Study of odd–even effects in physisorption and chemisorption of Ar, N2, O2 and NO on open shell Ag11–13+ clusters by means of self-consistent van der Waals density functional calculations

This journal is ©the Owner Societies 2019 Phys. Chem. Chem. Phys. Cite this: DOI: 10.1039/c9cp04865k Study of odd–even effects in physisorption and chemisorption of Ar, N 2 ,O 2 and NO on open shell Ag 11–13+ clusters by means of self-consistent van der Waals density functional calculations Eva M. Ferna ´ndez * a and Luis C. Balba ´s b We have studied the adsorption and coadsorption properties of one or more X = Ar, N 2 ,O 2 , and NO adsorbates on cationic silver clusters Ag 11–13+ , whose sizes are in the open shell region of metal clusters, aiming to understand the observed odd–even effects in the abundance spectra of Ag 11–13+ mX complexes. All calculations were performed self-consistently using a non-local van der Waals correlation functional, covering the different nature of the interactions between the silver substrate and the several adsorbates, which range from dispersion (London) forces for Ar, non covalent p–pinteractions for N 2 , charge-transfer interactions for O 2 and NO, and the covalent Ag–Ag bond in the nude silver cluster. Despite the wide interval of adsorption energies, spanning two orders of magnitude, we have been able to explain the following experimental facts. For X = Ar, N 2 , and O 2 reactions with Ag 11–13+ , it was observed in the mass spectra an abundance peak at n= 12 [M. Schmidt, et al.,ChemPhysChem, 2015, 16, 855]. In addition it was observed the competitive adsorption of two or more N 2 molecules, and the cooperative effect of adsorbing N 2 together with O 2 molecules. For X = NO, an abundance peak at n= 12 has been also observed [J. Ma, et al.,Phys. Chem. Chem. Phys., 2016, 18, 12819]. We find that the main factors determining these properties are the different core motifs of the cluster geometry (pentagonal bipiramid for Ag 11+ and Ag 13+ , but triangular prism for Ag 12+ ) and, on the other hand, the odd number of valence electrons for Ag 12+ , leading to a smaller HOMO–LUMO gap than those of its neighbours. Further details about the preferred adsorption sites, dipole moments, and dipole polarizabilities are also discussed. 1 Introduction Aside from their application in many branches of nanotechnology based products such as, for example, antimicrobial agents, 1 silver nanoparticles are being studied currently as a support for small molecules and radicals (N 2 ,O 2 ,NO,etc....), focussing on the understanding of their catalytical properties. 2,3 Much of the recent effort in this direction has dealt with neutral and anionic nanoparticles, 4–11 but interesting results have been also found recently for positively charged clusters. 2,11–14 The reactivity of bimetallic Ag n M m0 clusters towards small particles has been also explored. 15–18 The interaction of pure and bimetallic clusters with noble gases, like argon, has been studied in order to infer the particle morphology and to characterize its physisorption activity. 2,19 Bre ´chignac and coworkers 2,12 have extracted and rationalized general size-dependent trends about the reactivity of cationic silver clusters by analyzing the mass spectra of gas phase Ag n+ X clusters (nr70), X being one or more of Ar, N 2 ,andO 2 adsorbed molecules. For noble gases, the interaction was unambiguosly characterized as physisorption. However, the connection between the observed stability pattern of Ag n+ mAr complexes and the cluster geometry could not be clearly established. With respect to N 2 , they found that the adsorption signal behaves as that of rare gases, that is, in both cases the adsorption decreases with cluster size and shows peaks at the same sizes, suggesting that N 2 ,like noble gases, suffers physisorption. On the contrary, for oxygen adsorption, the mass spectra data indicate that molecular oxygen is chemisorbed (at 77 K) on Ag n+ up to at least n= 70, and the signal increases with cluster size. As a unified explanation of these general trends, Bre ´chignac and coworkers 2,12 conclude that the factor responsible for both N 2 physisorption and O 2 chemisorption is the surface charge density on the cluster cations, since it promotes N 2 physisorption and hinders electron transfer to O 2 , and both effects decrease when the surface charge density a Departamento de Fı ´sica Fundamental, Universidad Nacional de Educacio ´na Distancia, Madrid, Spain. E-mail: [email protected]ed.es b Departamento de Fı ´sica Teo ´rica, Universidad de Valladolid, 47011 Valladolid, Spain Received 2nd September 2019, Accepted 10th October 2019 DOI: 10.1039/c9cp04865k rsc.li/pccp PCCP PAPER Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online View Journal Phys. Chem. Chem. Phys. This journal is ©the Owner Societies 2019 decreasesastheclustersizeincreases. Superposed onto these general adsorption trends, notoriousvariationswithclustersize are observed, which are attributed to very different causes depending on the type of adsorbate and the electronic and geometric structure of the particular Ag n+ cluster. Thus, calculations for small size Ag n+ clusters 12 show that the binding energy of N 2 positively correlates with the coordination number of adsorption sites, and that physisorption at obtusecornersisstrongerthan that at acute ones. It was also observed competition between multiple N 2 physisorptions on small clusters, 2,12 that is, physisorption of N 2 at any site is reduced by the presence of other N 2 molecules on other sites. Anotherexperimentalfactisthatthose clusters with an adsorbed O 2 moleculeareabletoattractmore nitrogen than bare clusters. This cooperative effect is consistent with charge transfer from the cluster to the O 2 molecule, which enhancesthepositivechargeonthemetallicpartofthecluster, thus promoting N 2 physisorption. DFT calculations for neutral Ag n clusters (nr9) have predicted that dissociation of O 2 is preferred for larger sizes, while molecular adsorption is favored for nr5 sizes. 7 Dissociation of O 2 is reported in experiments 12,15 at temperatures higher than about 100 K. (Our calculations in the present paper are conducted at 0 K.) On the other hand, electronic shell closing effects, and the electron pairing energy, 9 arising from a small number of confined interacting electrons, originate the peaks and valleys which appear superimposed on the increasing trend with the size of cationic silver clusters with chemisorbed O 2 molecules. 