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Electronic Structures of Small (RuO) (n= 1 to 4) Nanoclusters and Their Anions and the Hydrolysis Reactions with Water Zongtang Fang, Michael A Outlaw, and David A Dixon J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b07226 • Publication Date (Web): 12 Sep 2017 Downloaded from http://pubs.acs.org on September 13, 2017

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The Journal of Physical Chemistry

Electronic Structures of Small (RuO2)n (n= 1 to 4) Nanoclusters and Their Anions and the Hydrolysis Reactions with Water Zongtang Fang, Michael A. Outlaw, and David A. Dixon* Department of Chemistry, The University of Alabama, Shelby Hall, Box 870336, Tuscaloosa, AL 35487-0336

Abstract Group 8 (RuO2)n (n= 1 to 4) nanoclusters, their anions and the hydrolysis reactions of the neutral clusters have been studied with the density functional theory (DFT) as well as coupled cluster CCSD(T) theory. The ground state is predicted to be a singlet and a doublet for the neutral RuO2 clusters and anionic clusters, respectively. The CCSD(T) method is required to predict the correct ground state. The calculated singlet-triplet gaps ( < 15 kcal/mol) and fluoride affinities ( < 95 kcal/mol) are smaller than those of the Group 4 (MO2)n and Group 6 (MO3)n metal oxide clusters. The electron affinities range from 2.2 to 3.4 eV showing that the RuO2 clusters are quite reducibile. Clustering energies and heats of formation are calculated. The water physisorption energies are predicted to be -10 to -20 kcal/mol with the adsorption energy for the singlet generally more exothermic than for the triplet. The hydrolysis reactions are exothermic for the monomer and dimer clusters and are slightly endothermic or neutral for the trimer and tetramer. H2O is readily dissociated on the monomer and dimer, but not on the trimer and tetramer. The physisorption and chemisorption energies are less exothermic and the barriers for the hydrolysis reactions are larger of RuO2 nanoclusters than for the corresponding Group 4 ZrO2 nanoclusters.

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Introduction Two different types of ruthenium oxide, RuO4 (+VIII) and RuO2 (+IV), are the most common. RuO4 is a colorless liquid at room temperature, whereas RuO2 is stable in the solid phase with a rutile structure in nature. 1,2,3 Both RuO2 and RuO3 molecules have been observed in solid matrices. 4,5 RuO2 can be deposited on various metal oxide substrates such as TiO2, WO3, Al2O3, and ZnO by grafting dopamine onto the unreactive surfaces from RuO4. 6 RuO2 films can be made by pulsed-chemical vapor deposition method using the RuO4 precursor. 7 RuO2 is widely used in heterogeneous catalysis, for example in electrocatalysis. RuO2 has been used for dimensionally stable anodes in the industrial scale cholor-alkali electrolysis process to produce Cl2 (chlorine evolution reaction: CER) and NaOH. 8, 9 RuO2 supported on TiO2 has been used for large scale manufacturing of chlorine via the catalytic oxidation of hydrogen chloride (Deacon reaction). 10 RuO2 is also used as the supported cocatalyst together with a photocatalyst to improve the efficiency of water splitting to produce hydrogen and oxygen (hydrogen evolution reaction: HER and oxygen evolution reaction: OER). 11,12,13,14 The presence of RuO2 is believed to improve the transfer of photogenerated holes and electrons.14 RuO2 can be reduced to Ru0 during catalytic reactions.16 RuO2 is also an active catalyst for biomass conversion reactions. 15, 16, 17, 18, 19 Of interest is the fact that solid RuO2 is actually metallic. 20 The (110) surface is the most dominant orientation for crystalline RuO2.31 The surface reactivity has been studied in terms of the adsorption of small molecules including O2, 21,22,23 CO,2,23, 24,25,26 H2,27 and water 28,29 on the RuO2 (110) surface. These molecules are stable on the surface either as a molecular adsorbate or can participate in dissociative chemisorption. The adsorption takes place mostly on coordinatively unsaturated Ru and under-coordinated bridging O sites. Those reactions are generally exothermic except for atomic hydrogen adsorption on a coordinatively unsaturated 2 ACS Paragon Plus Environment

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Ru site. Conversion of alcohols to aldehydes with oxygen has been efficiently catalyzed by a solid Ru-Co oxide in liquid phase under atmospheric pressure. 30 There is a substantial interest in the study of molecular structures and energetics for ruthenium oxide nanoclusters due to their interesting electrical, magnetic, optical, and catalytic properties. 31 Zeolite-confined RuO2 nanoclusters have been synthesized by a hydrothermal method and are efficient catalysts for the oxidation of alcohols 32,33 and cyclohexane. 34 TiO235 or Al2O335, 36 as well as carbon nanotube 37 , 38 supported RuO2 nanoparticles are also active heterogeneous catalysts for the aerobic oxidation of alcohols to alkenes or ketones. The mechanism of the production of ruthenium alkoxides as the key intermediate species has been proposed.35,36 Furthermore, Ru can be released in severe nuclear power plant accidents where steam is generated either from the coolant or as the power transfer agent. In the presence of air in this atmosphere, a variety of species can be generated including Ru oxides and hydroxides which can serve to disperse the radioactive contaminant isotopes

103

Ru and 106Ru. 39,40,41,42 Thus it is of

additional interest to understand the hydrolysis reactions of small nanoclusters of Ru containing O and OH. The lack of a detailed understanding of the structure-property relationships of RuO2 nanoparticles suggests that more information is required for such species to be used in practical applications. Vallet and coworkers studied the thermochemistry of gas phase mono ruthenium oxides and ruthenium oxyhydroxides because they are produced as fission products in in pressurized water nuclear reactors using both density function theory (DFT) and several post-HF methods. 43,44 They found that the CCSD(T) method gives better results than do CASSCF, MRCI and CASPT2 methods due to the need to treat dynamic correlation. The thermodynamic data at this high computational level provides a reliable database for the gas phase mono-ruthenium 3 ACS Paragon Plus Environment


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species and these values were used to determine the speciation of these species under severe nuclear reactor conditions. The RuO2 monomers to pentamers as well as their cations and anions have been studied at the DFT level with the B3LYP functional. 45 The hydrolysis reactions have been studied at the same level. These workers predict that three-dimensional structures are preferred with an increase in cluster size. Water physisorption on the cationic clusters are more exothermic than on the neutral clusters. This is also true for the water dissociative chemisorption reactions. Although, the small RuO2 clusters have been studied at the DFT B3LYP level,45 metallic RuO2 has a d4 valence electronic configuration on the metal and there are low lying excited states for each isomer so the DFT method may not provide accurate energies. Our preliminary results for the RuO2 dimers suggested that DFT/B3LYP does not give the correct ground state and that a higher level computational electronic structure method is required. The previous study on the heats of formation of gas phase mono-ruthenium oxides and oxyhydroxides43,44 showed there is a large deviation of the calculated thermochemical data between the DFT/TPSS 46 and CCSD(T) methods. Thus, the energetics for the small RuO2 clusters are not well-established based on the only available results with DFT. In this paper, we first study the molecular structure and energetics of small (RuO2) n (n = 1 to 4) nanoclusters with both DFT and CCSD(T) theory. The structures of energetically low lying isomers were predicted for different spin states (singlet, triplet, and quintet) to find the ground states. For the ground state isomers, the corresponding anionic clusters are calculated to obtain the electron affinities to investigate the reducibility of the metal center. 47 , 48 The fluoride affinities are calculated to predict the Lewis acid-base properties. The fluoride affinity (FA) of A is the negative of the reaction enthalpy at 298 K of the


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reaction A + F− → AF−. 49,50 The normalized clustering energies of the dimer, trimer and tetramer are also calculated. 51 In the second part, we focus on the interaction between water and (RuO2) n (n = 1 to 4) nanoclusters as RuO2 has been found to be an effective cocatalyst to improve the water splitting efficiency.11,12,52,53 We use both DFT theory and coupled cluster CCSD(T) theory to study the hydrolysis reactions of H2O on (RuO2) n (n = 1 to 4) nanoclusters. The water physisorption and chemisorption processes as well as the proton transfer to produce the hydroxide have been studied. The potential energies surfaces (PESs) are calculated for the ground state singlet and the first excited triplet clusters. Computational Methods The geometries for the neutral nanoclusters were optimized with the B3LYP 54 , 55 , BP86

56 , 57

and PW91 58 , 59 exchange correlation functionals at the DFT level. The B3LYP

functional was selected based on our previous work on the Group 4 (MO2)n and Group 6 (MO3)n metal oxide (MO) nanoclusters 60,

61, 62

and on the study of hydrolysis reactions of those MO

nanoclusters. 63,64,65 The spin unrestricted calculations with the B3LYP functional do not always predict the correct spin pairing of the spin-polarized alpha and beta orbitals for some doubly occupied molecular orbitals of the open shell molecules. Thus, there is more spin contamination using the B3LYP functional than the BP86 and PW91 functionals. The starting guesses of the structures of the nanolcusters for the geometry optimization are taken from our previous work on the Group 4 MO clusters. Vibrational frequencies were calculated to characterize the global minimum on the potential energy surface and to obtain the zero-point energy corrections (ZPEs) and the thermal corrections at 298 K, which were calculated by using the normal statistical mechanical expressions. 66 The aug-cc-pVDZ basis sets 67 for O and H and PP-based aug-cc5 ACS Paragon Plus Environment


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pVDZ-PP basis sets 68 for Ru were used for the DFT geometry optimization and frequency calculations. For simplicity, we denote these combined basis sets as aD. We used both the B3LYP and BP86 functionals and the aD basis set for the optimization of the anions and the same spin contamination issue for the B3LYP has been found for the open shell molecules. The DFT calculations were carried out with the Gaussian 09 program package. 69 The DFT/B3LYP optimized geometries for the ground state monomers and dimers with the singlet, triplet, and quintet states were used in single point energy calculations at the coupled cluster [CCSD(T)] level 70, 71, 72, 73 with the sequence of basis sets of aX (X = D, T, and Q),67,68 except for cases where the B3LYP geometry resulted in symmetry breaking. In these cases, the BP86 geometries were used. These CCSD(T) energies were extrapolated to the complete basis set (CBS) limit using a mixed Gaussian/exponential formula. 74 Although there is more spin contamination for the B3LYP calculations, the optimized geometries using the B3LYP and BP86 functionals do not differ by much. Thus the differences in the CCSD(T) energies from the use of geometries from different functionals is small. For the singlet and triplet Ru2O4, the CCSD(T) energies with the aT basis set differ by only 1.0 kcal/mol using the geometries optimized with the B3LYP and BP86 functionals. The electron affinities and fluoride affinities for the ground state monomer and dimer are also calculated at the CCSD(T)/CBS level. For the trimer and tetramer, the geometries optimized at the B3LYP/aD level are used for the singe point calculations at the CCSD(T) level, except for cases where the B3LYP geometry resulted in symmetry breaking. In these cases, the BP86 geometries were used. The electronic energies of the open-shell species are calculated with the R/UCCSD(T) approach where a restricted open shell Hartree-Fock (ROHF) calculation was initially performed


