Adsorption of Noble-Gas Atoms on the TiO2(110) Surface: An Ab Initio

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Adsorption of Noble-Gas Atoms on the TiO(110) Surface: An Ab Initio-Assisted Study with van der Waals-Corrected DFT Ali Abbaspour Tamijani, Akbar Salam, and Maria Pilar de Lara-Castells J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b05949 • Publication Date (Web): 26 Jul 2016 Downloaded from http://pubs.acs.org on July 31, 2016

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The Journal of Physical Chemistry

Adsorption of Noble-Gas Atoms on the TiO2(110) Surface: An Ab Initio-Assisted Study with van der Waals-Corrected DFT A. A. Tamijani,† A. Salam,† and M. P. de Lara-Castells∗,‡ Department of Chemistry,Wake Forest University, Winston-Salem, North Carolina 27109, United States, and Instituto de Física Fundamental (C.S.I.C.), Serrano 123, E-28006, Madrid, Spain E-mail: [email protected]

∗ To

whom correspondence should be addressed of Chemistry,Wake Forest University, Winston-Salem, North Carolina 27109, United States ‡ Instituto de Física Fundamental (C.S.I.C.), Serrano 123, E-28006, Madrid, Spain † Department

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Abstract Weakly bound noble gases (Ne, Ar, Kr and Xe) are being utilized as probes to monitor the photocatalytic activity of the TiO2 (110) surface. In this work, this adsorption problem is examined using different van der Waals-corrected DFT-based treatments on periodic systems. The assessment of their performance is assisted by the application of non-periodic DFT-based symmetry adapted perturbation theory [SAPT(DFT)]. It is further verified by comparing with experimentally-based determinations of the adsorption energies at one-monolayer surface coverage. Besides being dispersion-dominated adsorbate/surface interactions, the SAPT(DFT)based decomposition reveals that the electrostatic and induction energy contributions becomes highly relevant for the heaviest noble-gas atoms (krypton and xenon). The most reliable results are provided by the revPBE-D3 approach: it predicts adsorption energies of −118.4, −165.8, and −2231.7 meV for argon, krypton and xenon, which are within 6% of the experimental values, and attractive long-range tails which are consistent with our ab-initio benchmarking. Moreover, the revPBE density functional describes the short-range part of the potential energy curve more precisely, avoiding the exchange-only binding effects of the PBE functional. The non-local vdW-DF2 density functional performs well at the long-range potential region but largely overestimates the adsorption energies of noble gas atoms as light as argon. The Tkatchenko-Scheffler dispersion correction combined with the revPBE functional produces accurate estimations of the adsorption energies (to within 10%) but long-range attractive tails that decay too slowly. as in first-generation non-local vdW-DF density functional. Lateral interactions between co-adsorbate atoms contribute up to about 15−20%, being key in achieving good agreement with experimental measurements. The interaction with the noble-gas atoms reduces the work function of the TiO2 (110) surface, agreeing to the experimental observation of an inhibited photo-desorption of co-adsorbed molecular oxygen.

Introduction The adsorption of noble-gas atoms onto solid surfaces is nowadays attracting strong attention. Besides being stereotypical dispersion-dominated problems in surface science, noble gases are used 2 ACS Paragon Plus Environment

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in very recently developed experimental tools such as the new soft-landing deposition technique. 1,2 For the particular case of the TiO2 (110) surface covered by molecular oxygen, co-adsorbed noblegas atoms heavier than neon are being utilized to monitor its photo-catalytic activity. 3,4 As extensively reviewed by Yates’s 5–10 and Henderson’s groups, 11 the photo-catalytic activity of TiO2 surfaces is much influenced by the creation and dynamics of holes and electrons, with the holeelectron recombination limiting the photocatalyst efficiency. Molecular oxygen photo-desorption (PD) is usually employed as a probe to monitor the dynamics of photo-generated hole and electron carriers. 12–18 Yates’ group proposed a molecular oxygen PD picture according to which valenceband holes, created via ultraviolet (UV) irradiation above the material "band-gap", neutralizes the single charged O2 adsorbed on the surface, leading to the O2 desorption from the repulsive region of a "physisorbed" potential energy surface (see for example Ref. 10 and references therein). This picture was consistent with further experimental measurements, 15 the earliest quantum-mechanical studies of O2 photo-desorption, 19,20 and direct calculation of intersite hoppings in titanium dioxide, 21 suggesting a higher probability transfer of photoexcited holes as compared with photoexcited electrons in the material. Further scanning tunneling microscope (STM) measurements, 17,18 showed that anionic O2 species bound at non-vacancy sites are responsible of the O2 PD signal while those adsorbed on the vacancy sites experience photo-dissociation. More recent evidences of the charge transfer-mediated O2 PD mechanism in TiO2 have been obtained by the co-adsorption of "reporters" noble-gas atoms and molecular species. 3,4 The first study 3 has shown that when the TiO2 (110) surface is covered by O2 as well as physisorbed noblegas atoms, and then it is exposed to UV irradiation, the noble-gas atoms photo-desorb. In contrast, the Kr photo-desorption signal is very low or not recorded without chemisorbed oxygen. According to the interpretation of Petrik and Kimmel, 3 these findings are indicative of the excitation of O2 via the interaction with the hole-electron pairs created by UV irradiation. The electronically excited oxygen species would relax by energy transfer to the nuclear degrees of freedom of the co-adsorbed noble-gas atoms, leading to their desorption and the subsequent decrease of the O2 PD intensity. The second study 4 focuses on the microscopic mechanism quenching the O2 PD by 3 ACS Paragon Plus Environment


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co-adsorption, suggesting that co-adsorbed species inhibit the photo-generated hole transfer to the adsorbed O2 species. Interfacial dipole moments created by the coadsorbed layers, with the negative pole pointed towards the surface, would decrease the work function of the material, hindering then the hole migration to the interfacial layer where O2 is adsorbed. These photo-induced processes are naturally strongly determined by the specific interactions between the three basic components (noble-gas atoms, O2 , and the TiO2 (110) surface) so that their accurate description via first-principles methods is necessary. For this purpose, the detailed forms of the interaction potentials are necessary. Furthermore, according to the most recent experimental studies, 4 electrostatic-like interactions arising from the adatom polarization, influence the dynamics of charge carriers upon UV irradiation so that a detailed breakdown of the interaction energy components is also desirable. These challenges have been recently addressed for the specific case of the He/TiO2 (110) interaction. 2,22–24 Detailed studies of the Ar/TiO2 (110) and Xe/TiO2 (110) interactions have been reported by Gomes et al. 25,26 and Rittner et al. 27 using density functional theory (DFT), including van der Waals (vdW) corrections 26,28 This work extends previous firstprinciples studies of the He/TiO2 (110) complex 2,24 by considering noble gases atoms heavier than neon and the most stable adsorption site of the perfect TiO2 (110) surface (i.e., the fivefold Ti atom). The calculation of accurate global potentials describing the interaction of physisorbed atoms and molecules with solid surfaces is now at reach for modern ab-initio methodologies addressing intermolecular interactions as well as state-of-the-art vdW-corrected DFT-based treatments (for recent reviews see, e.g., Refs. 28,29). These methodological advances have been accompanied by theoretical analysis contributing to a deeper understanding of the electromagnetic charge fluctuations governing vdW interaction forces (see, e.g., Refs. 30,31). Due to the inability of standard semi-local density functionals to describe long-range (dispersion-like) correlation effects, the inclusion of dispersion corrections is the current standard in DFT-based calculations. During the last decade, many advanced vdW-corrected DFT methods have been developed and implemented into robust periodic codes, with numerous applications. Concurrently, an intense effort has been dedicated to advanced methods and algorithms making possible the upscaling of fully ab initio


