Jan 2, 2018 - Comparison of Performance of van der Waals Dispersion Functionals in Description of Water and Ethanol on Transition Metal Surfaces. Rafael Luiz Heleno Freire, Diego ... Impact of Bi Heterovalent Doping in OrganicâInorganic Metal Halid
Jan 2, 2018 - Comparison of Performance of van der Waals Dispersion Functionals in Description of Water and Ethanol on Transition Metal Surfaces. Rafael Luiz Heleno Freire, Diego Guedes-Sobrinho, Adam Kiejna, and Juarez L. F. Da Silva. J. Phys. Chem.
Jan 2, 2018 - Pairwise van der Waals (vdW) corrections have been routinely added to density functional theory (DFT) adsorption studies of inorganic or organic molecules on solid surfaces, however, comparative studies of the available pairwise correct
Jan 2, 2018 - A second extension of the DFT-D3 was made within the BeckeâJohnson (BJ) model framework as an alternative for the damping function, DFT-D3(BJ). This implementation is justified by the analytical Koide's(61) study about the dispersion
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Apr 24, 2017 - Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States. Â§ Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742 United S
Apr 24, 2017 - However, electronic structure methods are best suited to study a smaller number of materials with a focus on understanding the molecular level details of guest binding at the primary binding site (or sites) in MOFs. The ability of dens
Apr 24, 2017 - neutron powder diffraction (NPD) data for further comparison. All of the functionals are able to predict ..... vendors and used without further purification. Samples of all of ..... The authors declare no competing financial interest.
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Comparison of Performance of van der Waals Dispersion Functionals in Description of Water and Ethanol on Transition Metal Surfaces Rafael Luiz Heleno Freire, Diego Guedes-Sobrinho, Adam Kiejna, and Juarez L. F. Da Silva J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09749 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 3, 2018
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Comparison of Performance of van der Waals Dispersion Functionals in Description of Water and Ethanol on Transition Metal Surfaces Rafael L. H. Freire,† Diego Guedes-Sobrinho,‡ Adam Kiejna,¶ and Juarez L. F. Da Silva∗,§ †Department of Physical-Chemistry, S˜ao Paulo State University, 14800-060, Araraquara, SP, Brazil ‡Technological Institute of Aeronautics, 12228-900, S˜ao Jos´e dos Campos, SP, Brazil ¶Institute of Experimental Physics, University of Wrocław, Plac M. Borna 9, 50-204 Wrocław, Poland §S˜ao Carlos Institute of Chemistry, University of S˜ao Paulo, PO Box 780, 13560-970, S˜ao Carlos, SP, Brazil E-mail: juarez [email protected]
Pairwise van der Waals (vdW) corrections have been routinely added to density functional theory (DFT) adsorption studies of inorganic or organic molecules on solid surfaces, however, comparative studies of the available pairwise corrections, e.g., D2, D3, D3(BJ), TS, and TS+SCS, are quite scarce. We report DFT calculations within the Perdew–Burke– Ernzerhof (PBE) functional to assess the performance of the mentioned pairwise vdW corrections for well defined transition-metal (TM) systems, namely, the Cu, Pt, and Au bulks in the face-centered cubic structure, close-packed TM substrates (Cu(111), Pt(111), Au(111), Cu9 /Pt9 /Cu(111), Pt9 /Cu9 /Cu(111), Au9 /Pt9 /Au(111), Pt9 /Au9 /Au(111)), and the adsorption of water and ethanol on the selected substrates, which include strained Pt-monolayers, i.e., a good challenge for pairwise vdW corrections. In general, accounting for vdW interactions leads to smaller lattice constants, which is expected due to the attractive nature of the vdW corrections, and the D3, D3(BJ), and TS+SCS improves the DFT-PBE results, in contrast with D2 and TS. Compared with PBE results, the vdW corrections enhance the contraction of the topmost surface layers, which contributes to change the electronic structure, in particular, the d-band center shifts away from the Fermi energy (up to 0.3 eV) in most cases, while the work function changes by about 0.2 eV in the worst cases. As expected, the attractive nature of the vdW corrections helps to enhance adsorption energies by 3–4 times compared with DFT-PBE. However, the adsorption energy trends versus the d-band center are preserved for all vdW corrections, except for the DFT-D2 framework, which deviates substantially from the studied vdW corrections. Therefore, based on our results and analyses, we can conclude that the D3, D3(BJ), and TS+SCS corrections yield the best description for the selected systems.