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and the spin constraint was then relaxed in the coupled cluster calculation. 75,76,77 All CCSD(T) calculations were performed with the MOLPRO 2012.1 program. 78, 79 For the hydrolysis reactions, the reactions of up to two water molecules with the small clusters are studied. The potential energy surfaces are calculated for the ground state as well as the first excited state of the triplet state. The synchronous transit-guided quasi-Newton (STQN) method was used to search for the transition states, which are characterized by a single imaginary frequency. 80 The geometry optimizations were first performed with the B3LYP functional and the aD basis set. The DFT potential energy surfaces are benchmarked with the CCSD(T) method with the aD basis sets using the B3LYP geometries. The B3LYP energetic results for the trimer and tetramer do not agree well with the CCSD(T) results, so we tried the BP86 functional, which works better for the hydrolysis reactions of the trimer and tetramer. The CCSD(T) calculations were performed for the reactions with two water molecules involved for the monomer and dimer. Only the first water addition was calculated at the CCSD(T) level for the trimer and tetramer. We use the Feller-Peterson-Dixon (FPD) method 81, 82, 83 as implemented previously by us 84 for other transition metal oxide clusters for the calculation of the total atomization energies (TAE, ΣD0,0K) and the heats of formation of ground singlet state ruthenium oxides and oxyhydroxides. As noted above, the valence contributions are calculated using the DFT/B3LYP geometry at the CCSD(T) level with the sequence of basis sets of aX (X = D, T, and Q) and these energies were extrapolated to the complete basis set (CBS) limit using a mixed Gaussian/exponential formula.74 Core-valence (CV) correlation corrections for the 1s2 electrons on O and 4s24p6 electrons for the ruthenium were calculated at the CCSD(T) level with the augcc-pwCVTZ basis set for O and aug-cc-pwCVTZ-PP basis set for the metals. This basis set combination is denoted as awT. For RuO2, Ru2O4, RuO(OH)2, and Ru(OH)4, the CV corrections 7 ACS Paragon Plus Environment


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were calculated at the CCSD(T)/CBS level, which were derived using the same formula for the valence contributions. The spin-orbit (SO) corrections are derived from the atomic experimental value. 85,86,87 The scalar relativistic corrections (ΔERel) including the pseudopotential corrections were calculated at the second order Douglas-Kroll-Hess (DK) 88,89,90 level with the all-electron aug-cc-pwCVTZ-DK basis sets.

91 , 92 , 93 , 94

These basis sets are denoted as awT-DK. The

relativistic correction is given as the difference between ΔEawT-DK and ΔEawT.

The ΔERel is

derived from the calculations with the correlation of both valence and outer-core electrons. As the singlet ruthenium oxides and oxyhydroxides may have some multi-reference character with the T1 diagnostics ranging from 0.04 to 0.06, we use the PW91 orbitals as the initial wave functions for the coupled cluster calculations. This follows our previous work on transition metal oxide clusters, 95,51 where we used this approach to deal with potential multi-reference character leading to improved TAEs. The relativistic corrections are derived from the calculations using HF orbitals. The results with PW91 orbitals are noted as CCSD(T)/PW91. The calculations were performed on the local Xeon and Opteron based Penguin Computing clusters, the Xeon based Dell Linux cluster at the University of Alabama, the Opteron and Xeon based Dense Memory Cluster (DMC) and Itanium 2 based SGI Altix systems at the Alabama Supercomputer Center, and the Opteron based HP Linux cluster at the Molecular Science Computing Facility at Pacific Northwest National Laboratory. Molecular visualization was done using the AGUI graphics program from the AMPAC program package. 96 Results and Discussions The optimized geometries for the neutral and anionic clusters at the BP86/aD level as well as the CCSD(T) relative energies for different isomers are shown in Figures 1 and 2. The geometries at the B3LYP/aD level are shown in the Supporting Information (SI). We optimized 8 ACS Paragon Plus Environment

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the structures of the singlet, triplet, and quintet spin states for the neutral clusters. For the anionic clusters, the doublet, quartet and sextet spin states were optimized. Figure 1 only shows the spin state with the lowest energy for each conformation and the structures of the isomers in other spin states are shown in the SI. The relative energies for the neutral clusters with the B3LYP, PW91, and BP86 functionals are also shown in the SI. Neutral Cluster Structures and Energies All three DFT functionals give the same ground state for the monomer. The ground state of RuO2 monomer is predicted to be 1A1 in C2v symmetry (Figure 1). This is consistent with all previously reported calculations. 5,43,97,98 The O-Ru-O bond

1.694

1.699

1.689 153.6˚

1.890

RuO2 (1A1,C2v)

1.890

Ru2O4(1A1,C2v), 0.0

1.684

1.867 1.680

1.904

1.893

1.832

1.913

1.874 1.908

Ru3O6(1A1,C3v),

0.0

Ru3O6(1A,C1),

36.3

1.674 1.963 1.861

Ru3O6(1A,C2),

1.996

1.871

1.693 1.999

Ru2O4(3A˝,Cs), 33.9 1.905 1.686 2.021 1.948

1.880

1.898

1.692

2.046

1.885

Ru2O4(1Ag,C2h), 5.8

1.870

1.856

39.9

Ru3O6(1A′, Cs), 44.5

1.677 1.697

1.874

1.659 1.883

1.975 1.822

1.842

2.036

1.903

Ru4O8(1A1,C2v,a), 0.0

1.669 2.012 2.265 1.912 1.887 1.880

Ru4O8(1A1,C2v,b), 36.1 Ru4O8(1A1,Td), 38.7

Ru4O8(1A1,C2v,c),42.1

Figure 1. Molecular structures of the neutral (RuO2)n (n = 1 to 4) clusters. Bond distances in Å and Bond Angle in Degree at the BP86/aD Level. Relative energies in kcal/mol at the CCSD(T)/CBS//B3LYP/aD Level for the dimer and the CCSD(T)/aD//B3LYP/aD for the trimer and tetramer. 9 ACS Paragon Plus Environment


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angle is predicted to be 153.6˚ at the BP86/aD level. The Ru=O bond distance is 1.694 Å. The calculated bond distance and bond angle are close to previous results with the TPSSh-5%HF functional

(1.685

Å,

149.8°)

and

the

HF

method

(1.595

Å,

150.6°). At

the

CCSD(T)/CBS//B3LYP/aD level, the triplet and quintet isomers are of 11.0 and 26.4 kcal/mol higher in energy. The relative energies of the triplet and quintet isomers predicted by the DFT are smaller than the CCSD(T) values by up to 6 and 10 kcal/mol respectively. Previous work reported a singlet-triplet gap of 13.2 kcal/mol44 for RuO2 at the CCSD(T) level, which is consistent with our vertical excitation energy of 13.1 kcal/mol at the CCSD(T)/CBS level. The ground state of the dimer (RuO2)2) is predicted to be 1A1 in C2v symmetry with two Ru=O double bonds and four Ru-O single bonds. The 3A˝ state with the Cs symmetry (shown in the SI) is slightly higher in energy by 3.2 kcal/mol at the CCSD(T)/CBS//B3LYP/aD level. BP86/aD predicts the triplet (3A˝, Cs) to be the ground state and the singlet to be 5.9 kcal/mol higher in energy. The difference may be due to the correlation of the d electrons requiring a high level computational method such as CCSD(T) to obtain accurate relative energies. This is consistent with a previous study on the ruthenium oxide monomers showing better thermodynamic results predicted by the CCSD(T) than the other methods such as MRCI, CASPT2.44 The Ru=O bond distance of 1.635 Å in the ground state isomer 1Ru2O4 (C2v) is slightly shorter than that in the monomer. The Ru-O bond distance in 1Ru2O4 (C2v) is 1.907 Å. The singlet conformer in C2h symmetry (Figure 1) is predicted to be 5.8 kcal/mol higher in energy than the ground state at the CCSD(T)/CBS//B3LYP/aD level. The Ru=O and Ru-O bond distances are close to those in the lowest energy conformer. The triplet in Cs symmetry has a much higher energy than 1Ru2O4(C2v) with a difference of 33.9 kcal/mol. Both the B3LYP and


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PW91 functionals with the aD basis set predict the triplet to be the ground state with correpsonding singlet-triplet splittings of 3.0 and 5.4 kcal/mol. Consistent with the monomer and dimer, the ground state of the trimer is 1A1 in C3v symmetry with three Ru=O double bonds and six Ru-O single bonds (Figure 1). Jahn-Teller distortion effects for the triplet decrease its symmetry to Cs. The optimization of the triplet 3A′ in Cs symmetry with the B3LYP results in symmetry breaking to give a lower C1 symmetry. The excited triplet and quintet structures are shown in the SI. At the CCSD(T)/aT//B3LYP/aD level, the excited triplet state and the quintet state are 13.2 kcal/mol and 24.9 kcal/mol higher in energy than the ground state singlet. The Ru=O and Ru-O bond distances in 1Ru3O6 (C3v) are predicted to be 1.684 Å and 1.904 Å respectively at the BP86/aD level. The isomer in C1 symmetry for the singlet spin state is 36.3 kcal/mol higher in energy than the ground state at the CCSD(T)/aD//B3LYP/aD level. For the C2 symmetry structures, the singlet is predicted to be lower in energy than the triplet and the quintet. The energy of the higher energy singlet isomer Ru3O6 (1A´,Cs) is also lower than the triplet and the quintet at this geometry. For the conformations other than the ground state, the Ru=O bond distances range from 1.67 to 1.69 Å and the Ru-O bond lengths range from 1.80 to 2.00 Å. The ground state is again a singlet in C2v symmetry for the tetramer as shown in Figure 1. The first excited state is predicted to be 3A2 in C2v symmetry. For the triplet, symmetry breaking is also found with the B3LYP functional. The triplet-singlet splitting energy for the ground state isomer is predicted to be 9.7 kcal/mol at the CCSD(T)/aT//B3LYP/aD level. This gap decreases to 3.9 kcal/mol and 1.0 kcal/mol at the BP86/aD and the B3LYP/aD levels, respectively. The quintet for structure C2v,a is much higher in energy, 34.9 kcal/mol, than the ground state at the CCSD(T)/aD//B3LYP/aD level. The Ru=O and the Ru-O bond distances are generally consistent 11 ACS Paragon Plus Environment


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with those of the smaller nanoclusters. The other conformations for the tetramer have the singlet lower in energy than the quintet and triplet. These isomers are 35 to 40 kcal/mol higher in energy than the ground state at the CCSD(T)/aD//B3LYP/aD level. The Ru=O bond distances are predicted to be 1.64 to 1.66 Å and the Ru-O bond lengths are 1.80 to 2.03 Å depending on the structure. First Excited Neutral State The structures and the excitation energies for the first excitation states of the (RuO2)n (n = 1 to 4) nanoclusters are shown in Figure 2. The first excited states are

-67.8a -65.7b 3RuO

3Ru O 2 4

2

ΔES-T = FA = -90.4a EA = 2.69a

11.0a

2

ΔES-T = FA = -87.0a EA = 2.22a

0.0a

3Ru O 4 8

3Ru O 3 6

ΔES-T = 3.2a FA = -83.7a EA = 3.31c

ΔES-T = 13.2d FA = -81.2b EA = 3.99b

-49.1a -48.9b 1RuO

-72.6b

-91.3b

-92.8b 1Ru O 2 4

-59.1b

1Ru O 3 6

ΔES-T = FA = -93.2a EA = 3.17a

0.0a

ΔES-T = 9.2d FA = -87.6b EA = 3.26b

ΔET-Q =0.0b FA = -77.1b EA = 3.42b

1Ru O 4 8

ΔES-T = 0.0b FA = -88.0b EA = 2.86b

Figure 2. Singlet (bottom row) and first excited triplet states (top row) for the (RuO2)n (n = 1 to 4) nanoclusters. Electron affinities, fluoride affinities, and sequential clustering energies for the ground state singlet and first excited state triplet. a At the CCSD(T)/CBS//B3LYP/aD Level; b At the CCSD(T)/aT//B3LYP/aD Level. c At the CCSD(T)/CBS//BP86/aD Level; d At the CCSD(T)/aT//BP86/aD Level. 12 ACS Paragon Plus Environment