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calculations to large systems (see, e.g., Ref. 32 and following articles). Moreover, schemes combining fully ab-initio and DFT have been recently proposed and successfully applied to noble-gas atoms adsorbed on different supports. 2,24,33–36 Considering graphene, 35 it has been shown that the performance of periodic vdW-DFT might depend strongly not only on the specific treatment but also on the noble-gas atom size, reaching accurate descriptions for noble-gas atoms heavier than neon. That study used experimental measurements of the low-lying nuclear bound-state energies to assess the accuracy of vdW-DFT methods. For the same purpose, we use the very recent experimentally determined adsorption energies of Petrik and Kimmel 3 in this work. Additionally, the DFT-based symmetry-adapted perturbation theory [SAPT(DFT)] approach 37,38 has been applied to decompose the interaction energy between noble-gas atoms, employing a cluster model of the TiO2 (110) surface. The resulting dispersion energy contributions are extrapolated to the extended adatom/TiO2 (110) system and used to ratify the behaviour of the chosen vdW-DFT methods in the asymptotic long-range region. The dispersionless correlation terms are then added to periodic Hartree-Fock interaction energies to verify the adequacy of the vdW-DFT methods in the shortrange repulsive region. An objective behind the present study is thus to present an ab-initio-assisted (beyond DFT) route to guide the selection of a periodic vdW-corrected DFT treatment. The structure of this paper is as follows: Section 2 presents the structural models, the applied theoretical approaches, and the computational details of both the non-periodic SAPT(DFT) and the periodic vdW-DFT electronic structure calculations. The energy decomposition of the interaction of the noble-gas atoms with a finite cluster model of the TiO2 (110) surface is analyzed in Section 4. The assessment of the performance of periodic vdW-DFT treatments is discussed in Sections 5 and 6. Finally, Section 7 closes with concluding remarks and future prospects.



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Structural Models, Theoretical Approaches and Computational Details Structural Models The structural models used in this work are illustrated in Figure 1. The periodic calculations were carried out using the same 4×2 supercell (four triple layer TiO2 ) model reported in Ref. 23 (supplementary material) for the He/TiO2 (110) interaction. In this work, we have considered the most stable adsorption site (the fivefold Ti(5f) atom). The adsorption of the noble-has atoms has been modeled on one side of the slab and the vacuum region above the slab was 17 Å thick. Initial periodic calculations were carried out by freezing the positions of the O and Ti atoms to those determined by Busayaporn et al. 39 using X-Ray Diffraction (XRD). For the final calculations, however, the O and Ti positions were relaxed. Following Ref. 24, the hydrogen-saturated cluster of stoichiometry Ti9 O25 H14 (see Figure 1) was used in our finite cluster calculations. According to an accurate ab-initio study of the N2 /TiO2 (110) system by Rittner et al., 40 the Ti9 O25 H14 cluster is large enough to allow for a correct picture of the global interaction. The geometry of the cluster has been frozen to the experimental geometry of the TiO2 (110)–(1×1) surface. 39

Theoretical Approaches Theoretical Approaches Using Surface Cluster Models Using the cluster shown in Figure 1 to model the surface (lower panel), the SAPT(DFT) method has been applied to dissect the X/TiO2 (110) interaction energy (X= Ne, Ar, Kr, and Xe) adopting the Perdew-Burke-Ernzerhof (PBE) density functional. 41 The SAPT(DFT) method 37,38 decomposes the interaction energy as a sum of first- and second-order interaction terms, namely first-order electrostatic Eelec and exchange Eexch , second-order induction Eind and dispersion Edisp terms, along with their respective exchange corrections (Eexch−ind and Eexch−disp ). The δ (HF) estimate 42,43 of the higher-order induction plus exchange-induction contributions was added to the SAPT(DFT) 6 ACS Paragon Plus Environment

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interaction energies. In this work, the dispersion and exchange-dispersion SAPT(DFT) contributions were combined into the total exchange-repulsion portion, as were the induction, exchangeinduction and δ (HF) contributions into the total induction term. As already mentioned, the PBE density functional 41 was chosen and the approach will be referred to as SAPT(PBE). Theoretical Approaches Using Periodic Models Using the periodic model shown in Figure 1, different vdW-corrected DFT-based treatments have been considered along with the benchmark (correlation-free) Hartree-Fock counterpart. For the discussion of their performance in this work, it is instructive to decompose the total interaction total into Hartree-Fock E HF along with intermonomer and intramonomer correlation conenergy Eint int inter and E intra ), tributions (Eint int tot HF inter intra Eint = Eint + Eint + Eint .

(1)

For vdW-dominated interactions, the intermonomer correlation term can be well identified with the dispersion energy while the intramonomer correlation can be associated to a short-range dispersionless correlation contribution. Using semilocal density functionals, the long-range dispersion contribution is naturally missed, and many schemes have been developed to include it. In this work, we have added interatomic vdW −C6 /R6 two-body terms using the empirical DFT-D2

parameterization of Grimme and collaborators, 44 and the method of Tkatchenko and Scheffler (referred to as DFT-TS). 45 In both cases, damping functions are introduced to avoid the divergence of the 1/R6 term at short distances. Instead of considering each atom individually, the DFT-TS method is an "atom-in-molecule" approach based on the direct relationship between polarizability X is defined as and volume. 46 In particular, the effective polarizability of the noble-gas atom X, αeff

a function of the adatom/surface distance, 47 X αeff (Z) =

X (Z) Veff X Vfree−atom

!

X αfree−atom


(2)


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where Veff stands for the local Hirshfeld volume of the adatom, which is naturally determined by the electronic density. Both the DFT-D2 and the DFT-TS approaches have been extended over the last few years. Within the DFT-D3 framework, 48 the dispersion coefficients C6 are adjusted to the local chemical environment of the interacting atomic pairs. Furthermore, three-body dispersion corrections and higher-ranked Cn /Rn terms are introduced, by defining DF dependent scaling factors only for n > 6. Similarly, the DFT-TS method has been extended to include screening effects, beyond the pairwise additive approximation. 47 When modelling three-atom dispersion contributions, the tri-atomic Axilrod-Teller-Muto (ATM) triple-dipole interaction is typically considered. 49,50 These triple-dipole terms arise from the screening between fluctuating dipoles at three different bodies. The weight of three-body terms has been very recently calculated at coupled-cluster level for noblegas atoms adsorbed on carbon-based surfaces: 35 they account for 10−15 % of the total interaction energy, with the upper limit attained by the heaviest noble-gas atom (xenon). Using the semilocal PBE exchange-correlation density functional 41 as well as the revised revPBE version for the exchange part, 51 we have applied the DFT-D2 and DFT-D3 schemes along with the DFT-TS method in this work. The D3 corrections were calculated via an external code developed by Grimme and collaborators, 48,52 applying the zero-damping scheme. A second category of vdW-corrected DFT approaches has been developed by Langreth and co-workers. 53,54 It includes the long-range intermonomer correlation contributions via a non-local correlation functional of the electronic density. To avoid their overcounting at short range, it replaces the semilocal correlation functional by the purely local counterpart. Within this category, we have chosen the original vdW-DF approach, 53 that uses the revPBE exchange functional, 51 as well as the second-generation vdW-DF2 treatment. 54 The latter is based on the revised exchange PW86 functional 55,56 and a gradient correction for the non-local correlation functional evaluated on the basis of scaling laws for atoms.