As the workhorse in computational material science, standard density functional theory (DFT), 1,2 which is implemented in several computational codes, 3 commonly employs approximations for the exchange-correlation (XC) energy functional like the local density approximation 2,4 (LDA) or the generalized gradient approximation (GGA). 5–9 However, it is well established that the LDA/GGA approximations cannot provide a proper description of the asymptotic decreasing behavior of the long-range van der Waals (vdW) interactions, 10–13 which has motivated a large number of theoretical studies. For example, there are several reviews discussing the main challenges, improvements and, in particular, the importance of the vdW interactions for weakly bonded systems such as adsorption phenomena on surfaces, 14,15 water properties, 16,17 two-dimensional layeredmaterials, 18,19 biomolecules, 20,21 DNA, 22,23 interfaces, 24,25 and etc. Therefore, it is a problem that affects a wide range of applications, and hence, it has attracted great interest in the last years. Thus, along the years several theoretical approaches 26–33 have been reported with the aim to improve standard DFT calculations, which can be separated into two types: (i) parameter-free vdW density functional 34 (vdW-DF) approaches, which are based on the adiabatic connection formula; 35,36 (ii) the approaches based on the atom-pairwise potential interactions, where the vdW dispersion energy vdW , is added to the DFT total energy, E DFT . correction, Eenergy tot In the first case, the vdW corrections are “plugged in” dynamically 37 in the DFT-GGA calculations. For that, the vdW-DF1 formulation has been employed. 26,34 On the other hand, its later variants, i.e., vdW-DF2 32 and optB86b-vdW, 38 include empirical parameters, which helps to improve deficiences of the vdW-DF1 formulation like large intermolecular binding distances and inaccurate binding energies. 39 In the second scheme, the DFT+vdW total energy DFT+vdW = E DFT + E vdW . At least, five vdW is written as Etot energy tot corrections based on the atom-pairwise potentials have been
proposed and widely used, namely, D2, 29 D3, 30 D3(BJ), 40 TS, 31 and TS+SCS. 33 The DFT-D2, DFT-D3 and DFT-D3(BJ) frameworks were proposed by Grimme 29,30,40 as the principal representation of the empirical approaches, where DFT-D2 29 does not take into account environment effects, which were subsequently introduced in the DFT-D3 and D3(BJ) frameworks through the addition of the dependence on coordination number from the dispersion energy contributions in nth-order terms. However, even for the three-body term, the use of higher nth-order terms has presented an overestimation of lattice parameters for weakly bound bulk systems, and thus, the standard DFT-D3 has been recommended. 30,41 On the other hand, for DFT-D3(BJ), the replacement of the damping function by the Becke–Johnson (BJ) model provided better results for molecular systems involving non-bonded distances. 28,40,42,43 In the TS and TS+SCS corrections proposed by Tkatchenko and Scheffler, 31,33 the vdW correction is determined from the ground-state electron density of the system, which allows, to some extent, to capture intrinsic hybridization (or environment) effects through the polarizability computed for a Hirshfeld volume. 44 However, the TS correction 31 does not include interactions beyond the local environment (neighboring atoms), disregarding the effects relative to the fluctuating dipole interacting with more distant fluctuating dipoles, describing the screening effects which are intrinsic for metallic systems. In this sense, the main difference between the TS and TS+SCS corrections 31,33 arises from the addition of the self-consistent screening (SCS) effects, where the dipole long-range fluctuations are taken into account to compute the polarizability. 33 Thus, the TS+SCS is a variant of the TS correction in which short- and longrange effects are taken into account. However, it is important to mention that the atomic volumes are calculated from the neutral free atoms via Hirshfeld partitioning method, 44 which has been questioned for strongly polar systems. To treat this issue, Bu˘cko has proposed a modified version of Hirshfeld partitioning, 45 while Reilly and Tkatchenko a possible enhancement on the basis of the Wannier functions for a better description of delocalized states in metals. 46,47 Most of the pairwise vdW approaches available nowadays allows to combine a low (or medium) computational cost with a very good results. However, they cannot capture some many-body effects, like the screening of Coulomb interaction between electrons from different centres in the system or the dependence of the dispersion energy on the number of atoms. 47,48 At first, those effects will not play an important role for gas phase systems, but they may be crucial for condensed matter systems. 39 Such effects can be captured by high level theories based on the random phase approximation, however, at high computational cost. 47 To make it feasible, new methods beyond pairwise additivity have been proposed, like the Axilrod–Teller–Muto 49,50 or triple-dipole interactions, which were applied in the original D3 by Grimme. 30,51,52 The two extensions of the TS method also take care of such effects, namely the densitydependent TS+SCS, which capture environmental effects by the screening of the dispersion interactions and the many-
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body dispersion (MBD). 39,47,48,51,52 Despite of the advances in this field and many of these functionals being able to describe well the behavior of an atom in a molecule and the screening effects, some aspects like the N-dependence of the systems still remain unfeasible without to invoke RPA-like theories, which usually increase the computational cost. 48,52 This becomes even dramatic since the nonadditive effects tend to increase with the system size and lower dimensionality. 33,52 Although, our understanding of the vdW interactions have substantially improved in the last years, our understanding of applicability of vdW corrected functionals to different systems is not complete, since in many cases they are applied to molecular systems. In particular, there is a lack of detailed comparative studies using different dispersion functionals, which could provide possible connections between the properties of transition metal (TM) surfaces and of molecules adsorbed thereon. A useful and simple model system for such comparisons is water adsorbed on TM surfaces. Carrasco et al. 17 have studied water monomers adsorbed on TM surfaces using nonlocal vdW-DF functionals, and noticed an improvement in the adsorption energies as a result of an increasing water-metal interaction with respect to the standard DFT-PBE. Nadler and Sanz 16 have investigated the interaction between water and the Au(111) surface using DFT-D2 and optB86b-vdW functionals, further comparing with DFT-PBE. They showed that DFT-D2 gives unreasonable results for water monomers and, in general, the slab thickness has almost no influence on the properties of molecule. Park et al., 53 employed different vdW functionals to study bulk systems and diamond structures. 53 Similarly, Rego et al. 54 have studied the bulk properties of graphite, showing a global improvement for DFT-D3(BJ). However, only recently Chiter et al. 55 have studied different metallic surfaces using DFT-D2 and the vdW-DF/optB86b corrections. In general, all those studies reported a decreasing in the lattice parameter and magnetic moment, and an increased cohesive energy compared with standard DFTPBE calculations and experiment. Reckien, Eggers, and Bredow 56 studied the adsorption of benzene on different low Miller index coinage metal (Cu, Ag, and Au) surfaces. Using different DFT-D3 functionals, also including threebody terms, they conclude that better results can be obtained by using PBE-D3, PBE-D3(BJ) and RPBE-D3, despite of them overestimate the adsorption energies compared to experimental results. On the other hand, the functional RevPBE combined either D3 or D3(BJ) could not provide reliable results to benzene adsorption, being considered not suitable by the authors. 56 Such kind of studies are important to verify the reliability of vdW corrections and select the best ones, for similar cases, and to provide insights for new studies. Despite of several related previous works, there is still room to improve our atomistic understanding of the performance of the pairwise vdW schemes, in particular for challenge systems such as the adsorption of water and ethanol on strained TM substrates by the exploration of strained Pt skinlayers supported on close-packed TM surfaces. Thus, our
study focus on the bulk, clean surfaces, and adsorbate-metal properties, where well defined TM skin-layers under strain, e.g., Cu9 /Pt9 /Cu(111), Pt9 /Cu9 /Cu(111), Au9 /Pt9 /Au(111), Pt9 /Au9 /Au(111), were selected to study the performance of different vdW corrections. For comparison, we considered also the Cu(111), Pt(111), and Au(111) surfaces. For the vdW corrections, we employed the pairwise potential schemes, as implemented in the Vienna ab initio simulation package (VASP), 41,45,57–60 namely, D2, 29 D3, 30 D3(BJ), 30 TS, 31 and TS+SCS. 33 Furthermore, standard DFT-PBE calculations will be also reported.
