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[Shengzhou Li](https://orcid.org/0000-0001-6973-3825), [Tsuyoshi Miyazaki](https://orcid.org/0000-0003-3534-4404), [Ayako Nakata](https://orcid.org/0000-0002-3311-6283)

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[Theoretical search for characteristic atoms in supported gold nanoparticles: a large-scale DFT study](https://mdr.nims.go.jp/datasets/a9731622-528b-47bb-9b51-a968114aa3c7)

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Theoretical search for characteristic atoms in supported gold nanoparticles: a large-scale DFT study PAPER  Ayako Nakata  et al .  Theoretical search for characteristic atoms in supported gold nanoparticles: a large-scale DFT study ISSN 1463-9076rsc.li/pccpPCCPPhysical Chemistry Chemical PhysicsVolume 26Number 3014 August 2024Pages 20151–20720This journal is © the Owner Societies 2024 Phys. Chem. Chem. Phys., 2024, 26, 20251–20260 |  20251Cite this: Phys. Chem. Chem. Phys.,2024, 26, 20251Theoretical search for characteristic atoms insupported gold nanoparticles: a large-scale DFTstudy†Shengzhou Li, ab Tsuyoshi Miyazaki b and Ayako Nakata *abcThe size and site dependences of atomic and electronic structures in isolated and supported goldnanoparticles have been investigated using large-scale density functional theory (DFT) calculations usingmulti-site support functions. The effects of the substrate on nanoparticles with diameters of 2 nm andseveral different shapes have been examined. First, isolated gold nanoparticles with diameters of 0.6 nm(13 atoms) to 4.5 nm (2057 atoms), which have comparable sizes to nanoparticles used in experiments,were considered. To analyse huge amounts of data obtained from large-scale DFT calculations, weperformed principal component analysis (PCA), which helps systematically and efficiently clarify theelectronic structures of large nanoparticles. The PCA results reveal the site dependence of theelectronic structures. Notably, the atoms in the surface and subsurface have different electronicstructures to those located in the inner layers, especially at the vertexes of the particles. Theconvergence of local electronic structures with respect to the particle size has also been demonstrated.For supported nanoparticles, PCA helps indicate which atoms are affected, and how much, by thesubstrate. The correlation between the PCA results and site dependence of reaction activity is alsodiscussed herein.1. IntroductionNumerous metallic nanoparticle catalysts have been developedfor different types of reactions. For example, gold nanoparticlescan be used for CO oxidation and hydrogen generation.1 Thereactivity of nanoparticles is different from both bulk materialsand small clusters and significantly depends on the particlesize and the combination of nanoparticles and substrates.Oxide materials, such as MgO, TiO2, and CeO2, are commonlyused as substrates.1 Vertexes of nanoparticles and interfacesbetween nanoparticles and substrates are considered to be theactive sites in various reactions. The atomic-scale investigationof isolated and supported nanoparticles has been conductedboth experimentally2–5 and theoretically.6–16 First-principlesdensity functional theory (DFT) calculations are a powerful toolto investigate the atomic and electronic structures of materialsand have been widely applied to analyse catalytic reactions.However, the target system size of DFT calculations has beenlimited to less than a thousand atoms in most cases because thecomputational cost is high, scaling cubically with the number ofatoms (Natom). Even nanoparticles with diameters of 3 nm, whichare relatively small among the nanoparticles in practical use,consist of approximately one thousand atoms, and larger num-bers of atoms are required to include substrates in the models.Therefore, DFT calculations have been applied mainly to clustersconsisting of tens of atoms or periodic models representing theedge of nanoparticles, and there are few DFT studies on metallicparticles with diameters of several nanometers.14–16In the present study, we investigated the size and site depen-dences of the atomic and electronic structures of gold nano-particles of several nanometers in diameter using our large-scaleDFT code, CONQUEST.17–19 Using the multi-site support functionmethod implemented in CONQUEST, we can consider largemetallic systems consisting of several thousand atoms.20–23 Wealso investigated the interaction between 2 nm gold nanoparticlesand the substrate, namely MgO(100). The models contain approxi-mately three thousand atoms. To