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Computational Details Surface Cluster Calculations All surface cluster calculations were carried out employing correlation consistent basis sets with the

MOLPRO

package, 57 such as the (augmented) polarized correlation-consistent triple-ζ (aug-cc-

pVTZ) basis of Woon and Dunning, Jr. 58 The SAPT(PBE) calculations were performed using the computational setup reported in Ref. 24 but adopting the aug-cc-pV5Z basis set for Ne and Ar atoms, and the aug-cc-pVTZ-PP basis 59 together with the corresponding relativistic pseudopotentials for krypton and xenon, respectively. The exchange-correlation PBE potential was asymptotically corrected 60 with the ionization potential values reported in the NIST Chemistry Web Book for the noble-gas atoms. 61 For the cluster model of the TiO2 (110), an ionization potential value of ca. 5.0 eV was used instead. This value lies in the range of work function values characterizing TiO2 (110) surfaces 62 (in between 4.9 and 5.5 eV). A spatial grid in between 2.4 and 5.0 Å was considered. To estimate the dispersion energy contribution in the extended system, the evaluated SAPT(PBE) dispersion energies were fitted to the effective inter-atomic pairwise functional proposed by Szalewicz and collaborators 63,64 (referred to as Das ),

Das = ∑ − x

q C6XC6x R6X−x

p βX βx RX−x − f6

q C8XC8x R8X−x

p βX βx RX−x f8

(3)

where x numbers the atoms within the cluster and f6,8 are the damping functions of Tang and ToenX X nies. 65 We optimized the CX 6 , C8 and damping coefficients β of the noble-gas atom X, freezing

the parameters of the oxygen and titanium atoms to the values reported in Ref. 64. When extrapolating the dispersion contributions, we added a correction for the adatom basis set incompleteness (BSI). For this purpose, we carried out additional calculations with the aug-cc-pVTZ basis for neon and argon, and the aug-cc-pVQZ-PP basis for krypton and xenon. Specifically, the dispersion energies E disp evaluated at SAPT(PBE) level were extrapolated using the n−3 scheme to the complete basis set (CBS) limit of Helgaker and co-workers, 66 with n = 3 and 5 for neon and argon, 9 ACS Paragon Plus Environment


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and n = 3 and 4 for krypton and xenon, disp

Endisp = ECBS + A n−3

(4)

disp

where ECBS is the estimate for the CBS dispersion energy and A characterizes the convergence rate to the CBS limit. Next, adatom (X) CBS-accounting upscaling factors fX CBS were calculated as disp

the ratio between the ECBS values and those determined using the aug-cc-pV5Z (neon and argon) and aug-cc-pVTZ-PP (krypton and xenon) basis. It was found that these factors bear a weak dependence on the Z distance. For example, considering xenon, the upscaling factor varied from 1.18, at the repulsive region, to 1.16 and 1.17 at the potential well and the long-range potential regions, respectively. Finally, the extrapolated dispersion contributions were rescaled with the largest fCBS values, ranging from 1.04 to 1.18, obtaining an estimate of adatom BSI-corrected dispersion energies. Periodic Calculations To perform the periodic calculations, the computational setup reported in a previous study of the He/TiO2 (110) interaction 23 was applied. For this purpose, we used the ab initio total-energy and molecular-dynamics program

VASP

67,68

(Vienna Ab initio Simulation Package) based on the pro-

jector augmented-wave method, 68,69 using the PAW-PBE pseudopotentials supplied with the same code. They include 6, 12, and 8 valence electrons for O, Ti, and noble-gas atoms, respectively. As in Ref. 23, most of the calculations were performed using plane wave basis sets with a kinetic energy cutoff of 700 eV and a Gaussian smearing of 0.05 eV to account for partial occupancies, with the Brillouin zone sampled at the Γ point only. Applying the enhanced version of Markov and Payne, 70 monopole, dipole, and quadrupole corrections were accounted for along the Z-axis to avoid multi-pole creation. To assess the numerical accuracy of the periodic calculations, the well-depth of the Kr/TiO2 (110) potential energy curve (PEC) was recalculated with the revPBE-TS approach by improving the


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computational setup. By varying the kinetic energy cutoff from 700 to 1000 eV, using a Γ- centered 2×2×1 Monkhorst-Pack 71 k-point mesh instead of the Γ point only, the integration precision (from normal to accurate) and the convergence threshold for the self-consistent-field loop (from 10−4 to 10−7 eV), the well-depth was modified by less than 1 meV. Computationally intensive HF calculations were also performed by adjusting the integration precision to normal (PRECFOCK=Normal) in the VASP code. 72 Full non-local exchange calculations were carried out for NBANDS=1000. Besides the periodic calculations keeping the atomic positions within the model slab fixed to XRD experimental-based values, 39 relaxation calculations of the surface ionic positions were also performed. A much better agreement with experimental estimations of surface energies 73 was achieved upon relaxation. For example, applying the revPBE-TS approach, the surface energy value of 1.06 Jm−2 for the unrelaxed surface decreases to 0.26 Jm−2 when the ionic positions are relaxed. This value agrees very well with the lower limit of the experimental value (0.28 Jm−2 from Ref. 73). This reflects that the optimized structures of the bare surface with the chosen density functionals differ somewhat from the experimentally derived structure, it being more consistent with the approximative nature of the DFT methods not to constrain the geometry optimization (see also section six). Unless otherwise noticed, adsorbate-induced relaxations were not accounted for. All interaction energies were determined using the supermolecular approach as follows, tot Eint = EnNG/TiO2 (110) − EnNG − ETiO2 (110) /n

(5)

where n is the number of adsorbed noble-gas (NG) atoms, EnNG/TiO2 (110) is the total energy of the system, ETiO2 (110) stands for the energy of the substrate, and EnNG denotes the energy of the free NG atom. With n=1, the surface coverage (Θ) of 0.1 monolayer (ML) can be modelled. At one-monolayer coverage (Θ=1 ML), EnNG denotes the energy of the two-dimensional lattice formed by the NG atoms in the adsorption configuration but without the substrate (n = 8 considering the (4×2) supercell model). It is worth stressing that the experimentally determined adsorption energies per atom include the lateral NG-NG interactions at 1ML coverage and not



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only the NG/surface interaction. These energy contributions are implicitly accounted for, being lat = E tot (1ML) − E tot (0.1ML). This definition differs somewhat from that emdefined as, Eint int int

ployed in previous accurate studies of the interaction of NG atoms with metallic surfaces, 74 namely lat = (E Eint nNG − nENG ) /n. In fact, due to the close distance between Ti(5f) adsorption sites (about

3 Å), substrate-induced NG-NG interactions might play a significant role when co-adsorbed on TiO2 (110) at Θ=1 ML. Nuclear Bound States Calculations To evaluate zero-point vibrational energy contributions, the nuclear bound states were calculated using the Truhlar-Numerov procedure, 75 as described in Ref. 24. For this purpose, the potential energy curves as a function of the adsorbate-surface distance Z were first fitted following the procedure reported in Ref. 23 but adding damped C5 /Z5 long-range terms to the C3 /Z3 counterparts.

