Local Lewis Acidity of (TiO2)n (n = 7â10) Nanoparticles Characterized

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Local Lewis Acidity of (TiO) n=7-10 Nanoparticles Characterized by DFT-Based Descriptors: Tools for Catalyst Design Joakim Halldin Stenlid, Adam Johannes Johansson, and Tore Brinck J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09311 • Publication Date (Web): 21 Nov 2017 Downloaded from http://pubs.acs.org on November 21, 2017

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The Journal of Physical Chemistry

Local Lewis Acidity of (TiO2)n n=7-10 Nanoparticles Characterized by DFT-Based Descriptors: Tools for Catalyst Design

Joakim H. Stenlid1, A. Johannes Johansson2, and Tore Brinck1* 1

Applied Physical Chemistry, School of Chemical Science and Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden

2

Swedish Nuclear Fuel and Waste Management Company (SKB), Evenemangsgatan 13, Box 3091, SE-169 03, Solna, Sweden

* Corresponding author: Tore Brinck (E-mail: [email protected])

1 ACS Paragon Plus Environment

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ABSTRACT Transition metal oxide nanoparticles are common materials in a multitude of applications including heterogeneous catalysis, solar energy harvesting and energy storage. Understanding the particles’ interplay with their surroundings is key to their efficient usage and design. Herein two DFT-based descriptors are used to study local reactivity on (TiO2)n (n=7-10) nanoparticles. The local electron attraction energy [E(r)] and the electrostatic potential [V(r)], evaluated on isodensity surfaces, are able to identify and rank Lewis acidic sites on the particles with high accuracy when compared to the interaction energies of the Lewis bases H2O, H2S, NH3 and CO. These interactions are characterized as mainly electrostatically controlled. Given the local character, low computational cost and excellent performance of the ES(r) and VS(r) descriptors, they are anticipated to find widespread use in nanoparticle research and development.


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1. INTRODUCTION Transition metal oxides (TMOs) have long been recognized as valuable materials in chemical applications ranging from heterogeneous catalysis to electronics, solar energy harvesting and energy storage.1–6 A key to understanding and predicting the behavior of TMOs is studying their interactions with the surrounding media. The present work will exemplify how local descriptors based on density functional theory (DFT) can be used to rationalize adsorbate-oxide interactions using a series of (TiO2)n, n=7-10, TMO nanoparticles (NP). The community of computational and materials science has in later years witnessed a fast and fruitful development of linear scaling relations that link the adsorption energies of a few key species with e.g. catalytic efficiency of metal substrates.7–10 These adsorption energies may be obtained directly from experiments, from DFT calculations or by estimations based on some suitable descriptor. In the latter category the d-band model of Nørskov and coworkers holds a prominent position.11 Using the d-band model, one can correlate the position of a metal substrate’s d-band center with respect to the Fermi level to adsorbate interaction energies for series of congeneric metallic substrates. This relation can be used to compare, e.g., the catalytic properties of different metals and alloys.8,12 However, despite numerous promising efforts and despite the immense potential benefits, a model of similar simplicity and applicability as the d-band model is yet to be found for oxides and other semi-conducting materials.8,13–15 We will here demonstrate that the descriptors evaluated in this work display excellent potential for applications on TiO2 oxides, and potentially other oxide materials. In addition, the descriptors are local in their nature and can thus be used to evaluate site-resolved properties. This includes the ability to describe local reactivity at different positions on a single surface or particle, and hence the capacity to identify the most reactive sites, but the descriptors can also be used to compare the global reactivity of different surfaces and particles. In the present study we will evaluate the performance of two local DFT descriptors for characterizing site-resolved Lewis acidity of TiO2 NPs using the Lewis bases H2O, NH3, H2S



