crystals Article σ-Holes on Transition Metal Nanoclusters and Their Influence on the Local Lewis Acidity Joakim H. Stenlid 1 ID , Adam Johannes Johansson 2 and Tore Brinck 1,* 1 Applied Physical Chemistry, School of Chemical Science and Engineering, KTH Royal Institute of Technology, Teknikringen 36, SE-100 44 Stockholm, Sweden; [email protected] 2 Swedish Nuclear Fuel and Waste Management Company (SKB), Evenemangsgatan 13, Box 3091, SE-169 03 Solna, Sweden; [email protected] * Correspondence: [email protected]; Tel.: +46-8-790-8210 Academic Editors: Peter Politzer and Jane S. Murray Received: 10 June 2017; Accepted: 11 July 2017; Published: 14 July 2017 Abstract: Understanding the molecular interaction behavior of transition metal nanoclusters lies at the heart of their efficient use in, e.g., heterogeneous catalysis, medical therapy and solar energy harvesting. For this purpose, we have evaluated the applicability of the surface electrostatic potential [VS(r)] and the local surface electron attachment energy [ES(r)] properties for characterizing the local Lewis acidity of a series of low-energy TM13 transition metal nanoclusters (TM = Au, Cu, Ru, Rh, Pd, Ir, Pt, Co), including also Pt7Cu6. The clusters have been studied using hybrid Kohn–Sham density functional theory (DFT) calculations. The VS(r) and ES(r), evaluated at 0.001 a.u. isodensity contours, are used to analyze the interactions with H2O. We find that the maxima of VS(r), σ-holes, are either localized or diffuse. This is rationalized in terms of the nanocluster geometry and occupation of the clusters’s, p and d valence orbitals. Our findings motivate a new scheme for characterizing σ-holes as σs (diffuse), σp (localized) or σd (localized) depending on their electronic origin. The positions of the maxima in VS(r) (and minima in ES(r)) are found to coincide with O-down adsorption sites of H2O, whereas minima in VS(r) leads to H-down adsorption. Linear relationships between VS,max (and ES,min) and H2O interaction energies are further discussed. Keywords: σ-holes; surface electrostatic potential; local electron attachment energy; H2O interactions; transition metal nanoparticles; Lewis acidity 1. Introduction Surface maxima in the molecular electrostatic potential (VS,max) along the lateral extensions of intramolecular bonds are known as σ-holes [1]. These have been widely used to rationalize molecular interaction behavior and reactivity [2]. In the present contribution we introduce new categories of σ-holes based on the electronic origin of the VS,max; if the VS,max arises primarily as a consequence of electron deficiencies in the valence s-orbitals of the compound, we shall denote it an σs-hole. Similarly, VS,max originating from deficiencies in the p- or d-orbitals will be referred to as σp- or σd-holes. Mixtures of these exist. The new categorization is herein motivated by a detailed analysis of transition metal (TM) nanoclusters, and arises naturally from the occurrence of diffuse (non-directional) or localized (directional) σ-hole on the TM compounds. With some few exceptions, e.g., refs. [3–7], TM compounds have not commonly been characterized by surface electrostatic potential maps. We will here show that σ-holes are useful guides also for TM interactions with clear similarities to halogen or hydrogen bonding. Representative examples of σs- and σp-holes can be found on hydrogen and singly coordinated halogen (X = Cl, Br and I) atoms participating in hydrogen and halogen bonding. The VS,max of the hydrogen atom of e.g., HF (Figure1) arises because, upon formation of the covalent H–F bond, Crystals 2017, 7, 222; doi:10.3390/cryst7070222 www.mdpi.com/journal/crystals Crystals 2017, 7, 222 2 of 18 Crystals 2017, 7, 222 2 of 19 hydrogen atom of e.g., HF (Figure 1) arises because, upon formation of the covalent H–F bond, electronelectron density density is is relocatedrelocated fromfrom thethe non-bonding sides of of the the atoms atoms to to the the bonding bonding region region between between them.them. The The large large difference difference in electronegativityin electronegativit betweeny between H and H F furtherand F leadsfurther to aleads strong to polarization a strong towardspolarization F in thetowards bonding F inσ-orbital. the bonding The σ *-orbitalσ-orbital. is, The on theσ*-orbital other hand, is, on highly the other polarized hand, towards highly H polarized towards H but because it is unoccupied it will not compensate for the polarization of the but because it is unoccupied it will not compensate for the polarization of the σ-orbital. Consequently, σ-orbital. Consequently, the occupation of the σ-orbitals effectively results in a substantial electron the occupation of the σ-orbitals effectively results in a substantial electron deficiency on H. This is deficiency on H. This is manifested by a large positive electrostatic potential at the H atom—an manifested by a large positive electrostatic potential at