Analysis of the Interaction via Symmetry-Adapted Perturbation Theory Table 1: Decomposition of the X/(Ti9 O25 H14 ) interaction energy (X = Ne, Ar, Kr, and Xe) using the SAPT(PBE) method. The noble-gas atoms are located at the potential minima positions (Ze ) of the corresponding potential energy curves (see Figure 2). Values in parentheses correspond to experimental measurements of the X/TiO2 (110) binding energies at onemonolayer coverage of the noble-gas atoms. 3

Ze , Å Eelec , meV Eexch−rep , meV Eind , meV Edisp , meV Etot , meV Exp. (1ML)

Ne

Ar

Kr

Xe

3.20 −19.6 59.3 −6.53 −67.2 −34.0 −

3.25 −94.2 263.4 −50.0 −223.4 −104.2 [−125.4]

3.15 −213.1 511.6 −132.3 −342.8 −176.6 [−177.6]

3.25 −340.0 777.5 −216.2 −440.1 −219.0 [−246.0]


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Let us first focus on the breakdown of the interaction energy contributions as a function of the Z distance. Using the Ti9 O25 H14 cluster mimicking the surface, Figure 2 shows the different energy contributions, as calculated using the SAPT(PBE) approach. Placing the noble-gas atoms at the positions of the potential energy minima (Ze ), Table 1 collects these contributions. When analyzing Figure 2 and Table 1, the first thing to note is that the dispersion-less interaction is overly repulsive. In fact, the dispersion contribution is mainly responsible for the attractive nature of the noble-gas/surface interaction, determining it completely at the medium-range potential region (ca. 4.5−4.9 Å) and at larger distances. Naturally, the magnitude of the dispersion rises as the noble-gas atom size increases, but much less steeply than expected when considering the modification of the static dipole polarizabilities α X along the noble-gas series. Applying the X values of about 2.7, 11.2, 16.8 coupled-cluster method and including relativistic effects, αfree−atom

and 27.1 a.u have been reported for X = Ne, Ar, Kr, and Xe, respectively. 76 The atomic polarizability becomes about ∼4, 6 and 10 times larger when going from neon to argon, krypton, and xenon, respectively, while the dispersion energy contribution is enhanced by factors of about 3.3, 5.1, and 6.5 along the same sequence of noble-gas atoms (see Table 1). As discussed in Ref. 35 for the X/coronene interaction (X = Ne, Ar, Kr, and Xe), the dispersion energies scale with the dynamic polarizabilities of the noble-gas atoms and they vary with the distance Z from the noble-gas atom to the surface plane [see Eq. (1)]: Upon approaching the surface, the deviation of the effective atomic densities from the ideal free-atom densities may be more pronounced for the heaviest atoms due to the larger overlap with the substrate electronic density. At the vdW minima (see Table 1), the dispersion contributes to about 72% to the attractive portion of the interaction energy for neon. This percentage decreases to ca. 61%, 50%, and 44% along the noble-gas series. In its turn, as can be seen in Figure 2, the heavier the noble-gas atom the larger is the weight of the electrostatic and induction energy terms. The electrostatic term is defined as the Coulomb interaction between the electrons and nuclei of the two monomers (i.e., the noble-gas atom and the Ti9 O25 H14 cluster). The intensification of the electrostatic contribution along the noble-gas sequence reflects the stronger charge overlap between the monomer densities



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as the adatom size increases. This is naturally translated into much larger exchange-repulsion contributions for the heaviest atoms. Apparently, the evolution of the energy components along the noble-gas series is rather similar to that shown for the interaction with the coronene surface (see Fig. 4 of Ref. 35). However, it should be stressed that, while the induction energy component plays an insignificant role in coronene, it reaches very large values for the interaction of Kr and Xe atoms with the TiO2 -based cluster. The weighting of the dispersion also decreases as the atom size increases, but much more smoothly when it is adsorbed onto coronene (as high as 10%). The marked intensification of the induction interaction might reflect the formation of a weak adatomTi(5f) covalent bond at the potential energy minima via the hybridization of valence p and d adatom orbitals with Ti(3d) atomic orbitals, and the strong polarization of the adatom density towards the substrate, causing an increase in the magnitude of the adatom-induced "interfacial" dipole moments. Experimentally-determined values of the adsorption energies 3 of the noble-gas atoms onto TiO2 (110) are also shown in Figure 2 (cyan line) and Table 1. It can be noticed that the experimental values lie in between the well-depths calculated for the Ti9 O25 H14 cluster and those estimated for the extended TiO2 (110) system through the extrapolation of the dispersion contribution. It is implicitly assumed that the dispersionless interaction is not long-ranged and, then, reasonably well accounted for using our cluster model. Considering also that the experimental adsorption energies include lateral adatom-adatom interactions at one-monolayer coverage, 3 we conclude that the agreement between the experimental and theoretical binding energies is satisfactory (to within 16% and 9% on average).

Variation of the Work Function Upon Physisorption Applying the hybrid DFT/HF PBE0 approach, 77 we have calculated the ionization potential (IP) values of the adatom/Ti9 O25 H14 complexes. Without the adsorbate, the IP value is very close to the experimental value of the work function (WF) for a quasi-stoichiometry TiO2 (110) surface (5.9 eV). The estimated work function value decreases to 2.9−3.2 eV for the adatom/cluster complexes, 14 ACS Paragon Plus Environment

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without a substantial dependence on the specific noble-gas atom considered. The WF reduction of the TiO2 (110) surface upon physisorption has been invoked by Petrik et al. 4 to qualitatively explain the quenching of O2 PD upon noble-gas atom physisorption. Adsorbate-induced WF reduction can be identified with charge-transfer from the noble-gas atom to the substrate. Hence, the WF reduction can be correlated to the inhibited hole transfer through the material interfacial region, supporting the hole-mediated nature of the O2 PD mechanism first proposed by Yates, Jr. (see, e.g., Ref. 9).