and CO as probe adsorbates. The descriptors include the electrostatic potential, V(r),16 and the local electron attachment energy, E(r).17 These descriptors have shown excellent capabilities in predicting similar interaction behaviors for metal NPs as well as in nucleophilic organic reactions and weak interactions such as halogen- and hydrogen bonding.16–22 The studied probe molecules are common reactants, intermediates, (bi)products and catalytic poisons in industrially important processes (e.g. in the syngas and methanol, production, water-gas shift reaction, in the Claus process for desulfurization of hydrogen sulfide and the Haber-Bosch process for production of ammonia, which is used to produce artificial fertilizers) as well as in corrosive processes.2,23–29 For the purpose of optimization of catalytic proficiency, it is imperative to have a thorough atomistic understanding of the underlying interactions that govern the catalytic processes, as well as the processes leading to degradation of the catalyst, in order to guide the material’s design and fine-tune the operational conditions. In addition to the above, the interactions of H2O, NH3, H2S and CO with TiO2 is of interest in e.g. detoxification of waste water,30 photocatalytic water splitting,6,31,32 in dye-sensitized solar cells,33,34 gas purification,32,35–38 as sensor material39 as well as in CO oxidation and hydration.40 TiO2 NPs are ionic compounds formally comprised by Ti4+ and O2- ions. Therefore it is expected that regions of negative electrostatic potential are encountered in the vicinity of O2ions, and that positive electrostatic potential is built-up around Ti4+. In the following we will show that the fluctuations of V(r) over the Ti4+ when evaluated on a contour of constant electron density can be used to estimate the relative affinity of the Ti4+ sites’ for interactions with the H2O, H2S, NH3 and CO Lewis bases. Similar results are obtained for the E(r) property; we find that E(r) exhibits minima at Ti4+ sites, thus indicating that these have an increased susceptibly towards electron addition. When evaluated on isodensity surfaces, local maxima in V(r) on an isodensity surface and local surface minima in E(r) are denoted VS,max and ES,min, where VS,max are commonly referred to as σ-holes in the literature.41 The results for the VS,max and ES,min quantities show promise for future applications as reactivity descriptors in e.g. heterogeneous catalysis, but also in the study of nanotoxicology, and in nanoparticle


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sorption, agglomeration and degradation, as well as in general understanding of nanoparticle and oxide interaction behavior. The present study covers only molecular adsorption. More complex modes of interactions, such as dissociative adsorption, co-adsorption and adsorptions leading to strong local structural relaxation, are beyond the scope of the present paper but are potential topics for future evaluations of the descriptors.

2. THEORY The electrostatic potential of a polyatomic compound at a position r in space is rigorously defined as: =

− , | − | | − |

1

where RA and ZA are the coordinate and charge of the A:th nuclei, while ρ(r) is the electron density function. The first term corresponds to the nuclear contribution and dominates for positive regions of V(r), whereas the second, electronic term dominates in regions where V(r) is negative. The local electron attachment energy, E(r), is given by:17 =

. 2

Here εi is the energy of the i:th spin-orbital of the substrate and the summation runs over all virtual (unoccupied) orbitals of energy below the eigenvalue cut-off value of εi < 0. Within the generalized Kohn-Sham DFT (GKS-DFT) and on the basis of Janak’s theorem,42 i.e.

" ⁄" $ = , it follows that this cut-off is a sensible choice since an orbital with an energy

above this level would not bind an electron (given a frozen orbital description).17 The E(r)

property was introduced as the electron-accepting analog to the average local ionization energy Ī(r)43 that has been broadly applied in the study of molecular interactions and reactivity of electron donating compounds.44,45 E(r) can be decomposed into contributions from the electrostatic potential, the local orbital kinetic energy density ti(r) and the exchangecorrelation potential [VXC(r)] by:17,46



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1 = % & − + () * ,

3

where ti(r) = −½ψi*(r)∇2ψi(r). Hence V(r) and E(r) give complementary information where V(r) describes the purely electrostatic component of an interaction whereas E(r) also describes the interaction’s charge-transfer/polarization characteristics.17,46

3. COMPUTATIONAL METHODS All calculations were carried out in the Gaussian program suite47 employing the PBE048 density functional. The adsorbate structures were optimized in vacuo using the Pople style 631+G(d,p) basis set for the first and second row elements, and the effective core potential LANL2TZ+(f) basis set of Hay and Wadt49–51 for the Ti atoms. The latter is a triple-ζ version of the LANL2DZ basis set augmented with polarizing and diffuse functions. The final energies were obtained using the LANL2TZ+(f) basis set for Ti and a 6-311+G(2df,2p) basis set for the remaining atoms. Grimme’s D3 dispersion corrections52 with Becke-Johnson damping53 were added to the final energies. Eq. 3 below was used to calculate the interaction energies, ∆Eint. ∆Eint = Esub/ads – [Esub + Eads] (4) Here Eads, Esub and Esub/ads are the zero-point energies of the free adsorbate molecule, the bare (TiO2)n nanoparticle substrate and the (TiO2)n-adsorbate complex respectively. The convergence of all structures to local minima was confirmed by harmonic frequency calculations on the optimized structures. The VS(r) and ES(r) properties were evaluated by the in-house HS95 program (T. Brinck) using orbital energies and densities obtained with the PBE0 xc-functional and the LANL2TZ49–51 [Ti] and 6-311+G(2d,2p) [O] basis sets on the optimized (TiO2)n particles. Local VS,max and ES,min values were determined at the 0.001 a.u. isodensity surface and visualized with the Chimera software.54 The 0.001 a.u. isodensity surfaces have previously been found suitable for the evaluation of interactions with metal nanoparticles and for the interactions and reactions of organic compounds.16,20,21 Values of V(r) are reported as qV(r)