systematically and efficientlyanalyse the electronic structures of the three thousand atoms, weapplied statistical analysis to an atom-projected density of states(DOS). Several studies have used statistics and machine learningto analyse the DOS, either using descriptors based on domaina Department of Computer Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japanb Research Center for Materials Nanoarchitectonics (MANA), National Institute forMaterials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan.E-mail: NAKATA.Ayako@nims.go.jpc Precursory Research for Embryonic Science and Technology (PRESTO), JapanScience and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4cp01094aReceived 13th March 2024,Accepted 13th June 2024DOI: 10.1039/d4cp01094arsc.li/pccpPCCPPAPEROpen Access Article. Published on 21 June 2024. Downloaded on 8/2/2024 7:52:05 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article OnlineView Journal  | View Issuehttps://orcid.org/0000-0001-6973-3825https://orcid.org/0000-0003-3534-4404https://orcid.org/0000-0002-3311-6283http://crossmark.crossref.org/dialog/?doi=10.1039/d4cp01094a&domain=pdf&date_stamp=2024-06-26https://doi.org/10.1039/d4cp01094ahttps://doi.org/10.1039/d4cp01094ahttps://rsc.li/pccphttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4cp01094ahttps://pubs.rsc.org/en/journals/journal/CPhttps://pubs.rsc.org/en/journals/journal/CP?issueid=CP02603020252 |  Phys. Chem. Chem. Phys., 2024, 26, 20251–20260 This journal is © the Owner Societies 2024knowledge, such as d-band centres,24,25 or raw DOS values.26–29We performed principal component analysis (PCA) with raw DOSdata to directly compare the electronic structures of nanoparticleswith different sizes, with and without substrates, without relyingon domain knowledge.In the next section, we provide the computational details.Then, the atomic and electronic structures of isolated andsupported gold nanoparticles are discussed in the third section,based on the large-scale DFT calculation and PCA results. Thefinal section contains the conclusions of the present study.2. Computational detailsDFT calculations with periodic boundary conditions were per-formed using a large-scale DFT code, CONQUEST.17–19 The Per-dew–Burke–Ernzerhof generalised gradient approximation, anexchange–correlation functional,30 was used. Core electrons weredescribed by Hamman’s norm-conserving pseudopotential,31 andvalence electrons were described by real-space local orbital func-tions, which are pseudo atomic orbital (PAO) functions32,33 for thedouble-z polarisation (DZP) level. The radii of the PAO functionsof Au, Mg, and O atoms are given in Table S1 in the ESI.† Forsupported Au nanoparticles, we used the multi-site support func-tion method20–22 to reduce the number of local orbital functionswhile maintaining accuracy. The multi-site functions are con-structed for each atom in the system as the linear combinations ofPAOs that belong to the atom and its neighbouring atoms in agiven cutoff region,fia rð Þ ¼Xneighbor atoms of atom ikCia;mkwmk rð Þ (1)where fia(r) is the ath multi-site support function of atom i, wmk(r)is the mth PAO of the atom i’s neighbouring atom k, and Cia,mk is itslinear-combination coefficient. In the present study, we used thecutoff region of 13.0 bohr because our previous studies suggestedthat the cutoff region should include more than the second-neighbour atoms to obtain an accuracy comparable to the primi-tive PAOs.20,34 Although several studies have reported spin polar-isation in gold nanoclusters,35–38 spin-polarisation was notconsidered in the present study for simplicity. Dispersion energieswere considered using the DFT-D2 method.39The stabilised quasi-Newton method was used for geometryoptimisation with a threshold of 0.05 eV Å�1. We first optimisedthe structure of a bulk fcc gold crystal with a four-atom cubicsimulation cell using 8 � 8 � 8 Monkhorst–Pack k-point meshesand obtained the Au–Au bond length as 2.949 Å. Then, the initialstructures of cuboctahedral (Oh) nanoparticles were constructedbased on the optimised Au–Au bond length of bulk fcc gold. Weinvestigated the Oh gold nanoparticles with eight magicnumbers,40 namely Natom = 13 (Oh1), 55 (Oh2), 147 (Oh3), 309(Oh4), 561 (Oh5), 923 (Oh6), 1415 (Oh7), and 2057 (Oh8) atoms,which consisted of 1, 2, 3, 4, 5, 6, 7 and 8 shells, respectively(as shown in Fig. 1). For the MgO(100) surface, we first optimisedthe structure of the eight-layered clean surface model consistingof 32 atoms (B15 Å thick) using 3 � 3 � 1 k-points and thenconstructed a large surface model with an area of 38.5 