2 In the range of sizes n= 11–13, where no electronic shell closing effects occur, it can be expected subshell splitting due to oblate distortion of the geometry, 13,20 in addition to the odd–even effect caused by the electron pairing energy. Oxygen, as an electron acceptor, reacts with alkali and alkaline-earth species. Thus, it is observed that the alkaline-earth-like Ag 11+ (ten valence electrons) chemisorbs O 2 despite its paired electron configuration. Instead, even-n cationic clusters, which have an unpaired electron, are unreactive when they are just below the noble gas configurations, such as Ag 8+ and Ag 19–20+ .However,clusterswithanunpairedelectronnot far above the noble gas configuration, such as Ag 12+ ,behavelike an alkaki superatom and transfer that electron to O 2 ,whichwill appear as a superoxo-like chemisorbed molecular oxygen. No more than a single O 2 molecule adsorbed on Ag n+ with no22 was observed. 2 As noticed by Khanna and coworkers 8 for Ag 13 , anionic clusters with an odd number of Ag atoms (an even number of electrons) require spin accommodation to activate the O–O bond since the antibonding orbitals of the O 2 (triplet ground state) are filled. That spin conservation rule should hold also for cationic clusters. Thus, triplet oxygen reacts rapidily with all species in a doublet spin state (and possibly higher spin states), whereas it reacts much more slowly with species in a singlet state, 21 that is, clusters with low spin excitation energy bind O 2 strongly and then are more reactive. High spin excitation energy results from a distortion in the geometry, leading to a splitting of the D shell, and then to a large electron detachment energy and HOMO–LUMO gap at the subshell level. As proposed by Khanna and coworkers, 8 the ability of clusters to accommodate spin excitation and the modification of electronic shells via geometrical distortions can explain the observed variable reactivity of silver clusters with oxygen. That reasoning was also used to explain the observed odd–even effects in the reactivity of Al n and Ga n (n= 9–14) towards molecular oxygen. 22 Similar ideas concerning the role of the structural isomers in the adsorption of NO on Cu 13 have been also argued in a recent theoretical study by Iwasa and coworkers. 23 Small silver clusters are supposed to be the active phase in the Ag/Al 2 O 3 catalyst for selective catalytic reduction of nitrous oxides, NO x , in the presence of hydrocarbons 24,25 and ammonia. 26 As a first step to understand these processes, apart from the action of the support, density functional calculations have been done to explore NO x adsorption on pure and doped silver clusters, 7,18 as well as the Ag(111) surface 27 and AlN(0001) surface. 28 DFT calculations show that NO interacts weakly with Ag n clusters (nr8) and is preferably adsorbed in atop sites. 7 Experiments of adsorption and activation of NO on silver clusters with sizes up to one nanometer show that the interactions are dominated by electron transfer from silver to NO. 11 The adsorption of NO on Ag n Rh (nr15) occurs with enhanced reactivity compared to that on pure Ag n . 18 Calculations of NO adsorption on the Ag(111) surface 27 predict that all high symmetry sites on the Ag(111) surface are stable, with binding energy ranging from 0.17 (top) to 0.33 (fcc site). At fcc and bridge sites the NO axis is nearly perpendicular to the surface, while at the top site the NO axis is about 331off the surface normal. In this work we study, by means of spin dependent DFT calculations, the odd–even electronic effects on the the reactivity of Ag 11–13+ clusters towards one or more Ar, N 2 ,andO 2 molecules, as well as the conjoint adsorption of N 2 and O 2 . In addition we will consider the non dissociative adsorption of NO as a first step in thesearchfordissociationpathways of NO from several low-lying energy Ag 11–13+ structural isomers. In Section 2 we give details of the computational method used in this work. Section 3 contains the results and discussion organized in subsections for (i) pure cationic silver clusters, (ii) adsorption of one to three Ar atoms on these clusters, (iii) adsorption of one and two N 2 molecules, (iv) adsorption of a single O 2 molecule, (v) co-adsorption of O 2 and N 2 molecules, and (vi) adsorption of a single NO molecule. ConclusionsaregiveninSection4. 2 Computational methods In this work, DFT calculations were performed using the code SIESTA 29 with the self-consistent exchange and correlation potential given by the non local van der Waals (vdW) density functional of Klimes, Bowler, and Michaelides (KBM). 30 The core interactions were accounted for by means of norm conserving scalar relativistic pseudopotentials 31 in their fully nonlocal form, 32 generated from the atomic valence configuration 4d 10 6s 1 6p 0 for Ag, 2s 2 2p 4 for O, 2s 2 2p 3 for N and 4s 2 4p 6 for Ar. The core radii for (s, p, d) orbitals are, in a.u., (2.49, 2.59, 2.20), Paper PCCP Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online This journal is ©the Owner Societies 2019 Phys. Chem. Chem. Phys. (1.13, 1.13, 1.13), (1.23, 1.23, 1.23) and (1.58, 1.58, 1.84) for Ag, O, N and Ar, respectively. The pseudopotentials of Ag, O and Ar have been tested in previous work. 6,33 For the N 2 dimer we obtain a binding energy 4.72 eV, and a bond length 1.13 Å, to be compared to the measured values 4.90 eV and 1.10 Å, respectively. For 3 O 2 the calculated (experimental) values of the binding energy and bond length are 3.227 eV (2.558 eV) and 1.247 Å (1.208 Å), respectively. For the NO molecule, these values are 7.050 eV (6.515 eV) and 1.185 Å (1.151 Å), respectively. The matrix elements of the self-consistent potential were evaluated by integrating using a uniform grid. The grid fineness is controlled by the energy cutoff of the plane waves that can be represented in it without aliasing (150 Ry in this work). Flexible lineal combinations of numerical pseudo-atomic orbitals (PAO) are used as the basis set, allowing for multiple-zand polarization orbitals. Here we use DZ plus a p polarization orbital. To limit the range of PAOs, they were slightly excited by a common energy shift (0.001 Ry in this work) and truncated at the resulting radial node, leading to maximum cutoff radii, in au, of 9.49 (s), 5.73 (p), 6.39 (p) and 6.11 (p) for Ag, O, N and Ar, respectively. In the self-consistent field calculations, the density and energy tolerances were set to 10 4 e Bohr 3 and 10 3 eV, respectively. The equilibrium geometries resulted from unconstrained conjugate-gradient structural relaxation using the DFT forces until the force on each atom was smaller than 0.001 eV Å 1 . We considered several initial structures for each cluster taken from the low lying energy isomers of neutral and charged Ag clusters obtained in previous work using a number of different DFT approaches. 