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with q=1. Previous studies on Cu, Ag and Au nanoclusters have shown that the VS(r) evaluated with different classes of xc-functionals yield results of comparable quality for interactions analyses.20 It was also found for the metal nanoclusters that ES(r) performs well when using hybrid functionals of 10-15% of HF exchange admixture, but the predictive power of ES(r) in the form defined by eq. 5 decreases when used together with functionals of larger HF admixture or with range-separated functionals due to the tendency of these functionals to result in too few virtual orbitals with negative eigenvalues. However for metal oxides, a higher contribution from HF exchange is generally needed compared to pure metals to reproduce the band gap. It can be expected that this also holds for ES(r), and that the 25 % of HF exchange present in PBE0 is well balanced. Tests further show that triple-ζ plus polarization basis sets of varying size and origin all give results of good predictive quality.20

4. RESULTS AND DICUSSION 4.1. Adsorption structures The (TiO2)n nanoparticles were re-optimized from low-energy structures identified by Berardo et al.55 The particles are displayed in Figure 1 and belong to the Cs (n=7), C2h, (n=8), C1 (n=9), and C1 (n=10) symmetry point groups. All particles have a singlet (S=0) ground state multiplicity. The O2- ions are 4-fold to 1-fold coordinated, giving rise to two dangling Ti-O bonds per particle. The Ti4+ ions are mainly 4-fold coordinated, with the exception of the sites Ti(3) and Ti(5) of (TiO2)9 that are 6-fold and 5-fold coordinated respectively, as well as Ti(8) of (TiO2)10 that is 5-fold coordinated. The 4-fold coordinated Ti ions primarily have a tetrahedral coordination that for some sites is slightly distorted. This is obvious for certain (but not all) cases of Ti ions with dangling O bonds, whereas the distortion in most cases leads to a minor shift towards a trigonal pyramidal coordination pattern with the central Ti ion in the same plane as three O ions.



Figure 1. Showing the structures of the (TiO2)n particles. Ti ions in grey and O ions in red. Upon interaction with electron donating molecules (i.e. nucleophiles/Lewis basis), it is found that adsorption takes place at the Ti sites. Accounting for symmetry, the series of (TiO2)n nanoparticles have all together 27 unique Ti-adsorption sites. These are distributed as five (n=7), three (n=8), nine (n=9) and ten (n=10). In the present study, we have focused on the interactions with the small H2O, NH3, H2S and CO molecules for the assessment of local Lewis acidity of the TiO2 nanoparticles. Figure 2 shows the favored mode of interaction for molecular adsorption of H2O, NH3, H2S and CO onto the (TiO2)7 nanoparticle. We can also note that the interaction energy for the strongest adsorption of the probe molecules is essentially constant over the particles (Table 2). As demonstrated by the adsorption figures, H2O, NH3, and H2S interact with via an electron lone-pair positioned at the most electronegative atom, i.e. O, N and S, without forming H-bonds with the substrate O-atoms. Out of all interactions, the only exception to the above is H2O adsorption onto the Ti(1) site of (TiO2)7 where a H-bonds is formed as shown in Figure 2 and Figure 3. Interactions displaying both H-bonds and the lack of H-bonds, as well as mixtures of molecular and dissociative adsorption modes, have been reported previously for various TiO2 particles and surfaces.56–67


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Figure 2. Displaying adsorbate-(TiO2)7 structures for all of adsorbate molecules onto the Ti(1) site. Although H2S is considered a soft electrophile meaning that its interactions are expected to be charge-transfer rather than electrostatically controlled, its mode of interaction onto the (TiO2)n nanoparticles is dominated by electrostatics and very similar to those of H2O and NH3. Likewise, the CO displays a similar adsorption behavior despite the fact that it often rehybridizes and form complex binding to metal surface and particles.20,68–72 (CO is found to adsorb C-down in agreement with refs. 73,74.) The similarities in the interaction modes of the different particles is discussed in more detail below and is exemplified by the charge difference plots of Figure 3.