Theoretical Approach Computational Details
A Total Energy Calculations Our spin-polarized total energy DFT 1,2 calculations were based on the XC energy functional as proposed by Perdew– Burke–Ernzerhof (PBE). 9 To improve the description of the DFT-PBE calculations, we considered several vdW corrections based on pair-potential interactions, namely, D2, 29 D3, 30 D3(BJ), 30 TS, 31 and TS+SCS, 33 as implemented in VASP, 41,45,57–60 version 5.4.1. The vdW DFT+vdW , is obtained as the corrected DFT total energy, Etot DFT , i.e., sum of the self-consistent plain DFT total energy, Etot in our case is the DFT-PBE total energy, and the vdW energy vdW , based on pair-potential schemes, correction, Eenergy DFT+vdW DFT vdW Etot = Etot + Eenergy .
vdW is obtained from the following expression, Here Eenergy vdW Eenergy =
X X AB n=6,8
CnAB fd,n (RAB ) , RnAB
where sn is a scaling factor that depends on the selected exchange-correlation energy functional and on the vdW correction scheme. The CnAB parameter represents the averaged nth-order dispersion coefficients for each AB pairs, and hence, it plays the major role in the magnitude of the interactions. RAB is the atomic distance between the A and B atoms, while fd,n is a damping function employed to avoid near-singularities for small RAB distances, and also compensate short-range correlations commonly employed in density functionals. 47 In the DFT-D2 proposed by Grimme, 29 the C6AB parameters are empirically parameterized through the London formula in which the ionization potentials for each atom are obtained from hybrid DFT-PBE0 calculations. In contrast, the C6AB parameters for DFT-D3 are obtained from nonempirical calculations through the time dependent-density functional theory (TD-DFT) by using the Casimir–Polder expression, 30,40 as in the case of DFT-TS, discussed below. In the DFT-D2 framework, pairwise interactions for the A and B atoms are considered, 29 while the DFT-D3 scheme employs terms beyond the two-body interactions to describe the vdW in isotropic local neighborhood by the expansion of Eenergy
nth-order dispersion terms, i.e., the C8AB interactions are considered. 30 In VASP, the DFT-D3 implementation does not include the three-body terms as a default, which play a minor role in the vdW D3 energy correction for small and midsize molecules. 41,52 On the other hand, it can be significant for larger systems. 30,41 Despite of it, more careful analysis and studies about the inclusion of this term are needed, demanding many other tests which are not our focus at this time. A second extension of the DFT-D3 was made within the Becke–Johnson (BJ) model framework as an alternative for the damping function, DFT-D3(BJ). This implementation is justified by the analytical Koide’s 61 study about the dispersion forces between two atoms, in which the dispersion energy asymptotically reaches a constant for very close distances instead of zero as in the -D3 correction. 40,61 To include the environment effects on the electronic structure of the systems, in the TS and TS+SCS corrections proposed by Tkatchenko and Scheffler, 31,33 a less empirical approach based on the charge density of the system is taken into account to compute the C6AB , in contrast to the Grimme’s empirical approaches. Thus, while in DFT-D3 method the coordination number is taking into account in order to capture environment effects and then to adjust the C6AB coefficients, in DFT-TS method these effects are captured by relationship between the polarizability and Hirshfeld volumes, i.e., the C6AB parameters are defined based on the atomic polarizability and volume for the free atom reference system and the atom-in-a-molecule, 31 like a perturbation when the free atom is embedded in a molecular environment. The main difference between the TS and TS+SCS schemes comes from the inclusion of the self-consistent screening, where the dipole long-range fluctuations are accounted to compute the polarizability by using quantum harmonic oscillators on each atomic site of the system. This approach allows us to describe the non-isotropic environment typical of systems with low symmetry with relative efficiency. 33 Further details and applications of vdW corrections can be found elsewhere. 29–31,33,41,45,54,59,60,62 DFT+vdW , To obtain the vdW corrected DFT total energies, Etot the electron-ion core interactions were described using the projector augmented wave (PAW) method, 63,64 as implemented in VASP. 57,58 The valence electrons were described using the scalar-relativistic approximation, in which the spin-orbit coupling is not considered for the valence states. For all total energy calculations, the Kohn–Sham orbitals were expanded in plane-wave using a cutoff energy of 469 eV. However, for the stress tensor calculations to obtain the equilibrium volumes of the Cu, Pt, and Au bulk systems, since the convergence of the stress tensor components as a function of the number of plane waves is slow, we employed higher cutoff energies, namely, 834.1 eV, 497.4 eV and 496.7 eV, respectively. The compact TM(111) substrates were modeled using a 3×3 surface unit cell and the repeated slab geometry with six metal atomic layers and a vacuum region of 20 Å, while the water and ethanol in gas-phase were modeled using a cubic box with 20 Å edge, which yields negligible interaction among the molecule and its images. Furthermore, for
the spin-polarized free-atom calculations, we employed an 3 orthorhombic box with 20.0 × 21.8 × 21.0 Å , which helps to yield the correct occupation of the free-atom electronic states, in particular, for partially occupied p- and d-states. To describe the surface Brillouin zone (BZ), for work function calculations and Bader analysis, we applied a 4 × 4 × 1 k-point mesh, while for density of states (DOS) calculations related to the adsorbed systems, we employed higher k-point density, namely, a 8 × 8 × 1 k-point mesh, which provides an accurate DOS. For the molecules (water, ethanol) and free-atoms in gas-phase, we employed only the Γ-point due to the lack of dispersion in the electronic states. For all calculations, the total energy convergence parameter was set up to 10−6 eV, while the equilibrium structures were obtained once all atomic forces on all atoms were smaller than 0.01 eV/Å.