8,9,14,34–38 Our calculations in the present paper are conducted at 0 K. We use the KBM self-consistent non local van der Waals density functional 30 to properly take into account the electronic dispersion effects that occur in the physisorption of Ar and N 2 on silver clusters. This kind of functional is essential to accurately describe critical electronic properties of metallic systems, such as the dipole moment and static polarizability of sodium 39 and gold 33 clusters. Another example is the explanation of the photoelectron spectrum of Au 12 , for which detailed experimental features 40 are well described theoretically by a suitable combination of the density of states of a planar isomer and that of a three-dimensional isomer, 33 both obtained with the KBM exchange–correlation functional. Recent benchmarking of several van der Waals dispersion approaches 41 shows that the vdW-DF2 kind of functionals (KBM used here is one of them) perform better than those semiempirical functionals based on many body dispersion methods, when compared with CCSD(T) results for the intermolecular interaction energy in a large set of test molecules. We have performed GGA/PBE calculations for pure cationic silver clusters and for the adsorption of a single molecule of Ar, N 2 , and O 2 . The sequence of isomers of pure clusters in Table 1 only changes for the first and second isomers of Ag 11+ . The adsorption energy of Ar (N 2 )is larger (smaller) using VDW than using GGA/PBE, and the adsorption energy of O 2 is nearly the same within both functionals. The higher computational costs of the vdW-DF2 self consistent treatment compared to those of semiempirical and single point treatments are compensated by the improved theoretical description, which is reflected in better understanding of the studied physisorption and chemisorption processes. 3 Results and discussion 3.1 Structure of Ag n + clusters with n= 11–13 In Fig. 1 are presented the optimized equilibrium geometries of three low energy Ag n+ clusters with n= 11 (first row), n=12 (second row), and n= 13 (third row). The two numbers below each geometry are the total energy (in eV) with respect to the lowest energy isomer, and the modulus of the electrical dipole moment. The orientation of the dipole moment for each structure is indicated by an arrow. We observe that the lowest energy geometries of Ag 11+ and Ag 13+ are both grown from a pentagonal bipyramid (whose axis is along the line joining two atoms labeled with a black star in Fig. 1). For the lowest energy Ag 11+ isomer we see an additional pentagonal bipyramid whose axis is an edge of the other pentagon (and vice versa). The nearly degenerate isomer of Ag 11+ at only 0.004 eV higher energy, which will be denoted as Ag 11+ * in the following, contains also a pentagonal bipyramid motif, with three Ag atoms capping three consecutive faces on a side of the pentagon plane, and another Ag atom bridging one edge of the pentagon and bonding to one of the capping atoms. The geometrical motif of the third isomer of Ag 11+ in Fig. 1 is a triangular prism, whose edge connecting the acute corners of the trianglesismarkedwithredcross symbols. The lowest energy geometry of Ag 12+ contains a triangular prism motif, with five Ag atoms capping their five faces (three squares and two triangles) plus another Ag atom binding to the Ag caps of a triangle and a square. The second isomer of Ag 12+ is formed by a compact arrangement of tetrahedra, and the third isomer shows the pentagonal bipyramid motif. The lowest energy isomer of Ag 13+ contains again the pentagonal bipyramid motif, and the second Table 1 In the columns from left to right are given, for Ag 11–13+ clusters in their minimum energy state, the cluster symbol, spin multiplicity, binding energy per atom (see eqn (1)), mean Ag–Ag bond length, HOMO–LUMO gap, average coordination (twice the average number of bonds per atom; the maximum Ag–Ag distance is fixed to 2.9 Å), modulus of the dipole moment (see eqn (2)), mean static dipole polarizability (see eqn (4)), and polarizability anisotropy (see eqn (5)). The isomer Ag 11+ *, at only 0.004 eV higher total energy than Ag 11+ (see Fig. 1), is also included Cluster 2S + 1 E bind (eV) % d Ag–Ag (Å) H–L (eV) hCoor.i|m| (Debye)  a/n(Å 3 )Da/n(Å 3 ) Ag 11+ 1 1.745 2.838 1.121 3.454 0.512 5.476 2.682 Ag 11+ * 1 1.745 2.839 0.732 3.272 0.507 5.278 2.140 Ag 12+ 2 1.734 2.856 0.117 4.000 0.227 5.283 1.870 Ag 13+ 1 1.772 2.806 0.770 2.924 0.214 5.358 3.099 PCCP Paper Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online Phys. Chem. Chem. Phys. This journal is ©the Owner Societies 2019 isomer maintains that motif. This second isomer was also found by Chen and coworkers 9 as the third isomer of the neutral species. The third isomer of Ag 13+ in Fig. 1 is a bilayer structure which was also found by Khanna and coworkers 13 as the first isomer of the cationic species. Certainly, we do not pretend to establish a general law for the structural motifs of cationic silver clusters in the range of sizes 7–13 atoms. Simply, by checking previous work (e.g. ref. 37 and references therein), we have verified that the geometry of many low lying energy isomers in that range contains either the triangular prism or the pentagonal bipyramid as a structural motif. Then, we realize that the lowest energy isomer of Ag 7+ , Ag 9+ ,Ag 11+ and Ag 13+ contains the pentagonal bipyramid, whereas the triangular prism motif appears in the lowest energy isomer of Ag 10+ and Ag 12+ (but not in Ag 8+ ). The relation between the electronic and ionic structure of metal clusters with nearly free valence electrons, such as the alkali and the noble metal ones, is far from being understood, apart from some semi-phenomenological rules provided by the non-spherical jellium model for those cases with non closed electronic shells. 42 Here we study the odd–even structural effect in Ag 11–13+ clusters, that is, the alternation of pentagonal bipyramid and triangular prism motifs, on the adsorption properties of Ar, N 2 , and O 2 on these non-closed shell clusters. The interplay between the atomic geometry and odd–even electron number with respect to the reactivity of neutral and negatively charged silver clusters towards O 2 , in the region of sizes n= 8–18 atoms, has been examined by Khanna and coworkers. 8,13,43 The clusters in that region, whose shell model electronic configuration evolves from 1S 2 1P 6 to 1S 2 1P 6 1D 10 closed shells, suffer subshell splitting and strong rearrangement of the 1P x ,1P y ,1P z ,1D z 2 ,1D xz ,1D yz ,1D xy , and 1D x 2 y 2 subshells due to a deviation from the nearly spherical atomic geometry. 