Figure 3. Density difference maps for CO, H2O, NH3 and H2S upon interaction with the (TiO2)7 particle at position Ti(1), i.e. the most favored adsorption site. H2O is shown in an Hbonding (relaxed) and non-H-bonding (constrained) conformation. This is the only example out of all adsorption structures where a H-bond is formed. Coloring: depletion=blue, buildup=purple. We can draw some general conclusions with regards to the adsorption behavior of the probe molecules by comparing their ground state properties in Table 1 to the computed TiO2 interaction details. Firstly, the average interaction distances of the probe molecules follow the variations in the van der Waals radius of the interacting atoms closely: H2O < NH3 < CO < H2S. Moreover, the interactions are accompanied by an average electron-transfer (as determined by NBO analysis75) to the TiO2 particles in the order H2S > CO > NH3 > H2O. Somewhat surprisingly, the trend from the average charge transfer is qualitatively inversed compared to the average interaction energy; the NH3 corresponds to the strongest interaction followed by H2O, CO and H2S. This is due to the large electrostatic contribution to the interaction, as elaborated on further on in the discussion, and is reflected by the fact that the surface (VS,min) and spatial (Vmin) minima of V(r) at the probe molecules correctly rank their relative average interaction energies as H2O > NH3 > H2S > CO (Table 1 and Figure 4). In


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contrast, the charge-transfer/polarization descriptor ĪS,min gives an incorrect ordering of the H2O and H2S molecules for the TiO2 interactions – thus, again indicating a generally small charge-transfer/polarization component to the interaction energy. In summary, the inversed trend between the computed NBO charge-transfer and TiO2probe molecule interaction energies is a reflection of the fact that a larger charge-transfer and/or redistribution of the electronic configuration does not necessarily lead to stronger interaction energies. Instead it is the combined interaction with constructive and destructive contributions that determines the interaction energy, which can be referred to as an example of “capitalistic chemistry”.76

Table 1. Average adsorption details for H2O, H2S NH3 and CO upon adsorption to the (TiO2)n, n=7-10, particles. Included are the average adsorption distance (̅-. ), adsorbent van

der Waals radii (rvdw)[a] and expected interaction distances (rexp)[b]. All distances are given in Å. Included are also the average interaction energy (∆Eint) in eV, the NBO charge transfer (∆qNBO)[c] in a.u., VS,min and Vmin[d] at the interacting probe atom in kcal mol-1 and their distances to the probe atom, as well as ĪS,min in eV.

0 1/ rvdW rexp ∆Eint ∆qNBO VS,min dTi-Vs,min Vmin dTi-Vmin ĪS,min / H2O 2.17 1.52 2.2 -0.91 -0.20 -33.9 1.82 -47.5 1.27 9.95 H2S 2.69 1.80 2.5 -0.54 -0.33 -18.0 2.29 -22.1 1.84 8.01 NH3 2.21 1.55 2.3 -1.24 -0.26 -37.6 2.06 -64.1 1.28 7.83 CO 2.41 1.70 2.4 -0.50 -0.31 -12.2 1.98 -15.5 1.59 10.9 [a] van der Waals radii of the interacting atom of the probe molecule.77 [b] Based on sum of rvdw and, the crystal ionic radius of Ti4+ of 0.745Å.78 [c] Average charge transferred to (TiO2)n upon interaction derived from NBO analysis.75 [d] Minimum in the (surface) electrostatic potential at the site of interaction of the probe molecule determined at the PBE0/6311+G(2d,2p) level of sophistication, at the 0.001 a.u. isodensity surface for VS,min.



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Table 2. Interaction energies at the favored site for the individual particles and adsorbents. See table S1-S4 of the supporting information for a full account of all adsorption energies.

H2O H2S NH3 CO

n=7 -1.20 -0.79 -1.53 -0.71

n=8 -1.09 -0.75 -1.50 -0.66

n=9 -1.18 -0.81 -1.55 -0.71

n=10 -1.20 -0.84 -1.59 -0.71

Figure 4. Surface electrostatic potential, VS(r), of the H2O, H2S, NH3 and CO Lewis basis determined at the PBE0/6-311+G(2d,2p) level of theory on the 0.001 a.u. isosurface. Note that the VS,min of largest magnitude of CO is located at the C atom (left CO figure), whereas a weaker minimum appears on the O atom (right CO figure of reduced size). Coloring (colors centered on given value) in kcal mol-1, VS(r): blue < -15 < cyan < -5 < green < 10 < yellow < 20 < red.