results. Considering all image cells, the minimum distances between molecule atoms in different unit (image) cells (lateral distance between molecules) ranged from 4.2 Å to 7.3 Å, where the small distances are obtained for Cu-based systems due to the smaller lattice parameter of bulk Cu. Thus, the lateral interactions between the molecule and its images are negligible, and cannot affect the conclusions obtained in this work. For substrates and adsorbed systems, the atoms from the slab bottom layer were kept frozen in their bulk positions, and the remaining layers and molecule were allowed to relax. As the molecules were adsorbed on one side of the substrate slab, these systems have a lack of inversion symmetry, and the charge density behaves differently on each side of substrate. Consequently, the dipole correction should be applied to compute a reliable work function.
B Atomic Structure Configurations
To access the performance of the pairwise vdW corrections for the adsorption of molecular species on strained TM substrates, we selected Pt(111) skin-layers supported on Cu(111) and Au(111), which can provide a wide range of chemical environments due to differences in the lattice constants of the bulk Cu, Pt, and Au systems, e.g., 3.61 Å, 3.92 Å, and 4.08 Å, respectively. A careful identification of such substrates is a challenge by its own, and hence, it was discussed in our previous work. 65 Thus, based on that, we selected the following seven substrates: Cu(111), Pt(111), Au(111), Cu9 /Pt9 /Cu(111), Pt9 /Cu9 /Cu(111), Au9 /Pt9 /Au(111) and Pt9 /Au9 /Au(111). As adsorbates, we selected water and ethanol due to their great importance for a wide range of studies, e.g., water splitting, 66,67 hydrogen production from ethanol steam reform, 68,69 ice-formation on solid surfaces. 70,71 From previous studies, 17,69,72–75 both water and ethanol have a preference for low-coordinated sites and preferentially bind through the anionic oxygen atom to an one-fold site (on-top), which is related to the strong O-TM interaction because of electronegativity differences. Furthermore, water molecule has an almost parallel configuration on the TM surfaces, 75 which is in good agreement with previous theoretical 17,69,76 and experimental results. 77,78 However, for ethanol adsorption, in most of the cases the C – C bond has an almost parallel configuration with respect to the surface, but it may be perpendicular if the OH group presents an angular torsion. 69,75,79 So, in the case of ethanol it is important to consider both isomers, namely trans- and gaucheethanol. 75,80 In our studies, for each substrate, a monomer of water or ethanol was adsorbed on one side of the slab in the on-top adsorption site. In the case of ethanol adsorption, three initial configurations were considered, namely, transethanol with C – C bond parallel and perpendicular to the surfaces, and one gauche-ethanol perpendicular to the surfaces. For water, one configuration parallel to the surface was considered for all DFT-PBE and DFT-vdW functionals. These configurations were considered based on previous theoretical 17,69,72,73,75,76,79,81–83 and experimental 77,80,84,85
Results and discussion
A Bulk Properties The bulk properties, namely, lattice constant, a0 , cohesive energy, Ecoh , elastic constants (C11 , C12 , C44 ), and bulk modulus, B0 (B0 = (C11 + 2C12 )/3), are summarized in Table 1 for Cu, Pt, and Au in the face-centered cubic (fcc) structure along with the experimental results. 86 The experimental results obtained at room temperature were not extrapolated to zero temperature, however, according to Haas et al., 87 zero-point energy and thermal fluctuations provide corrections to the experimental lattice constants smaller than 0.007 Å for the considered systems. Additionally, the zero-point energies computed from the Debye temperature provide values of the order of 0.03 eV/atom. 86 The zeropoint vibration can affect both absolute energy and the energy against volume curve, and it should taken into account for very accurate comparisons. 88 However, in our case, the changes in deviations between theory and experiment are of the order of 0.2 % for the lattice constants and about 1.0 % for the cohesive energies. In view of that, the comparison with the uncorrected values does not affect trends for the considered systems. As expected, DFT-PBE yields a0 larger than the experimental results 86 by 0.5 %, 1.3 %, and 1.7 % for Cu, Pt, and Au, respectively, which is consistent with previous DFT-PBE results employing different DFT implementations. 53,55,75,89 All the considered vdW corrections add an attractive contribution to the DFT-PBE total energy, and hence, a reduction in the aDFT-PBE parameter 0 for all systems is expected, which was indeed observed in our results. However, the magnitude of the reduction is dependent on the vdW correction used and the substrate chemical composition. For example, for Cu, DFT-TS yields the worst result, i.e., underestimates a0 by 1.9 %, which is consistent with previous results. 90 The addition of screening effects via the TS+SCS correction reduces the relative error to about −0.3 %, which clearly indicates the importance of the screening effects. The D2, D3, and D3(BJ) vdW corrections yield similar relative error, −1.4 %,
Table 1 Bulk properties of Cu, Pt, and Au in the face-centered cubic structure calculated with several vdW corrections. Equilibrium lattice constant, a0 in Å, cohesive energy, Ecoh in eV/atom, elastic constants, Ci j in Mbar, and bulk modulus, B0 in Mbar, where B0 = (C11 + 2C12 )/3. Experimental results are reported for a0 , Ecoh , and B0 . 86 The values in parenthesis are the deviation, ∆ in %, relative to experimental results obtained at 300 K, namely, ∆ = 100( X DFT − X Exp. )/X Exp. .