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the triplet for the monomer to the tetramer. The respective excitation energies (∆ES-T, singlettriplet gaps) are 11.0, 3.2, 13.2, and 9.2 kcal/mol at the CCSD(T)/CBS//B3LYP/aD level for the monomer and dimer and at the CCSD(T)/aT//B3LYP/aD level for the trimer and tetramer. The corresponding excitation energies for the monomer and dimer are 9.5 and 2.2 kcal/mol at the CCSD(T)/aT//B3LYP/aD level. The small singlet-triplet gaps are consistent with the metallic property of bulk RuO2. The excitation energies are much smaller than the corresponding values for the Group 4 MO2 (M = Ti, Zr, Hf) nanoclusters.60,61 The electron spin densities (ESD) for the triplet isomers from the Mulliken population analysis are shown in Figure 3. The calculated spin density values at the B3LYP/aD, BP86/aD,

Ru2O4 (3A˝, Cs) a

RuO2 (3B1, C2v) a

Ru3O6 (3A′, Cs) a

Ru2O4 (3A˝, Cs)b

Ru4O8 (3A2, C2v) a

Figure 3. Mulliken spin densities of the triplet (RuO2)n (n =1 to 4) clusters with an isovalue of 0.02 a.u. a At the BP86/aD Level; b At the B3LYP/aD Level.



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PW91/aD levels are in the SI. The three functionals generally give consistent spin densities with the exception of the dimer. For 3RuO2, the spin localizes on the metal. At the B3LYP/aD level, the spin for 3Ru2O4 lies on two metals, one terminal oxygen and two bridge oxygen atoms. There is 1.2e localized on the metal bound to the excited terminal oxygen. Only 0.2e is predicted on the other metal. At the BP86/aD and PW91/aD levels, the spin densities on the two metals do not differ as much as that predicted with the B3LYP functional. The use of the geometries from the different functionals for the dimer did not affect the CCSD(T) results. Generally consistent with the monomer, the spin mostly lies on the metals for the trimer and there is only a small spin on the oxygen atoms. For the tetramer, there is ~ 0.3e on each of the terminal oxygen atoms. The remaining spin is on the two metals bonded to the terminal oxygens. NPA Charge Analysis The natural charges on Ru and O atoms for both the singlet and triplet neutral clusters are determined using NBO6 99,100 for the natural population analysis (NPA) with the B3LYP, BP86, and PW91 functionals and the results are shown in the SI. The natural charges from different functionals are generally consistent with B3LYP predicting slightly more negative charges on Ru than BP86 and PW91. For the monomer, the charge on Ru is calculated to be 1.24e with the B3LYP, which is substantially lower than the charge on Zr (1.94e) 61 for ZrO2 predicted by the same functional. Thus, much less ionic character for RuO2 is predicted than that of the same row ZrO2. This is in part due to the presence of the extra 4d electrons on Ru as compared to Zr, even though both are in the formal +IV oxidation state. The natural charge on Ru is even lower than that on Ti (1.52e) from TiO2.61 From the monomer to the trimer, the natural charges on Ru remain essentially the same. The most positive charge, 1.53e at the B3LYP/aD level, occurs on the Ru bound to a terminal =O in the tetramer. The difference in the metal charge for the same size singlet and triplet clusters is small. 14 ACS Paragon Plus Environment

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Normalized and Sequential Clustering Energies Table 1 shows the normalized clustering energies (NCE, Eq. 1) and the sequential clustering energies (SCE, Eq. 2) for both the singlet and ΔE(NCE)0K = {nE[(RuO2)] - E[(RuO2)n]}/n

(1)

ΔE(SCE)0K = E[(RuO2)n] - E[(RuO2)n-1] - E[RuO2]

(2)

triplet RuO2 clusters. The NCEs and SCEs are calculated from the clusters on the same spin state. The NCE of the dimer is much smaller than that of the trimer or the tetramer. The NCEs of the trimer and tetramer are comparable and are predicted to be 50 to 60 kcal/mol. The calculated NCEs follow the order of dimer < trimer < tetramer. For the same size of cluster, the NCE for the triplet is 5 to 7 kcal/mol larger than for the singlet. For the dimer, the difference of the NCE at the CCSD(T)/aT level and CCSD(T)/CBS level is 0 for the singlet and 1.1 kcal/mol for the triplet respectively. The NCEs at the CCSD(T)/aT level and CCSD(T)/CBS level differ by 0.2

Table 1. Calculated Normalized Clustering Energies (NCE) and Sequential Clustering Energies (SCE) in kcal/mol for (RuO2)n with the DFT and CCSD(T) Methods. B3LYP

BP86

PW91

Ru2O4 Ru3O6 1 Ru4O8 3 Ru2O4 3 Ru3O6 3 Ru4O8

24.3 41.8 45.5 32.1 46.5 51.6

31.0 56.9 58.2 37.3 57.9 61.3

31.3 58.0 59.8 38.9 59.5 63.5

1

-48.6 -76.9 -56.7 -64.3 -75.3 -66.9

-61.9 -108.8 -62.1 -75.5 -98.2 -71.6

-62.7 -111.3 -65.1 -77.9 -100.7 -75.3

Molecule 1 1

Ru2O4 Ru3O6 1 Ru4O8 3 Ru2O4 3 Ru3O6 3 Ru4O8 1

CCSD(T)/ CCSD(T)/ CCSD(T)/ CCSD(T)/C aD aT aQ BS Normalized 23.2 24.5 24.5 24.5 47.9 47.2 47.1 47.0 51.6 50.2 49.9 49.8 29.9 32.8 33.5 33.9 50.3 52.3 56.0 57.4 Sequential -46.4 -48.9 -49.1 -49.1 -97.2 -92.8 -92.1 -91.8 -63.0 -59.1 -58.6 -58.4 -59.8 -65.7 -67.0 -67.8 -91.3 -91.3 -73.0 -72.6 15

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and 0.4 kcal/mol for the trimer and tetramer respectively. Thus, it is safe to estimate the NCEs using the CCSD(T)/aT results. The B3LYP functional underestimates the NCEs compared to the best CCSD(T) results by 7 kcal/mol. On the contrary, the BP86 and the PW91 functionals overestimate the NCEs by 9 kcal/mol in comparison with the best CCSD(T) predictions. The SCEs follow the order of trimer > tetramer > dimer and are highly exothermic with the SCE for the formation of the trimer significantly more exothermic than for the dimer or tetramer. The energetic results show that the small clusters can condense to form larger cluster. On the basis of the SCE of (RuO2)n (n = 2 to 4) clusters, the trimer and tetramer are more stable than the dimer. At the CCSD(T) level, the difference due to the use of different double zeta and triple zeta basis sets is up to 4 kcal/mol. Similar to the prediction of the NCEs, B3LYP underestimates the SCEs and the BP86 and PW91 functionals overestimate the SCEs compared to the best CCSD(T) results. The DFT errors can be up to 20 kcal/mol. Heats of Formation The calculated total atomization energies and heats of formation of (RuO2)n (n= 1 to 4) clusters with the use of the HF and PW91 orbitals are shown in Table 2. The heat of formation of the Ru atom has some variation in it. Vallet and coworkers recommend a value of 152.5 ± 0.5 kcal/mol44 at 298 K based on the experimental heat of formation of RuO4 and their calculated energies. This value is in agreement with that of Zimmerman et al 101 of 153.0 ± 1.0 kcal/mol from the photochemical decomposition of RuO4. These values differ from the tabulated value of 155.1 ±0.7 kcal/mol. 102 For this study, we use the Vallet and coworkers value adjusted to 0 K using -0.4 kcal/mol from the tabulated values of Yungman 103 giving 152.1 kcal/mol. The use of PW91 and HF orbitals for predicting the valence and core-valence contributions to the TAE differ by 1.0, 3.2, 10.1, and 11.3 kcal/mol for the monomer, dimer, trimer and tetramer respectively and the use of PW91 orbitals gives larger contributions to the TAE. The relativistic 16 ACS Paragon Plus Environment

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Table 2. Total Atomization Energies and Heats of Formation for the Ground State Singlet (RuO2)n (n = 1 to 4) Clusters with the Use of Both HF and PW91 Orbitals a for the CCSD(T) Calculations. Orbs

ΔEZPEb

ΔECBSc

ΔECV,awTd

ΔECV,CBSe

ΔESOf

ΔERelg

ΣD0,0Kh

ΔHf,0Ki

ΔHf,298Kj

RuO2 (C2v)

HF

-2.97

242.51

0.21

-0.12

-4.38

1.63

236.9

33.2

33.5

RuO2 (C2v)

PW91

-2.97

240.64

3.80

3.51

-4.38

1.63

237.9

32.2

32.5

Ru2O4 (C2v)

HF

-7.74

535.49

5.11

3.54

-8.76

1.85

524.4

15.7

15.8

Ru2O4 (C2v)

PW91

-7.74

532.90

12.22

10.80

-8.76

1.85

527.6

12.5

12.6

Ru3O6 (C3v)

HF

-12.49

872.02

11.00

-13.1

-0.39

857.0

-46.8

-46.8

Ru3O6 (C3v)

PW91

-12.49

871.67

21.43

-4.38

-0.39

867.1

-56.9

-56.9

Ru4O8 (C2v)

HF

-17.26

1175.09

11.63

-17.5

-0.04

1151.9

-71.7

-72.1

Ru4O8 (C2v)

PW91

-17.26

1173.62

24.36

-8.76

-0.04

1163.2

-82.9

-83.4

Molecule

a

The PW91 orbitals are only used for the valence and core-valence calculations and ΔERel is taken from the results with the use of HF

orbitals. b From BP86/aD . c CBS value extrapolated from the CCSD(T)/aX energies. d Calculated from the CCSD(T)/awT energy differences with and without correlating the Ru 4s24p6 and O 1s2 electrons. e CBS value extrapolated from the CCSD(T)/awX energies. f

Experimental atomic spin-orbit corrections (−0.22 and −3.94 for O and Ru) from References 85,86, and 87. g ΔEawT-DK -ΔEawT with

the correlation of Ru 4s24p6 and O 1s2 electrons. hΣD0, 0K = ΔECBS + ΔEZPE + ΔECV + ΔESO +ΔERel. ΔECV,CBS is used for the monomer and dimer and ΔECV,awT is used for the others. i ΔHf, 0K [(RuO2)n] = n ΔHf, 0K (Ru) + 2n ΔHf, 0K (O) − ΣD0, 0K [(RuO2)n]. ΔHf,0K is 58.98±0.02 kcal/mol for O, 152.1±0.5 kcal/mol for Ru. j ΔHf,298K [(RuO2)n] = ΔHf,0K [(RuO2)n] + ΔH0K→298K [(RuO2)n] − n ΔH0K→298K (Ru) – 2n ΔH0K→298K (O). ΔH0K→298K is 1.04 kcal/mol for O, 0.4 kcal/mol for Ru.