4.2. Local Lewis Acidity As described in the introduction, previous studies of molecular16–18 as well as metal nanoparticle interactions,19–21 have found that the electrostatic potential V(r) and the local electron attachment energy E(r) evaluated on a isodensity surface of a compound provide a good description of the local electron accepting ability, i.e. the local Lewis acidity. Specifically, local surface maxima in V(r), VS,max, and local surface minima E(r), ES,min, indicate sites susceptible to interactions with nucleophiles/Lewis bases. In other words, areas of high positive surface electrostatic potential of a compound and/or large negative surface local electron attachment energy are likely to interact with Lewis bases. In addition it has


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been found that the relative magnitudes of the VS,max and ES,min, scale linearly with local interaction energies and reactivity trends. These features makes it possible to compare the behavior for different sites within a compound, but also, e.g., the reactivity variations for a set of different compounds: i.e. both regio- and compound selectivity are attainable. It has also been found that VS(r) and ES(r) provide complementary information on the character of the interaction; whereas VS(r) reflects the electrostatic contributions, ES(r) is more involved and includes contributions associated with the charge-transfer capacity and local polarizability of the studied compound. In this respect, differences in the performance of E(r) compared to V(r) could be used as an indicator of whether a studied interaction is electrostatically or charge-transfer/polarization controlled.

Figure 5. Electrostatic potential VS(r) and local electron attraction energy ES(r) mapped on the 0.001 a.u. isodensity surfaces of the (TiO2)7 particles. Included is also the lowest unoccupied molecular orbital. Coloring (colors centered on given value); VS(r) in kcal mol-1: blue < -30 < cyan < -15 < green < 25 < yellow < 90 < red; ES(r) in eV: green > -10.0 > yellow > -25 > red. Similar figures for (TiO2)8, (TiO2)9, and (TiO2)10 particles are included in the supporting information (Figure S1).



Figure 5 displays the V(r) and E(r) properties mapped on the 0.001 a.u. isodensity surface of (TiO2)7. Similar figures for the (TiO2)8, (TiO2)9, and (TiO2)10 particles are included in the supporting information (Figure S1). The VS(r), as well as the ES(r), identify the Ti sites as the Lewis acidic centers, i.e. VS,max and ES,min are located at the Ti ions. This is in line with the adsorption patterns of the electron donating probe molecules H2O, NH3, H2S and CO that all favor adsorption to the Ti sites. On the basis of minima in VS(r) (marked by blue areas, the most negative, in e.g. Figure 5) we can further recognize that the surface exposed O ions are likely Lewis basic sites. In contrast to VS(r), ES(r) cannot be used to identify Lewis basic sites. Instead one should apply the local average ionization energy Ī(r) of Sjoberg et al.43 for a corresponding examination of charge-transfer/polarization contributions to the Lewis basicity. This is, however, beyond the scope of the present study. We can further note that the magnitudes of both the VS,max/min and ES,min are much larger than those identified on e.g. neutral molecules or metal particles,17,20–22 in line with the ionic character of the TiO2 compounds. Included in Figure 5 is also the LUMO orbital, which for the studied particles cannot be recommended as a sole indicator of local Lewis acidity. For the case of (TiO2)7, the LUMO does, apart from incorrectly marking out a number of O atoms as Lewis acidic, gives more limited information than VS(r) and ES(r) on the site specificity for the various Ti sites. In order to illustrate the applicability of the VS(r) and ES(r), we will use (TiO2)7 as an example. The interaction properties of (TiO2)7 can be dissected by analysis of the site-specific information in Table 3. We find that both VS,max and ES,min identify the Ti(1) sites as the most Lewis acidic followed by Ti(6=7) > Ti(3) > Ti(4=5) > Ti(2). The same order is reflected by the H2O interaction energies where, for instance, the interaction energies and VS,max correlate linearly with a coefficient of determination (R2) of 0.976. (Linear relations between descriptor values and interaction energies are further discussed below in section 3.3.) We also find that partial atomic charges according to the NBO75 and Merz-Singh-Kollman79,80 schemes do not capture the adsorption trends correctly. However, it can be noted when analyzing (TiO2)7, as well as the other TiO2 particles, that sites with a low (high) NBO charge are commonly, but 14 ACS Paragon Plus Environment

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not always, associated with a weaker (stronger) interactions. A full account of all the local descriptor values for all particles is included in the supporting information in Table S5. The results for the (TiO2)7 particle show that VS,max is a better descriptor for electrostatic interactions than qNBO. By analyzing the VS,max for the various adsorption sites of all the TiO2 particles, distinct groups emerge divided into weak and strong VS,max respectively. This grouping is clearly displayed in e.g. Figure 6. Interestingly, all Ti sites of weak VS,max are associated with some coordination discrepancy. This includes sites that either have a higher coordination (5- or 6-fold), or sites where Ti is coordinated to a dangling O. For certain sites, this is compensated by a clear distortion of the coordination pattern and the site still displays a larger (‘normal’) VS,max. This can be understood in terms of the balance between the ionic charge and the exposure of the ion; a large ionic charge favors interaction, but if the cation is largely embedded by O2-, as in the case of sites of higher coordination numbers, the effective electrostatic potential felt by the adsorbate at the interaction site will be low relative other sites, and the interaction energy comparable small. We note that Ti sites of 5- and 6-fold coordination are common in crystal structures. Initial studies on periodic model systems indicate that the descriptors are capable of reproducing interaction behavior also for crystalline oxides. This will be further evaluated in a future study.