20,42 Thus, for silver clusters with 10–14 valence electrons, the atomic arrangement is prolate (the cluster geometry spreads along one axis more than along the other two axes). Nevertheless, the detailed arrangement of the different S, P, and D subshells depends on the charge state. For example, calculations for 14 valence electron silver clusters (Ag 15+ ,Ag 14 ,andAg 13 )show that the HOMO level has different orbital character (subshell), Fig. 1 In the first, second, and third rows are shown the geometries of three low energy isomers of Ag 11+ ,Ag 12+ , and Ag 13+ , respectively. Below each geometry is given the energy (in eV) with respect to the lowest energy isomer, and the modulus of the electric dipole moment (in Debye). The arrow attached to the structures indicates the direction of the dipole moment. Other electronic and structural properties are given in Table 1. In this figure we emphasize that most geometries contain either a pentagonal bipyramid motif (whose axis is denoted by two black star (*) symbols), or a triangular prism motif (with the side conecting the two acute corners marked with two red cross symbols). Paper PCCP Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online This journal is ©the Owner Societies 2019 Phys. Chem. Chem. Phys. which is more important for the reactivity, and also a different HOMO–LUMO gap. 8,13,43 Apart from the HOMO–LUMO gap, other possible manifestations of the splitting and rearrangement of subshells (which can also be understood as a crystal field splitting of the jellium-model energy levels) are the inexistence of odd–even effects in the calculated removal energy of one 13 and two 14 Ag atoms out of Ag 10–14+ clusters, as well as in their average binding energy. 9,14 In Table 1 are given the spin multiplicity, binding energy per atom, average bond length, HOMO–LUMO gap, and the average coordination per atom for the smallest energy configuration of Ag 11–13+ clusters and for the nearly degenerate isomer Ag 11+ *, which has only 0.004 eV higher total energy than Ag 11+ . In the last three columns of Table 1 are given the modulus of the dipole moment, the mean dipole polarizability, and the the polarizability anisotropy. The binding energy per atom is defined in eqn (1), where E(X) is the total energy of species X: E bind (Ag n+ )=[(n1)E(Ag) + E(Ag + )E(Ag n+ )]/n(1) We see in Table 1 that the binding energy is higher for odd n than for even nclusters, that is, those clusters with an even number of electrons have extra binding energy, which can be attributed to the electron pairing energy. 9 Thus, having a higher multiplicity has a cost in the binding energy of silver clusters with few 1D valence electrons. This fact is also noticeable in the HOMO–LUMO gap. It is well known that clusters with higher HOMO–LUMO gaps are less reactive than those with smaller ones. With respect to structural effects, the average bond length and the average coordination number are both larger for Ag 12+ (odd number of electrons) than for Ag 11+ and Ag 13+ . We will see below that these properties are related to the physisorption interaction with Ar and N 2 molecules. The smaller binding energy of Ag 12+ with respect to its neighbours correlates with its smaller abundance observed in mass spectra, see, for example, the recent results by Luo and coworkers. 44 (Incidentaly, the geometry reported by Luo and coworkers 44 as the ground state of Ag 11+ corresponds to that of our isomer at 0.094 eV higher energy shown in Fig. 1.) The electric dipole moment is obtained from the numerical integration mj¼eðrjrðrÞd3rþeZ X R Rj(2) where r j and R j are electronic and nuclear Cartesian coordinates, respectively, r(r) is the electron density, and Zis the ionic charge. The static dipole polarizability can be obtained from the induced component of the dipole moment in the presence of an external electric field F: 39 aij ¼mjðþFiÞmjðFiÞ 2Fi ;i;j¼x;y;z:(3) In the polarizability calculations, we employ external electric field values F i = 0.000 and 0.002 a.u. along the three Cartesian directions, a total of six additional calculations for each cluster. For each value of the external electric field, we self-consistently optimize both the electron density and the structure of the cluster with the same force tolerance (1 meV Å 1 ) as in the zero field calculations. We assume that the chosen field intensities are well within the linear regime, where the above relations for the polarizability are valid. Test calculations for Ag 11+ with F i = 0.000 and 0.001 a.u. do not change the result significantly. The three diagonal elements of the polarizability tensor are extracted from the linear fits of the dipole moment components against the external field components, and the mean polarizability is calculated as  a= Tr(a ij )/3. (4) The polarizability anisotropy is calculated (ignoring the non diagonal a ij elements) as Da¼1 ffiffiffi 2 p½ðaxx ayyÞ2þðayy azzÞ2þðazz axxÞ2 1 2:(5) Notice in Table 1 that Ag 12+ has the smaller polarizability with the smaller anisotropy value (except the low lying isomer Ag 11+ *, whose  a/nvalue is only 0.005 Å 3 smaller). The modulus of the calculated dipole moments in Table 1 indicates that n= 11 cations are about twice more polar than n= 12 and n= 13 ones. In Fig. 1 is indicated by an arrow the direction of the dipole moment. The electric dipole moment is very sensitive to the precise nuclear positions, and different theoretical methods can predict different global minimum structure and also different electronic screening properties (and shape distortions), which affect the m-value. The localization of holes of charge on the clusters, that is, the information about the dipole moment, is given in Fig. 1 in a crude gross manner. More specifically, Bader analysis shows that all the atoms in the cationic silver clusters lost charge with respect to their charge in the neutral cluster, and the minimum (maximum) charge lost by a single atom is 0.056, 0.041, and 0.037 (0.121, 0.127, and 0.123), in |e|units,forclusters with 11, 12, and 13 atoms, respectively. Interestingly, for the Ag 11+ * isomer the minimum and maximum loss of charge are 0.014 and 0.146, respectively. The dipole contribution to the measured effective cluster polarizability at finite temperature Tis 45 aeff ¼ aþm2 3kT;(6) where kis Boltzmann’s constant. That correction is important at low temperatures for clusters with permanent dipole moments. Using the values of  aand mof Table 1 in eqn (6) we estimate that theeffectivepolarizabilitya eff of Ag 12+ should be equal to that of Ag 13+ at B185 K, a temperature higher than that in the experiments of Bre ´chignac and coworkers, 2 and far beyond the validity of eqn (6). The calculated mean polarizabilities per atom of Ag 11–13+ clusters given in Table 1 are slightly smaller than those calculated for isoatomic neutral species. 13,46 Since the mean static polarizability of metallic clusters is related directly to the volume of the (electron cloud of the) cluster, 42,47 the difference PCCP Paper Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online Phys. Chem. Chem. Phys. This journal is ©the Owner Societies 2019 between the polarizability of cationic and neutral species is due to the smaller size of the cation electron cloud with respect to that of its neutral species. On the other hand, the odd–even alternation of the mean polarizability per atom is related to the odd–even number of valence electrons, or, correspondingly, the even–odd number of atoms. 