i.e., the improved versions of the Grimme vdW corrections (coordination effects, damping function, etc) do not yield better results for aCu 0 . In contrast, for Pt and Au, the D3 and D3(BJ) yield the best results, while the results obtained with TS and TS+SCS are slightly worse, see Table S1. In general, vdW corrections contribute to increase in the cohesive energy for bulk TMs, 53,55,75,91 which can be attributed to the attractive vdW character, which is also enhanced by the overestimation of the C6 coefficients obtained from free atoms. Because of metallic screening, they can be quite different from those within metallic bulk environment, as pointed previously in the case of DFTTS. 90,92 However, for DFT-TS+SCS, the accounting of the screening effects helps to reduce the vdW interactions and thus to improve Ecoh in some cases. 91 For instance, in case of Pt bulk, the Ecoh for DFT-TS+SCS is 1.4 % larger than experimental one, while for the other vdW corrections it exceeds 4 %. Despite of that, valuable improvements are observed when vdW corrections are included. For Au bulk all DFT-vdW functionals work better than DFT-PBE, and the best results for Ecoh were obtained by using DFT-D3 (−2.9 %) and D3(BJ) (−3.1 %). In this particular case, TS and TS+SCS work poorly, but still provide better results than PBE (−20.2 %) or DFT-D2 (19.2 %), namely −10.2 % and −12.6 % larger than experimental Ecoh . Our results agree reasonably well with those of recent theoretical studies, 53,55,93,94 even though the comparison with experimental results, in most cases, show large deviations. The accurate description of cohesive properties of metallic
systems including dispersion contributions remains a major challenge, in order that it requires a more detailed treatment of the polarizability due to localized ions and metallic electrons. 90 We calculated also the elastic constants and bulk moduli for Cu, Pt, and Au, Table 1, which can be used to assess the performance of the vdW corrections near the equilibrium configuration as it depends on the second derivative of the potential energy at the equilibrium volume. Our PBE results are consistent with previous theoretical results, 87,95,96 while there are larger deviations compared with the experimental data. 86 Part of the error is related to the errors in the equilibrium volume, which can affect the agreement of the elastic constant and bulk moduli with the experimental results. 89,93,96 As obtained for a0 , the DFT-D2 framework yields the worst performance among the vdW corrections, i.e., the results are worse than with PBE, while the D3(BJ) and TS performs badly for the shear modulus, i.e., C44 . Overall, from our analysis in Table S1, the best performance is obtained by the DFT-D3 and DFT-TS+SCS, which even improve the results compared with DFT-PBE for particular elastic constants.
B Clean Surface Properties The calculated electronic parameters of considered substrates are summarized in Table 2. Additionally, structural results for the interlayer relaxations (∆di j = 100(di j − d0 )/d0 , where d0 and di j are the unrelaxed and relaxed interlayer
Table 2 Electronic parameters calculated with different vdW corrections: occupied d-band center, εd in eV, and work function, Φ in eV. Results for εd are given as an average over the atoms located in the topmost surface layer (L1 ).
distances), effective coordination number (ECN), and average bond lengths (dav ) are summarized in Tables S2 and S3. In most cases, the interlayer distances between the three outermost layers, d12 and d23 (where, 1 represents the topmost layer, followed by inner layers 2 and 3) are not affected by the addition of vdW corrections. For instance, for closepacked surfaces the variation of the interlayer distance, d12 (d23 ), is less than 0.03 Å (0.06 Å), and the average d12 (d23 ) considering all functionals are 2.06 Å, 2.30 Å and 2.43 Å (2.04 Å, 2.24 Å and 2.36 Å) for Cu(111), Pt(111), Au(111), respectively. For Pt-monolayers, the variations in d12 and d23 are the same as for close-packed surfaces, except for Pt9 /Au9 /Au(111), where larger differences are seen for d12 , 0.41 Å. On the other hand, the second layer, d23 , remains well-behaved as in other cases. In the particular case of Pt9 /Cu9 /Cu(111), DFT-PBE provides d12 = 2.23 Å with no rumpling, while there is a rumpling for all the vdW corrections, which increases d12 from 2.27 Å for DFT-D2 to 2.64 Å for DFT-TS+SCS, with a strongly rumpled surface (cf. Figure 1 and Table S2). Additionally, for close-packed surfaces, the vdW corrections provide a small expansion in the interlayer distance between the topmost and the adjacent layer (∆d12 > 0, except for DFT-TS+SCS), and a compression (∆d23 < 0) in the interlayer distance between the second and third outermost layer, as can be seen in Table S2. We have also evaluated ∆di j due to the supported Ptmonolayers, namely, Pt9 /Cu9 /Cu(111) and Pt9 /Au9 /Au(111), since it is possible to compare d23 and d0 in this cases. As for close-packed surfaces, for these surfaces DFT-vdW gives a compression in the d23 distance (∆di j < 0), where larger ones were observed for DFT-TS+SCS, in most cases. The larger differences between d12 and d23 for Pt9 /Cu9 /Cu(111) reflect the strong rumpling observed for this systems by using DFT-vdW, mainly for the TS and TS+SCS corrections. For Au(111), we obtained ∆d12 = 1.47 % for DFT-PBE, which perfectly agrees with the experimental value of 1.5 % obtained by Nichols et al., 97 while for DFT-D2, we have found ∆d12 = 5.18 %, i.e., far way from the experimental value. However, using TS+SCS, we obtained ∆d12 = 1.13 %, which agrees well either, and represents a large improvement compared with TS. The DFT-D2 results are quite away from experimental results, and it is consistent with the results reported by Chiter et al. 55 , which observed similar discrepancies between DFT-D2, DFT-PBE, and different DFT-