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corrections to the pseudopotential are predicted to increase the TAEs by up to 2 kcal/mol. The predicted heat of formation of RuO2 with the use of PW91 orbitals, 32.5 ± 0.5 kcal/mol is consistent with the Zimmerman experimental value of 32.5 ± 2.0 kcal/mol.102 The predicted heat of formation of RuO2 with the use of HF orbitals, 33.5 ± 0.5 kcal/mol is identical to the value predicted by Vallet and coworkers as the methods used based on the FPD approach are very similar.43 The total atomization energies for the ruthenium oxyhydroxides species formed in the hydrolysis reactions are shown in Table 3. The TAEs for the mono- and diruthenium oxyhydroxides are calculated with the FPD method. Both HF and PW91 orbitals are used for the CCSD(T) calculations of the valence and core-valence contributions. The use of PW91 orbitals gives larger valence and core-valence contributions than those obtained with the HF orbitals. The results from the two sets orbitals differ by up to 2 kcal/mol and 5 kcal/mol for the mono- and diruthenium oxyhydroxides respectively. The relativistic corrections to the pseudopotential are less than 0.5 kcal/mol for the mono- and diruthenium oxyhydroxides. For the tri- and tetraruthenium oxyhydroxides, the FPD TAEs are too computationally expensive for those species with C1 symmetry. We calculated the heats of formation at 298K of those oxyhydroxides from the heats of formation of the pure dimer and trimer clusters and mono ruthenium oxyhydroxides at the CCSD(T)/CBS level and the reaction energies of clustering reactions (1) – (4) at the CCSD(T)/aT level at 298 K. The reaction energies include the valence contribution at the Ru2O4 + RuO(OH)2 → Ru3O5(OH)2

(1)

Ru2O4 + Ru(OH)4 → Ru3O4(OH)4

(2)

Ru3O6 + RuO(OH)2 → Ru4O7(OH)2

(3)

Ru3O6 + Ru(OH)4 → Ru4O4(OH)4

(4)


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Table 3. The Total Atomization Energies at 0 K (ΣD0,0K, kcal/mol) for Ruthenium Oxyhydroxide Species (RuxOyHz (x =1 to 4, y = 3 to 10, z = 2, 4)) with the Use of Both HF and PW91 Orbitals a for the CCSD(T) Calculations. Molecule Orbs ΔEZPEb ΔEaTc ΔE CBSd ΔECV,awDe ΔECV,awTf ΔECV,CBSg ΔESOh ΔEReli ΣD0,0K j RuO(OH)2 HF -17.88 490.98 503.78 6.89 3.80 2.73 -4.60 0.09 484.1 RuO(OH)2 PW91 -17.88 487.66 499.50 10.40 8.80 7.84 -4.60 0.09 484.9 Ru(OH)4 HF -34.15 732.10 748.15 6.56 2.98 2.06 -4.82 -0.27 711.0 Ru(OH)4 PW91 -34.15 727.39 743.39 11.27 9.74 8.98 -4.82 -0.27 713.1 Ru2O3(OH)2 HF -23.38 777.52 798.25 13.86 6.77 -8.98 0.47 773.1 Ru2O3(OH)2 PW91 -23.38 774.70 794.43 20.08 15.44 -8.98 0.47 778.0 Ru2O2(OH)4 HF -39.04 1022.00 1046.98 14.65 7.37 -9.20 0.04 1006.2 Ru2O2(OH)4 PW91 -39.04 1016.98 1040.59 22.15 17.82 -9.20 0.04 1010.2 Ru3O5(OH)2 HF -28.34 1079.27 22.26 -13.36 Ru3O4(OH)4 HF -43.18 1311.26 22.18 -13.58 Ru4O7(OH)2 HF -32.62 1373.59 31.80 -17.30 Ru4O6(OH)4 HF -48.11 1599.71 32.33 -17.96 a The PW91 orbitals are only used for the valence and core-valence calculations and ΔERel is taken from the results with the use of HF orbitals. b At the BP86/aD level. c At the CCSD(T)/aT level. dCBS value extrapolated from the CCSD(T)/aX energies. e Calculated from the CCSD(T)/awD energy differences with and without correlating the Ru 4s24p6 and O 1s2 electrons. f Calculated from the CCSD(T)/awT energy differences. g CBS value extrapolated from the CCSD(T)/awX energies. h Experimental atomic spin-orbit corrections (0, −0.22 and −3.94 for H, O and Ru) from References 85,86, and 87. i ΔEawT-DK -ΔEawT with the correlation of Ru 4s24p6 and O 1s2 electrons. j ΣD0, 0K = ΔECBS + ΔEZPE + ΔECV + ΔESO +ΔERel. ΔECV,CBS is used for RuO(OH)2 and Ru(OH)4 and ΔECV,awT is used for Ru2O3(OH)2 and Ru2O2(OH)4.



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CCSD(T)/aT level, the core-valence contribution at the CCSD(T)/aWD level and the ZPE and thermal contributions at the BP86/aD level. As an example, ΔHf,298K(Ru3O5(OH)2) = ΔHf,298K (Ru2O4) + ΔHf,298K (RuO(OH)2) + ΔH298K(rxn) where ΔH298K(rxn) is the electronic energy for reaction (1) at the CCSD(T)/aT level plus the additional corrections. The calculated reaction energies, ΔH298K(rxn) are shown in the Supporting Information. The heats of formation for the ruthenium oxyhydroxides are shown in Table 4. The use of PW91 orbitals gives heats of formation that are 2 to 10 kcal/mol more negative than the use of

Table 4. Heats of Formation of Ruthenium Oxyhydroxide Species (RuxOyHz (x =1 to 4, y = 3 to 10, z = 2, 4)) with the Use of Both HF and PW91 Orbitals for the CCSD(T) Calculations. Molecule

a

CCSD(T)/HF ΔHf,0K

a

CCSD(T)/PW91

ΔHf,298K

ΔHf,0K

a

ΔHf,298K

b

Expt,298K d

RuO(OH)2

-51.8

-53.2 b

-52.6

-54.1 b

-44.7

Ru(OH)4

-116.4

-119.9 b

-118.6

-122.1 b

-118.3

Ru2O3(OH)2

-70.8

-72.5 b

-75.6

-77.4 b

Ru2O2(OH)4

-141.6

-145.0 b

-145.6

-149.1 b

Ru3O5(OH)2

-109.6 c

-113.6 c

Ru3O4(OH)4

-168.2 c

-173.6 c

Ru4O7(OH)2

-135.1 c

-146.0 c

Ru4O6(OH)4

-188.1 c

-200.4 c

ΔHf, 0K (RuxOyHz) = x ΔHf, 0K (Ru) + y ΔHf, 0K (O) + z ΔHf, 0K (H) − ΣD0, 0K (RuxOyHz). ΔHf,0K

is 51.63 kcal/mol for H, see Table 2 for O and Ru. b ΔHf,298K (RuxOyHz) = ΔHf,0K (RuxOyHz) + ΔH0K→298K (RuxOyHz) − x ΔH0K→298K (Ru) – y ΔH0K→298K (O) – z ΔH0K→298K (H). ΔH0K→298K is 1.01 kcal/mol for H, See Table 2 for O and Ru. c Derived Heats of formation from the reaction energies for reactions (1) to (4). d Ref. 104. 20 ACS Paragon Plus Environment

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HF orbitals depending on the size of the oxyhydroxide clusters. At the CCSD(T)/HF level, the heat of formation of RuO(OH)2, -53.2 ± 1.0 kcal/mol is ~ 8 kcal/mol more negative than the only available experimental value of -44.7 kcal/mol. 104 However, our predicted value is consistent with Vallet and coworkers value of -51.4 ± 0.7 kcal/mol43 with a difference of only 2 kcal/mol. The calculated heat of formation of Ru(OH)4, -119.9 ± 1.0 kcal/mol agrees well with the experimental value of -118.3 kcal/mol104 and Vallet and coworkers value of -120.4 ± 0.7 kcal/mol.30 Average Bond Dissociation Energies The ruthenium oxygen bond dissociation energies (BDE) can be estimated from the TAE using the same method as we used for the MO2 (M = Ti, Zr, Hf) 60,61

and MO3 (M = Cr, Mo, W)62,84 clusters. The average BDE of Ru=O in RuO2 is estimated to

be one half of the TAE of RuO2. We use the TAE calculated with the use of HF orbitals to compare to the same row Zr=O and Mo=O bond energies which were reported using the same type orbitals. The difference in bond energies using the HF and PW91 orbitals is small. The average Ru=O BDE is predicted to be 118.5 kcal/mol from the TAE of RuO2 calculated with the FPD method. The terminal Ru=O bond in RuO2 clusters is different from the Ru-O bond on crystal surfaces where the unsaturated Ru atom is usually bonded with bridge or 3-fold coordinated O atoms and the terminal Ru=O bond is not present. 105 The average BDEs for Zr=O and Mo=O are 164.3 and 137.4 kcal/mol at the same level.84 Thus, the Ru=O bond energy is weaker than the Zr=O and Mo=O bond energies. We can directly compare the Ru=O BDE to that in Zr=O as they are both in the formal +IV oxidation. The Ru=O BDE is substantially lower than that in Zr=O in part due to the presence of the two lone pairs containing 4d electrons on Ru in contrast to the lack of any repelling metal valence electrons on the Zr. In addition, we note that



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the difference in the atomization energies between Zr and Ru is less than 10 kcal/mol so this cannot account for the difference. Assuming the Ru =O bonds in Ru2O4 (1A1, C2v) is the same as that in RuO2, we can estimate the Ru-O BDE to be (ΣD0,0K(Ru2O4) – 2 x BDE(Ru=O))/4 = 72 kcal/mol. The Ru-O single bond energy is also weaker than the Zr-O and Mo-O bond energies which are predicted to be 114 and 97 kcal/mol84 by using a similar approach. Similarly, we can estimate the Ru-O single bond energy in Ru3O6 (1A1, C3v) to be (ΣD0,0K(Ru3O6) – 3 x BDE(Ru=O))/6 = 84 kcal/mol, 12 kcal/mol larger than the Ru-O single bond energy in Ru2O4, suggesting that there is less strain in the trimer than in the dimer. Anionic Cluster Structures and Relative Energies The structures for the anions optimized at the BP86/aD level are shown in Figure 4. The ground state of the monomer is 2A1 in C2v symmetry, which is consistent with the previous DFT report with both the B3LYP and BP86 functionals.5 The Ru=O bond distance is predicted to be 1.722 Å and the bond angles is 151.3˚ and this geometry is consistent with the predicted results with the B3LYP (1.743 Å, 150.7˚) and the BP86 (1.736 Å, 155.2˚) using the 6-31+G(d) basis set for O and the Los Alamos ECP plus DZ basis set for Ru.5 The bond distance in the anionic cluster is slightly longer than the neutral. The relative energies of the quartet and sextet to the ground doublet at the CCSD(T)/CBS//B3LYP/aD level are 18.8 and 47.5 kcal/mol respectively. The ground state of the anionic dimers is 2B2 in C2v symmetry. The B3LYP functional gives a symmetry broken structure for the dimer anion. The doublet C2h anion structure is predicted

to

be

11.8

higher

in

energy

than

the

ground

state

anion

at

CCSD(T)//CBS//B3LYP/aD level. The doublet anion Cs symmetry isomer with one Ru=O


the

Page 23 of 65

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1.720

1.713

1.722 151.3˚

1.921

1.942

RuO2- (2A1,C2v)