46 Khanna and coworkers 13 found that neutral silver clusters with odd-numbers of atoms have larger polarizability per atom than those with even-numbers of atoms by about 0.1 Å 3 per atom. That difference is smaller than that found here between the two isomers of Ag 11+ , see Table 1, which, then, should be due to their different geometry. Notice in Table 1 that the average Ag–Ag distance and the average coordination are not very different for the Ag 11+ and Ag 11+ * isomers, indicating a similar size of the ionic structure. The dipole moments of these isomers have also similar values. However, the size of their electron clouds, as measured by the dipole polarizability, is clearly different. Also their HOMO– LUMO gap values substantially differ. Then, the subtle difference in the electronic configurations, particularly the electronic spill-out of the valence electron cloud induced by the different geometry of these isomers, is responsible for their different polarizability and HOMO–LUMO gap values. The electronic spill-out, d, is defined as the difference between the radii of the electron cloud ( a 1/3 ) and the jellium model (r WS n 1/3 ), where r WS is the Wigner–Seitz radius, whose experimental value 48 is 1.60 Å. Thus, for n= 11, 12, and 13, the spill-out values are (in Å) 0.362, 0.324, and 0.352, respectively (0.314 for Ag 11+ *). With respect to neutral silver clusters, in the range of sizes n= 9–15 there are available polarizability measurements 49 only for clusters with odd numbers of atoms (n= 9, 11, 13, and 15). Calculations for neutral silver clusters by McKee and Samokhvalov 14 led to polarizability values slightly decreasing in the range n= 11–14. Older calculations 13,46 led to very small differences (o0.07 Å 3 per atom) between odd and even values of polarizability in that range of sizes, with valleys at even numbers of atoms (up to n= 13). Our calculations for the mean polarizability of cationic silver clusters with n= 11–13 (see Table 1) show an odd–even behaviour, with a valley at n= 12 (odd number of electrons). We stress again that calculated dipole moments, which we use to calculate the dipole polarizability tensor by means of eqn (3), are very sensitive to the cluster geometry and to the level of exchange–correlation description used in calculations. 33,39 In this work we will use the mean polarizability as a quantitative indicator of the volume of the electron cloud, and the polarizability anisotropy as an index of the asphericity of that electron cloud. One consequence of the anisotropy, Da, is that the dispersion force between molecules becomes dependent on their mutual orientation, originating steric forces, which may be repulsive. Although Ag 12+ has a larger Ag–Ag average distance than its neighbour clusters, its polarizability (the volume of its electron cloud) is smaller. As the volume is a physical property, related to the amount of space occupied by the particle, the polarizability and polarizability anisotropy of silver clusters will have some relevance in the physisorption interactions with different atoms and molecules that we study in this work. On the other hand, we will use the HOMO–LUMO value as an indicator of stability against electronic transitions. Clusters with unpaired valence electrons are, in principle, more reactive to chemisorption interactions than those with paired electrons. 3.2 Physisorption of 1, 2, and 3 Ar atoms For m= 1–3 and n= 11–13, we have probed all possible configurations of Ag n+ Ar m complexes resulting from adding an Ar atom to the lowest energy isomer Ag n+ Ar m1 . Throughout this paper we will denote with a dot the physisorption of particle X on Ag n+ clusters: Ag n+ X. In the first to fourth columns of Fig. 2 are shown the lowest energy geometries of silver–Ar complexes formed after adsorption of m= 1, 2, and 3 Ar atoms (first, second, and third row, respectively) on Ag 11+ (first column), Ag 11+ * (second column), Ag 12+ (third column), and Ag 13+ (fourth column). In all cases the Ar atoms are adsorbed on top of Ag atoms whose coordination is smaller than the average one (except for Ag 13+ mAr and Ag 11+  2Ar, see Table 2) and the substrate geometry is not modified after absorption. In Table 2 are given the adsorption energy (see eqn (7)), the bond distance Ar to the cluster, the site coordination ratio, and the charge accumulated on the Ar atoms, for one, two, and three Ar atoms adsorbed on Ag 11–13+ clusters. The coordination ratio is defined as the quotient between the coordination of the adsorption site and the average coordination of the cluster given in Table 1. To obtain the coordination ratio the maximum Ag–Ag distance was fixed at 2.9 Å. The adsorption energy of an atom/molecule X on the Ag n+  mX complex is defined as: E ads =E(Ag n+ (m1)X) + E(X) E(Ag n+ mX) + DZPE (7) where E(Y) is the total energy of species Y, and DZPE = ZPE(Ag n+ (m1)X) + ZPE(X) ZPE(Ag n+ mX), (8) is the contribution of the zero point energy (ZPE) correction. The accumulated charge on one, two, and three adsorbed Ar atoms given in Table 2 is calculated by means of the Bader method 50 (using a cutoff energy of 300 eV). Notice that the charge on the first adsorbed Ar atom will change after the adsorption of the second Ar atom, and so on. Thus, the Ar atom adsorbed on Ag 11+ 2Ar brings the accumulated charge on the Ar atoms from 0.022 |e|to0.015 |e|, that is, the third Ar atom acts as an electron acceptor instead of an electron donor. As for the kind of interactions between rare gases and cationic silver clusters, it was suggested by experiments 2 that they were not chemical, but of physical character instead, leading then to physisorption rather than chemisorption processes. This suggestion is confirmed by inspecting in Table 2 the small adsorption energy (column 2), the large bond-length (column 3), and the small charge on Ar atoms (column 5) for one, two, and three Ar atoms adsorbed on Ag 11–13+ clusters. In addition, we can observe odd– even effects in the trends of these magnitudes with size. Thus, for n= 12 complexes, the distance Ar–Ag is larger, and the binding energy is smaller, than for their n=11andn=13neighbours. Paper PCCP Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online This journal is ©the Owner Societies 2019 Phys. Chem. Chem. Phys. (An exception is the distance Ar–Ag in Ag 11+ 3Ar, which can be related to the positive charging of the third Ar atom already commented on above.) In addition, the coordination ratio is also smaller for the n= 12 complexes. On the other hand, we know from mass espectrometry experiments 2 that the capability of Ag 12+ to adsorb Ar atoms is larger than that of neighbor clusters. Since the calculated binding energies of the n=12complexesaresmaller than those of their neighbours, we can discard chemisorption as the leading interaction of Ar with silver clusters. A qualitative explanation of the trend of binding energies is that the physisorption interactions between Ar and silver clusters must be governed by dispersion (London type) forces, which are proportional to the polarizability and ionization potential of the Ar atom and silver cluster. The polarizability of Ag 12+ is the smaller one among those for Ag 11–13+ clusters in their ground state (see Table 1), and also