, 2.852	22.0
Pt2-(B)	–132.0	2.002, 1.985	2.009	2.021	2.874, 1.630	8.3
Pt3	–167.5	1.948, 1.964, 1.989, 2.124	2.021	2.067	2.999, 2.832	9.8
Pt4	–180.3	1.978, 2.068, 1.973, 1.981	2.046	2.050	2.897, 2.704	3.6
Pt5	–173.0	1.950, 1.976, 1.934, 1.997	2.099	––	2.840, 2.750	13.9

Table 4

Key parameters of Pt on di-vacancy defect (C94H26) (k is 1 or 6) in Figure 6. Separations of a Pt atom from orange atoms (Pt-C(orange)), those of carbon atoms from a Pt atom except for the nearest Pt atom (other Pt-C), and those between the two orange atoms (C-C). Bond lengths are in Å. The Ebind and ΔE(Pt) values are given in kcal/mol.

	E bind	Pt-C(orange)	other Pt-C	C-C Bond	ΔE(Ptk)
Pt1	–106.1	1.999, 1.985, 1.999, 1.985	––	2.846, 2.846	––
Pt6(i)-(A)	–106.7	2.010, 2.001, 2.091, 2.117	2.088,2.033	2.810, 2.940	12.7
Pt6(i)-(B)	–106.3	2.014, 2.101, 2.109, 2.008	2.087,2.108	2.918, 2.921	14.8
Pt6(ii)-(C)	–94.5	2.014, 2.119, 2.088, 2.005	2.206,2.314, 2.084, 2.119	2.928, 2.921	17.3
Pt6(ii)-(D)	–85.1	1.994, 2.021, 2.036, 2.114	2.040	2.836, 2.941	17.9

Figure 6

Optimized geometries for Pt6 cluster on the di-vacancy-type defect in the singlet state (Pt6-C94H26). Optimized bond lengths are given in Table 4.

Table 5

Key parameters of Pt on tri-vacancy defect (C93H26) (k is 1 or 6) in Figure 7. Separations of a Pt atom from orange atoms (Pt-C(orange)) and those from the red atom (Pt-C(red)). Separations of carbon atoms from a Pt atom except for the nearest Pt atom (other Pt-C), and those between the two orange atoms (C-C). Bond lengths are in Å. The Ebind and ΔE(Pt) values are given in kcal/mol.

	E bind	Pt-C(orange)	Pt-C(red)	other Pt-C	C-C Bond	ΔE (Ptk)
Pt1	–162.6	2.114, 2.333, 2.097, 2.641	2.059	––	2.637, 2.641	––
Pt6(i)-(A)	–198.2	1.992, 1.959, 1.971, 1.969	2.105	2.054	2.753, 2.830	12.2
Pt6(i)-(B)	–193.4	2.006, 1.988, 1.974, 1.938	2.144	2.130	2.825, 2.746	5.9
Pt6(ii)-(C)	–188.4	1.971, 2.081, 1.970, 1.969	2.046	2.378, 2.217, 2.107	2.924, 2.922	20.0
Pt6(ii)-(D)	–142.0	2.006, 2.015	2.021	2.130, 2.231	2.710	17.9

Corresponding optimized structures for the smaller Pt clusters adsorbed (k = 2, 3, 4, and 5) are also displayed in Figure 8–Figure 10.

Figure 8

Optimized geometries for Pt cluster (k = 2~5) on the mono-vacancy-type defect in the singlet state (Pt-C95H26). Optimized bond lengths are given in Table 6.

Figure 10

Optimized geometries for Pt cluster (k = 2~5) on the tri-vacancy-type defect in the singlet state (Pt-C93H26). Optimized bond lengths are given in Table 8.

Table 6

Key parameters of Pt on mono-vacancy defect (C95H26) (k = 2 ~ 5) in Figure 8.

