The number of surface gold atoms contained in each hemispherical Au NP nanoparticle (n S ) (Scheme S2b) was calculated as follows: π 2 D2, = ρ [hkl]

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1 Supporting Information Controlled Loading of Small Au n Clusters (n = 10 39) onto BaLa 4 Ti 4 O 15 Photocatalysts: Toward an Understanding of Size Effect of Co-Catalyst on Water Splitting Photocatalytic Activity Yuichi Negishi, *,,,# Yoshiki Matsuura, Ryota Tomizawa, Wataru Kurashige, Yoshiki Niihori, Tomoaki Takayama, Akihide Iwase,, and Akihiko Kudo *,, Department of Applied Chemistry, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, , Japan. Photocatalysis International Research Center, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, , Japan. # Department of Materials Molecular Science, Institute for Molecular Science, Myodaiji, Okazaki, Aichi , Japan. I. Calculation methods The number of gold atoms contained in each hemispherical Au NP nanoparticle (n) (Schemes S1b and S2a) was calculated as follows: n = πρn A D D 3, (S1) 6M where D is the particle diameter (nm) measured from TEM (Figure 9), π is circular constant (3.14), ρ is the density of bulk gold (19.32 g cm 3 ), 1 N A is Avogadro constant ( mol 1 ), and M is the atomic weight of gold (197 g mol 1 ). The calculated n values of the nanoparticles of different sizes are summarized in Table S1. The number of surface gold atoms contained in each hemispherical Au NP nanoparticle (n S ) (Scheme S2b) was calculated as follows: n S = ρ [hkl] π 2 D2, (S2) where ρ [hkl] is the density of gold atom at [hkl] surface of bulk Au, as described in the following equations using a as lattice constant of bulk gold ( nm): 1 4 ρ [111] =, (S3) 2 3a ρ [110] = 2 a 2. (S4) The calculated values of ρ [111] and ρ [110] were and 8.50 nm 2, respectively. The calculated n S values of the nanoparticles of different sizes are summarized in Table S1. The total number of surface gold atoms in Au NP -BaLa 4 Ti 4 O 15 (N S ) prepared with a gold ratio of S1

2 0.1 wt% (Scheme S2c) was calculated as follows: n N S = N S[hkl] n P = 3ρ M [hkl] ρn A 10 N P 21 D (S5) D where N is the total number of gold atoms, calculated as for Au NP -BaLa 4 Ti 4 O 15 prepared with 500 mg BaLa 4 Ti 4 O 15 at a gold ratio of 0.1 wt%. P is the existence probability of a nanoparticle of a given size; P can be calculated from the core size distribution (Figure 9), and the obtained values are summarized in Table S1. Note that all the surface atoms of different-sized gold nanoparticles (Figure 9) are accounted for in this calculation (Scheme S2c). When the nanoparticles consist of [111] surfaces only, a maximum N S value is obtained (i.e., , as calculated from Equation S5). In contrast, when the nanoparticles consist of [110] surfaces only, a minimum N S value is obtained (i.e., , as calculated from Equation S5). However, because the actual gold nanoparticles are expected to be composed of several surfaces containing [111] and [110] surfaces, an N S value in the range of ( ) is expected. Thus, the ratio of the surface gold atoms in Au NP -BaLa 4 Ti 4 O 15 can be estimated at % by dividing the minimum and maximum N S values, respectively, with the value of N ( ) (see Section 3.2.). D II. Schemes Scheme S1. Schematic of the geometrical structures used for comparing the number of surface gold atoms in (a) Au 10 -BaLa 4 Ti 4 O 15 and (b) Au NP -BaLa 4 Ti 4 O 15. Scheme S2. Schematic of (a) gold atoms contained in each hemispherical Au NP nanoparticle, (b) surface gold atoms contained in each hemispherical Au NP nanoparticle, and (c) the total surface gold atoms in Au NP -BaLa 4 Ti 4 O 15. S2