the ionization potential of Ag 12+ is the smaller one in that range of sizes. In addition, the dispersion forces depend on the distance between Ar and the silver cluster as d Ar–Ag6 ,thatis,largerd Ar–Ag distances yield lower interactionenergies,ascanbeseeninTable1. A possible explanation of the experimental peak at n=12 observed in the Ar adsorption abundance spectra 2 must rest on Table 2 Adsorption energy (see eqn (7)), average distance Ar–Ag, coordination ratio, and charge accumulated on the Ar atoms, for 1 Ar/2 Ar/3 Ar atoms adsorbed on Ag 11–13+ clusters (see Fig. 2). The site coordination ratio given in column four is defined as the quotient of the coordination of the adsorption site with the average coordination of the cluster substrate given in Table 1. In the last column is given the effective physisorption energy density, defined in eqn (9), where the values of hcooriand  aare taken from Table 1 Compound E ads (eV) % d Ar–Ag (Å) Coor. ratio Charge (|e|) E eff ads (eV Å 3 ) Ag 11+ Ar 0.071 3.155 0.868 0.012 0.493 Ag 11+ 2Ar 0.067 3.173 1.013 0.022 Ag 11+ 3Ar 0.115 3.297 0.965 0.015 Ag 11+ *Ar 0.070 3.135 0.917 0.013 0.477 Ag 11+ *2Ar 0.076 3.137 0.764 0.013 Ag 11+ *3Ar 0.080 3.127 0.713 0.040 Ag 12+ Ar 0.062 3.185 0.500 0.010 0.563 Ag 12+ 2Ar 0.049 3.210 0.750 0.017 Ag 12+ 3Ar 0.067 3.183 0.750 0.030 Ag 13+ Ar 0.074 3.090 1.026 0.016 0.525 Ag 13+ 2Ar 0.083 3.126 1.197 0.021 Ag 13+ 3Ar 0.086 3.153 1.140 0.029 Fig. 2 Lowest energy equilibrium geometry of Ag n+ mAr complexes for m= 1 (first row), m= 2 (second row), and m= 3 (third row). The first and second columns correspond, respectively, to adsorption of Ar on the lowest energy isomer of Ag 11+ , and on the near degenerate Ag 11+ * isomer (see Fig. 1). The third and fourth columns correspond to Ar adsorption on the lowest energy isomer of Ag 12+ , and Ag 13+ , respectively. PCCP Paper Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online Phys. Chem. Chem. Phys. This journal is ©the Owner Societies 2019 the geometrical features of silver clusters rather than adsorption energies and local electronic effects. Bre ´chignac and coworkers 2 have suggested that the coordination number of the surface atoms may be used as a measure of the interaction between rare gases and silver clusters. On one hand, the calculated average coordination number of Ag 12+ is larger than that of the neighbour clusters, that is, more Ag atoms in a volume unit interact with Ar atoms. On the other hand, recall that the mean polarizability of a molecule represents somehow the effective volume of the electron cloud. Thus, the product of binding energy times the average coordination, divided by the mean polarizability: E eff ads =E bind hcoori/ a(9) represents an effective interaction per volume unit of Ag n+ silver clusters with Ar atoms. That effective interaction is given in the last column of Table 2, and it is higher for Ag 12+ than for its neighbours, pointing to Ag 12+ as the more effective cluster in the range n= 11–13 for Ar physisorption, which agrees with the experimental facts. In adition, the polarizability asymmetry is smaller for Ag 12+ , that is, the dispersion forces are less dependent on the mutual orientation between Ar and the silver cluster. On the other hand, previous calculations for small cationic silver clusters suggest that rare gases prefer corner and edge adsorption sites. 12 We observe in Table 2 that the coordination ratio of the adsorption site is clearly smaller for Ag 12+ than for its neighbour clusters, that is, corners and edges are preferred. In this way, occupation of low coordination sites should increase the average coordination of available physisorption sites, and then the factor hcoori/ a, which is multiplied by the adsorption energy to obtain the effective physisorption energy density of a given Ag n+ mAr (m=0,1,2,...) complex, also increases. In summary, both experimental facts, the Ar absorption peak at n= 12 and the preference for corner and edge adsorption sites, are related, according to our calculations, to odd– even geometrical and electronic effects of Ag 11–13+ clusters, namely (i) the differences in their geometrical motifs (pentagonal bipyramid for odd-nand triangular prism for even-n), and (ii) to the effective volume of their electron clouds as given by their dipole polarizabilities. 3.3 Physisorption of one and two N 2 molecules It is well known that the N 2 molecule is unreactive toward most reagents because of its strong triple bond, large HOMO–LUMO gap, and nonpolarity. Recently, several experimental and theoretical studies about the reactivity in the gas-phase of metal clusters with N 2 have been reported, see the recent work of Zhao and coworkers 51 and references therein. Here we focus on the experimental results for the adsorption of N 2 on Ag n+ clusters reported by Bre ´chignac and coworkers, 2 particularly on those with n= 11, 12, and 13. In the first and second columns of Fig. 3 are shown the adsorption geometries of one and two N 2 molecules on the smallest energy configuration of Ag 11–13+ clusters and the Ag 11+ * Fig. 3 In the first to third columns are shown the adsorption geometries of N 2 ,2N 2 ,andO 2 molecules, respectively, on the lowest energy Ag 11–13+ clusters and Ag 11+ * isomer. The adsorption of O 2 distorts the geometry of the silver clusters, particularly that of Ag 12+ . In column four are shown the adsorption geometries of N 2 on the Ag n+ O 2 clusters of the third column. Paper PCCP Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online This journal is ©the Owner Societies 2019 Phys. Chem. Chem. Phys. isomer. In Table 3 are given the adsorption energy (see eqn (7)), bond length of physisorbed N 2 ,averagedistanceofN 2 to the cluster, site coordination ratio, accumulated charge on the N 2 molecules, and HOMO–LUMO gap for the complexes shown in Fig. 3. In the last two columns of Table 3 are given the magnitude of the electric dipole moment and the mean polarizability as defined in eqn (2) and (4), respectively. We see in Fig. 3 that N 2 binds on top of Ag atoms, which is a signal of possible physisorption, because it has been noted experimentally that N 2 physisorption is enhanced in upright positions at edges and corners of charged particles 2,52,53 (in particular nickel and other 3d metal clusters). That feature was also obtained by means of DFT calculations for the adsorption of several N 2 molecules on small Ag n+ clusters. 12 As expected for physisorption interactions, we see in Table 3 that the N–N distance in the adsorbed N 2 does not differ appreciably from that calculated for the free molecule, 1.13 Å. Other signtures of physisorption shown in Table 3 are the small adsorption energies, the large % d N 2 –Ag distances to the Ag substrate (smaller, however, than those % d Ar–Ag in Table 2), and the small charging of N 2 . The charge accumulated on the first and first plus second physisorbed N 2 molecules is given in the sixth column of Table 3, as calculated by means of the Bader method. 