Table 3. Site resolved information for the (TiO2)7 particle. Included are the H2O interaction 6

energy, (Δ3457 ) in eV, VS,max in kcal mol-1 (strictly given as qV for q=1), ES,min in eV, and atomic partial charges in a.u. according to the NBO (qNBO)75 as well as to the Merz-SinghKollman schemes (qESP).79,80 [a] See Figure 1 for the numbering of the sites. Ti site Δ 67 VS,max ES,min qNBO qESP 345 1 -1.23 154.6 -56.28 1.57 2.02 2 -0.38 32.7 -4.73 1.47 2.15 3 -1.08 120.4 -36.86 1.58 2.43 4=5 -0.97 98.8 -23.46 1.49 2.29 6=7 -1.20 134.2 -46.11 1.59 2.35 4+ 2[a] Here using the crystal ionic radii of Ti and O from ref. 78 for the qESP.



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4.3. Linear relationships As discussed above, the VS(r) and ES(r) probes can be used to identify Lewis acidic sites. The remaining question is whether Lewis acidity descriptors are able to retrieve the interaction energy trends of the H2O, NH3, H2S and CO molecules? This is indeed demonstrated by the correlation of the graphs in Figure 6 and the results presented in Table 4. Included in the correlations of Figure 6 are all unique adsorption sites of the considered TiO2 nanoparticles, while Table 4 also gives the corresponding correlations resolved for each particle. The good overall trends with R2-values ranging from 0.96 to 0.91 for VS,max and 0.93 to 0.91 for ES,min for the different adsorbates are quite impressive given the multitude of sites included.

Table 4. Correlations indicated by R2 between probe molecule interaction energies and local descriptor values VS,max and ES,min obtained at the 0.001 a.u. isodensity surface for all individual (TiO2)n, n=7-10, clusters.[a] n=7

n=8[b]

n=9

n=10

Total

VS,max H2O 0.976 0.976 0.917 0.976 0.949 H2S 0.972 0.999 0.921 0.976 0.956 NH3 0.964 0.998 0.828 0.934 0.915 CO 0.986 0.999 0.900 0.985 0.962 ES,min H2O 0.911[c] 0.927 0.899 0.943 0.908 H2S 0.918[c] 0.991 0.908 0.967 0.930 NH3 0.904[c] 0.995 0.876 0.975 0.917 CO 0.947[c] 0.991 0.845 0.947 0.914 [a] H-bonding was not observed except for the H2O adsorption onto position Ti(1) of (TiO2)7. [b] Note that there are only three unique adsorption sites on (TiO2)8, hence the reported R2 values should be used with caution. [c] When evaluated at 0.004 au isosurface of (TiO2)7, ES,min display increased R2 correlations: H2O=0.960, H2S=0.966, NH3=0.958 and CO=0.982. Analyzing the results adsorbate by adsorbate, one find that VS,max display better correlation with H2O interaction energies than ES,min for all series; thus corroborating the conclusions that


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the H2O interaction is more electrostatically than charge-transfer/polarization controlled. The same conclusion can be drawn also for the remaining adsorbates with the possible exception of NH3 where ES,min gives a better correlation for the (TiO2)9 and (TiO2)10 particles. We note, however, that E(r) has a large contribution from V(r), and that VS,max and ES,min have an overall mutual correlation of R2=0.944. Nonetheless, the results for the (TiO2)9 and (TiO2)10 suggest that the NH3 interactions indeed have a substantial charge-transfer/polarization component. This is in line with the comparable low ĪS,min of NH3 that is benefiting chargetransfer and polarization, and the fact that NH3 displays the strongest interactions among the considered adsorbates (Table 1); a strong electrostatic interaction is expected to be accompanied by a significant polarization effect, which is a second order correction to the electrostatics (see also discussion below on the charge-difference plots in Figure 3). In general, however, the H2O, H2S, NH3 and CO interactions appear to be electrostatically controlled. The dominance of electrostatics is expected considering the ionic character of the TiO2 particles and the large values of VS(r) compared to, for instance, aromatic molecules17 and metal nanoparticles of Ag, Au and Cu.20 In the case of the metal nanoparticles, a mixed charge-transfer/polarization and electrostatic control is instead seen for several of the CO, H2O, H2S and NH3 adsorbates.