Ru2O4- (2B2,C2v), 0.0a

1.744 1.903 1.918 1.917 1.739 1.917 1.950 1.878

1.922 1.710 1.897

1.729 1.708 1.954 1.854 1.994 1.951 1.922 1.879 1.886

0.0

Ru3O6- (2A′,Cs, b),

24.3

1.856 1.887 1.893 1.702

Ru4O8- (2A, C2), 0.0

2.124

Ru2O4- (2A˝,Cs), 50.2 1.915 1.728 1.948 1.980 1.818

1.980

24.8

Ru3O6- (4A′, Cs, c), 38.0

2.014 2.041 1.698

1.901

Ru4O8- (2B1,C2v, a), 6.9

1.727

1.665 2.004

1.901

1.979 1.827

2.032

1.894

Ru3O6- (2A,C1),

1.703 1.855 1.701

1.851

Ru2O4- (2Bg,C2h), 11.8a

1.913

Ru3O6- (2A˝,Cs, a),

1.868

Ru4O8- (2A1,C2v. b) , 43.5

Figure 4. Molecular structures of the anionic (RuO2)n- (n = 1 to 4) clusters. Bond distances in Å and Bond Angle in Degree at the BP86/aD Level. Relative energies in kcal/mol at the CCSD(T)/CBS//B3LYP/aD Level for the dimer and the CCSD(T)/aD//B3LYP/aD for the trimer and tetramer. a The relative energies are at the CCSD(T)/CBS//BP86/aD Level.

double bond and six Ru-O single bonds is at a much higher energy, 50.2 kcal/mol, as compared to the ground C2v isomer. The Ru-O bond distances range from 1.70 Å to 1.73 Å. The quartet and sextet anions shown in the SI are higher in energy by 12 to 19 kcal/mol than the ground state anion. The optimization of the quartet and sextet anion with the Cs conformation results in a structural transformation to the isomers in C2v symmetry.



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The ground state of the anionic trimers is a 2A˝ in Cs symmetry. At the BP86/aD level, the optimized Ru=O bond distances are comparable to that in the monomer and dimer anions. The Ru-O bond distance ranges from 1.90 to 1.92 Å. At the CCSD(T)/aD level, the quartet and the sextet Cs,a isomers (shown in the SI) are 4.7 kcal/mol and 27.2 kcal/mol higher in energy than the doublet. The lowest energy anionic clusters in the other conformations (Figure 2) are generally in the doublet spin state except for the Cs,c isomer which is a quartet. The higher energy doublet isomers have relative energies of ~ 25 to 38 kcal/mol compared to the ground state. The bond distances in the higher energy anionic trimers are predicted to be 1.70 to 1.74 Å for the Ru=O double bond and 1.82 to 2.00 Å for the Ru-O single bond respectively. The lowest energy structure of the anionic tetramers is predicted to be 2A in C2 symmetry as shown in Figure 2. At the CCSD(T)/aD level, the quartet state of the C2 isomer (shown in the SI) is 9.2 kcal/mol higher in energy. Again, the Ru=O and Ru-O bond distances are comparable to those for the smaller clusters. The anionic clusters in other conformations (Figure 2) have the doublet state lower in energy than the quartet and sextet. The C2v, a isomer is only 6.9 kcal/mol higher in energy than the ground state anionic structure. The C2v,b isomer is much higher in energy, 43.5 kcal/mol, as compared to the ground state. The optimized bond lengths range from 1.67 to 1.70 Å for the Ru=O double bond and 1.85 to 2.16 Å for the Ru-O single bond depending on the molecular structures. Electron Localization in the Anions We first discuss the orbitals for the neutrals. The hybrid B3LYP and pure BP86, PW91 functionals predict similar type of highest occupied molecular orbitals (HOMO) of the ground state (RuO2)n (n =1 - 4) clusters for the monomer and dimer, but not for the trimer and tetramer. The HOMOs predicted by the BP86 and PW91 functionals are


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consistent. The HOMOs and the singly occupied molecular orbitals (SOMO) of their anionic clusters at the BP86/aD level are shown in Figure 5. The results calculated at the B3LYP/aD

HOMO (b1) of 1RuO2(C2v), SOMO (a1) and ESP of 2RuO2- (C2v)

HOMO (b2) of 1Ru2O4(C2v), SOMO (b2) and ESP of 2Ru2O4- (C2v)

HOMO (e) of 1Ru3O6(C3v), SOMO (a˝)and ESP of 2Ru3O6- (Cs)

HOMO (b2) of 1Ru4O8(C2v), SOMO (b1) and ESP of 2Ru4O8- (C2v) Figure 5. HOMO of the ground state (RuO2)n (n =1-4) clusters and SOMO and Electron Spin Density (ESD) of their Anions at the BP86/aD level.



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level are shown in the SI. The HOMO of neutral RuO2 is Ru 4dπ with a small component of O 2pπ. For Ru2O4, the HOMO is dominated by Ru 4dπ character on the two metals at the BP86/aD level. The B3LYP functional predicts an additional small component of O 2pσ on the two bridge oxygen atoms. For Ru3O6, the doubly degenerate HOMO predicted by the BP86 functional is a mixture of Ru 4dσ, 4dπ, and 4dδ orbitals. In contrast, significant Ru 4dσ character on the three metal atoms with a small component of O 2pσ is predicted for the a1 symmetry HOMO of Ru3O6 at the B3LYP/aD level. The HOMO of Ru4O8 is predicted to have b2 and a2 symmetry with the BP86 and B3LYP functionals respectively. At the BP86/aD level, the HOMO is mostly a combination of Ru 4dσ orbitals on the two metals bonded to the =O atoms. There is also a small component from the O 2pσ orbital from the =O atom in the HOMO of Ru4O8. At the B3LYP/aD level, the HOMO is mainly dominated by the Ru 4dπ and 4dδ orbitals from the two metal bonded to four –O atoms. The HOMO has a small portion of O 2pπ orbital from the terminal =O atom. The SOMO of RuO2- is dominated by the Ru 4dσ orbital with the BP86 functional. B3LYP predicts additional Ru 4s character for the SOMO of RuO2-. For the dimer, the BP86 and B3LYP functionals predict the same type of SOMO. The SOMO of Ru2O4- is mostly a mixture of Ru 4dσ and 4dπ orbitals. There is also a small O 2pσ component on the two =O atoms. Symmetry breaking is predicted and decreases the symmetry to Cs when an electron is added to the neutral C3v trimer using both the BP86 and B3LYP functionals. The SOMO of Ru3O6- is consistent at both the B3LYP/aD and BP86/aD levels and is a mixture of Ru 4dπ and 4dδ orbitals. Although the same symmetry of b1 is predicted for the SOMO of Ru4O8- by both the B3LYP and BP86, the character of the SOMO is different for the two functionals. At the BP86/aD level, the SOMO of Ru4O8- is dominated by Ru 4dσ orbital on the two metal bonded to all bridge –O atoms. 26 ACS Paragon Plus Environment

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There is only a slight Ru 4dπ orbital character on the other two metals for the SOMO of Ru4O8-. At the B3LYP/aD level, the SOMO of Ru4O8- involves mostly a Ru 4dδ orbital on the two metals bonded to two =O atoms with a component of O 2pπ on the bridge O between those two metals. The lowest unoccupied molecular orbitals (LUMO) (shown in the SI) of the neutral clusters are generally consistent with the SOMOs of the anionic clusters. Electron Affinities Figure 2 and Table 5 show the electron affinities (EA) of the RuO2 clusters. We calculated the electron affinities using the ground state doublet anions for both the singlet and the triplet clusters as the addition of an electron on both the singlet and triplet will result in the same anionic clusters. Depending on the size of the cluster, the EAs range from 2.2 eV to 3.4 eV for the ground state RuO2 clusters. The calculated EAs follow the order of monomer < tetramer < dimer < trimer for the singlet and monomer < tetramer ≈ dimer < trimer for the Table 5. Calculated Electron Affinities at the B3LYP/aD, BP86/aD, CCSD(T)/aD//B3LYP/aD , CCSD(T)/aT//B3LYP/aD, and CCSD(T)/CBS//B3LYP/aD Levels in eV.a Molecule 1 RuO2 1 Ru2O4 1 Ru3O6 1 Ru4O8 3 RuO2 3 Ru2O4 3 Ru3O6 3 Ru4O8 a

B3LYP 2.49 3.29 3.83 3.54 2.76 3.16 4.04 3.69

BP86 2.48 3.38 3.36 3.14 2.66 3.15 3.76 3.31

CCSD(T)/aD CCSD(T)/aT CCSD(T)/aQ CCSD(T)/CBS 2.19 2.19 2.20 2.22 3.30 3.16 3.17 3.17 2.69 3.42 2.88 2.86 2.45 2.60 2.66 2.69 3.22 3.25 3.29 3.31 3.13 3.99 3.13 3.26

The addition of an electron to both the singlet and triplet clusters leads to the formation of the

same ground state doublet anions.



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triplet. The BP86 and B3LYP functionals predict EAs within 0.4 eV compared to the best CCSD(T) values. Again, the BP86 results for the EAs are slightly more consistent with the CCSD(T) results than the B3LYP EAs. The current DFT results for the electron affinity of RuO2 agree well with a previous report of 2.5 eV using the same functional and different basis sets,5 but all of the DFT results are too high by ~ 0.3 eV as compared to the CCSD(T)/CBS value. The reducibility of the RuO2 clusters characterized by the EAs are comparable to the corresponding Group 6 MO3 (M = Cr, Mo, W) nanoclusters 106,107,108 and larger than the Group 4 MO2 (M = Ti, Zr, Hf) nanoclusters.60,61 As a result of its ease-of-reduction, RuO2 is a significantly stronger oxidizer than TiO2, consistent with its behavior as an oxidation catalyst. Fluoride Affinities (Lewis Acidities) The fluoride affinity describes the electron pair donoracceptor ability and the Lewis acid-base strength. The calculated fluoride affinities (FA) at the CCSD(T) level for both the singlet and the triplet RuO2 clusters are shown in Figure 2 and Table 6. The FAs at the B3LYP/aD, BP86/aD levels are also shown in Table 6. The molecular structure for the optimized Lewis adducts are shown in the SI. The predicted FAs range from 80 to 95

Table 6. Calculated Fluoride Affinities at the B3LYP/aD, BP86/aD, CCSD(T)/aD//B3LYP/aD , CCSD(T)/aT//B3LYP/aD, and CCSD(T)/CBS//B3LYP/aD Levels in kcal/mol. Molecule 1 RuO2 1 Ru2O4 1 Ru3O6 1 Ru4O8 3 RuO2 3 Ru2O4 3 Ru3O6 3 Ru4O8

B3LYP -87.0 -91.2 -85.8 -83.2 -90.9 -82.6 -89.6 -90.7

BP86 -90.3 -95.7 -76.5 -85.5 -89.7 -80.0 -81.4 -87.4

CCSD(T)/aD -86.9 -96.3 -77.0 -90.2 -88.0 -84.8 -79.1 -86.2

CCSD(T)/aT CCSD(T)/aQ CCSD(T)/CBS -87.2 -87.1 -87.0 -93.7 -93.3 -93.2 -77.1 -88.0 -89.9 -90.2 -90.4 -84.1 -83.9 -83.7 -81.2 -87.6