	E bind	Pt-C(orange)	Pt-C(red)	other Pt-C	C-C Bond	ΔE(Ptk)
Pt2-(A)	–131.7	1.964, 2.006	1.969	––	2.755	29.6
Pt2-(B)	–146.1	1.965, 1.965	1.942	––	2.743	9.0
Pt3-(A)	–132.4	1.971, 1.972	1.971	––	2.715	0.9
Pt3-(B)	–126.9	1.952, 1.976	1.962	––	2.790	2.5
Pt4(ii)-(A)	–139.7	1.983, 1.984	1.967	––	2.759	7.4
Pt4(ii)-(B)	–140.0	1.981, 1.987	1.987	2.054	2.743	7.4
Pt4(i)	–128.3	1.953, 1.966	1.960	2.227	2.757	19.8
Pt5(ii)-(A)	–140.5	1.976, 1.976	1.980	––	2.753	4.3
Pt5(ii)-(B)	–147.8	1.982, 1.982	2.002	2.105	2.741	5.4
Pt5(i)	–132.4	1.947, 1.966	1.972	2.211, 2.275	2.790	4.6

Table 7

Key parameters of Pt on di-vacancy defect (C94H26) (k = 2 ~ 5) in Figure 9.

	E bind	Pt-C(orange)	other Pt-C	C-C Bond	ΔE(Ptk)
Pt2-(A)	–91.2	1.999, 2.028, 2.038, 2.066	––	2.831, 2.904	10.6
Pt2-(B)	–59.2	1.934, 1.935, 1.997, 1.997	––	2.786, 2.740	7.1
Pt3-(A)	–70.9	2.025, 2.118, 2.025, 2.119	2.045, 2.046	2.893, 2.893	9.6
Pt3-(B)	–63.2	1.990, 2.013, 2.125, 2.199	2.081, 2.082	2.791, 2.976	7.0
Pt3-(C)	–57.6	1.972, 1.987, 1.971, 1.986	––	2.690, 2.690	1.1
Pt4(i)-(A)	–84.8	2.034, 2.035, 2.101, 2.100	2.053, 2.054	2.852, 2.853	6.4
Pt4(i)-(B)	–75.8	2.004, 2.005, 2.064, 2.134	2.067, 2.066	2.786, 2.896	4.7
Pt5(i)-(A)	–93.4	2.005, 2.006, 2.085, 2.099	2.122, 2.138	2.917, 2.923	12.3
Pt5(i)-(B)	–81.3	1.991, 2.001, 2.113, 2.123	2.053, 2.082	2.806, 2.932	13.4

Figure 9

Optimized geometries for Pt cluster (k = 2~5) on the di-vacancy-type defect in the singlet state (Pt-C94H26). Optimized bond lengths are given in Table 7.

Here Etotal(n class="Chemical">Pt-C96–H26) is the total energy of an optimized C96–H26 geometry, Etotal(C96–H26) is that of the optimized C96–H26 geometry, and Etotal(Pt) is that of the optimized Pt cluster. For the DFT calculations of the binding energies, a counterpoise correction for basis set superposition error (BSSE) was included [55]. When an Ebind value has a negative sign, the binding of a Pt cluster or the Pt atom into C96–H26 is energetically preferable. As shown in Table 3–Table 5, the calculated Ebind values in the single Pt addition are similar to those reported in [35]. These similarities verify the reliability of our DFT results.

Looking at the Ebind values, the bindings of a Pt cluster into the n class="Gene">sp2 surface are strongly facilitated by introducing vacancy-type defects. In fact, their stabilizing energies (–Ebind) in stable Pt-C95H26 structures are around 150 kcal/mol. These values are much larger than the pristine cases (about 50 kcal/mol [22]). Similar enhancement in the stabilization energies was also found in the Pt-C94H26 and Pt-C93H26 structures. Judging from the Ebind values, reactivity of vacancy-type defects toward Pt clusters declines in the order: tri-vacancy > mono-vacancy > di-vacancy. These results suggest that the tri-vacancy defect is more suitable for binding of Pt clusters into carbon surface rather than the mono- and di-vacancy defects.

From Table 3–Table 8, we see different behaviors between the three types of defect in terms of dependences of the Ebind values on Pt cluster size. Most stable n class="Chemical">Pt-C95H26 structures except for Pt3-C95H26 have Ebind values similar to that in Pt1-C95H26. In contrast, the Ebind values in Pt-C94H26 and Pt-C93H26 are deviated from those in Pt1-C94H26 and Pt1-C93H26. When a Pt cluster binds into the di-vacancy-defect, their Ebind values are smaller than the Pt1-C94H26 value. However, these absolute values increase gradually with an increase of the cluster size, and seem to converge to the Pt1-C94H26 value at k = 6. In the Pt-C93H26 cases, the Ebind values, being around 180 kcal/mol, are always larger than the Pt1-C93H26 value.