Å � 38.5 Å.The vacuum gap was set to 15 Å. For the calculations of supportedgold nanoparticles, we placed gold nanoparticles with a diameterof 2.25 nm on the MgO surface. Several shapes of the supportednanoparticles were considered; these were constructed by remov-ing the bottom layers of Oh4. Because the calculated Au–Audistance in the (100) plane in bulk Au (2.95 Å) and the O–Odistance in the clean MgO(100) surface (3.02 Å) only had a 2.3%mismatch, the interfacial gold atoms in the bottom layer of thenanoparticle were initially placed approximately above the Oatoms in the MgO surface, which was reported to be a stableconfiguration,8 although the orientation of the nanoparticles onthe substrate was not fully investigated in the present study. Theinitial distances between the bottom layer of the nanoparticlesand the MgO surface were set to 2 Å. The structures of thenanoparticles and the upper two layers of the MgO substrate wereoptimised by G-point sampling.The cohesive energy (Ec) was calculated as follows:Ec = Enanoparticle/Natom � EAu atom (2)The interaction energy between the nanoparticle and thesubstrate (Eint) and the adsorption energy of a molecule (or anatom) (Ead) were calculated as the energy differences before andafter adsorption:Eint = �(Enanoparticle�substrate � (Enanoparticle + Esubstrate))(3)Ead = �(Enanoparticle�substrate�molecule� (Enanoparticle�substrate + Emolecule)) (4)The DOS was calculated using the Gaussian smearing func-tion with s = 0.005 Hartree for each eigenstate of the electronicHamiltonian. Local DOS (LDOS) was calculated by theFig. 1 Optimised structures of Oh1–Oh8 gold nanoparticles and thelayered (shell) structure of Oh6.Paper PCCPOpen Access Article. Published on 21 June 2024. Downloaded on 8/2/2024 7:52:05 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4cp01094aThis journal is © the Owner Societies 2024 Phys. Chem. Chem. Phys., 2024, 26, 20251–20260 |  20253projection of DOS for atom i was performed using the weight w:wni ¼XajbcniaSia;jbcn�jb (5)where a and b are the indices of local functions of atoms i and j,S is the overlap matrix of local functions, and cnia and cnib arethe coefficients of the nth Kohn–Sham orbital for the athand bth local orbital functions of atoms i and j, respectively.We examined the basis-set dependence of the LDOS, which isdiscussed in the ESI.†To analyse the LDOS, PCA was performed using scikit-learn41 to reduce the dimensionality of the LDOS without losingimportant information in the raw LDOS.4,42 In the presentstudy, the LDOS was expressed as a high-dimension vectorusing the values on the grid points with the interval of 0.225mHartree for the energy region of �11.3 to 12.8 eV around theFermi level (EF), resulting in high dimensional (3543) raw LDOSdata. Then, the input data for PCA was constructed as a matrixX3543,Natomconsisting of the LDOS of Natom atoms. The PCAcomponents were obtained as the eigenvectors of the covar-iance matrix of X, and the components with the first andsecond largest proportions of variance were used to reducethe original dimension to two dimensions (2D). We performedPCA for the isolated nanoparticles Oh1–Oh8. Then, we appliedthe PCA components of the isolated Oh4 nanoparticle to thesupported nanoparticles, to project the LDOS of the atoms inthe supported nanoparticles directly to the 2D-PCA map thathad already been obtained for Oh4.3. Results and discussion3.1 Size and site dependences in isolated nanoparticlesFirst, we investigated the site and size dependences of the atomicand electronic structures of isolated gold nanoparticles. It hasbeen shown that gold nanoparticles consisting of specificnumbers (i.e., magic numbers) of atoms are relatively more stable.We investigated Oh gold nanoparticles with eight magic numbersfrom 13 atoms (Oh1) to 2057 atoms (Oh8), as explained in theprevious section. The diameters (rd) of the eight nanoparticles inthe optimised structures are 0.57, 1.12, 1.68, 2.25, 2.81, 3.38, 3.95,and 4.52 nm, respectively. The calculated cohesive energies forOh1–Oh8 are 2.24, 2.91, 3.17, 3.32, 3.43, 3.49, 3.54, and 3.58 eV peratom, respectively. Here, the cohesive energy of the nanoparticlebecomes closer to that of bulk fcc gold, 3.83 eV per atom (3.81 eVper atom by experiment43). The tendency of larger particles tohave larger cohesive energies is similar to the results reported inthe previous studies.4,5 Fig. 2 shows the intra-shell Au–Au bondlengths in the optimised structures, in which more outer shellshave wider bond-length distributions. The maximum differencesof the bond lengths in the particle surface (i.e., the outermostlayer) are 0.186, 0.216, 0.217, 0.212, 0.250, 0.212, and 0.219 Å forOh2–Oh8, respectively. This means that the site dependence of thebond length is larger in the outer shell. The Au–Au bond lengthsin faces are longer than those in edges in all particles, whichmeans that the particle surface is not flat but slightly round.Next, the size dependence of the electronic structures of thegold nanoparticles was investigated. Fig. 3 shows the total DOSof Oh1–Oh8. The band in the range from �6 to �2 eV originatesmainly from d electrons (d-band). Compared with the d-band forbulk fcc gold, the shapes of the d-bands for the nanoparticles aresharper, and the centres of the d-bands are shifted closer toFermi level (EF). Additionally, the electronic structures of smallnanoparticles, such as Oh1–Oh3, are still discrete, especially inthe unoccupied states, whereas larger nanoparticles have morecontinuous (i.e., metallic) electronic structures and do notchange much depending on size. This result is consistent withthe experimental reports demonstrating that the electronicstructure changes around the diameter of 2 nm.1,44The site dependence of the electronic structures of thenanoparticles was investigated by projecting the DOS to eachFig. 2 Calculated intralayer Au–Au bond lengths [Å] in gold nanoparticles with (a) 13 (Oh1), (b) 55 (Oh2), (c) 147 (Oh3), (d) 309 (Oh4), (e) 561 (Oh5), (f) 923(Oh6), (g) 1415 (Oh7), and (h) 2057 (Oh8) atoms. The x-axes correspond to the indices of the layers in the nanoparticles. Black dotted lines correspond tothe bond length in the bulk fcc gold crystal.PCCP PaperOpen Access Article. Published on 21 June 2024. Downloaded on 8/2/2024 7:52:05 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4cp01094a20254 |  Phys. Chem. Chem. Phys., 2024, 26, 20251–20260 This journal is © the Owner Societies 2024atom in the nanoparticles. The LDOS of the atoms at the vertex,in the edge, and the (100) and (111) faces of Oh6 are presentedin Fig. 4. The vertex atom has a characteristic electronicstructure; that is, the d-band of the vertex atom is much sharperand the d-band centre is closer to EF compared with those ofthe atoms in the edge and faces. This suggests that the vertexatom is an active site in the nanoparticle, based on d-bandcentre theory.45,46 It’s also reported experimentally by Fenget al. that Au vertex sites are the dominant Au active sites.47Fig. 4(a)–(d) focusses on the atoms at the representativepositions, although there are many more atoms in the nano-particles. To systematically and efficiently investigate the elec-tronic structures of all atoms in the large systems anddetermine the characteristic atoms among them, we appliedPCA to the raw LDOS data. Fig. 4(e) shows the PCA result forOh6 with 923 atoms, in which the LDOS data with B3543dimensions were reduced to 2D. There are 923 points thatcorrespond to the electronic structures of the 923 atoms in thefigure, plotted according to the principal component scores forthe first and second components as a 2D map. The difference ofLDOS is quantified as the position difference of the data pointsin the PCA map. The proportions of variance of the first andsecond PCA components are 0.810 and 0.100, which means thatthe two components include most of the information for theraw data in high dimensions.In Fig. 4(e), the data points are roughly distributed into threeareas, namely the right, upper left, and lower left areas, and thepoints in these three areas correspond to the atoms in the surface(6th layer), subsurface (5th layer), and the inner layers (1st to 4thlayers), respectively. The first PCA component divides the atoms inthe surface from the other layers, and the second PCA componentdivides the atoms in the subsurface from the others. Thisindicates that the surface and subsurface have characteristicelectronic structures, whereas the electronic structures of theinner layers are more similar to each other, almost converging.Thus, by simultaneously analysing the electronic structures of allatoms, we can demonstrate how deeply the electronic structure isaffected by forming a nanoparticle. Considering the right area inFig. 