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kcal/mol. The singlet trimer has the lowest FA and the triplet dimer has the highest FA. The predicted FAs for both the singlet and triplet are comparable. The predicted FAs with the B3LYP and BP86 method are within 5 kcal/mol of the best CCSD(T) results. The BP86 functional performs slightly better than the B3LYP does in terms of the FAs. The Lewis acidities of RuO2 nanocluster are not as large as those of the Group 4 MO2 (M = Ti, Zr, HF) nanoclusters, which have FAs of ~ 100 to 150 kcal/mol.51 Hydrolysis Reactions The potential energy surfaces for the hydrolysis of both the singlet and triplet (RuO2)n (n = 1 to 4) clusters calculated at the CCSD(T)/aD//B3LY/aD level are shown in Figures 6 to 9. For the trimer and tetramer, the reactions with the addition of one water molecule are shown in the text and the reaction for the second water addition is shown in the SI. As the BP86 functional gives better reaction energies for the trimer and tetramer than do the B3LYP functional, we use the BP86 results for the discussion of the second water addition reaction. The results with the B3LYP functional are also shown in the SI. The physisorption energies, dissociative chemisorption energies, and the reaction barriers from the complex are summarized in Table 7 and discussed in more detail below. Hydrolysis Reactions for the Monomer The potential energy surface for the monomer is shown in Figure 6. On the potential energy surface of the ground state singlet, the reaction begins with a Lewis acid-base addition of water to the metal center (physisorption) with the formation of a donor-acceptor dative bond. This step is exothermic by -21.9 and -22.2 kcal/mol at the CCSD(T)/CBS//B3LYP/aD and CCSD(T)/aD//B3LYP/aD levels respectively. The RuO(OH)2 (1d) is generated by a proton transfer to a terminal oxygen atom with an exothermicity of -26.3 and -25.8 kcal/mol at the CCSD(T)/CBS//B3LYP/aD and CCSD(T)/aD//B3LYP/aD levels, respectively. The transition state is calculated to be just below the reactant asymptote at the 29 ACS Paragon Plus Environment


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Singlet Triplet 6.9 5.8 5.8

1H O 2

RuO2(1a) 0.0 0.0 0.0

5.1 −0.7 21.5

T.S. (1c) 1.9 0.2 −0.5

−11.8 −25.1

RuO2·H2O(1b) −22.2 −22.1 −21.9

1H O 2

0.7 RuO(OH)2(1d) −34.4 −25.8 2.6 −26.4 RuO(OH)2·H2O(1e) −26.3 −37.0 −36.7

7.2 T.S. (1f) −18.9 −18.1

−20.4 15.2 Ru(OH)4(1g) −35.7 −35.7

Figure 6. Potential energy surfaces for the hydrolysis of the singlet and triplet RuO2 clusters . CCSD(T)/aD//B3LYP/aD = blue, CCSD(T)/aT//B3LYP/aD = crimson, and CCSD(T)/CBS//B3LYP/aD = purple. 30 ACS Paragon Plus Environment

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(a)


2.2*

Singlet Triplet

1H O 2

2.2* Ru2O4(2a) 0.0

−5.0 −16.6 5.7 Ru2O4·H2O(2b) −22.3

10.9 T.S. (2c) −15.9

−17.9

−14.3

6.8

16.1 1H O 2

Ru2O3 (OH)2(2d) −30.4

−26.9 16.0

Ru2O3 (OH)2·H2O(2e) −42.9


−22.6

T.S. (2f) −24.7

21.9

Ru2O2 (OH)4(2g) −44.5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

(b)

2.2*

1H O 2

4.0

−1.2

2.2* Ru2O4(2a) 0.0

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−16.6

3.7 T.S. (2h) −4.8

11.3 −13.3

1H O 2

5.7

1.7

Ru2O4·H2O(2b) −22.3

Ru2O3 (OH)2(2i) −15.0

T.S. (2k) −7.2 −24.2 2.7

Singlet Triplet

Ru2O3 (OH)2·H2O(2j) −26.9

−23.5 15.9 Ru2O2 (OH)4(2l) −39.4

Figure 7. Potential energy surfaces for the hydrolysis of the singlet and triplet Ru2O4 clusters at the CCSD(T)/aD//B3LYP/aD level. (a) Proton transfer to a bridge –O atom. (b) Proton transfer to a terminal =O atom. a At the CCSD(T)//aT//B3LYP/aD level. 32 ACS Paragon Plus Environment

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(a)

Singlet Triplet 14.4 10.1

10.1

1H O 2

Ru3O6(3a) 0.0

6.9

1.8 11.3

9.5

6.0 T.S.(3c) 7.5 Ru3O5 (OH)2(3d) 3.5

Ru3O6·H2O(3b) −9.5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(b)

24.0 8.2 10.1

10.1

1H O 2

Ru3O6(3a) 0.0

15.5 T.S. (3e) 15.5 15.8 1.8 Ru3O5 (OH)2(3f) 0.0

11.3 Ru3O6·H2O(3b) −9.5

Figure 8. Potential energy surfaces for the hydrolysis of the singlet and triplet Ru3O6 clusters at the CCSD(T)/aD//B3LYP/aD level. The Triplet (3a) is Calculated at the CCSD(T)/aD//BP86/aD level. (a) Proton transfer to a terminal =O atom. (b) Proton transfer to a bridge –O atom.


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(a)

Singlet Triplet 17.1 9.5

4.0 1H O 2

9.5 Ru4O8(4a) 0.0

−8.5

13.6

T.S. (4c) 4.8 13.1 Ru4O7(OH)2(4d) 8.8

11.5 Ru4O8·H2O(4b) −20.0



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(b)

19.3 9.5 9.5

9.3

1H O 2

Ru4O8(4a) 0.0

− 3.3

8.3

T.S. (4f) 10.0

9.5

Ru4O7(OH)2(4g) − 1.2

12.1 Ru4O8·H2O(4e) − 15.4


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(c)

20.8 2.4

T.S. (4h) 18.4 Ru4O7 (OH)2 (4i) 12.5

9.5 9.5

1H O 2

Ru4O8(4a) 0.0

15.3 2.8

− 3.3 12.1 − 15.4

Ru4O8·H2O(4e)

Figure 9. Potential energy surfaces for the hydrolysis of the singlet and triplet Ru4O8 Clusters at the CCSD(T)/aD//B3LYP/aD level. The Triplet (4a) is Calcualted at the CCSD(T)/aD//BP86/aD level. (a) Water addition to an Ru bonded to all bridge –O atoms. (b) Water addition to a Ru bound to a =O and two –O atoms and proton transfer to a terminal =O atom. (c ) Water addition to a Ru bound to a =O and two –O atoms and proton transfer to a bridge –O atom.



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Table 7. Calculated Reaction Barriers from the Reactant Complexes (∆H‡298K, kcal/mol) and Physisorption (∆Hphy,298K, , kcal/mol )and Dissociative Chemisorption Enthalpies (∆Hchem,298K, kcal/mol) for the First Addition of H2O at the CCSD(T)/aD//B3LYP/aD Level. Reaction

∆H‡298K

a

Singlet

∆Hphy,298K

∆Hchem,298K

Triplet Singlet Triplet

Singlet

Triplet

RuO2 (1a) + H2O → RuO(OH)2 (1d)

23.8b

6.9

-22.7 b

-7.3

-27.4 b,c

-32.1

Ru2O4 (2a) + H2O → Ru2O3(OH)2 (2d)

5.8

10.7

-23.6

-16.8

-31.8

-15.1

Ru2O4 (2a) + H2O → Ru2O3(OH)2 (2i)

20.8

10.8

-23.6

-16.8

-14.6

-15.8

Ru3O6 (3a) + H2O → Ru3O5(OH)2 (3d)

16.2

11.7

-10.2

-9.1

2.3

-1.6

Ru3O6 (3a) + H2O → Ru3O5(OH)2 (3f)

24.6

21.5

-10.2

-9.1

-1.2

4.2

Ru4O8(4a) + H2O → Ru4O7(OH)2 (4d)

32.4

25.1

-20.4

-18.4

7.9

3.3

Ru4O8(4a) + H2O → Ru4O7(OH)2 (4g)

24.5

22.0

-16.0

-13.6

-2.4

-2.8

Ru4O8(4a) + H2O → Ru4O7(OH)2 (4i)

35.4

21.0

-16.0

-13.6

11.5

4.9

a

See Figures 6 to 9 and Supporting Information for the molecular structures of the reactants,

transition states, and products. For the reactions involving the triplet states, H2O is in the singlet state.

b

At the CCSD(T)/CBS//B3LYP/aD level for the singlet. c -29.2 kcal/mol derived from the

heats of formation.

CCSD(T)/CBS//B3LYP/aD level. The second water addition is similar to the first and is less exothermic. The physisorption and chemisorption energies for the second water addition are only -10.3 and -9.3 kcal/mol at the CCSD(T)/aT//B3LYP/aD level. The activation energy for the second proton transfer is predicted to be 18.6 kcal/mol at the CCSD(T)/aT//B3LYP/aD level, which is larger than the exothermicity of the second water addition. The reaction energies derived from the heats of formation for the hydrolysis of the monomer can be compared to that from Vallet and coworkers44. Our reaction energy for the formation of RuO(OH)2 (1d) using the predicted heats of formation is -29.2 kcal/mol, which is 2 kcal/mol more exothermic than 38 ACS Paragon Plus Environment

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Vallet’s value of -27.1 kcal/mol. Their predicted reaction energy for the formation of Ru(OH)4 (1g) from RuO2 and two H2O differs by only 0.5 kcal/mol from our value. For the triplet, the reaction mechanism is similar to that for the singlet. At the CCSD(T)/aD//B3LYP/aD level, physisorption for the first water addition on the triplet RuO2 is exothermic by -6.5 kcal/mol, much less exothermic than for the singlet. The transition state for the first proton transfer is 1.1 kcal/mol above the triplet reactant asymptote. The chemisorption energy to generate 3RuO(OH)2 is comparable to the singlet. The reaction energetics for the second water addition are similar to that for the singlet. Hydrolysis Reactions for the Dimer The potential energy surfaces for the hydrolysis of the dimers are shown in Figure 7. The initial step is similar to that for the monomer with an exothermicity of -21.9 and -18.3 kcal/mol on the singlet and triplet potential energy surfaces respectively at the CCSD(T) level. Proton transfer to a bridge –O atom from the Lewis acid-base Ru2O4∙H2O complex is shown in Figure 7a. For the singlet, the barrier is only 6.5 kcal/mol and the formation of the hydroxide is exothermic by -29.9 kcal/mol. Thus water should readily dissociate on the dimer to produce the hydroxide. The reaction for the second water addition (Figure S6a) is similar to the first with smaller exothermicities for both the physisorption and chemisorption processed. The activation barrier for the second proton transfer is predicted to be 18.3 kcal/mol at the CCSD(T)/aD//B3LYP/aD level. The barrier energy for the second proton transfer is larger than for the first. For the triplet, the reaction mechanism is the same as that on the singlet potential energy surface. The barrier energy for the first proton transfer is slightly larger than the second proton transfer.