50 We see that only for the Ag 12+ cluster do the first and second N 2 adsorbed atoms donate electronic charge to the silver substrate, and just the contrary occurs for Ag 13+ . Instead, the first adsorbed N 2 donates electronic charge to Ag 11+ and Ag 11+ * and the second adsorbed N 2 accepts electronic charge from the silver substrate. Thus, N 2 can be considered as an amphoteric species, which either donates or accepts electrons from metal species. The smallest adsorption energy, the largest % d N 2 –Ag distance, and the smallest coordination ratio in Table 3 correspond to Ag 12+ mN 2 . As these features also appear for Ag 12+ mAr (see Table 2), one is tempted to assume an analogous explanation of the observed peaks in the abundance spectra of N 2 and Ar adsorption on Ag n+ clusters. However, the N 2 adsorption energies are more than two times larger than those for Ar adsorption, although still they are about one order of magnitude smaller than those of typical covalent interactions (see the binding energies of Ag atoms in Table 1). In addition, the % d N 2 –Ag distances are B0.8 Å smaller than the % d Ar–Ag distances. Thus, although the physisorption mechanism based on (London) dispersion forces (used above to rationalize the Ar adsorption energies) may also explain the trend of the N 2 adsorption energies, the full interaction of N 2 with Ag n+ clusters must involve other components, like a dipole-induced dipole mechanism (Debye forces), or, more probably, a non-covalent mechanism based on p–por cation–pinteractions. That cation–pinteraction is surprisingly strong, 44 and could explain the exceptional adsorption energy of N 2 on Ag 11+ N 2 .p–pinteractions are associated with the overlap between the p-orbitals of a molecular system. With respect to the 4d electrons of silver we recall that the s–d promotion energy in the valence region is much higher than that for copper and gold condensates, because the eigenvalues of the s (d) valence electrons of silver are less (more) deeply bound than their counterparts of copper and gold. Thus, the participation of 4d electrons in the frontier orbitals and bonding of silver clusters with ligands like N 2 islessimportantthanthatofthesandpcomponents. In order to better understand the bonding character of nitrogen molecules to silver clusters we discuss now the orbital projected density of states (PDOS) of Ag n+ mN 2 complexes with n= 11–13 (including Ag 11+ *) and m= 0, 1, 2, which is presented in Fig. 4 and, with a focus around the Fermi level, in Fig. 5. First we can distinguish in all cases a region between 6.0 and 2.5 eV delimited and dominated by the 4d orbital of Ag. The PDOS of that big 4d peak at these energies is presented only between 5.0 a.u. and 5.0 a.u. to allow us to display details of the other components. In that region of energy there is a net hybridization of the 4d orbital with the 5s and 5p orbitals of Ag, having nearly the same shape in all the cases. The exception is Ag 12+ mN 2 , whose PDOS shows a small difference with the other aggregates for all mvalues, probably due to its different structural motif. The PDOS of 2s, 2p, and 3d of nitrogen in the region between 6.0 eV and 2.5 eV is shown with more detail in Fig. 5, where we can see that Ag 12+ mN 2 (m=1,2) shows two lobes instead of the three lobes shown by the other aggregates. The region below 7.0 eV is dominated by the orbitals 2s, 2p, and 3d of nitrogen, and their shapes do not change (only the amount of charge) after the adsorption of the second N 2 (except, slightly, for Ag 13+ 2N 2 ). On the other hand, in the region of positive energies larger than 1 eV (see Fig. 4), Table 3 Adsorption energy, bond length of physisorbed N 2 , mean distance N 2 –Ag, site coordination ratio, accumulated charge on the N 2 molecules, electric dipole moment and mean static dipole polarizability per atom for one and two molecules adsorbed on Ag 11–13+ clusters with the smallest energy geometry and isomer Ag 11+ * (see the first and second columns of Fig. 3). The site coordination ratio is defined as the quotient of the coordination of the adsorption site with the average coordination of the silver cluster given in Table 1 Complex E ads (eV) d N–N (Å) % d N2–Ag (Å) Coord. ratio Charge (|e|) H–L gap (eV) |m| (Debye)  a/n(Å 3 ) Ag 11+ N 2 0.165 1.129 2.434 0.866 0.005 0.831 2.350 6.144 Ag 11+ 2N 2 1.145 1.130 2.490 0.866 0.013 0.823 1.317 3.123 Ag 11+ *N 2 0.174 1.128 2.445 1.220 0.007 0.839 2.438 5.666 Ag 11+ *2N 2 0.171 1.130 2.416 0.916 0.012 0.783 4.014 7.037 Ag 12+ N 2 0.137 1.129 2.497 0.750 0.006 0.176 2.361 6.543 Ag 12+ 2N 2 0.139 1.129 2.502 0.875 0.009 0.178 2.122 4.274 Ag 13+ N 2 0.212 1.129 2.395 1.711 0.002 0.954 2.095 5.720 Ag 13+ 2N 2 0.158 1.129 2.439 1.027 0.020 0.946 2.572 6.040 PCCP Paper Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online Phys. Chem. Chem. Phys. This journal is ©the Owner Societies 2019 minimum value at n= 12 to a maximum HOMO–LUMO for Ag 12+ O 2 . Comparing the adsorption energy of N 2 on Ag n+ with that on Ag n+ O 2 we see that the adsorption energy slightly decreases in the oxidized clusters (except for n= 11), and the charging of N 2 is similar in both cases (except for n= 13). Thus, we assume that the N 2 bonding mechanism is similar for Ag n+ and Ag n+ O 2 . The major differences occur in the trend of the HOMO–LUMO values. The adsorption of N 2 on Ag n+ O 2 nearly maintains the HOMO–LUMO gap of odd-naggregates but it results twice the HOMO–LUMO in the case of n= 12 (which stabilizes that aggregate with respect to its neighbours against further N 2 adsorption). The consecutive adsorption of O 2 and N 2 on Ag n+ clusters switches their semiconductor character from low (high) HOMO LUMO for even-n(odd-n) values towards the opposite behavior. Thus, Ag 12+ O 2 is stabilized by the cooperative adsorption of N 2 . In the case of NO adsorption, the favoured cluster is again Ag 12+ for similar reasons to O 2 chemisorption. The adsorption mechanism is illustrated by examining the projected density of states of Ag n+ NO complexes. The HOMO–LUMO gap of Ag 12+ NO still is smaller than that of its neighbours, and then more reactive. Thus, that cluster could adsorb another NO molecule, originating dimerization 61 or reactions towards Ag 12+ NO 2 . 11 Finnally, as an overview about the reactivity trends of Ag n+ X compounds (X = N 2 ,O 2 , NO) when adsorbed on, for example, TiO 2 surfaces, we extract from our calculations two phenomenological rules, assuming that the HOMO eigenvalue of these compounds may serve as an index of reactivity (R) in such systems: 63 (i) For all nvalues, R(Ag n+ O 2 )4R(Ag n+ NO) 4R(Ag n+ N 2 ). (ii) For a given X (X = N 2 ,O 2 , NO) the reactivity of a compound with n= 12 is smaller than that of compounds with n= 11 and 13. Conflicts of interest The authors declare no competing financial interest. Acknowledgements We acknowledge the support of the Ministerio de Ciencia, Innovacio ´n y Universidades of Spain through FEDER (Project PGC2018-093745-B-I00), and Junta de Castilla y Leo ´n (Project VA124G18). E. M. F. is thankful for the RyC contract (ref. RYC2014-15261) of the Spanish Minister of Economy, Industry and Competitiveness. Notes and references 1 J. R. Morones, J. L. Elechiguerra, A. Camacho, K. Holt, J. B. Kouri, J. T. Ramirez and M. J. Yacaman, Nanotechnology, 2005, 16, 2346–2353. 