To understand the energetics in the optimized n class="Chemical">Pt-C96–H26 structures (Table 3–Table 8), let us first look at in detail geometrical features of Pt1-C96–H26. These key geometrical parameters in the Pt1-C96-H26 configurations (lengths of newly formed Pt-C bonds and of lengthening CC bonds) are listed in Table 3–Table 5.

In these tables, we can distinguish two types of the formed Pt-C bond, by whether a n class="Chemical">Pt atom binds into orange or red atoms. When the single Pt atom binds into the mono-vacancy defect, it inserts between the orange atoms in the five-membered ring, and then two P-C(orange) bonds are formed newly. As a result of the Pt addition, the separation between the orange atoms lengthens from 1.754 to 2.764 Å. At the same time, the Pt atom also coordinates to the unsaturated red atom. The binding Pt atom lifts from the sp2 surface, because the hole is not large enough to accommodate the Pt atom. Similar Pt lifting can be seen in the Pt1-C94H26 configuration, where the Pt atom inserts between orange atoms in both five-membered rings, and it breaks the connections. The degree of Pt lifting in Pt1-C94H26 is less significant than that in Pt1-C95H26, due to relatively larger hole in C94H26.

In contrast, the hole of C93H26, surrounded by ten n class="Chemical">carbon atoms, can house the Pt atom, and therefore the binding Pt atom is on the sp2 surface. Then, four Pt-C bonds are formed, accompanying the cleavage of the bonds between orange atoms in the five-membered rings. Moreover, the Pt binding into the unsaturated C atom was also seen. When a Pt cluster binds into a vacancy-type defect, slightly longer separations of the nearest Pt atom from reactive (orange and red) atoms were found. Despite the stabilization operated between a Pt cluster and C96–H26, slightly longer Pt-C bonds imply weakening interactions of the nearest Pt atom from the reactive carbon atoms compared with Pt1-C96–H26 case.

Compensating the weakening of the interactions, remaining Pt atoms of a clusters are additionally bound to n class="Chemical">carbon atoms of a defective site to maximize the Pt-C interactions. Then their clusters are more or less deformed from the most stable configuration in the gas-phase [56,57,58]. The degree of cluster deformation was estimated by using ΔE(Pt), defined as [E(Pt on surface) – E(Pt)], where E(Pt on surface) is the total energy of Pt cluster taken from an optimized Pt-C96–H26 structure and E(Pt) is that of the optimized geometry for the bare Pt cluster. Positive ΔE(Pt) values in Table 3–Table 8 suggest destabilization from cluster deformation upon the interactions with a vacancy-type defect. Although we cannot find a clear correlation between Ebind and ΔE(Pt) values, the balance between the stabilization from the Pt-C bond formation and the destabilization from the cluster deformation is a key in determining the stability. From Figure 5–Figure 7 and Figure 11, we found clear differences between Pt-C93H26 and Pt-C95H26 (Pt-C94H26) in terms of the number of Pt atoms binding directly into orange atoms in the defective site to cleave connections between adjacent orange atoms.

Figure 11

Optimized geometries for the singlet Pt atom on the mono-, di-, and tri-vacancy-type defects in the triplet state (Pt1-C95H26, Pt1-C94H26, and Pt1-C93H26, respectively). Optimized bond lengths are given in Table 3–Table 5.

In Pt-n class="Chemical">C95H26 (Ptk-C94H26), one Pt atom participates in cleaving the orange connection(s), irrespective of the cluster size. In the tri-vacancy cases containing larger ten-membered ring, two Pt atoms in a cluster bind to the defective site to split two orange connections. The accommodation of two Pt atoms cannot be seen in the Pt1-C94H26 structure, and thus the significant enhanced stabilization in Pt-C93H26 is understandable. Moreover the acceptability of the ten-membered-ring to trap Pt atoms differentiates C93H26 from C95H26 and C94H26 in terms of their reactivity toward Pt clusters. Due to the strong interactions between a Pt6 cluster and a vacancy-type defect, we can see unique orbital features, which cannot be seen in C96–H26 (Figure 12).

Figure 12

Orbital energies (eV) in the frontier orbital region of the optimized Pt6-C95H26, Pt6-C94H26, and Pt6-C93H26 configurations whose structures are given in Figure 5–Figure 7. The HOMO-LUMO gaps are given. Orbitals originated from 5d(Pt) orbitals are denoted by blue bars, and those with no or less 5d(Pt) orbital contribution are denoted by black bars.