The singlet triplet energy gaps range from 2 to 22

kcal/mol and the singlet triplet gaps for the complexes, transition states and the hydroxides are larger than that for the bare metal-oxide cluster. 39 ACS Paragon Plus Environment


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The reactions for proton transfer to a terminal =O oxygen are shown in Figure 7b. The singlet transition state for the first proton transfer is 3.7 kcal/mol higher in energy than for the triplet transition state. As the ground state of Ru2O4∙H2O complex is predicted to be the singlet with the singlet triplet energy gap of 5.7 kcal/mol, the barrier energy on the singlet potential energy surface for the first proton transfer is larger than that for the triplet. Dissociative chemisorption is still exothermic for both the singlet and triplet. The barrier energy for a proton transfer to a terminal =O atom is much smaller than proton transfer to a bridge on the singlet potential energy surface. For the second water addition (Figure S6b), the second proton transfer is similar to the first. Again, the transition state for the singlet is 11.3 kcal/mol higher in larger than the triplet. The tetra-hydroxide after the addition of two water molecules for the triplet has a higher energy than the singlet. We note that the water complexes as well as the hydroxides are comparable in energy for both the singlet and triplet for the addition of the first water. Hydrolysis Reactions for the Trimer The potential energy surfaces for the hydrolysis reactions for the first water addition on the trimer at the CCSD(T)/aD//B3LYP/aD level are shown in Figure 8. The results for the second water addition at the DFT level are shown in the SI. Again, the reaction begins with the formation of a Lewis acid-base complex. For the singlet, the physisorption energy is predicted to be -9.5 kcal/mol, which is less exothermic than that for the monomer and dimer. A proton transfer to a terminal =O atom (Figure 8a) is preferred over that to a bridge –O atom (Figure 8b). This is different from the hydrolysis reaction for the dimer. The energy barriers are predicted to be 17.0 and 25.3 kcal/mol for the proton transfer to a terminal =O and a bridge –O respectively. The dissociative chemisorption step to form the dihydroxide Ru3O5(OH)2 (3d) containing two terminal =O atoms is slightly endothermic with the reaction energy of 3.5 kcal/mol. The formation of Ru3O5(OH)2 (3f) via a proton transfer to a bridge –O 40 ACS Paragon Plus Environment

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atom is an energetically neutral reaction. On the triplet potential energy surface, the Lewis acidbase interaction is slightly less exothermic than that for the singlet with an energy of -8.3 kcal/mol. The proton still prefers to transfer to a terminal =O atom. Dissociative chemisorption for the formation of triplet 3Ru3O5(OH)2 (3d) and 3Ru3O5(OH)2 (3f) is slightly exothermic and endothermic with the energies are -1.4 and 4.4 kcal/mol respectively. The DFT results for the addition of up to two water molecules are shown in Figure S7 in Supporting Information. On the PES of proton transfer to a terminal =O atom (Figure S7a), B3LYP predicts the triplet transition state and dihydroxide species to be lower than the singlet in energy for the first water addition. However, BP86 and CCSD(T) predict the singlet to be of lower energy than the triplet. Similarly, the triplet of the water complex and the hydroxide in the second water addition are predicted to be lower in energy than the singlet by B3LYP. However, BP86 predicts the singlet of the two species to be lower in energy than the triplet. Based on the comparison to the CCSD(T) results for the first water addition, BP86 gives more reasonable predictions for the second water addition than does B3LYP. Proton transfer to a terminal =O atom to form the tetrahydroxide is an endothermic process for both the singlet and triplet at the BP86/aD level. The energy barrier for the triplet is smaller than that for the singlet. Similar to the proton transfer to a terminal =O atom, the reaction for a proton transfer to a bridge –O atom in the second water addition is also predicted be endothermic on both the singlet and triplet PESs (Figure S7b). This process has a larger energy barrier for the triplet than that for the singlet. Hydrolysis Reactions for the Tetramer The results for the first water addition on the tetramer at the CCSD(T)/aD//B3LYP/aD level are shown in Figure 9. The most exothermic water addition takes place on a metal bound to all bridge –O atoms (Figure 9a). The physisorption energies are 41 ACS Paragon Plus Environment


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predicted to be -20.0 and -18.0 kcal/mol for the singlet and triplet respectively. The respective energy barriers for a proton transfer to a bridge –O atom are 33.1 and 25.6 kcal/mol for the singlet and triplet. Similar to the trimer, the reaction for the formation of hydroxide Ru4O7(OH)2 (4d) is endothermic for both the triplet and singlet. The reactions for water addition to a metal bonded to a terminal =O atom and three bridge –O atoms are shown in Figures 9b and 9c. The water cluster interaction energies are predicted to be -15.4 and -12.8 kcal/mol for the singlet and triplet respectively. For the singlet, proton transfer to a terminal =O atom is preferred over proton transfer to a bridge –O atom, consistent with the reaction for the trimer. The respective energy barriers are 25.4 and 36.2 kcal/mol and the respective hydrolysis reaction energies are -1.2 and 12.5 kcal/mol. For the triplet, the barrier energies for proton transfer to a terminal oxygen and to a bridge oxygen are comparable with a difference of only 0.9 kcal/mol. The chemisorption for proton transfer to the terminal oxygen is less endothermic than to the bridge oxygen with the reaction energies of 8.3 and 15.3 kcal/mol respectively. As the BP86 functional performs better than the B3LYP functional, we use it to describe the addition of the second water. The second water addition on an active metal bound to a terminal =O atom at the BP86/aD level is shown in Figure S8b. Proton transfer to a terminal =O atom (Figure S8a) is more preferable than that to a bridge –O atom (Figure S8b). At the BP86 level, the barrier energy for the second proton transfer to a terminal =O atom is 3.7 and 3.9 kcal/mol larger than that to a bridge –O atom for the singlet and the triplet respectively. The reaction of the second proton transfer to a terminal =O atom is endothermic by 2.9 and 2.2 kcal/mol for the singlet and triplet respectively. The reaction of the second proton transfer to a bridge –O atom more endothermic by ~ 5 kcal/mol at the BP86/aD level.


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We also studied a second water addition to a Ru bound to a terminal =O atom after the first water addition to a similar Ru atom and the DFT results are shown in S8d. At the BP86/aD level, the barrier energy for a proton transfer to a terminal =O atom (Figure S8c) is smaller than that to a bridge –O atom (Figure S8d) for both the first and the second water addition. The hydrolysis reaction for the second water addition is generally endothermic with one exception of the proton transfer to a terminal =O atom on the singlet PES, where dissociative chemisorption is predicted to -6.7 kcal/mol at the BP86/aD level. Physisorption and Dissociative Chemisorption Energies The calculated reaction barriers from the reactant complex and the physisorption (Lewis acid-base adduct formation) and dissociative chemisorption (product produced by proton transfer) energies for the first addition of H2O on both the singlet and triplet clusters at 298K are shown in Table 7. The physisorption energies for the singlet are larger than that for the triplet for the monomer and dimer. For the trimer and tetramer, the predicted physisorption energies on the singlet and triplet clusters are comparable with the adsorption energy on the singlet slightly more exothermic than the triplet. In terms of the energy barriers for the ground state singlet, the energy barrier depends on the cluster size and the oxygen atom to which the proton is transferred. A proton transfer to a bridge –O atom has a smaller energy barrier than that to a terminal =O atom for the dimer. However, proton transfer to a terminal =O atom is preferred for the trimer and tetramer. The energy barrier for the triplet is generally larger than for the singlet with the exception of the proton transfer to a bridge –O atom on the dimer. We note that the energy barriers are comparable for proton transfer to a terminal =O and a bridge –O atoms for the dimer and tetramer on the triplet PES. The hydrolysis reactions are exothermic for the monomer and dimer for both the singlet and triplet. For the dimer, the chemisorption energies are larger for proton transfer to a bridge –O atom than to a terminal –O 43 ACS Paragon Plus Environment


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atom on the singlet PES. However, these energies are comparable on the triplet PES. For the trimer and tetramer, the hydrolysis reactions are either slightly exothermic or endothermic depending on the cluster and the reaction. These chemisorption energies range from -3 to 10 kcal/mol. The transition state is below the reactant asymptote for the monomer and dimer and above the reaction asymptote for the trimer and tetramer. Thus, water should readily dissociate on the monomer and dimer clusters, but not on the trimer and tetramer clusters. Thus, the smaller nanoclusters can readily hydrolyze but after the dimer, it is unlikely that the larger clusters will hydrolyze. The water physisorption energies for the singlet RuO2 monomer and dimer are comparable to those for the second row Group 4 ZrO2 monomer and dimer64

The water

physisorption energies for the singlet trimer and tetramer are much smaller than those for ZrO2 clusters. The much lower exothermicities for the trimer and tetramer are in part due to the much smaller Lewis acidity (smaller fluoride affinities) of RuO2 clusters than the ZrO2 clusters.64 Our previous work64 showed that the hydrolysis reactions on small ZrO2 clusters are very exothermic, which is different from the current work on small RuO2 clusters, where slightly endothermic processes are predicted for the trimer and tetramer. The exothermicity for the RuO2 monomer and dimer chemisorption reactions is also smaller than those for the corresponding ZrO2 clusters. The barrier energies for the proton transfer for RuO2 clusters are much larger than those for the ZrO2 clusters64. Our calculations of the hydrolysis reaction for the singlet monomer and dimer can be compared to the water adsorption on the RuO2 (110) surface calculated with the PBE functional. 109 In that work, molecular water adsorption on the most active coordinatively unsaturated Ru site is very exothermic. The predicted strong binding energy of -33 kcal/mol is 10 44 ACS Paragon Plus Environment

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kcal/mol larger than our predictions of ca. -23 kcal/mol of water on the singlet monomer and dimer. On the RuO2 (110) surface, the splitting of H2O to form two OH groups is predicted to be slightly more exothermic by 0.7 kcal/mol than the formation of molecular bound water on RuO2 (110). Similarly, we predict the hydroxides via the dissociative chemisorption of the first water are ca. -5 and -7 kcal/mol lower in energy than the Lewis acid-base water-cluster adducts for the singlet monomer and dimer respectively. The barrier for proton transfer on the RuO2 (110) surface is only 0.7 kcal/mol, which is smaller than our CCSD(T) values of 23.8 and 5.8 kcal/mol for the monomer and dimer. The lower barrier on RuO2 (110) is in part due to the more exothermic water physisorption process on the coordinatively unsaturated sites (cus) and the unsaturated coordination environment. This difference between the cluster and the bulk surface suggests that the reactivity of the Ru metal center is dependent on both the coordinative and chemical environment. This is an interesting difference as the results for other transition metal oxides often show that the behavior of the cluster and the bulk is similar. The energy for molecular water adsorption on the RuO2 (110) surface is larger than our prediction of water physisorption energies on the trimer and tetramer in part due to the nonexistence of coordinatively unsaturated Ru atom sites in our clusters. As shown above, the water physisorption energies and chemisorption energies on the monomer and dimer are generally more exothermic than the trimer and tetramer. For the tetramer, the water physisorption on a Ru atom bound with three bridge -O atoms is more preferable than on a Ru atom bound with a terminal =O and three bridge –O atoms due to a steric effect, which is consistent with our previous work on the hydrolysis of group 4 metal oxide clusters.63,64 These properties for the small (RuO2)n (n = 1 to 4) cluster suggest that the bigger RuO2 clusters will be more likely less effective to react with water if there are no unsaturated 45 ACS Paragon Plus Environment