2 M. Schmidt, A. Masson, H.-P. Cheng and C. Bre ´chignac, ChemPhysChem, 2015, 16, 855–865. 3 B. Sun and A. S. Barnard, Nanoscale, 2017, 9, 12698–12708. 4 Y. D. Kim and G. Gantefo ¨r, Chem. Phys. Lett., 2004, 383, 80–83. 5 L. D. Socaciu, J. Hagen, J. Roux, D. M. Popolan, T. M. Bernhardt, L. Woste and S. Vajda, J. Chem. Phys., 2004, 120, 2078–2081. 6 E. M. Ferna ´ndez, M. B. Torres and L. C. Balba ´s, in Density functional studies of noble metal clusters. Adsorption of O 2 and CO on gold and silver clusters, ed. J. P. Julien, J. Maruani, D. Mayou, S. Wilson and G. Delgado-Barrio, Springer, 2006, vol. 15. 7 S. Klacar, A. Hellman, I. Panas and H. Gronbeck, J. Phys. Chem. C, 2010, 114, 12610–12617. 8 Z. Luo, G. U. Gamboa, J. C. Smith, A. C. Reber, J. U. Reveles, S. N. Khanna and A. W. Castleman, J. Am. Chem. Soc., 2012, 134, 18973–18978. 9 M. Chen, J. E. Dyer, K. Li and D. A. Dixon, J. Phys. Chem. A, 2013, 117, 8298–8313. 10 M.-S. Liao, J. D. Watts and M.-J. Huang, J. Phys. Chem. C, 2014, 118, 21911–21927. 11 J. Ma, X. Cao, H. Liu, B. Yin and X. Xing, Phys. Chem. Chem. Phys., 2016, 18, 12819–12827. 12 Y.-N. Wu, M. Schmidt, J. Leygnier, H.-P. Cheng, A. Masson and C. Bre ´chignac, J. Chem. Phys., 2012, 136, 024314/1–8. 13 G. U. Gamboa, A. C. Reber and S. N. Khanna, New J. Chem., 2013, 37, 3928–3935. 14 M. L. McKee and A. Samokhvalov, J. Phys. Chem. A, 2017, 121, 5018–5028. 15 T. M. Bernhardt, J. Hagen, S. M. Lang, D. M. Popolan, L. D. Socaciu-Siebert and L. Wo ¨ste, J. Phys. Chem. A, 2009, 113, 2724–2733. 16 D. Palagin and J. P. K. Doye, Phys. Chem. Chem. Phys., 2016, 18, 22311–22322. 17 S. Kohaut and M. Springborg, J. Cluster Sci., 2016, 27, 913–933. 18 P. L. Rodriguez-Kessler, S. Pan, E. Florez, J. L. Cabellos and G. Merino, J. Phys. Chem. C, 2017, 121, 19420–19427. 19 A. Shayeghi, R. Scha ¨fer, D. M. Rayner, R. L. Johnston and A. Fielicke, J. Chem. Phys., 2015, 143, 024310. 20 P. V. Nhat, N. T. Si and M. T. Nguyen, J. Mol. Model., 2018, 24, 209. 21 R. Burgert, H. Schno ¨ckel, A. Grubisic, X. Li, K. H. Bowen, G. F. Gantefo ¨r, B. Kiran and P. Jena, Science, 2008, 319, 438–442. 22 M. Neumaier, M. Olzmann, B. Kiran, K. H. Bowen, B. E. S. T. Stokes, A. Buonaugurio,R.BurgertandH.Schno ¨ckel, J. Am. Chem. Soc., 2014, 136, 3607–3616. 23 T. Iwasa, T. Sato, M. Takagi, M. Gao, A. Lyalin, M. Kobayashi, K.-I.Shimizu,S.MaedaandT.Taketsugu,J. Phys. Chem. A, 2019, 123, 210–217. 24 P. Sazama, L. Capek, H. Drobna, Z. Sobalik, J. Dedecek, K. Arve and B. Wichterlova, J. Catal., 2005, 232, 302. 25 J. P. Breen and R. Burch, Top. Catal., 2006, 39, 53–58. 26 D. E. Doronkin, S. Fogel, S. Tamm, L. Olsson, T. S. Khan, T. Bligaard, P. Gabrielsson and S. Dahl, Appl. Catal., B, 2012, 113–114, 228–236. Paper PCCP Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online This journal is ©the Owner Societies 2019 Phys. Chem. Chem. Phys. 27 B. W. J. Chen, D. Kirvassilis, Y. Bai and M. Mavrikakis, J. Phys. Chem. C, 2019, 123, 7551–7566. 28 P. Strak, K. Sakowski, P. Kempisty, I. Grzegory and S. Krukowski, J. Phys. Chem. C, 2019, 123, 10893–10906. 29 J. M. Soler, E. Artacho, J. D. Gale, A. Garcı ´a, J. Junquera, P. Ordejo ´n and D. Sa ´nchez-Portal, J. Phys.: Condens. Matter, 2002, 14, 2745. 30 J. Klimes, D. R. Bowler and A. Michaelides, J. Phys.: Condens. Matter, 2009, 22, 02201. 31 N. Troullier and J. L. Martı ´ns, Phys. Rev. B: Condens. Matter Mater. Phys., 1991, 43, 1993. 32 L. Kleinman and D. M. Bylander, Phys. Rev. Lett., 1982, 48, 1425. 33 E. M. Ferna ´ndez and L. C. Balba ´s, Phys. Chem. Chem. Phys., 2011, 13, 20863–20870. 34 V. Bonac ˇic ´-Koutecky´, J. Pittner, M. Boiron and P. Fantucci, J. Chem. Phys., 1999, 110, 3876. 35 P. Weiss, T. Bierweiler, S. Gilb and M. Kappes, Chem. Phys. Lett., 2002, 355, 355. 36 R. Fournier, J. Chem. Phys., 2001, 115, 2165. 37 E. M. Ferna ´ndez, J. M. Soler, I. L. Garzo ´n and L. C. Balba ´s, Phys. Rev. B: Condens. Matter Mater. Phys., 2004, 70, 165403. 38 E. M. Ferna ´ndez, J. M. Soler, I. L. Garzo ´n and L. C. Balba ´s, Int. J. Quantum Chem., 2005, 101, 740–745. 39 A. Aguado, A. Vega and L. C. Balba ´s, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 84, 165450. 40 W. Huang and L. S. Wang, Phys. Rev. Lett., 2009, 102, 153401. 41 J. Claudot, W. J. Kim, A. Dixit, H. Kim, T. Gould, D. Rocca and S. Lebe `gue, J. Chem. Phys., 2018, 148, 064112. 42 W. A. de Heer, Rev. Mod. Phys., 1993, 65, 611. 43 A. C. Reber, G. U. Gamboa and S. N. Khanna, J. Phys.: Conf. Ser., 2013, 438, 012002. 44 M. Yang, H. Wu, B. Huang and Z. Luo, J. Phys. Chem. A, 2019, 123, 6921–6926. 45 I. Vasiliev, S. Ogut and J. R. Chelikowsky, Phys. Rev. Lett., 1997, 78, 4805. 46 M. Yang, K. A. Jackson and J. Jellinek, J. Chem. Phys., 2006, 125, 144308. 47 K. R. S. Chandrakumar, T. K. Ghanty and S. K. Ghosh, J. Phys. Chem. A, 2004, 108, 6661. 48 T. Lu ¨nskens, P. Heister, M. Tha ¨mer, C. A. Walenta, A. Kartouzian and U. Heiz, Phys. Chem. Chem. Phys., 2015, 17, 1751. 49 H. Handschuh, C.-Y. Cha, P. S. Bechthold, G. F. Gantefo ¨r and W. Eberhardt, J. Chem. Phys., 1995, 102, 6406. 50 R. F. W. Bader, Atoms in Molecules: A Quantum Theory, Clarendon, Oxford, New York, 1990. 51 Y. Zhao, J.-T. Cui, M. Wang, D. Yubero-Valdivielso, A. Fielicke, L.-R. Hu, X. Cheng, Q.-Y. Liu, Z.-Y. Li, S.-G. He and J.-B. Ma, J. Am. Chem. Soc., 2019, 141, 12592–12600. 52 J. H. Parks, L. Z. J. Ho and S. J. Riley, J. Chem. Phys., 1994, 100, 7206–7222. 53 E. F. Rexer, J. Jellinek, E. B. Krisinel and E. K. Parks, J. Chem. Phys., 2002, 117, 82–94. 54 P. K. Chattaraj, Chemical Reactivity Theory: A Density Functional View, CRC Press, Taylor and Francis Group, Boca Raton, FL, 2009. 55 T. M. Bernhardt, Int. J. Mass Spectrom., 2005, 243, 1–29. 56 E. M. Ferna ´ndez, P. Ordejo ´n and L. C. Balba ´s, Chem. Phys. Lett., 2005, 408, 252–257. 57 M. B. Torres, E. M. Ferna ´ndez and L. C. Balba ´s, J. Phys. Chem. A, 2008, 112, 6678. 58 M. Schmidt, A. Masson and C. Bre ´chignac, J. Chem. Phys., 2005, 122, 134712. 59 M. V. den Bossche and H. Gro ¨nbeck, J. Phys. Chem. C, 2017, 121, 8390–8398. 60 S. Abujarada, et al.,Phys. Chem. Chem. Phys., 2019, 21, 10939. 61 N. Takagi, K. Ishimura, R. Fukuda, M. Ehara and S. Sakaki, J. Phys. Chem. A, 2019, 123, 7021–7033. 62 T. Ghanty and S. K. Ghosh, J. Phys. Chem., 1996, 100, 12295. 63 T. Kamachi, T. Tatsumi, T. Toyao, Y. Hinuma, Z. Maeno, S. Takakusagi, S. Furukawa, I. Takigawa and K. Shimizu, J. Phys. Chem. C, 2019, 123, 20988–20997. PCCP Paper Published on 11 October 2019. Downloaded by Universidad de Valladolid Biblioteca on 11/7/2019 9:30:23 AM. View Article Online