4(e), the points of the vertex atoms are separated from thoseof the other atoms on the surface, suggesting that the electronicstructures of vertex atoms are different from the other atoms.To investigate which parts of LDOS is found to be differentby PCA, the weights of the two PCA components in Fig. 4(e) areprovided in Fig. 5(a) and (b), which represent the parts of theLDOS with significant differences. The first PCA componenthas a large positive peak at �2.646 eV and a large negative peakat �6.578 eV. Comparing the LDOS of the atoms at the vertexposition in the surface (Fig. 5(c)) and the subsurface (Fig. 5(d)),the LDOS of the surface atom is higher around �2.646 eV andlower around �6.578 eV than that of the subsurface atom.For the second component, there are large peaks around�5.864 and �6.803 eV. The differences around these energyregions are clearly observed when comparing the LDOS of theatoms in the subsurface (Fig. 5(d)) and the 4th layer (Fig. 5(e)).Fig. 3 Total density of states (DOS) for gold nanoparticles with (a) 13 (Oh1), (b) 55 (Oh2), (c) 147 (Oh3), (d) 309 (Oh4), (e) 561 (Oh5), (f) 923 (Oh6), (g) 1415(Oh7), and (h) 2057 (Oh8) atoms (EF is set to be zero). The DOS of bulk fcc gold is provided at the top for comparison. Note that the present total DOS isdefined for the whole system, not per atom.Paper PCCPOpen Access Article. Published on 21 June 2024. Downloaded on 8/2/2024 7:52:05 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4cp01094aThis journal is © the Owner Societies 2024 Phys. Chem. Chem. Phys., 2024, 26, 20251–20260 |  20255Fig. 6 shows the PCA results for Oh1–Oh8 and corresponds tothe size dependence of ‘‘local’’ electronic structures, whereasFig. 3 corresponds to the size dependence of the global electro-nic structure for whole nanoparticles. In Fig. 6, the points arecategorised in the three areas for all eight nanoparticles, andthe distribution of the points in the three areas starts conver-ging roughly from Oh4. The results indicate that the electronicstructure change by forming nanoparticles occurs only in thesurface and subsurface for any size of nanoparticles and thatnot only the electronic structure of the whole nanoparticle butalso the local electronic structures start converging from theparticle size of B2 nm. Furthermore, the points are distributedmore widely in Oh8 than in Oh4, indicating that the sitedependence of the electronic structure is larger in largernanoparticles. The weights of the PCA components in Fig. 6are provided in Fig. 7. Since the PCAs were performed sepa-rately, we obtained different PCA components for Oh1–Oh8. ThePCA components in Fig. 7 also become similar from Oh4 sincethe LDOS is almost converged. For Oh1 in which there are only 2kinds of atomic positions, only the first component is useful forthe classification. Note that we did not use descriptors based ondomain knowledge, such as the d-band centre, but still distin-guished the atoms with different electronic structures.3.2 Atomic and electronic structures of supportednanoparticlesNext, we investigated the atomic and electronic structures ofgold nanoparticles supported by the MgO(100) substrate. In thepresent study, we chose Oh4 as the model of the gold nanopar-ticle on the MgO substrate because the electronic structure ofOh4 can be considered ‘‘metallic’’, based on the discussion inthe previous section. It has been observed experimentally thatthe lower part of the gold nanoparticle near the substrate ismissing.1,48 Therefore, in the present study, we investigatednanoparticles with several shapes, in which the lower layers ofthe nanoparticle are missing, as shown in Fig. 8(a1)–(e1). Theinterfacial area between the nanoparticle and the substratebecomes wider when more of the lower part of the nanoparticleis missing, and the interaction energies (Eint) between thenanoparticles and the substrates gradually increase as theinterfacial areas increase. The heights of the Mg and O atomsin the MgO surface (Dh) are also provided in Fig. 8(a2)–(e2). Thehorizontal axis in Fig. 8(a2)–(e2) corresponds to the distancefrom the centre of the nanoparticle to Mg or O atom in xy-plane. Note that O is higher than Mg in the surface far from thenanoparticle, which is consistent with the previous studies forthe clean MgO(100) surface.49 It is found that the heights of thesurface atoms near the nanoparticles are lower than those ofthe other surface atoms, indicating that the MgO surfaces areconcave under the nanoparticle. In the figure, the magnitude ofthe concave Dhc is defined as the height difference between thelowest atom and the atom furthest from the nanoparticle foreach of Mg and O. The concaves around the nanoparticleswhose lower layers are missing (Fig. 8(b2)–(e2)) are larger thanthat around the perfect nanoparticle (Fig. 8(a2)).Then, we investigated the electronic structures of supportedgold nanoparticles. The LDOS of the atoms in the supportednanoparticles was calculated. Using the first and second compo-nents obtained for isolated Oh4 nanoparticles, the LDOS of thesupported nanoparticles was projected directly onto the PCA mapof the isolated Oh4 nanoparticle, as shown in Fig. 9. Owing to thedirect projection, we can compare the differences in the positionof the points between the isolated and supported nanoparticles inFig. 