vdW frameworks. In summary, because of their attractive character, vdW corrections yield an additional compressive strain in the substrates, which contributes to affect the structural properties of the topmost surface layers. For example, the effective coordination number decreases along with a decreasing in the weighted average bond length, dav , which leads to a shift in the center of gravity of the substrate occupied d-band states (d-band center) further away from the Fermi level. 98,99 Such behavior is observed even for DFT-PBE, mainly for monolayer substrates, which undergo either compressive or expansive strain, and is more pronounced in the second outermost layer for all systems, where the d-band system shifts down even further from the Fermi level. Based on the d-band model, 100,101 qualitatively, we should observe a decrease in the substrates reactivity, or at least a reduction of their interaction with the adsorbates. However, the attractive vdW corrections contribute to an increase in the molecule–substrate interaction. This points on their dominant contribution to the adsorbate–substrate interaction compared with the small shift in the d-band center. It is obvious that the second layer does not interact directly with possible adsorbates, giving an even smaller contribution to the molecule–substrate interaction, and the down-shift of dband, as possible result from dav (and also d23 ) compression, just reinforced this fact. The work functions for all substrates were slightly affected by vdW corrections when compared with DFT-PBE, e.g., changing less than 0.1 eV, which is an upper limit reached for Pt(111) substrate (DFT-TS). As in our previous works, 65,75,89,102 the work function for TM monolayers depends on the type of the chemical species which form the substrate and are exposed to the vacuum region. Therefore, the vdW corrections provide only a small contribution to the substrates work function, giving similar values as for DFTPBE. Thus, although they contribute to the contraction of the distance between surface atoms, they do not lead to any abrupt changes in the surface charge distribution, except when there are surface distortions.
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Figure 1 Side views of ethanol lowest energy adsorption configurations for all DFT-PBE and DFT-vdW frameworks considered, which are indicated on top of the columns. The upper three rows present the close-packed FCC(111) substrates, and the remaining rows Pt-monolayers. The respective top views are presented in the SI.
β β −TM
The analyzed geometric parameters of adsorbed ethanol and water molecules are defined in Figure 2. In Figure 1, we show the side views of the lowest energy configurations to the adsorbed ethanol systems. Top and side views of the lowest energy configurations for adsorbed water are presented in Figure S1, while top views for adsorbed ethanol are presented in Figure S2. As obtained in previous studies, 17,69,75,76,81 the water molecule binds to TM surfaces with the O atom pointing to an on-top site, and the HOH plane almost parallel to the surface. The β angles, which represent the O – H bonds tilt (β1 and β2 , respectively O – H1 and O – H2 ) relative to the surface, are smaller than 13◦ for all functionals and usually are positive, which means that the O – H bond points to the vacuum region (cf. Figure 2). However, for Au(111), Au9 /Pt9 /Au(111) and Pt9 /Cu9 /Cu(111) the O – H bond points to the surface (β < 0). Comparatively, β is larger for DFTPBE, DFT-TS and DFT-TS+SCS in most of cases, showing a more flat orientation for DFT-D2, DFT-D3 and DFT-D3(BJ) (β ± 5◦ ). Large deviations are observed for Pt9 /Cu9 /Cu(111) substrate because of its surface distortions. These results are presented in Figure S3 in the SI.
1 Lowest Energy Adsorbate Configurations
For ethanol molecule, DFT-vdW functionals, predominantly, favor a C1 – C2 bond arrangement almost parallel to the surface, α ≈ 10◦ (cf. Figure S3), where the C1 and C2 denote carbon atom bound and not bound to the O,
Figure 3 Water and ethanol molecule distance from the surface, dO−TM , in Å, which is the O distance from the nearest TM substrate atom, for different DFT-vdW functionals.
respectively, being farther from the surface (cf. Figure 2). This behavior is expected due to the contribution of the carbon chain to the interaction with the surface. For water molecule the main contribution is from the O atom. Thus, the ethanol carbon chain contributes to dO−TM closer to the substrate, as vdW interaction consequence, when compared to the water for all the vdW corrections. The exception is for Pt9 /Cu9 /Cu(111) substrate (DFT-TS+SCS), in which the strong surface rumpling contributes to an increase in the dO−TM , Figure 3. In general, ethanol and water show quite a similar behavior regarding both the substrates and DFT-vdW functionals. For example, generally, substrates with top Pt-monolayer show a decrease in the molecule-substrate distance, dO−TM , compared with close-packed substrates, as shown in Figure 3. Thus, the dO−TM distances follow the trend Cu9 /Pt9 /Cu(111) < Cu(111) < Pt9 /Au9 /Au(111) ' Pt(111) < Au9 /Pt9 /Au(111) < Au(111) < Pt9 /Cu9 /Cu(111). The Pt9 /Cu9 /Cu(111) substrate is an exception due to the surface rumpling. Moreover, dO−TM changes slightly from one vdW correction to another. We have also considered the displacement from the on-top site, ∆O , for both molecules (cf. Figure S4), where, in general, the vdW corrections indicating a high-coordination site preference. 69 For water adsorbed systems, there are only small shifts, which, mostly, vary from 0.05 Å to 0.3 Å. Exceptions were found for Au(111) and Au9 /Pt9 /Au(111) substrates (DFT-D2), and Pt9 /Cu9 /Cu(111) (DFT-TS), where ∆O = 0.57 Å, 0.49 Å and 0.54 Å, respectively. Furthermore, the TS correction shows an even stronger preference for on-top position than DFT-PBE in this case (cf. Figure S4). For ethanol, ∆O varies from 0.05 Å to 0.6 Å. The only case out of this range was for Pt9 /Cu9 /Cu(111) (DFT-TS+SCS), where ∆O = 1.04 Å. Comparatively, DFT-TS predicts ethanol adsorption in on-top site as most preferable for all considered substrates, with a stronger binding than that resulting from DFT-D3 and DFT-D3(BJ), and even from DFTTS+SCS. Calculations performed using DFT-TS+SCS, DFT-
Figure 4 Adsorption energies of water and ethanol as a function of the d-band center position of the non-adsorbed surfaces. The energy zero is at the Fermi level.
