DFT Study for Supported Pt Catalysts Focusing on the Chemical Potential

To study the physicochemical properties of supported Pt catalysts, we performed DFT calculations for the supported Pt3 clusters with various oxides. We determined that the chemical potential (μ) of the supported Pt cluster (μPt/MOx) could be described by averaging the μ values of the isolated Pt3 clusters and support oxides without Pt species (μMOx). The proportional value of the molar fraction of supported Pt species (mol%) should be used as the weighted factors for calculation of the average value. As a result, μPt/MOx could be expected to become μMOx for the actual Pt catalysts, because of their low Pt loadings (∼1 wt% ∼ 0.1 mol%). [DOI: 10.1380/ejssnt.2018.209]


I. INTRODUCTION
Many scientists studying catalyst chemistry have been interested in the Pt-oxide interaction, because the catalytic activities of supported Pt catalysts are strongly dependent on the kind of support oxides (Al 2 O 3 , SiO 2 , etc.) [1][2][3]. Our previous work [1] was carried out by focusing on the HSAB (hard soft acid base) concept [4,5] and DFT calculations to understand the Pt-oxide interaction. We showed that some physicochemical properties of the supported Pt catalysts, such as the oxidation states of Pt, Pt diameter and catalytic activities, have a relationship with the chemical potential (µ) of the support oxides [1]. For example, the support oxides with high µ values (basic oxide) tend to maintain smaller Pt particles after their thermal aging, moreover, the basic oxide tends to oxidize the supported Pt species. The opposite tendency could be obtained by using the support oxides with low µ values (acidic oxide). This knowledge indicated that we can predict the physicochemical properties of catalysts by estimation of the µ values based on the DFT calculations.
We postulated there was still room for further improvement regarding our previous studies. It could be suggested that µ of the supported Pt clusters are more important parameters than µ of the support oxide, to understand the physicochemical properties of the supported Pt catalysts. This study will try to formalize our previous knowledge by focusing on µ of the supported Pt clusters.

A. Computational details
The DFT calculations were carried out using a method similar to our previous work [1]. The DFT calculations were performed for the slab models of 28 kinds of support oxides (Al 2 O 3 , SiO 2 , etc.) with a 100-200Å 2 area of the base, ca. 6Å thickness and 40Å vacuum layer. The Pt 3 cluster and O 2 molecule were also considered. We also performed the DFT calculations for the structure models of the supported Pt 3 clusters on the 28 kinds of support oxides. All of the DFT calculations were carried out under the periodic boundary condition by DMol 3 [6] with GGA-PBE [7]/ DSPP-DND [8]. The Brillouin zone (BZ) integration was performed by the Monkhorst-Pack scheme [9] using a grid of k-points with spacing of 0.05Å −1 . The chemical potential (µ) can be defined by Eq. (1) [4,5].
for periodic boundary 1 2 (E HOMO + E LUMO ) for non periodic boundary (1) E VBM , E CBM , E HOMO , and E LUMO were the eigen values of the valence band maximum, conduction band minimum, highest occupied molecular orbital, and lowest unoccupied molecular orbital, respectively. Namely, µ for the support oxide (µ MOx ), Pt 3 cluster (µ Pt ), and supported Pt 3 cluster (µ Pt/MO x ) could be obtained immediately after the DFT calculations.

B. Experimental details
Various Pt catalysts were prepared by the impregnation method or evaporation and dryness method using Pt(NO 2 ) 2 (NH 3 ) 2 solutions. The amounts of the supported Pt species were set to 0.21 mol%. All of the Pt catalysts were aged at the 650 • C, ambient air condition for 2 h. The catalytic activities were tested by using simulated diesel automotive exhaust gas (8 vol% O 2 , 850 ppm C 3 H 6 , 350 ppm NO, 10 vol% H 2 O, 10 vol% CO 2 , N 2balance). The XAFS (X-ray adsorption fine structure) analyses were also carried out for the Pt catalysts after the activity tests in the transmission mode at SAGA-LS BL11 and Aichi-SR BL11S2. More detailed information is described in our previous study [1].