4 Local electronic structure analysis of the Oh6 gold nanoparticleswith of 923 atoms. (a)–(d) LDOS for atoms at the vertex, edge, and (111)and (100) faces of the nanoparticle (EF is set to be zero). (e) LDOSdistribution of the 923 atoms in 2D space by PCA. Black, purple, yellow,pink, blue, green, and red points correspond to the LDOS of the atoms atthe centre and in the 1st, 2nd, 3rd, 4th, 5th and 6th (surface) layers of thenanoparticle, respectively. For the surface atoms, circle, square, diamond,and star symbols are used for the LDOS of the atoms in the vertex, edge,(111) and (100) faces, respectively.PCCP PaperOpen Access Article. Published on 21 June 2024. Downloaded on 8/2/2024 7:52:05 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4cp01094a20256 |  Phys. Chem. Chem. Phys., 2024, 26, 20251–20260 This journal is © the Owner Societies 2024a PCA map, which corresponds to the electronic structure changeinduced by the MgO substrate. When a point of the supportednanoparticle is shifted from that of the isolated nanoparticle, itmeans that the electronic structure of the corresponding atomis changed by the MgO substrate. In the centre areas of thePCA maps, there are several points for the supported nano-particles but no point for the isolated nanoparticle. The centrepoints correspond to the electronic structures of the gold atoms atthe interface between the nanoparticle and the substrate. Thus,the PCA map reveals the large electronic structure changes in thegold atoms at the interface. Fig. 9(a0) shows the PCA results of thesupported nanoparticle, in which the particle shape is the same asthat in Fig. 9(a) but the position of the nanoparticle is different(i.e., the gold atoms in the interface are located above the MgFig. 5 Weights of (a) first and (b) second principal components in the PCA for the LDOS of the gold nanoparticle consisting of 923 atoms in six layers(Oh6). LDOS of the atoms at the vertex positions in (c) the surface, (d) subsurface, and (e) 4th layer in Oh6. The positions of the large peaks at �2.646 and�6.578 eV in (a) and �5.864 and �6.803 eV in (b) are highlighted in red, blue, yellow and green in (c)–(e), respectively.Fig. 6 LDOS distributions for the atoms in gold nanoparticles with (a) 13 (Oh1), (b) 55 (Oh2), (c) 147 (Oh3), (d) 309 (Oh4), (e) 561 (Oh5), (f) 923 (Oh6),(g) 1415 (Oh7) and (h) 2057 (Oh8) atoms in 2D space by PCA. Red, green, and blue points correspond to the LDOS of atoms at the surface, subsurface, andinner layers of the nanoparticle, respectively. For the surface atoms, circle, square, diamond, and star symbols are used for the LDOS of atoms in thevertex, edge, (111) and (100) faces, respectively.Paper PCCPOpen Access Article. Published on 21 June 2024. Downloaded on 8/2/2024 7:52:05 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4cp01094aThis journal is © the Owner Societies 2024 Phys. Chem. Chem. Phys., 2024, 26, 20251–20260 |  20257atoms of the surface). Comparing Fig. 9(a) and (a0), the distribu-tions of the points in the centre areas differ, but the positions ofthe other points are more similar. This means that the electronicstructures of the interface atoms largely depend on the particlepositions, whereas those of the other atoms depend less on thepositions. Moreover, there are two points corresponding to thevertex atoms v1 and v2 in Fig. 9(a2)–(d2), which are not located atthe interface, although v2 is closer than v1 to the substrate. Thepoint of v2 is further than that of v1 from the point of the vertexatom in the isolated nanoparticle v0, especially in the nano-particles whose lower layers are missing, as shown in Fig. 9(b2)–(d2). These point distributions indicate that the electronic struc-tures of the atoms that are not directly located at but, rather, nearthe interface are also slightly affected by the substrate, whereasthe atoms far from the interface are barely affected.To investigate the relationship between the PCA result andthe reactivity, we calculated the adsorption energies Ead of ahydrogen atom (H) and an O2 molecule at the vertex atoms ofthe isolated nanoparticle (v0) and the vertex atoms at the v1 andv2 sites of the supported nanoparticles. As shown in Table 1,the Ead of v2 is larger than that of v1 for all supportednanoparticles. The O–O bond elongation