D3 and DFT-D3(BJ) give ∆O of similar magnitude (cf. Figure S4). 2 Adsorption Energies The adsorption energy calculated using DFT-vdW functionals was found to be substantially increased in comparison to DFTPBE results, Figure 4. Table 2 and Table S4 show that the changes in the d-band center are small, and, as expected, the addition of vdW interactions does not change substantially the system electronic structure. Thus, vdW corrections contribute, mainly, to an increase of the pair-potential interaction between the molecule and substrate through the addition of the dispersion energy, which consequently yields an effect on the computed adsorption energy. Namely, the adsorption energies calculated by using DFTvdW frameworks are 3 to 4 times larger than those of DFTPBE. Thus, by increasing the molecule-substrate interaction the vdW interactions make the system energetically more stable. This effect is important, for example, to understand the adsorption energies by comparing their magnitudes for water and ethanol, in which it is clear the carbon chain contributes to the increasing of the ethanol adsorption energy when compared with water for all DFT-vdW functionals. However, in general, the TS+SCS correction, which gives the smallest contribution to the dispersive energy for bulk systems, presumably as a result from dipole screening effects, provides adsorption energies which are larger than DFTPBE, but smaller than from other DFT-vdW approaches. Therefore, comparatively, the interaction between the carbon chain and the substrate for ethanol provides a lower energetic contribution through the long-range interactions given by the dipole screening effects. From Figure 4, we can see that the adsorption energies plotted as functions of d-band center position by using different functionals follow a similar tendency for both molecules, wherein: DFT-D2 > DFT-D3 > DFT-D3(BJ) > DFT-TS > DFT-TS+SCS > DFT-PBE. The adsorption energy increases as the d-band center gets closer to the Fermi level, in a reasonable agreement with the d-band model, 100
and with a similar order of functionals conserved. The adsorption energy calculated by using DFT-D2 functional exhibits much larger deviations than the other ones, and it seems to be less reliable for the transition metal surfaces analyzed. The large deviations can be ascribed to the lack of parameters which take into account environment variables, as the coordination number which was added in the later versions, 30,40 or fixed parameters like C6 and the polarizabilities. 29 We found that the adsorption of both water and ethanol molecules on the Pt9 /Cu9 /Cu(111) substrates induces a strong rumpling of the substrate surface, which originates from the combined effects of strain through the Cu and Pt lattice mismatch and the use of DFT-vdW frameworks. Therefore, as consequence, the number of low-coordinated sites is higher, which contributes to a stronger molecule-substrate interaction as indicated by the higher adsorption energy of molecules for the DFT-vdW calculations. For example, the rumpling is quite pronounced for DFT-TS+SCS, where one can observe a substantial decrease in the effective coordination number with a shift up in the d-band center, in contrast to its down-shift induced by compressive strain. In the remaining cases the rumpling was not so strong. The strong rumpling of the Pt9 /Cu9 /Cu(111) substrate may indicate limitations in the application of DFT-vdW frameworks to surface systems, i.e., once the main differences involve the empirical (DFT-D2, DFT-D3 and DFT-D3(BJ)) and semi-empirical (DFT-TS and DFT-TS+SCS) nature of the functionals, it becomes difficult to compare one to each other, mainly for different schemes. Furthermore, even after the efforts have been made to add vdW interactions beyond two-body, as given by DFT-D2 to DFT-D3 and DFT-TS to DFT-TS+SCS, more studies are needed to better understand them. 3 Work Function Change and Charge Transfer In general, the substrate work function changes upon the adsorption of molecular species due to the changes in the electrostatic potential near to the surface induced by the adsorbates, which correlates with the charge transfer among the adsorbates and substrates, and as expected, the magnitude of the changes depend on the DFT framework. Except few cases, the TM substrates reduce their work function upon the the adsorption of water or ethanol, Table 3, where the reduction is larger for ethanol due to extended size compared with water. As expected, the vdW corrections affect the work function change, however, those changes are indirectly due to the changes in the equilibrium structures as the vdW corrections cannot affect the electron density or electrostatic potential directly. The DFT-D3 and DFT-D3(BJ) functionals provided work function changes of similar magnitude and smaller than those obtained with DFT-PBE and other vdW functionals, in particular, the DFT-D2 framework. A quantitative description of the charge transfer can be obtained from the Bader charge analysis, and the effective Bader charge (cationic or anionic) can be obtained from the difference of the number of valence electrons and total Bader charge. From our results, the water and ethanol effectively lost
charge to the substrates, e.g., smaller than 0.05 e for most of the systems, and about 0.1 e for Pt(111) and Pt9 /Au9 /Au(111). The effective charges on the metal atom, QBM , nearest to O do not change much and exhibit a small charge loss (QBM > 0), typically of 0.1 e and 0.3 e for the DFT-vdW functionals. It means, the TM atom has a cationic character, while O is anionic, and thus, enhancing the Coulomb interaction between them. 75 However, a distinctly different behavior can be observed for ethanol/Pt9 /Cu9 /Cu(111) system (DFTTS+SCS), in which the metal atoms of the top layer show, in general, a small charge gain (QBM < 0). As already discussed, in this case a strong surface rumpling occurs, which substantially affects the charge distribution and the molecule-substrate interaction. A comparison of the different TM substrates shows that those which contain Cu atoms in the first layer, i.e., are exposed to the vacuum region, exhibit the highest electronegativity difference, contributing to the highest anionic magnitude for the O atom on the substrate. Consequently, there is a Coulomb contribution when the atom in the on-top site of the substrate is cationic (cf. Tables S5 and S6) for all systems. For example, the Pauling electronegativities for the Pt, Au, Cu, H, C, and O are 2.28, 2.54, 1.90, 2.20, 2.55 and 3.44, respectively. As showed for the adsorption energies data, this result helps to explain the interaction strength between molecule’s oxygen and the substrate, however, the charge distributions from the electronegativities comparison have no correlation with the adsorption energies for the different DFT-vdW functionals.