Noble-Gas Atoms Adsorption onto the Unrelaxed TiO2(110) Surface: Ab initio-Assisted Benchmarking Table 2: Interaction energies (in meV) and adatom/surface distances (in Å, in square brackets) at the potential minima of the X/TiO2 (110) PECs shown in Figure 3 (X = Ne, Ar, Kr, and Xe). Values in parentheses correspond to experimental measurements at one-monolayer coverage (Θ = 1) of the noble-gas atoms 3 while the theoretical values correspond to Θ = 0.1. Method

Ne

Ar

Kr

Xe

revPBE-D2 revPBE-D3 revPBE-TS vdW-DF2 PBE-D2 PBE-TS vdW-DF Exp. (1ML)

−43.43 [3.29] −53.91 [3.20] −66.36 [3.42] −96.74 [2.86] −89.69 [2.90] −99.50 [3.05] −113.4 [3.04] −

−74.22 [3.61] −148.3 [3.33] −151.2 [3.64] −197.8 [3.20] −162.5 [3.19] −250.7 [3.20] −211.2 [3.41] (−125.4)

−117.2 [3.58] −202.8 [3.40] −190.5 [3.70] −228.7 [3.33] −229.7 [3.25] −308.5 [3.39] −245.0 [3.52] (−177.6)

−169.4 [3.75] −264.8 [3.51] −263.3 [3.73] −283.2 [3.55] −308.7 [3.40] −403.3 [3.50] −298.8 [3.72] (−246.0)

For complexes with the noble-gas atom on the Ti5 f adsorption site, Figure 3 shows the interaction potential determined with different periodic vdW-corrected DFT approaches, with the slab geometry frozen to the experimental-based atomic positions. 39 The main parameters characterizing these interaction potentials (well-depths and equilibrium distances) are collected in Table 2 along with those evaluated with the revPBE-D2 and PBE-TS treatments. From Figure 3 and Table 2, 15 ACS Paragon Plus Environment


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it can be seen that, with the exception of the revPBE-D2 treatment, the DFT-based approaches provide larger binding energies than those measured in samples at one-monolayer coverage of the noble gases. Besides the contribution of lateral interactions between co-adsorbed atoms, the lack of surface relaxation effects is partly responsible for this behaviour (see next section). As can be seen in Table 2, the equilibrium distances lie in the range [2.9−3.8] Å depending on the noble-gas atom and the specific vdW-corrected DFT method.

Benchmarking of the Long-Range Dispersion Tails In order to guide the comparison between different approaches, Figure 3 also shows the SAPT(PBE) dispersion energies, as extrapolated to the extended system and corrected for adatom basis-set incompleteness. It should be stressed that the adequate performance of the extrapolation scheme has been demonstrated in previous studies of the He/TiO2 (110) interaction. 2,24 From Figure 3, it is clearly apparent that the long-range vdW-DF and revPBE-TS dispersion tails decay too slowly as compared with the SAPT-based ab-initio benchmarking. Contrarily, the long-range potential region determined with the Grimme D3 dispersion correction 48 and the second-generation vdWDF2 method closely follows the SAPT-based counterpart. The improvement in going from the DFT-D2 treatment 44 to the DFT-D3 approach is evident, especially for the Ar/TiO2 (110) complex. In addition to a local chemical correction, the DFT-D3 treatment includes three-body dispersion corrections to the DFT-D2 scheme. 48 As previously discussed, 78 the gradient correction factor of the non-local vdW-DF2 functional 54 follows atomic scaling laws instead of that of the electron gas with a slower varying density, as in the vdW-DF precursor. 53 This explains why the attractive vdW-DF long range tail decays too slowly. The slow decay of the revPBE-TS dispersion in the medium- and long-range region might be explained by the lack of long-range screening effects in the original Tkatchenko-Scheffler (TS) model.


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Benchmarking of the Short-Range Potential Region After assessing the performance of vdW-DFT dispersion corrections, the next step is to analyze the adequacy of the underlying DFT approach in describing the short-range dispersionless interaction. The dispersionless interaction energy can be tentatively approximated as follows: disp−less

Eint

SAPT(PBE) SAPT(PBE) HF HF − Eint /cluster /periodic ≈ Eint /periodic + Etot − Edisp

The resulting potential energy curves are represented in Figure 4 along with those determined in periodic calculations with either the Hartree-Fock method or the PBE and revPBE density functionals. For all the noble-gas atoms, the dispersionless correlation contribution at short-range is repulsive and increases exponentially as the adatom/surface distance decreases. However, the heavier the adatom, the less repulsive is the dispersionless correlation contribution. Thus, at the potential wall, the total dispersionless and Hartree-Fock interaction energies becomes very close to each other for the heaviest atom (xenon). From Figure 4, it can be noticed that the revPBE interaction potentials follow our best estimations for the dispersionless potential energy curves. Contrarily, the PBE-based interaction potentials deviate very significantly from both revPBE and estimated dispersionless counterparts. Since PBE and revPBE approaches differ in the parametrization characterizing the exchange density functional, and the PBE interaction potential bear pronounced potential minima which are absent in the revPBE cases (see Figure 4), it follows that the PBE minima are exchange-induced contributions which can be attributed to the self-interaction shortfall. 80 It should be pointed out that the extreme shallow minima predicted by the revPBE treatment arise from an induction energy contribution. Similar conclusions have been reached in previous studies of He/TiO2 (110) 2,24 and vdW-dominated adsorbate/graphene interactions. 35,78 Although there exists no unique way of defining different correlation contributions in DFT, a localized molecular orbital decomposition energy analysis 81 indicated that the PBE approach underestimates the repulsive exchange-repulsion contribution to the He/TiO2 (110) interaction. 24 17 ACS Paragon Plus Environment


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Based on a previous analysis by Jordan and collaborators, 82 it could also be argued that the PBE approach is accounting for short-range dispersion-like correlation in the adatom/TiO2 (110) interaction, as arising from the overlap of the monomer (adatom and substrate) densities. Within the DFT-D2 scheme, the damping function contained in the D2 dispersion correction avoids the overcounting of these short-range contributions by pure density functionals which are assumed to already include them. As a matter of fact, the scaling factor of the D2 dispersion functional depends on the specific density functional in question such as the PBE treatment. The PBE scaling factor has been employed to calculate the revPBE-D2 interactions energies. From these considerations, it is easy to understand why the revPBE-D2-based well-depths are grossly underestimated while the values predicted by the PBE-D2 treatment are much more sensible estimations (see Table 2). It also serves to clarify why the replacement of the D2 by the zero-damping D3 correction in the revPBE approach produces very reasonable well-depth values: the D3 scheme is free of density-functional dependent scaling factors for the leading C6 dispersion coefficients. The same arguments can be applied to justify the good performance of the revPBE-TS approach. The opposite holds true when the PBE-TS treatment is applied, resulting in significantly overshot well-depths whatever the noble-gas atom may be. On the whole, our benchmarking reveals that, between the different choices to account for the dispersion in vdW-corrected DFT, the DFT-D3 and vdW-DF2 treatments predict long-range dispersion tails closely following the SAPT-based counterparts. At the short-range potential region, the comparison of vdW-uncorrected DFT interaction energies with our ab initio-based estimations shows that the revPBE approach yields potential energy curves which are consistent with the dispersionless picture of the interaction as opposed to those determined with the PBE treatment. This qualitatively explains why the inclusion of the Tkatchenko-Scheffler (TS) dispersion correction on top of the PBE interaction energies cause severe overbinding effects while very sensible well-depths are predicted by the revPBE-TS method. At this point, it should be mentioned that the dispersionless density functional (dlDF) of Pernal et al. 63 is explicitly designed to avoid the problem of overcounting vdW corrections in DFT


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treatments. When combined with dispersion contributions evaluated at coupled-cluster level of theory on surface cluster models (the so-termed dlDF+D∗as approach 33 ), it has provided a very good performance for the He/TiO2 (110) interaction, 2,24 as verified with the method of increments of Stoll. 83 It has also been validated by comparing with experimental measurements of the interaction between noble-gas atoms (He, Ne, Ar, Kr, and Xe) and molecular hydrogen with graphite. 35,84 A very good agreement with vdW-DF2-based determinations of silver/graphene 78 and argon/gold interaction potentials 34 has also been revealed. A preliminary estimation of the Ar/TiO2 (110) potential minimum with the dlDF+D∗as method (see supplementary material of Ref. 2) provides a value (−121.33 meV) agreeing well with the experimental determination (−125.6 meV).