the H atom—an σs-hole since it originates in σs-hole since it originates in the hydrogen s-orbital occupation. Simultaneously a negative the hydrogen s-orbital occupation. Simultaneously a negative electrostatic potential is built up on electrostatic potential is built up on F. Due to the spherical symmetry of the H 1s orbital, the F. Due to the spherical symmetry of the H 1s orbital, the corresponding σs-hole is diffused over the corresponding σs-hole is diffused over the entire H end of the molecule. This explains the weak entire H end of the molecule. This explains the weak directionality of H-bond interactions, which directionality of H-bond interactions, which often deviate significantly from 180° [8]. In the often deviate significantly from 180◦ [8]. In the following we will show that common features of following we will show that common features of σs-holes are their diffuse and non-directional ss-holes are their diffuse and non-directional character. VS,max have also been used to rationalize character. VS,max have also been used to rationalize the formation of non-covalent bonds between thehalogen formation atoms of and non-covalent electron donating bonds between compounds, halogen i.e., halogen atoms and bonds electron [9,10]. donating In contrast compounds, to hydrogen i.e., halogenbonds, halogen bonds [9 bonds,10]. In are contrast highly todirectional. hydrogen This bonds, can halogen be attributed bonds to are the highly partial directional. occupation This of the can be attributed to the partial occupation of the valence p- rather than s-orbitals. Figure1 includes the valence p- rather than s-orbitals. Figure 1 includes the example of the I2 molecule. The intramolecular examplebonding of in the I2 Iis,2 molecule. by and large, The intramolecularthe consequence bonding of the inmixing I2 is, byof andtwo large,I 5pz theorbitals, consequence leading ofto thea σ σ σ mixingσpz-bond of twowhere I 5 pthez orbitals, σpz-orbital leading is occupied to a pz-bond and the where σ*pz-orbital the pz-orbital is unoccupied. is occupied Similarly and the to *HF,pz-orbital this isgives unoccupied. rise to electron Similarly deficiencies to HF, this in givesthe lateral rise to extensions electron deficiencies of the I–I bond, in the with lateral two extensions corresponding of the I–IVS,max bond, at the with edges two of corresponding the σ-framework.VS,max Usingat thethe edgesprinciples of the forσ σ-framework.-hole categorization Using thefrom principles above, the for σV-holeS,max categorizationof halogen atoms from should above, be the denotedVS,max σofp-holes halogen due atoms to the should p-origin be denotedof the hole.σp-holes Owing due to tothe the p-originlargely ofdirectional the hole. character Owing to of the the largely pz orbitals, directional the σp character-holes are ofhighly the p zlocalizedorbitals, in the theσp direction-holes are of highly the localizedσ-bond. inConsequently, the direction the of thehalogenσ-bond. bond Consequently, interactions are, the halogenin contrast bond to hydrogen interactions bonds, are, infound contrast to be to hydrogendirectional bonds, with A···X–R found to angles be directional close to 180° with [8]. A ··· X–R angles close to 180◦ [8]. ForFor TM TM compounds, compounds, we we analogously analogously find find that areasthat ofareas high of electrostatic high electrostatic potential potential are sometimes are localizedsometimes along localized the extension along the of extension TM–TM of bonds. TM–TM In addition,bonds. In multipleaddition,V multipleS,max may VS,max arise may on arise the same on atomthe same corresponding atom corresponding to up to one toσ-hole up to per one TM–TM σ-hole bond. per TM–TM This can bond. be traced This to can the be partially traced occupied to the d-orbitalspartially occupied of the TM d-orbitals compound of the and TM will compound thus be and called willσ thusd-holes. be called The squareσd-holes. planar The square Pt4 cluster planar of FigurePt4 cluster1 can beof takenFigure as 1 an can example. be taken Pt as has an a 5example.d96s1 valence Pt has configuration a 5d96s1 valence and accordinglyconfiguration the and local electronaccordingly deficiencies the local of electron Pt4 are adeficiencies consequence of Pt of4the are redistributiona consequence of of both the redistributions- and d-orbital of densitiesboth s- and (the minord-orbital mixing densities of 6p (the-orbitals minor is mixing here neglected of 6p-orbitals for the is sakehere ofneglected simplicity). for the The sakes-deficiencies of simplicity). promote The s-deficiencies promote the creation of areas of high electrostatic potential on the corners of Pt4. The the creation of areas of high electrostatic potential on the corners of Pt4. The corners do, however, corners do, however, not correspond to maxima as the VS(r) profile is also affected by the not correspond to maxima as the VS(r) profile is also affected by the d-occupation.