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coordinative or sterically favorable Ru atoms to bind a water molecule. The larger proton transfer barriers on our small clusters, especially for the trimer and tetramer, than on the crystal RuO2 (110) surface109 show that the reactivity of larger clusters is more dependent on the structural environment of the active metal center than on the size of the metal oxide cluster. DFT Performance The three DFT functionals give similar relative energies for the monomer. For the dimer, none of the functionals give the correct ground state and the CCSD(T) method requires at least a triple zeta basis set to predict the correct ground state. The pure BP86 and PW91 functionals predict better relative energies for the trimer and tetramer than B3LYP as compared to the CCSD(T) results. The relative energies predicted by the BP86 and PW91 functionals are generally consistent. Similarly, BP86 also performs better than B3LYP for the prediction of the cluster properties such as the electron affinities and the fluoride affinities. The calculated HOMOs and LUMOs for the ground state singlet clusters as well as the singly occupied molecular orbitals (SOMO) and the highest doubly occupied molecular orbitals (DOMOs) for the first excited triplet clusters with the B3LYP and BP86 functionals are shown in the SI as are the orbitals at the HF/aD level for the singlet and the ROHF/aD level for the triplet, which are used for the CCSD(T) calculations. B3LYP, BP86 and HF give the same type of HOMO and LUMO for the singlet monomer. For the singlet dimer, the Ru 4d character for the HOMO predicted by the BP86 is slightly different from that with the other two methods. The Ru 4d character of the LUMO of the singlet dimer depends on the computational method. Although all three methods predict the same type of LUMO for the singlet trimer, the predicted HOMO at the BP86 level is different from that of both B3LYP and HF. For the tetramer, all three methods give three different sets of HOMO and LUMO orbitals. Differences in the SOMO and DOMOs with the three different methods are also found for the triplet clusters. The difference becomes 46 ACS Paragon Plus Environment

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more pronounced as the cluster becomes bigger. This is probably due to fact that the Ru with the +IV oxidation state has 4 d electrons which can be filled in 5 different d orbitals and the molecule has some multi-configuration character.

As the cluster grows, more Ru atoms

contribute more d electrons which can form more low-lying states. Thus, the differences in the LUMO, HOMO as well as the SOMOs for the anion for the trimer and tetramer are larger than that for the dimer. The T1 diagnostics for the CCSD(T)/aT calculations with the use of the HF orbitals for the clusters are shown in the Supporting Information. The T1 diagnostics for the singlet and triplet RuO2 clusters ranges from 0.04 to 0.06 and from 0.05 to 0.08 respectively. Thus the triplet has more multi-configuration character than the singlet. For both the singlet and triplet, the T1 diagnostic increases as the cluster increases and more multi-configuration character is predicted for the trimer and tetramer than that for the monomer and dimer. The use of the PW91 orbitals significantly reduces the T1 values. In addition, spin unrestricted B3LYP does not give the same set of α and β orbitals of the DOMOs for the triplet trimer and tetramer clusters. In contrast, BP86 generally gives consistent α and β orbitals for the DOMOs. The inconsistency of the spin-polarized α and β orbitals for the open shell molecules results in more spin contamination with the use of the B3LYP functional than the pure BP86 and PW91 functionals. Thus, the ‘cleaner’ DFT orbitals from BP86 make it perform better than B3LYP for the prediction of the relative energies as well as the cluster properties of the small RuO2 clusters. A similar trend can be found for the hydrolysis reactions, where BP86 performs better than B3LYP for prediction of the reaction energetics as well as the singlet-triplet gaps for the various species on the PES.



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For the monomer PES, the DFT results with the B3LYP and BP86 functionals are shown in the SI. DFT predicts the same reaction mechanism as that given by CCSD(T). The potential energy surfaces calculated with the B3LYP and BP86 functionals are generally semiquantitatively consistent with the CCSD(T) results.

For the singlet, the physisorption and

dissociative chemisorption energies are within 5 kcal/mol of the CCSD(T) results. The energy barrier predicted by CCSD(T) is up to 2 kcal/mol larger than that predicted by DFT. For the triplet, the physisorption energies at the CCSD(T)/aD//B3LYP/aD level are slightly more exothermic than the DFT results. The chemisorption energies predicted by DFT are more exothermic than by CCSD(T) for the first water addition. For the second water addition, a slightly less exothermic reaction energy is predicted by DFT than that by CCSD(T). In terms of the energy barriers, the difference can be up 7 kcal/mol by three different methods and the DFT barriers are smaller than the CCSD(T) barriers. The performance of the B3LYP and BP86 functionals for the hydrolysis of the dimer is generally consistent with that for the monomer and the results are shown in the SI. We still calculated the energies on the potential energy surfaces relative to the singlet even though DFT does not give the correct ground state for the dimer. Again, DFT generally underestimates the physisorption energies and the barrier energies for both the first and the second water addition as compared to the CCSD(T) predictions. This is similar to what was found for the hydrolysis reactions63,64 of the Group 4 (MO2)n and the reactions of alcohols with Group 6 (MO3)n clusters.47,48 For the reaction of proton transfer to a bridge –O atom, BP86 underestimates the chemisorption energy by 10 kcal/mol for the second proton transfer on the singlet PES and B3LYP overestimates the chemisorption energy by 5 kcal/mol for the first proton transfer on the triplet PES. Different from the reaction with a proton transfer to a bridge –O atom, the 48 ACS Paragon Plus Environment

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dissociative chemisorption energies for the proton transfer to a terminal =O atom are overestimated by DFT as compared to CCSD(T). In addition, B3LYP does not always predict the correct ground state for the species on the PES. For example, the water complex after the second water addition is predicted to be a ground state singlet by both BP86 and CCSD(T). However, B3LYP predicts the triplet of that water complex to be slightly lower in energy than the singlet. Thus DFT with the B3LYP and BP86 functionals only gives semi-quantitative results. Consistent with the monomer and dimer, the physisorption energy and the barrier energy calculated at the BP86/aD level are generally smaller than the CCSD(T) predictions for the first water addition reaction to the trimer. The DFT results for the potential energy surfaces for the tetramer are shown in Figure S8 in Supporting Information. Similar to the reactions on the trimer, the BP86 functional gives better reaction energies than does the B3LYP functional. For the water addition to a Ru bound to all bridge –O atoms (Figure S8a), BP86 underestimates the physisorption energies and the barrier energies for both the singlet and triplet compared to the CCSD(T) results. BP86 gives slightly exothermic hydrolysis reactions for the first water addition. Conclusions The structural and energetic properties of small (RuO2)n (n= 1 to 4) nanoclusters and their anions have been studied with the density functional theory (DFT) as well as coupled cluster CCSD(T) theory. The ground state of RuO2 clusters is predicted to be a singlet and the ground state for the anionic clusters is predicted to be a doublet with the CCSD(T) method. High level computational methods such as CCSD(T) are required to predict the correct ground state of RuO2 clusters. The singlet-triplet gaps are predicted to be less than 15 kcal/mol for the monomer to the 49 ACS Paragon Plus Environment


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tetramer and the gap for the dimer is only 3.2 kcal/mol. Less ionic character is predicted for small RuO2 clusters than that for the corresponding Group 4 metal oxide clusters. The clustering energy for the dimer is less than that for the trimer and tetramer. The electron affinities range from 2.2 to 3.4 eV showing somewhat that the RuO2 clusters can be readily reduced, so the clusters may be strong oxidizers. The calculated fluoride affinities are < 95 kcal/mol, and are smaller than the Group 4 (MO2)n and Group 6 (MO3)n clusters. The calculated heat of formation for the RuO2 monomer is consistent with previous experimental and computational values. The hydrolysis reactions of neutral RuO2 clusters have been studied with the same methods to predict the interaction between RuO2 and water as RuO2 is potentially an active catalyst for water splitting. The reactions of H2O with the metal site having a Ru=O bond and/or Ru−O bonds as well as H transfer to both terminal =O atoms and bridge –O atoms were studied. For the monomer and dimer, the physisorption energies for the first addition of H2O to the clusters are predicted to be -10 to -20 kcal/mol and the physisorption energies on the singlet clusters are more exothermic than for the triplet. For the trimer and tetramer, the predicted physisorption energies on the singlet and the triplet are comparable. For the ground state singlet, the reaction barrier for the proton transfer to a bridge –O atom is smaller than to a terminal =O atom for the dimer. A proton is preferably transferred to a terminal =O for the trimer and tetramer. The predicted proton transfer barriers have a broad range and are dependent on the reaction and the cluster. The hydrolysis reactions of monomer and dimer clusters are exothermic. For the trimer and tetramer, the reactions are slightly endothermic or thermoneutral. H2O is readily dissociated on the monomer and dimer, but not on the trimer and tetramer. Comparing to Group IV (ZrO2)n nanoclusters, we find that the physisorption and chemisorption energies are less exothermic and the barriers are larger for the hydrolysis reactions of the (RuO2)n 50 ACS Paragon Plus Environment

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nanoclusters. The BP86 functional works better than the B3LYP for prediction of the energetics of both the pure clusters and the hydrolysis reactions due to less spin contamination using the pure DFT functional. The (RuO2)n (n = 1 to 4) nanoclusters are characterized by small singlet triplet gaps suggesting that even these small nanoclusters are approaching metallic behavior. Behaving as cocatalysts, RuO2 nanoclusters have the potential to narrow the bandgap of the photocatalyst and improve the efficiency of capturing light because of their low-lying excited states. The different reactivity of H2O on our small RuO2 nanoclusters and on the coordinatively unsaturated sites of RuO2 (110) (discussed above) suggests that even larger RuO2 nanoclusters could be efficient catalysts for splitting water if surface-like unsaturated sites exist on the clusters. The current work on small RuO2 nanoclusters provides a starting point for further study of the molecular structures and energetics of larger nanoclusters leading to an improved understanding of structure-activity relationships in transition metal oxide nanoclusters. We also note that the new thermodynamic quantities can be used in thermodynamic models for predicting the Ru inventory present in severe nuclear reactor incidents under the exposure of steam and air. Acknowledgments This work was supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, U.S. Department of Energy (DOE) (catalysis center program). DAD also thanks the Robert Ramsay Chair Fund of The University of Alabama for support. Supporting Information. Complete citations for References 69 and 79. Figures: Optimized geometries at the B3LYP/aD level; Relative Energies for the neutral and anionic clusters with the DFT and CCSD(T) methods; HOMO, LUMO of the neutral clusters and SOMO of the anions at the B3LYP/aD level; Hydrolysis reaction PES with the B3LYP and BP86 functionals; DFT and 51 ACS Paragon Plus Environment


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HF HOMO and LUMO orbitals for the ground state singlet clusters; DFT and HF DOMO and SOMO orbitals for the triplet clusters. Tables: Calculated spin density values with the DFT; NPA Charges on Ru with the B3LYP, BP86, and PW91. Reaction energies for reactions (1) to (4) at the CCSD(T)/aT level; T1 Diagnostic at the CCSD(T)/aT level; Zero-Point energies, DFT and CCSD(T) electronic energies for all neutral and anionic clusters as well as the reactants, transition states, and products on the PES; and Cartesian coordinates for clusters and the species on the PES. This material is available free of charge via the internet at http://pubs.acs.org.


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TOC Graphic

FA EA

-90.4 2.69 ΔES-T

-81.2 3.99

-83.7 3.31

11.0

-72.6

-91.3

-67.8

Triplet

13.2

3.2

9.2 -59.1

-92.8

-49.1

-87.6 3.26

Singlet FA EA

-87.0 2.22

-93.2 3.17

-77.1 3.42


-88.0 2.86

Electronic Structures of Small (RuO2) - ACS Publications

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