is also larger in v2Fig. 7 Weights of the first and second principal components in the PCA for gold nanoparticles with (a) 13 (Oh1), (b) 55 (Oh2), (c) 147 (Oh3), (d) 309 (Oh4),(e) 561 (Oh5), (f) 923 (Oh6), (g) 1415 (Oh7) and (h) 2057 (Oh8) atoms.Fig. 8 (a1)–(e1) Optimised structures of the nanoparticles with the diameter of 2 nm in different shapes supported by MgO(100) substrate (yellow: Au,blue: Mg, red: O), provided with the interaction energy between the nanoparticles and substrate Eint [eV]. (a2)–(e2) Heights of the surface Mg and O atomsDh [Å] in the structures of (a1)–(e1). The height of the O atom furthest from the nanoparticle is set to zero. The horizontal axis corresponds to the distancer [Å] from the centre of the nanoparticle to Mg or O atom in xy-plane. Dhc correspond to the height differences between the lowest atom and the furthestatom for each element (e.g. red arrow for O and blue arrow for Mg in (b2)).PCCP PaperOpen Access Article. Published on 21 June 2024. Downloaded on 8/2/2024 7:52:05 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4cp01094a20258 |  Phys. Chem. Chem. Phys., 2024, 26, 20251–20260 This journal is © the Owner Societies 2024than in v1, which indicates that adsorption with larger Ead leadsto larger bond elongation. These results suggest that the vertexatoms near the substrate, whose points are shifted significantlyin the PCA map, are activated more than those far from thesubstrate because of the substrate effect, even if they are notlocated directly at the interface. Comparing the particles withdifferent shapes, the order of Ead and O–O bond elongation atthe v2 site is sNP-a t sNP-b o sNP-c o sNP-d, which suggeststhat the vertex nearer to the substrate is more active. For sNP-d,the adsorbed O2 molecule is close to the surface and theFig. 9 (a)–(e) Two-dimensional PCA map of the supported nanoparticles with the shapes in Fig. 9(a1)–(d1). The PCA results of the supportednanoparticles are presented with blue points. The colour depth of the blue points corresponds to the distance of the gold atoms from the MgO substratesurface. The PCA result of the isolated nanoparticle is presented with yellow points for comparison. (a2)–(d2) Enlarged figures of the squarely-surrounding areas in (a)–(d) with the corresponding atomic sites (v1 and v2). v0 in (a2)–(d2) correspond to the points of the vertex atom in the isolatednanoparticle. Cross, triangle, circle, square, diamond and star symbols corresponds to the atomic positions, inside layers, subsurface and surface vertex,edge, (111) and (100) faces in Oh4, respectively.Table 1 Adsorption energies Ead [kcal mol�1] of a hydrogen atom and an O2 molecule and O–O bond elongations DrO–O [Å] for adsorption to theisolated nanoparticle Oh4 and the supported nanoparticles with the shapes shown in Fig. 8(a1)–(d1) (sNP-a–sNP-d). The adsorption sites v0, v1, and v2are shown in Fig. 8(a2)–(d2)Isolated nanoparticle Supported nanoparticleParticle shape Oh4sNP-a sNP-b sNP-c sNP-dAdsorption site v0 v1 v2 v1 v2 v1 v2 v1 v2AdsorbateH Ead 75.6 76.3 77.0 75.0 76.3 74.5 75.7 76.0 80.2O2 Ead 27.6 22.5 23.0 22.2 22.5 22.6 23.9 22.9 37.4DrO–O 0.043 0.047 0.047 0.048 0.048 0.049 0.051 0.050 0.098Paper PCCPOpen Access Article. Published on 21 June 2024. Downloaded on 8/2/2024 7:52:05 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4cp01094aThis journal is © the Owner Societies 2024 Phys. Chem. Chem. Phys., 2024, 26, 20251–20260 |  20259molecule interacts not only with the vertex atom but also withthe surface. Although it is difficult to make rigorous conclu-sions because the absolute differences between the Ead and theO–O bond elongation are subtle in the present calculation, theresults suggest that conducting the PCA of the LDOS data isuseful for identifying the potential active sites.4. ConclusionsThe present study has proposed a method to analyse thedifference of the local electronic structure in large systemssystematically and quantitatively by the combination of large-scale DFT calculations and PCA. The size and site dependencesof the atomic and electronic structures of isolated and sup-ported gold nanoparticles were investigated by the combinationof large-scale DFT calculations and statistical analysis. Thelarge-scale DFT calculations with the CONQUEST code forisolated gold nanoparticles with several diameters rangingfrom 0.55 nm to 4.52 nm revealed that the DOS of thenanoparticle converges according to its size, and the nano-particles with diameters of B2 nm or larger have continuous(i.e., metallic) electronic structures. To investigate the sitedependence