III. RESULTS AND DISCUSSION
A. Chemical potentials of supported Pt species Figure 1 shows the relationship between µ Pt/MO x and µ MOx estimated by the DFT calculations. There was a linear relationship between µ Pt/MO x and µ MOx , however, these values did not perfectly correspond. This result could be understood by referring to a previous research study regarding electronic devices. The charge transfer phenomena should occur at the metal-semiconductor interface, and µ of the metal-semiconductor interface (CNL: charge neutrality level) could be described by the average value of µ of the metal and µ of the semiconductor. Moreover, the DOS (density of state) values should be used as weighting factors for estimation of the CNL [10]. We can suggest the semi-theoretical equation to estimate µ Pt/MO x by analogy of knowledge about the metal-semiconductor interface (CNL) as Eq. (2).
C 1 , C 2 , and C 3 were the numbers of valence electrons per Pt atom, the numbers of valence electrons per cation in the support oxide and the numbers of valence electrons per O 2− anion, respectively. Moreover, l, m, and n were the number of Pt atoms, the numbers of cations of the support oxide and the numbers of O 2− anions, respectively. It is possible to define C 1 = 10, because of the electron configuration of the Pt atom (5d 9 6s 1 ). This study treated the cations as having the electron configurations of a noble gas (e.g., Al 3+ , Si 4+ , Ti 4+ , and V 5+ have electron configurations similar to Ar), moreover the electron configuration of O 2− corresponds to that of Ne, thus C 2 and C 3 could be determined as 8 (two s electrons and six p electrons). The verification of Eq. (2) could be achieved by comparison of the predicted µ Pt/MO x and DFT value. For example, our DFT calculation was performed for Pt 3 /Ti 24 O 48 and µ Pt3/Ti 24 O48 was estimated to be −5.7 eV [1]. On the other hand, we also obtained µ Pt3 = −4.4 eV and µ Ti24O48 = −6.4 eV [1]. Thus we can predict µ Pt3/Ti 24 O48 = −6.2 eV based on these µ Pt3 and µ Ti24O48 values, Eq. (2) and l = 3, m = 24, n = 48. Figure 2 shows the correlation between the µ Pt/MO x values by the DFT calculations and Eq. (2). It could be suggested that The typical Pt amounts for the practical Pt catalysts were nearly 1-5 wt% [1][2][3]. Thus, the number of Pt atoms (l) can be ignored (l ≪ m and l ≪ n). As a result, the semi-theoretical formula predicts that µ Pt/MO x becomes close to µ MOx for practical Pt catalysts [Eq. (3)].
This idea seems to support some previous knowledge. The physicochemical properties of the Pt catalysts, such as the chemical states of Pt and the catalytic activity, well correspond to the physicochemical properties of the support oxides, such as the O 1s binding energy [2] and acid strength [3]. Our idea indicates that the physicochemical properties of the supported Pt catalysts strongly depend on the support oxides, because µ Pt/MO x well correspond to µ MOx .

B. Comparison among catalytic activities and chemical potentials
Table I summarizes the Pt particle diameter and specific surface area (SSA) by the CO pulse method and N 2 physisorption method, respectively. TiO 2 , V 2 O 5 , and MoO 3 had low SSA values, and the Pt species tend to become large on these oxides. The Pt species on the Al 2 O 3 , SiO 2 , Y 2 O 3 , ZrO 2 , and La 2 O 3 maintained a small size. Figure 3 shows the results of the activity test for  Figure 4 shows the relationship between the obtained TOF values and µ MOx based on the DFT calculations. The highest TOF seems to be obtained when the support oxides with µ of ca. −6 eV was used. −6 eV was similar to µ of O 2 molecules (µ O2 = −5.8 eV). The reason for this coincidence could be explained by the following consideration. According to the literature [11,12], the binding energy between a metal (Pt, Pd, Rh, etc.) and oxygen well corresponds to their catalytic activities for the C 2 H 4 oxidation reaction. Moreover, the catalyst having the binding energy of 100 kJ/mol could provide the highest C 2 H 4 oxidation activity. On the other hand, the binding energy of the supported Pt species and O 2− anion could be estimated in the following way. First, one Pt atom in the supported Pt particles receives the Thus, I E and E A could be estimated as shown by Eq. (7).
The reaction energy of the dissociative adsorption of the O 2 molecule on the supported Pt species could be estimated as shown by Eq. (8).
If we can assume that the catalysts having a 100 kJ/mol binding energy between Pt and oxygen could provide the highest C 3 H 6 oxidation activity as well as C 2 H 4 oxidation activity, our experimental results (Fig. 4) could be easily understood. Namely, the combination of the obtained relationships, Eq.  Figure 5 shows the XAFS results for the Pt catalysts after the activity test. The Pt species on the Y 2 O 3 and La 2 O 3 showed stronger whiteline intensity, namely, the Pt species were in the oxidized state on these oxides. In contrast, the Pt species on the MoO 3 , V 2 O 5 , and TiO 2 showed similar spectra as the Pt foil, i.e., the Pt species maintained a metallic state on these support oxides. The Pt species on the Al 2 O 3 , SiO 2 , and ZrO 2 surfaces could be considered as a mixture of metallic and oxidized Pt species, because their XAFS spectra had intermediate properties between the XAFS of the Pt foil and PtO 2 . The valence of the Pt species could be quantitatively analyzed by the linear combination fitting (LCF) method. Figure 6 shows the relationship between the valence of the Pt species and µ MOx . It was found that the Pt species maintain the metallic state on the support oxide having the low µ MOx values, moreover, the oxidation of the supported Pt species tend to be enhanced on the support oxide having the high µ MOx values. The threshold of whether the supported Pt species tend to be oxidized or maintain the metallic state was around µ MOx ∼ = −6 eV. Equation (8) could also explain about XAFS result. In the case of µ MOx ≫ µ O2 (−5.8 eV), the supported Pt clusters have the stronger Pt-O interaction (∆E becomes a greater negative value), and oxidation of the Pt species could be expected to be enhanced. In case of µ MOx ≪ µ O2 (−5.8 eV), the supported Pt clusters are hardly oxidized, because the adsorption energy (∆E) calculated by Eq. (8) becomes a positive value (endothermic reaction).
Finally, we want to propose that µ of the supported Pt species tend to become values similar to µ of the support oxides. This idea could explain some of the physicochemical properties of the supported Pt catalysts, such as the catalytic activity and chemical state of the Pt species.

IV. CONCLUSION
The DFT calculations were carried out for supported Pt 3 clusters on 28 kinds of support oxides. The chemical potential (µ) of the supported Pt species could be described by µ of the Pt clusters in a vacuum and µ of the support oxides. For the actual Pt catalysts, their µ values should become similar to µ for the support oxides. Thus, the physicochemical properties of the supported Pt catalysts strongly depend on µ of the support oxides. Finally, we successfully explained the XAFS results and C 3 H 6 oxidation activities by the obtained idea.