Bare Surface Relaxation and Lateral Interaction Effects Including Bare Surface Relaxation-Induced Contributions Table 3: Atomic displacements (in Å) away from the TiO2 (110)-(1×1) surface along the [110] direction (perpendicular to the surface plane). A positive value indicates that, upon relaxation, the atom moves toward the bulk. These atomic displacements are calculated by taking as the reference the experimentally-determined atomic positions from surface x-ray diffraction (SXRD) measurements, which are also shown along with those arising from low-energy electron diffraction (LEED) experiments (see Ref. 39). Method

Ti5 f

Ti6 f

Op

Ob

revPBE-D2 revPBE-TS vdW-DF2 PBE-D2

0.04 0.01 −0.06 0.07

−0.15 −0.17 −0.30 −0.08

−0.06 −0.09 −0.18 −0.01

−0.10 −0.12 −0.26 −0.03

−0.24±0.03 −0.25±0.01

−0.08±0.05 −0.10±0.04

−0.19 ±0.08 −0.17 ±0.03

LEED 39 XSRD 39

0.19±0.03 0.11±0.01

Let us now analyze the effects from relaxing the atomic positions in the slab modeling the bare TiO2 (110)-(1×1) surface. It should be stressed that, in the relaxed surface, the atomic positions are considerably displaced as compared with ideal bulk-terminated positions. According to recent 19 ACS Paragon Plus Environment


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surface x-ray diffraction measurements in the TiO2 (110)-(1×1) surface, 39 the Ti(5f) atoms lie beneath the basal plane by 0.11 ± 0.01 Å whereas the bridging oxygen atoms experience a vertical displacement away from the bulk of 0.10 ± 0.04 Å. In the unrelaxed surface calculations (see previous section), the atomic positions within the slab were fixed to these experimental-based values. As the next step, we performed additional relaxations of the slab geometry. These geometry optimizations were accomplished without including the adsorbate. As can be noticed in Table 3, the atomic displacements from experimentally-determined values are not negligible, especially when the vdW-DF2 method is applied. Interestingly, all the methods tend to intensify the shifting of the surface atoms from bulk-terminated positions, as estimated from the experimental measurements. By comparing the results obtained with revPBE-TS, revPBE-D2 and PBE-D2 approaches (see Table 3), it can also be noticed that the calculated atomic shifts depend more on the semilocal density functional than on the specific vdW correction. With the exception of the strong relaxation experienced by the Ti6 f atom and those evaluated with the vdW-DF2 approach, the deviations from XSRD data range from 0.01 to 0.1 Å. On the whole, they are rather moderate when considering the experimental error bars (in the range of [0.01−0.08] Å) and the slight influence of the applied technique (XSRD or LEED) in the measured values (see Table 3 and Ref. 39). Ideally, the optimized slab geometry with each DFT approach would correspond to the unrelaxed experimentally derived structure. Thus, the average of the differences between theoretical and experimentallydetermined atomic positions serves as an indication of the uncertainty limit of each DFT method to predict structural parameters (ca. 0.2 Å for the vdW-DF2 treatment and about 0.1 Å for the other vdW-corrected DFT approaches). In order to analyze the influence of the bare surface relaxation in the interaction energies, Table 4 collects the new set of well-depths and equilibrium distances. By comparing them with their counterparts obtained on the unrelaxed surface (see Table 2), notice that the surface relaxation is responsible for small enlargements of the equilibrium distances (by about 0.1 Å and less than 6%), irrespective of the noble-gas atom considered. Contrarily, it bears a diverse impact on the binding energies of the different noble-gas atoms, attaining also a remarkable dependence on the


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Table 4: Interaction energies (well-depths, in meV) and adatom/surface distances (in Å, in square brackets) at the potential minima for the X/TiO2 (110) complexes (X = Ne, Ar, Kr and Xe). The geometry of the TiO2 (110) slab corresponds to that obtained upon relaxation of the atomic positions with each of the considered approaches (see Table 3). Values in parentheses correspond to experimental measurements at one-monolayer (1ML) coverage of the noblegas atoms 3 while the theoretical values were obtained at 0.1 ML coverage. Theoretical values from previous studies 25–27 are also shown. Method

Ne

Ar

Kr

Xe

revPBE-D2 revPBE-D3 revPBE-TS vdW-DF2 PBE-D2 Theo.

−36.98 [3.46] −51.00 [3.30] −62.03 [3.53] −82.45 [3.05] −78.96 [3.03] −

−67.76 [3.75] −138.5 [3.41] −142.8 [3.76] −174.5 [3.40] −144.6 [3.30] −42 [3.6] 25

−97.54 [3.80] −184.5 [3.49] −179.8 [3.83] −202.1 [3.52] −201.6 [3.44] −

Exp. (1ML)

−

(−125.4)

(−177.6)

−137.3 [3.89] −236.3 [3.63] −230.9 [3.94] −245.4 [3.75] −262.0 [3.55] −295 [3.3] 27 −280 26 (−246.0)

chosen vdW-DF approach. It increases the absolute value of the slab energy and then, see Eq. (4), decreases the strength of the adatom/slab interaction. For the lightest atom (neon), the well-depth decreases from 6%, as determined with the revPBE-TS treatment, to 17%, as evaluated with the vdW-DF2 approach. Notice also that the heavier the noble-gas atom, the larger the surface relaxation influence on the well-depth. For example, the binding characterizing the interaction of xenon with the unrelaxed surface differs by 12−23% from that obtained when surface relaxation effects are accounted for. In fact, the oxygen atoms adjacent to the Ti(5f) site (termed O p , see Fig. 1) move outwards from the bulk when the surface geometry is relaxed (see Table 3). As a result, the effective adatom-O p exchange-repulsion increases, especially for the adatoms with the largest vdW radii. Although the relaxations of atomic positions from experimental values are moderate when the bare surface geometry is optimized, they bear a relevant influence on the adsorbate binding energies, especially for the heaviest adatoms, making them closer to the experimental values. Once again, it reflects an enhanced consistency when adsorption energies are calculated using bare surface structures optimized with the same density functionals. It has also been found that additional (adsorbate-induced) surface relaxations at Θ = 0.1 ML further decrease the binding energies 21 ACS Paragon Plus Environment


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but to a much lesser extent than the bare surface optimization (e.g., 6% vs. 0.05% for neon when the revPBE-TS method is applied). Focusing on the equilibrium adatom/surface distances determined with the revPBE-D3 approach (see Table 4), they agree to within 0.1 Å with those evaluated for noble gases adsorbed on the graphite surface in Ref. 35: 3.3 Å (neon and argon), 3.5 Å (krypton) and 3.7 Å (xenon). These adatom/graphite interaction potentials were validated against experimental measurements of the supported nuclear bound-states. The largest difference is found for xenon (3.6 vs. 3.7 Å), for which, however, the available experimental value (on graphite) is 3.59 ± 0.05 Å. 85 A very similar vertical distance (3.6 ± 0.05 Å) and adsorption energy (200−230 meV) has also been mea-

sured for the Xe/Ag(111) complex 86 (see also Ref. 87). The results shown in Table 4 are also consistent with those reported in earlier works addressing the noble-gas atoms interaction with TiO2 (110). 25–27 The largest differences are found for the Ar/TiO2 (110) complex, which can be attributed to the lack of a vdW correction. 25 Hence, the revPBE-D3 treatment not only provides interaction potentials agreeing very well with our ab-initio benchmarking, at both short- and longrange regions, but also very sensible estimates for the energy and positions of the potential minima.