of the electronic structures, the LDOS was calcu-lated for all atoms. Because we used large simulation modelscontaining several thousand atoms, it was not straightforwardto investigate the LDOS for all atoms and identify atoms thathave characteristic electronic structures. To overcome thisproblem and systematically and efficiently analyse the LDOSof several thousand atoms in the nanoparticles, we performedPCA. For the nanoparticles of B2 nm or larger in diameter, thePCA results of the LDOS were categorised into three groups: theatoms in the surface, subsurface, and inner layers. Differencesin the electronic structure were only found in the surface andsubsurface, whereas the electronic structures of the inner layersalmost converged. Conventionally, it has been assumed thatseveral outer layers of the nanoparticle have different electronicstructures from the bulk system because of surface effects, butour large-scale DFT calculation combined with PCA providesinsight into how deeply the change in the electronic structureextends into the nanoparticles.We have also investigated the effect of the substrate on theelectronic structure of the nanoparticles. The DFT calculationsof gold nanoparticles on the MgO(100) substrate, consisting ofapproximately three thousand atoms in total, were performedusing multi-site support functions. Notably, the optimisedstructures of the MgO surface were concave near the nanopar-ticle. The LDOS of the gold atoms in the supported nano-particles were investigated by projecting their DOS with thePCA components obtained for the isolated nanoparticle, whichenabled the direct comparison of the LDOS for the isolated andsupported nanoparticles in a 2D-PCA map. By comparing thepositions of the points for the isolated and supported nano-particles in the PCA map, we determined the atoms that arelargely affected by the MgO substrate. Most of the largelyaffected atoms are located at the interface between thenanoparticle and the substrate, and several atoms are affectedeven though they are not located directly at the interface. Thecomparison of the adsorption for a hydrogen atom and an O2molecule to the vertex atoms in the isolated and supportednanoparticles shows that the vertex atom, which is found to bemore strongly affected by the substrate has larger adsorptionenergy and O–O bond elongation, indicative of the correlationbetween the electronic structure and the reactivity. This resultis encouraging, suggesting that we can predict active sites inlarge systems from the information on local electronic struc-tures in future work. Moreover, the large-scale DFT calculationcombined with PCA in the present study is not limited to thepresent systems but applicable to many kinds of problems, forexample, the effect of the combinations of other nanoparticlesand substrates, the effect of defects and dopants and so on. Thepresent method can be also applied to various materials, notonly to catalysts. Managing huge amounts of data has been oneof the long-standing problems in large-scale calculations, andthe present method may help to overcome the problem.Data availabilityThe CONQUEST code for large-scale first-principles density func-tional theory calculations can be found at https://github.com/OrderN/CONQUEST-release with DOI: 10.5281/zenodo.3943720.The version of the code employed for this study is version 1.0.5.Conflicts of interestThere are no conflicts to declare.AcknowledgementsThe authors appreciate Prof. Yoshitada Morikawa and Prof.Takato Mitsudome at Osaka University for their valuable dis-cussion. This work is supported by the World Premier Interna-tional Research Centre Initiative (WPI Initiative) on MaterialsNanoarchitectonics (MANA), JST PRESTO (Grant No.JPMJPR20T4), JSPS Grant-in-Aid for Transformative ResearchAreas (A) ‘‘Hyper-Ordered Structures Science’’ (Grant No.JP20H05883 and JP20H05878), JSPS Grant-in-Aid for ScientificResearch (Grant No. JP18H01143), and MEXT ‘‘Program forPromoting Research on the Supercomputer Fugaku’’ (Grant No.JPMXP1020230325). Calculations were performed using theNumerical Materials Simulator at NIMS. We thank RobertIreland, PhD, from Edanz (https://jp.edanz.com/ac) for editinga draft of this manuscript.References1 T. Ishida, T. Murayama, A. Taketoshi and M. Haruta, Chem.Rev., 2020, 120, 464–525.2 H. Yoshida, Y. Kuwauchi, J. R. Jinschek, K. Sun, S. Tanaka,M. Kohyama, S. Shimada, M. Haruta and S. Takeda, Science,2012, 335, 317–319.PCCP PaperOpen Access Article. Published on 21 June 2024. Downloaded on 8/2/2024 7:52:05 AM.  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