IV Discussion and Summary In this work, we performed a systematic investigation of the performance of several vdW corrections based on pairpotential interactions to the DFT-PBE framework, namely, the D2, D3, D3(BJ), TS and TS+SCS schemes. For that, we selected the adsorption of water and ethanol on challenge close-packed substrates, e.g., Pt skin-layers under different strain, namely, Cu9 /Pt9 /Cu(111), Pt9 /Cu9 /Cu(111), Au9 /Pt9 /Au(111) and Pt9 /Au9 /Au(111). Furthermore, for comparison, calculations were performed also for Cu(111), Pt(111) and Au(111). In general, the equilibrium lattice constants of Cu, Pt, and Au in the fcc structure agrees well with the experimental results within a relative error smaller than 2.2 %. For Cu, the vdW corrections does not yield improvements, however, DFT-D3, DFT-D3(BJ), DFT-TS, and DFT-TS+SCS yield smaller relative errors than DFT-PBE for Pt and Au, while DFT-D2 yield the worst results. DFT-PBE yields nearly the experimental cohesive energy for Cu, and hence, due to the attractive nature of the vdW corrections, all the DFTvdW frameworks overestimate the cohesive energy. The best performance is obtained for Au, in particular because DFTPBE underestimates the cohesive energy by about 20 %, and hence, the attractive vdW correction compensante this effect, in particular, D3 and D3(BJ), while DFT-D2 yields similar error as DFT-PBE but in opposite direction. All the vdW corrections enhance the magnitude of the elastic constants
compared with DFT-PBE, which clearly indicates a change in the shape of the potential energy near the equilibrium volume. For Cu, the relative error compared with experimental results increase substantially, which is not the case for Pt and Au, where the D3(BJ) and TS+SCS corrections contribute to improve the DFT-PBE results, however, as for a0 and Ecoh , we do not recommend the D2 and TS corrections for the elastic constants. For clean TM surfaces, we found a decreasing in the weighted average bond lengths, dav , upon the addition of the vdW corrections with the DFT-PBE framework, which can be explained by the decreasing in the bulk lattice parameter for vdW corrections. Thus, in agreement with the d-band model, 69,98,100 there is a slight down-shift of the d-band center, which may contribute to decrease in the adsorbatesubstrate binding energy. However, the overall effect is an increase, by about 3–4 times, in the molecule adsorption binding energy calculated in the DFT-vdW frameworks compared to DFT-PBE, which can be explained also by the attractive nature of the vdW correction. The pairwise interactions between the molecule and the substrate atoms affect the magnitude of the vdW correction energy, and then can indirectly contribute to the adsorption binding energy, i.e., dispersion energy contribution dominates over the d-states down shift. In some cases, the magnitude of adsorption energy reaches ≈ 1 eV which is very expressive, considering the weak character of interaction of water and ethanol adsorbed on TM substrates. The smallest adsorption energies are observed for DFT-TS+SCS functional as a result of the inclusion of long-range effects given by the dipole fluctuation, which causes a decrease in the vdW energy correction. Finally, the rumpling of the Pt9 /Cu9 /Cu(111) substrate upon the water or ethanol adsorption, observed using DFTvdW functionals, changes its geometry compared with DFTPBE, indicating possible limitations of these functionals. We can also argue that the strong decrease in the bulk lattice parameter for Cu, may contributes to the final substrate arrangement. Furthermore, it affects the adsorption energy, either by decreasing it by shifting down the d-band center, or by increasing it through an increase in the number of lowcoordinated sites. Supporting Information Available: Extra data and analyses are provided in the Supporting Information. This material is available free of charge via the Internet at http:
−1.22 −1.32 −0.67 −1.34 −0.68 −0.78 −1.16
−1.16 −1.31 −0.64 −1.36 −0.72 −0.80 −1.16
−1.19 −1.22 −0.73 −1.40 −1.06 −0.83 −1.28
−1.18 −1.39 −0.77 −1.36 −0.29 −0.84 −1.23
//pubs.acs.org/. Acknowledgement We thank the National Counsel of Technological and Scientific Development, CNPq, the Coordination for the Improvement of Higher Level Education, CAPES, the S˜ao Paulo Research Foundation, FAPESP, and the infrastructure provided to our computer cluster by the S˜ao Carlos Center of Informatics, University of S˜ao Paulo. The authors acknowledge also the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources of the SDumont supercomputer, which have contributed to the research results reported within this paper. URL: http://sdumont.lncc.br, and the Advanced Scientific Computational Laboratory, LCCA-USP.
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