Comparison with Experiment: Including Lateral Interactions To compare with the experimental adsorption energies at 1ML coverage of Petrik and Kimmel, 3 it is necessary to include the energy contributions from lateral interactions between co-adsorbed atoms. It should be stressed that the distance between Ti(5f) adsorbed sites (about 3 Å) is shorter than the adatom-adatom equilibrium distance in gas-phase (about 4.36 Å for the Xe2 dimer 61 ). As lat = E tot (1ML) − mentioned above, this contribution has been evaluated as the energy difference Eint int

tot (0.1ML). It is clear that the modification of the effective adatom-adatom interaction due to Eint

substrate-induced effects is thus accounted for. Choosing four vdW-corrected DFT methods, Table 5 shows the lateral interaction contributions (∆Elat ) as well as those arising from surface relaxation effects (∆Erel ) and zero-point vibrational energies (∆EZPV ). Our final estimations of the adsorption energies (Efinal tot ) are also collected along 22 ACS Paragon Plus Environment

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Table 5: Summary of the main contributions to the X/TiO2 (110) adsorption energy (X = Ne, Ar, Kr, and Xe): (1) well-depth of the potential energy curve for the noble-gas atom (0.1 ML) adsorbed on the Ti(5f) site [Eunrel (0.1 ML)]; (2) substrate relaxation energy contribution [∆Erel (0.1ML)]; (3) lateral interaction energy contribution at one-monolayer coverage [∆Elat (1ML)]; and (4) zero-point vibrational (ZPV) energy contribution [∆EZPV ]. The resulting theoretical estimations for the adsorption energies [Efinal tot (1ML)] are tabulated along exp with those experimentally-determined [Etot (1ML)] from Ref. 3 . The absolute percentage deviations from experimental values (%Dev.) are also collected, including an average over all noble-gas atoms (%Average). Dashes indicate that ∆Elat values were assumed to be the same as determined with the revPBE-TS approach. PBE-D2

Eunrel tot , meV ∆Erel , meV ∆Elat , meV ∆EZPV , meV Efinal tot , meV exp Etot , meV %Dev. %Average

revPBE-TS

Ar

Kr

Xe

Ar

Kr

Xe

−162.5 +17.8 −16.2 +3.60 −157.3 −125.4 25.6

−229.2 +27.7 −11.6 +2.57 −210.5 −177.6 18.5 16.2

−308.7 +46.7 +25.1 +2.28 −234.6 −246.0 4.6

−151.2 +8.40 +18.5 +2.35 −122.0 −125.4 2.7

−190.5 +10.7 +17.1 +1.88 −160.2 −177.6 9.8 6.9

−263.3 +32.4 +3.20 +1.68 −226.0 −246.0 8.1

vdW-DF2

Eunrel tot , meV ∆Erel , meV ∆Elat , meV ∆EZPV , meV Efinal tot , meV exp Etot , meV %Dev. %Average

revPBE-D3

Ar

Kr

Xe

Ar

Kr

Xe

−197.8 +23.3 −13.1 +3.26 −184.3 −125.4 47.0

−228.7 +26.6 −6.30 +2.58 −206.0 −177.6 16.0 23.9

−283.2 +37.8 +18.5 +2.44 −224.5 −246.0 8.7

−148.3 +9.80 − +1.94 −118.1 −125.4 5.6

−202.8 +18.3 − +1.61 −165.8 −177.6 5.8 6.0

−264.8 +28.5 − +1.43 −231.7 −246.0 5.8



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with the experimental values. As expected from steric considerations, the lateral interaction energy contributions become repulsive for xenon adatoms when considering the PBE-D2 and vdWDF2 treatments. Interestingly, the repulsive lateral interaction energy contribution decreases as the adatom size increases when determined with the revPBE-TS treatment instead. Using the same method, the opposite trend is found when the lateral interaction is calculated without the presence of the substrate, making clear that this effect is substrate-induced. Without considering substratemediated interactions between co-adsorbates, the lateral interaction is predicted to be repulsive, irrespective of the chosen method. Contrarily, the PBE-D2 and vdW-DF2 treatments predict attractive interactions between co-adsorbed Ar and Kr atoms. As mentioned in the analysis of the SAPT-based energy decomposition, the induction contribution to the adsorbate/substrate interaction is much larger in TiO2 (110) than that estimated in less polarizable surfaces such as graphite, 35 especially for the krypton and xenon adsorbates. Hence, it seems plausible that the adatom-adatom exchange-repulsion energy might be compensated by the attractive interaction between adatominduced interfacial dipoles. Attractive lateral interactions have also been theoretically predicted for adsorbate/Mg(0001) complexes by Cheng et al. 88 On the TiO2 (110) surface, an increase in the magnitude of the adatom-induced surface dipole when raising the noble-gas atom coverage (i.e. instead of the expected depolarization) might also be consistent with the observed decrease of the PD signal from co-adsorbed O2 molecules in the experiments carried out by Petrik and Kimmel. 3 In fact, as mentioned above, a further decrease of the material WF (see section three) upon augmenting the adatom coverage would lead to a more pronounced inhibition of the hole-mediated transfer mechanism driving O2 PD. As can be observed in Table 5, the net-lateral interaction contributes less than 20% to the adsorption energy, with the equilibrium adatom/surface distances differing by 0.01−0.1 Å from those determined at 0.1 ML coverage (shown in Table 4). Vibrational zero-point energies represent a minor fraction of the interaction (below 3%). With relative deviations below 6%, the revPBE-D3 treatment provide the best estimates of the adsorption energies followed by the revPBE-TS approach bearing a mean deviation percentage of 7%. As also found in Ref. 35, the vdW-DF2


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method becomes rather accurate for xenon but its performance clearly deteriorates as the adatom size decreases (see Table 5). The same trend can be observed for the PBE-D2 approach. Potential error sources such as the consideration of the Ti(5f) adsorption site only are not expected to modify the overall good agreement with experimental measurements. Thus, preliminary calculations have showed that the global interaction potentials are strongly peaked when the noble-gas atoms are located at the Ti(5f) sites. Hence, the motion of the noble-gas atoms at one-monolayer coverage is expected to be rather hindered. Surface relaxation effects upon physisorption have also been explored at one-monolayer surface coverage: They decrease the adsorption energies by less than 8% using the revPBE-TS treatment, the influence being much less pronounced for the lightest adatom (e.g. 1% for neon). Future work will consider both additional adsorption sites and adsorbate-induced relaxations at one-monolayer surface coverage.