Figure 6. Correlation plots for ∆Eint of the various probe molecules onto the (TiO2)n particles versus VS,max (top) and ES,min (middle) at the site of interaction, as well as the multi-linear correlation with VS,max of the Ti site and Vmin [spatial minimum in V(r)] of the interacting atom of the probe molecule (bottom): R2 = 0.963. The displayed trends include sites from all particles combined while Table 4 reports correlations for each individual particle.


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In contrast to the mainly electrostatic picture of the interactions obtained above, NBO analysis suggests a rather large amount of charge-transfer by electron donation to the TiO2 particles upon adsorption of all probe molecules (Table 1). We claim that this, in fact, fits well into the picture and that the ∆qNBO reflects the polarization of electron density of the probe molecules towards the Ti-bond in order to accommodate a stronger Coulombic interaction. In support to the above, the interactions can be further analyzed by the use of the charge difference plots of Figure 3. As described in section 3.1, the adsorbates here display rather similar interaction behavior, although the evaluated probe molecules in certain aspects have largely dissimilar properties (Table 1). H2O and NH3 are for instance known as hard adsorbates, meaning that their interactions are usually electrostatically controlled, whereas H2S is a soft Lewis base that commonly interacts in a charge-transfer controlled manner. Upon adsorption on metallic surfaces, the CO molecule is, furthermore, known to have a complex interaction pattern accompanied by large valence rehybridization68,72 and a mixture of charge donation and back-donation.69–71,76 Nevertheless, all adsorbates seem to behave similarly upon interaction with TiO2 as highlighted in Figure 3 where the adsorption at the most favored site of (TiO2)7 is displayed as example. Upon interaction, electron density is built-up in the area in-between the TiO2 and the adsorbate, while electron density is depleted at the Ti-site. Altogether this leads to a larger negative charge accumulation at the adsorbates and a larger positive charge accumulation on the particle that facilitates a strong Coulombic interaction. In addition one can notice that the adjacent O sites on the TiO2 build up extra electron density, while the H-atoms of H2O, NH3 and H2S lose density. This should favor a fractional amount of H-bonding in the interaction. However, among the adsorbates, only the H2O adsorbate bends towards one side to form an H-bond. This, i.e. adsorption to Ti(1) of (TiO2)7 is also the only interaction among all considered where an explicit H-bond is being formed (section 3.1). Nonetheless, minor contributions from subtle interactions between H of the adsorbates and adjacent O particle atoms could be reflected in the small deviations in the 19 ACS Paragon Plus Environment


trends of Figure 6. This could also explain why CO is the adsorbate with best correlations amongst the probe molecules, since this is the only compound that lacks the ability to form Hads-OTiO2 interactions. In addition to the above, dispersion interactions (not directly captured by the descriptors) and adsorbate induced structure reconstruction are other factors leading to reduced correlations. The interactions can also be studied particle by particle. For the (TiO2)8 there are only three distinct adsorption sites, hence the correlations given for this particle alone should be used with caution. For the remaining particles the (TiO2)7 and (TiO2)10 display results that are throughout consistent with the overall results, whereas the (TiO2)9 particle shows weaker correlations. This can, by and large, be traced back to two outlier sites, Ti(5) and Ti(9), in all data series but the ES,min-NH3. These two sites are associated with coordinative anomalies as outlined previously; Ti(5) has a 5-fold coordination whereas Ti(9) is attached to a dangling O atom. This gives rise to considerable geometrical redistribution upon adsorption of the probe molecules, but to a lesser degree for NH3. Similarly are the outliers of the other particles typically coordinatively discrepant sites, e.g. Ti(8) of (TiO2)10. The (TiO2)9 is, however, the particle with the largest prevalence of coordinatively discrepant sites, four out of nine, which can explain its lower general correlations in Table 4. Since VS,max and ES,min are expected to give different and complementary information, an attractive approach is to estimate the interaction energies by a linear combination of the two properties, this because we thereby, presumably, can capture a larger portion of the interaction. The above approach has previously been successfully applied to Au, Ag and Cu nanoparticles as well as in organic molecular interactions.20,81,82 However for the present interactions, the description of adsorption trends cannot be improved significantly by this method, which further underlines the large electrostatic contribution to the variations in the studied TiO2 interactions. Instead, an interesting procedure is to form linear combinations of the VS,max at the interaction Ti site with the VS,min at the interacting atom of the probe molecule (Table 1). Such a dual descriptor is able to retrieve the interaction energy for all particles and all probe molecules simultaneously. The overall R2 of VS,max for the joint linear correlation 20 ACS Paragon Plus Environment