In fact, 5d(Pt)-based orbitals, given by blue bars in Figure 12, appear in the frontier orbital regions of the n class="CellLine">Pt6-C94H26 and Pt6-C93H26 configurations. As the most striking case, we can see in Figure 13 that the Pt6(i)-C94H26(B) configuration has the HOMO and LUMO consisting of 5d(Pt) orbitals. On the other hand, levels of 5d(Pt)-based orbitals in the Pt6-C95H26 strongly depend on their cluster-shape. In the Pt6(i)-C95H26(A) and Pt6(ii)-C95H26(C) configurations, such 5d(Pt)-based orbital lies larger than 1.3 eV above the LUMO, whereas the LUMO+1 consists of 5d(Pt)-based orbitals in the other Pt6-C95H26 configurations.

Figure 13

Frontier orbitals (the HOMO and LUMO) in the Pt6(i)-C94H26(B) configuration (Figure 6) are given as a representative Pt6-C96–H26 configuration.

2.3.2. Triplet State

As shown in Figure 12, the all optimized geometries in the single state have relatively small HOMO-LUMO gaps (0.29 ~ 0.40 eV). Thus, higher n class="Gene">spin states can be energetically stable relative to the singlet states. Along the assumption, we obtained their triplet states, and estimated the energy difference between the two spin states (ΔEstate(Pt6-C96–H26)), as tabulated in Table 9.

Table 9

Energy difference between the singlet and triplet states in the Pt6-C96–H26 configurations (ΔEstate in kcal/mol) a.

	Pt6(i)-(A)	Pt6(i)-(B)	Pt6(ii)	Pt6(iii)
Clusters on C95H26	–14.3	–17.8	–14.0	b
Clusters on C94H26	–23.3	–16.2	–23.3	–38.5
Clusters on C93H26	–15.0	–23.7	–13.7	b

a ΔEstate(Pt6-C96–H26) = Etotal(triplet state) – Etotal(singlet state). Negative ΔEstate values indicate that the triplet state of a Pt6-C96–H26 configuration is energetically stable relative to the singlet state. ΔEstate in kcal/mol; b we could not obtain the optimized geometry in the triplet state.

Table 9 shows that their triplet spin states are energetically stable relative to the singlet states, as expected. According to DFT calculations, most n class="Chemical">Pt6-C96–H26 configurations have radical Pt6 clusters on defective graphene patches As representative cases, spin density distributions on the Pt6(i) cluster binding into C95H26 or C94H26 are shown in Figure 14. Figure 14 shows that substantial spin densities appear on the adsorbed clusters in the three Pt6-C96–H26 configurations (Pt6(i)-C95H26(B), and two Pt6(i)-C94H26 configurations), whereas the Pt6(i)-C95H26(A) configuration does not have such radical cluster due to the absence of 5d(Pt)-based frontier orbitals (Figure 12). In the three configurations with radical clusters, a variety of the spin density distributions was found. In the Pt6(i)-C95H26(B) and Pt6(i)-C94H26(B), the spin density distributions are strongly deviated from those in the bare Pt6 cluster, whereas the Pt6(i)-C94H26(B) has similar distributions. Furthermore, we found a relationship between spin densities of Pt clusters and those on the defective sp2 surface. When spin density distributions of the Pt cluster of a Pt6-C96-H26 configuration are (not) similar to the bare case, spin densities are (not) delocalized over the carbon surface. Similar tendencies were found in spin density distributions of the stable triplet Pt13-C96–H26 configurations [59], because radical Pt clusters exist on the defective graphene patches as shown in Figure 15.

Figure 14

Spin density distributions of representative Pt6-C96–H26 configurations (Pt6(i) cluster on C95H26 or C94H26 in two binding fashions, displayed in Figure 5 and Figure 6). Isosurface α- and β-spins are given by pink and blue, respectively.

Figure 15

Spin density distributions of representative Pt13-C96–H26 configurations. Isosurface α- and β-spins are given by pink and blue, respectively.

Spin density distributions of representative n class="Chemical">Pt6-C96–H26 configurations (Pt6(i) cluster on C95H26 or C94H26 in two binding fashions, displayed in Figure 5 and Figure 6). Isosurface α- and β-spins are given by pink and blue, respectively.