Conclusions and Future Prospects With the main purpose of predicting the adsorption energies of noble-gas atoms onto the TiO2 (110) surface, we have combined vdW-corrected DFT and Hartree-Fock treatments for periodic structures with the SAPT(DFT) method for the finite-size surface model Ti9 O25 H14 . To compare with recent experimental measurements by Petrik and Kimmel, 3 lateral interactions and surface relaxation effects have been included in the periodic calculations. Our main findings can be summarized as follows: 1) The SAPT(DFT)-based energy decomposition clearly shows that the X/Ti9 O25 H14 (X = Ne, Ar, Kr, and Xe) interaction is dispersion-dominated. However, as the noble-gas atom mass increases, induction and electrostatic energy contributions start to play a very relevant role. This is explained as the result of the formation of an "interfacial" surface dipole of significant magnitude. It is further demonstrated that the adsorption of noble-gas atoms lowers the material WF by about 3 eV (ca. 50%). These ab initio determinations provide support to the suggestions by Petrik et al. 4 to explain the reasons why the noble-gas atoms inhibit the photodesorption from co-adsorbed O2



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molecules, assuming the hole-mediated mechanism proposed by Yates., Jr. (see, for example, Ref. 9). 2) The SAPT(DFT)-based dispersion energies are consistent with the long-range tails of the interaction potentials determined via the vdW-DF2 and DFT-D3 approaches. VdW-DF and revPBETS method provide dispersion contributions decaying more slowly as the atom/surface distance increases. By adding SAPT(DFT)-based dispersionless correlation contributions to the HartreeFock interaction energies for periodic structures, we have estimated dispersionless interaction potentials, which are rather well reproduced by the revPBE treatment. The opposite holds for the PBE density functional, which is attributed to exchange-only contributions. According to the ab initio-assisted benchmarking, the revPBE-D3 approach seems to provide the better performance for the short- and long-range potential regions. 3) The optimization of the bare surface structure with the chosen vdW-corrected DFT methods decrease the adsorbate binding energies by up to 20% from those calculated with the experimentally derived structure, making them closer to the experimentally measured adsorption energies. 4) The average deviation percentage of atomic displacements in the bare TiO2 (110) surface from experimental measurements 39 is about 0.1−0.2 Å. The revPBE-D3 treatment predicts equilibrium adatom/TiO2 (110) distances in the range of 3.3−3.6 Å, agreeing very well with either experimental or ab initio studies of noble-gas atoms adsorbed onto graphite and metallic surfaces. 5) Lateral interactions at one-monolayer coverage modifies the adsorption energies by up to 20%. After including them, agreement with experimental measurements to within 6% and 10% is achieved by applying the revPBE-D3 and revPBE-TS treatments. In conclusion, we have applied vdW-corrected DFT and Hartree-Fock treatments for periodic structures along with the SAPT(DFT) method for finite surface fragments to estimate adsorption energies. Their accuracy has been validated with experimental measurements. Furthermore, new physical insights into the interaction of noble-gas atoms with the TiO2 (110) surfaces have been revealed, for which not only the dispersion but also the induction and electrostatic interactions play an important role. It has also been found that lateral interactions between co-adsorbates are more


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complex than expected, deviating significantly from those existing without the substrate. This is also consistent with very recent experimental measurements revealing that the vdW interaction between noble-gas atoms co-adsorbed at a molecular network on Cu(111) is strengthened by a factor of up to two through adsorption-induced effects. 89 To deepen into the microscopic mechanisms driving substrate-induced lateral interactions between noble-gas atoms on titanium dioxide is thus an interesting direction for future research.

Acknowledgement The authors wish to thank Wake Forest University (USA) and the CESGA Super-Computer Center (Spain) for providing extensive computational resources, as well as the DEAC and CESGA cluster staffs for their valuable technical support throughout this work. This work has been partly supported by the COST Action CM1405 "Molecules in Motion (MOLIM)" and the Grant No. FIS2011-29596-C02-01 from the Spanish Dirección General de Investigación Científica y Técnica. One of the authors, Ali Abbaspour Tamijani, wishes to extend his sincere gratitude to Profs. Timo Thonhauser and Natalie Holzwarth, from the Physics Department of Wake Forest University, for useful discussions related to this work.

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°

Z/A

Z/A

400

400

Kr/TiO2(110) Exp.

Xe/TiO2(110) Exp.


200

100

revPBE-TS vdW-DF PBE-D2 100

-100

-200

-200

-300

-300

5

6

7

8

SAPT(PBE) Dispersion Energy Ext.

0

-100

4

vdW-DF2

200

0

3

revPBE-D3

300

Energy / meV

300

Energy / meV

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


3

°

4

5

6

°

Z/A

Z/A

Figure 3: Interaction potentials of X/TiO2 (110) complexes (X = Ne, Ar, Kr, and Xe) using different vdW-corrected DFT approaches. Z is defined as the vertical distance of the noble-gas atom above the surface Ti5 f atom, as shown in Figure 1. The TiO2 (110) slab geometry is frozen to experimental-based atomic positions. 39 The dispersion energies determined with the SAPT(PBE) approach using the Ti9 O25 H14 surface cluster and extrapolated to the extended systems are also shown (see main text).



Ne/TiO2(110), EHartree-Fock

Ar/TiO2(110), EHartree-Fock

revPBE

E 100

E Hartree-Fock

+E

E

revPBE

100

PBE

E

disp-less/corr

(Ne/Ti9O25H14)

E

Energy / meV

Energy / meV

E

50

0

Hartree-Fock

PBE

disp-less/corr

+E

(Ar/Ti9O25H14)

50

0

-50

-50 2

3

4

5

6

7

2

3

4

5

°

6

7

6

7

°

Z/A

Z/A

400

400

Kr/TiO2(110), E

Hartree-Fock

Xe/TiO2(110), EHartree-Fock

revPBE

E

320

ErevPBE

320

EPBE E

Hartree-Fock

+E

EPBE

disp-less/corr

(Kr/Ti9O25H14)

E

240

Energy / meV

240

Energy / meV

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

Page 40 of 41

160

disp-less/corr

+E

(Xe/Ti9O25H14)

160

80

80

0

0

-80

Hartree-Fock

-80 2

3

4

5

6

7

2

3

°

4

5

°

Z/A

Z/A

Figure 4: Interaction potentials for the X/TiO2 (110) interaction (X = Ne, Ar, Kr, and Xe) using the Hartree-Fock method and the PBE and revPBE density functionals. Z is defined as the vertical distance of the noble-gas atom above the surface Ti5 f atom, as shown in Figure 1. The TiO2 (110) slab geometry is frozen to experimental-based atomic positions. 39 The dispersionless interaction energies determined by adding SAPT(PBE)-based dispersionless correlation contributions to the Hartree-Fock energies are also shown (see main text). 79


Page 41 of 41

TOC Graphic 0

-100

Energy / meV

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


Theo. Eads(1ML)

Exp. Eads(1ML)

Theo. Eads(1ML)

Exp. Eads(1ML)

O(planar) O(bridging)

O(bridging)

X = Ne, Ar, Kr, Xe

-200 Theo. Eads(1ML)

Exp. Eads(1ML) X=Ne(0.1ML)

Ti(6f)

Ar(0.1ML)

-300

Kr(0.1ML)

revPBE-D3, X/TiO2(110) 3

4

Xe(0.1ML)

5

6

7

Ti(5f)

Ti(5f)

8

Z / A°


Ti(6f)

Adsorption of Noble-Gas Atoms on the TiO2(110) Surface: An Ab Initio

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