3 III. Results Table S1. Estimated values for gold nanoparticles of different sizes D (nm) a n b n S[111] c n S[110] d P e 8 15,827 1, ,535 1,766 1, ,913 2,181 1, ,145 2,639 1, ,417 3,140 1, ,915 3,685 2, ,824 4,274 2, ,330 4,906 3, ,618 5,582 3, ,874 6,302 3, ,282 7,065 4, ,030 7,872 4, ,301 8,723 5, ,158 10,554 6, a Diameter of the gold nanoparticles measured from TEM analysis of Au NP -BaLa 4 Ti 4 O 15 (Figure 9). b Number of gold atoms contained in each gold nanoparticle calculated by Equation S1. c Number of surface gold atoms contained in each gold nanoparticle calculated using Equations S2 and S3 under the assumption that the gold nanoparticles are composed of [111] surfaces only. d Number of surface gold atoms of each gold nanoparticle calculated using Equations S2 and S4 under the assumption that the gold nanoparticles are composed of [110] surfaces only. e Existence probability of a nanoparticle of a particular size, as calculated from the core size distribution (Figure 9). Table S2. Comparison data of Au 10 -BaLa 4 Ti 4 O 15 and Au NP -BaLa 4 Ti 4 O 15 ratio a photocatalyst surface gold atoms b activity c activity per surface atom d Au 10 -BaLa 4 Ti 4 O e Au NP -BaLa 4 Ti 4 O f Au NP -BaLa 4 Ti 4 O a Ratio was normalized by fixing the values obtained for Au 10 -BaLa 4 Ti 4 O 15 at 1. b Data were calculated under the assumption that all gold atoms of Au 10 -BaLa 4 Ti 4 O 15 are located on the surface (Scheme S1). The values indicate that the number of surface gold atoms in Au 10 -BaLa 4 Ti 4 O 15 can be ~17 28-fold higher than that of Au NP -BaLa 4 Ti 4 O 15 (see Section 3.2.). c Water splitting photocatalytic activities (Figure 8). d The values indicate that the activity per gold atom on the surface was lower by 75 85% in Au 10 -BaLa 4 Ti 4 O 15 relative to that in Au NP -BaLa 4 Ti 4 O 15 (see Section 3.2.). e The nanoparticles are composed of [111] surfaces only. f The nanoparticles are composed of [110] surfaces only. S3

4 Figure S1. Optical absorption spectra of different aqueous solutions containing Aun(SG)m clusters. The spectra are consistent with those reported in the literature,3 indicating that highly pure Aun(SG)m clusters were obtained. Figure S2. Photographs Au25-BaLa4Ti4O15. of (a) BaLa4Ti4O15, S4 (b) Au25(SG)18-BaLa4Ti4O15, and (c)

5 Figure S3. TEM images of the different (a) Aun(SG)m clusters, (b) Aun(SG)m-BaLa4Ti4O15, and (c) Aun-BaLa4Ti4O15 for Group 1 samples (n = 10, 15, 18, 25, 39). S5

6 Figure S4. TEM images of the different (a) Aun(SG)m clusters, (b) Aun(SG)m-BaLa4Ti4O15, and (c) Aun-BaLa4Ti4O15 for Group 2 sample (n = 22, 29, 33). S6

7 Figure S5. Time course of water splitting over Au n -BaLa 4 Ti 4 O 15 photocatalysts of Group 1 samples (n = 10, 15, 18, 25, 39; 0.1 wt% Au). IV. References (1) National Astronomical Observatory Ed. Chronological Scientific Tables 2014; Maruzen Co. Ltd: Tokyo, Japan, (2) Wyckoff, R. W. G. Crystal Structure, Second Edition; Interscience Publisheres: New York, USA, (3) Negishi, Y.; Nobusada, K.; Tsukuda, T. Glutathione-Protected Gold Clusters Revisited: Bridging the Gap between Gold(I)-Thiolate Complexes and Thiolate-Protected Gold Nanocrystals. J. Am. Chem. Soc. 2005, 127, S7