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including the interaction energies of all molecules of all particle sites is 0.385. By formation of the dual descriptor, a correlation of R2=0.928 can be obtained. If one instead uses the spatial minimum in the electrostatic potential (Vmin, i.e. without constraining the location to an isosurface) of the probe molecule, the R2 can be increased to 0.963. This is in line with previous findings that Vmin generally is a better interaction descriptor than VS,min for characterizing Lewis basicity.83 To conclude, it is appealing to elaborate on the transferability of the results of the descriptors to similar systems. One such aspect is to use calibration curves from a set of particles for estimations of the interactions of others. Due to the localized character of the electronic structure of oxides, as opposed to e.g. metallic materials, it is expected that the chemical behavior of larger compounds is rather well represented by smaller model systems. As a test, we can here e.g. use the (TiO2)7 and (TiO2)8 particles to form a linear calibration curve (∆Eint=0.0069VS,min+0.22) for H2O interactions on other TiO2 compounds. Applying this relation on the (TiO2)9 and (TiO2)10 particles a RMSD of 0.07 eV is obtained compared to our previously determined DFT interaction energies. Hence this could be a useful future approach to apply the descriptors for fast estimations of interaction energies of large particles. In summary, the ability to form linear combination as described above is in line with the established linear scaling relationships between adsorbates of various kinds onto various metal surfaces7–10 and reinforces a great promise for future applications of the V(r) and E(r) descriptors.

5. CONCLUSIONS The Lewis acidity of four (TiO2)n, n=7-10, nanoparticles have been evaluated in the framework of density functional theory (DFT) by studying the adsorption behavior of the electron donating probe molecules: H2O, NH3, and H2S, and CO. This was compared to information provided by two local DFT descriptors determined at the ground states of the oxide particles and evaluated at isodensity contours of 0.001 a.u. The descriptors comprise the surface electrostatic potential VS(r) and the local surface electron attraction energy ES(r).



It has been found that the DFT descriptors can identify the Lewis acidic sites of the TiO2 particles. Local maxima in VS(r) and local minima in ES(r) are found in the proximities of the Ti ions. The VS,max and ES,min coincide without exception with the adsorption sites of the probe molecules. It is also demonstrated that both VS(r) and ES(r) can rank the relative Lewis acidity of the individual adsorption sites and effectively reproduce trends in interaction energies for all adsorbates. The results of this study are promising for future applications of the descriptors as general tools for evaluations of oxide and electron-donor interactions, this in addition to the previously demonstrated capacity of the descriptors to characterize the interactions of metal nanoparticles as well as molecules. We thereby predict a wide applicability in heterogeneous catalysis as well as in sorption studies with relevance in e.g. corrosion, particle transportation and chromatography. An obvious limitation of the current study is that the evaluations of the descriptors are carried out versus computational data while, ideally, one should strive to perform the assessment against experimental results. Although high quality experimental adsorption data are scarce for nanoparticles of the considered sizes, reliable experimental studies have been conducted for extended metal84 and, to a limited degree, oxide surfaces.85 Accordingly future evaluations of the V(r) and E(r) descriptors should expand in this direction. Initial studies on crystalline surfaces of metals and oxides are showing promising results and will be the focus of a proceeding investigation.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: XXXX. Interaction energies, VS,max and ES,min, and Cartesian coordinates of the investigated particles (PDF).

AUTHOR INFORMATION Corresponding Authors *(T.B.) E-mail: [email protected]. 22 ACS Paragon Plus Environment

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ORCID Joakim Halldin Stenlid: 0000-0003-3832-2331, Adam Johannes Johansson: 0000-0001-76867776, Tore Brinck: 0000-0003-2673-075X

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work was supported by the Swedish Nuclear Fuel and Waste Management Company (SKB) and by the School of Chemical Science and Engineering at KTH (via its excellence award to J.H.S.). The calculations were performed at resources provided by the Swedish National Infrastructure for Computing (SNIC) at the National Supercomputer Centre (NSC) in Linköping University as well as by the PDC Center for High Performance Computing (PDC-HPC).

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Local Lewis Acidity of (TiO2)n (n = 7â10) Nanoparticles Characterized

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Local Lewis Acidity of (TiO2)n (n = 7â10) Nanoparticles Characterized