Finally, let us compare the spin density distributions on n class="Chemical">Pt6 clusters on defective sp2 surfaces (Figure 14) with the pristine case (Figure 2). As mentioned above, spin density maps on Pt6 cluster on pristine C96H26 are similar to those in the bare cluster. However, such similarity cannot be always found in the defective graphene cases. The different tendencies come from whether underlying carbon atoms have radical characters or not in Figure 2 and Figure 4. In the pristine patch, underlying carbon atoms do not have radical characters, and they cannot perturb spin density distributions of the absorbed cluster. In contrast, unpaired electrons exist on underlying carbon atoms in the defective sites, and thus spin density distributions of the adsorbed clusters are modulated by the Pt-C interactions. Therefore, perturbation of the radical sp2 surface by introduction of vacancy-type defects can change characters of adsorbed Pt clusters.

Spin density distributions of representative n class="Gene">Pt13-C96–H26 configurations. Isosurface α- and β-spins are given by pink and blue, respectively.

The DFT findings are important in the catalytic activity of Pt clusters on n class="Gene">sp2 surface, because the supported clusters can serve as active site for catalytic reactions. For example, if radical Pt clusters exist on carbon surface, it can cleave the H-H bond of hydrogen molecules in a homolytic manner. Otherwise, the H-H bond is activated by the clusters via a non-radical mechanism in [22]. Thus, the DFT calculations propose that one can change chemical reactivity of Pt clusters on graphene patches by introducing of vacancy-type defects on the surface.

3. Experimental

To investigate interactions of Pt clusters with n class="Chemical">C96H26, we carried out DFT calculations implemented in the Gaussian 03 and 09 program packages [60,61]. Adsorbed clusters that we considered consist of one, six, and thirteen Pt atoms. To perform the calculations, a hybrid Hartree–Fock/density functional theory method, B3LYP [62,63,64,65,66] was used. The B3LYP method consists of the Slater exchange, the Hartree–Fock exchange, the exchange functional of Becke [62,63,64], the correlation functional of Lee, Yang, and Parr (LYP) [65], and the correlation functional of Vosko, Wilk, and Nusair (VWN) [66]. In general the hybrid B3LYP method has been reported to provide excellent descriptions of various properties. The Gaussian-type basis set we used for the C and H atoms is 6-31G* [67], and that for the Pt atom is the quasi-relativistic effective core potential RECP and valence basis sets recommended by Stuttgart group (SDD) [68]. The SDD RECP is adjusted to total valence energies of a multitude of atomic references states, which are quantum mechanical observables [68]. As indicated in the previous papers [69,70,71,72,73,74,75,76], the B3LYP/6-31G* calculations correctly reproduce experimental data for C60, especially its IR and Raman vibrational frequencies. According to the theoretical report by Nova et al. [77], the method of our choice (B3LYP/SDD + 6-31G*) is appropriate to reproduce experimental values in terms of Pt-C bonds in Pt complexes [77]. The computational method is also suitable to study transition metals adsorbed on graphene. In fact, Pt-C bond lengths obtained from the B3LYP/SDD + 6-31G* calculations fall in the range reported from other theoretical reports [24,30].

4. Conclusions

Density functional theory (DFT) B3LYP calculations were employed to investigate the adsorption of n class="Chemical">Pt cluster (k is 1–6, and 13) into a nanometer-size graphene patch (C96H26) with or without vacancy-type defects. According to the DFT calculations, removing a few carbon atoms (n) from C96H26 results in the formation of five-membered rings as well as coordinatively unsaturated carbon atoms. Introduction of a vacancy-type defect on C96H26 strongly affects spin density distributions in its stable triplet state. Although spin densities appear only on edge carbon atoms of the triplet C96H26 structure, defective graphene patches have radical carbon atoms at the center where the reactive carbon atoms exist. These spin density distributions differentiate characters of Pt clusters adsorbed on defective graphene patches from those on the pristine. According to the DFT calculations, spin density maps of Pt clusters on C96H26 are similar to those of the corresponding bare clusters. In contrast, Pt clusters interact strongly with radical carbon atoms in defective graphene patches, and thus spin density distributions of the adsorbed Pt clusters are usually deviated from the bare cases. Consequently, DFT calculations propose that characters of Pt clusters adsorbed on the sp2 carbon surface can be modulated by introducing vacancy-type defects.