Quantum Monte Carlo Studies of CO Adsorption on Transition Metal

Jun 3, 2019 - The adsorption of carbon monoxide on transition metal surfaces, especially on ... It seems that both the hybrid functionals which includ...
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Quantum Monte Carlo Studies of CO Adsorption on Transition Metal Surfaces Published as part of The Journal of Physical Chemistry virtual special issue “Hai-Lung Dai Festschrift”. Cheng-Rong Hsing,† Chun-Ming Chang,*,‡ Ching Cheng,¶ and Ching-Ming Wei*,†,§ †

Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan ¶ Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan § Institute of Physics, Academia Sinica, Nankang 11529, Taiwan

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‡

S Supporting Information *

ABSTRACT: The adsorptions of CO molecule on various fcc(111) surfaces (Rh, Ir, Pt, and Cu) have been studied by diffusion quantum Monte Carlo (DMC) calculations, and the results show that the top site is the most stable adsorption site on all the four surfaces, in agreement with experiments. In particular, the site preference including the bridge site for CO/Pt(111) is predicted, i.e., the top site is most preferred followed by the bridge site while the hollow sites are much less favorable, in accordance with the existing experimental observations of the bridge-site adsorption, yet never on the hollow sites. Compared to the DMC results, density functional theory (DFT) calculations with the generalized-gradient approximation (GGA) predict very similar adsorption energies on the top site, but they overestimate those on the bridge and hollow sites. That is, although the nonlocal exchange-correlation contribution is small for the single-coordinated top-site adsorption, it is essential and required to be properly included for a correct description of the higher coordinated bridge- and hollow-sites adsorptions. These altogether explain why the top site adsorption for CO on Rh, Pt, and Cu(111) surfaces was not predicted correctly by the previous standard local or semilocal DFT calculations.

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INTRODUCTION The adsorption of carbon monoxide on transition metal surfaces, especially on noble metals such as rhodium and platinum, is an important mechanistic step in many industrial catalytic processes and has been studied extensively both theoretically1−17 and experimentally.18−28 However, there exists a well-known discrepancy between experiments and theoretical calculations about the stable adsorption site, especially for CO/Pt(111), which is often referred to as the “CO adsorption puzzle”.1 The stable adsorption site for CO on Pt(111) surface has been studied by low-energy electron diffraction,18,19 vibration spectroscopy,20 and scanning tunneling microscopy,21 which all concluded the top site as the most preferred adsorption site. Besides this, the coexistence of top and bridge site adsorptions was also asserted18−22 while the hollow site adsorption has never been observed.18−22 On the other hand, density functional theory (DFT)29,30 calculations based on both local density approximations (LDA)31 and generalized gradient approximation (GGA)32 have wrongly predicted the fcc hollow site as the most stable adsorption geometry for CO on Pt(111) surface.1 Similarly, several DFT calculations using GGA and RPBE33 approximation functionals predict the hollow sites as the preferred CO adsorption sites for CO/Cu(111) and CO/Rh(111),2−4 in contrast to the © 2019 American Chemical Society

experimentally observed top-site adsorption at low coverage.23,25 In order to determine the reason for the discrepancy between theory and experiment, variants of Kohn−Sham density functional theory have been applied to this prototype CO/Pt(111) system, which proposed that the current approximations to DFT underestimated the CO preference for low-coordination sites1 and the conventional LDA or GGA semilocal functionals would not resolve this discrepancy. With the hybrid functionals that combined a fixed fraction of the nonlocal Hartree−Fock exchange with the semilocal functionals, the correct adsorption site (top site) and adsorption energy for CO on Cu(111) were indeed predicted.5,6 However, for the open shell transition metals, especially for Pt, the problem persisted and the hollow site was still preferred.6 The correct site order was predicted by the semilocal BLYP and the corresponding hybrid B3LYP functionals, but it came with a price of the overall reduced performance of metal properties including lattice constant and surface energy,7,8 and the adsorption energy became slightly endothermic on the coinage Received: April 22, 2019 Revised: June 2, 2019 Published: June 3, 2019 15659

DOI: 10.1021/acs.jpcc.9b03780 J. Phys. Chem. C 2019, 123, 15659−15664

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The Journal of Physical Chemistry C metal surface.7 In short summary, not all the semilocal functionals or hybrid functionals can predict a consistent adsorption site for CO on transition-metal surfaces. Furthermore, the van der Waals functionals with nonlocal correlation were also proposed to be a solution for the CO adsorption puzzle9 as the top adsorption site for CO/Rh(111) was correctly predicted. Nevertheless, the discrepancy for CO/ Pt(111) still remained unresolved.9 It seems that both the hybrid functionals which include nonlocal exchange and the van der Waals functionals which include nonlocal correlation would improve the accuracy, leading to the correct predicted adsorption site for CO on some fcc(111) surfaces. Moreover, some other methods such as the meta-GGA,10 screened-exchange hybrid functional,11 and posterior empirical extrapolation correction12 were also proposed to deal with this puzzle and improvements were shown for some systems. However, all these methods are not really ab initio (parameter-free) methods, and their accuracy depends on the parameters in the functionals. Therefore, the parameter-free random phase approximation (RPA) method was proposed for a better treatment of the correlation energy. It is at present the only ab initio method that describes adsorption and surface energies accurately at the same time and predicts the correct adsorption site for CO adsorption on various transition metal surfaces.13,14 However, the RPA calculated energy difference between the hollow and top site adsorption for CO/Pt(111) is very small (almost degenerate) while the hollow site adsorption has never been observed experimentally. Furthermore, the bridge site adsorption was not included in the RPA works, in spite of the fact that it has been observed experimentally18−22 which implies that it should be more stable than the hollow site for CO/Pt(111). Besides the RPA method, there is another alternative parameter-free method which can be used to treat the nonlocal exchange and correlation energies accurately, i.e., the quantum Monte Carlo (QMC) calculations.31,34 QMC methods have been performed previously to study the dissociation of H2 on Mg(0001)35 and the surface reaction of H2 + Cu(111).36 In this study, we have used the diffusion quantum Monte Carlo method to calculate the adsorption energies for CO on Rh, Ir, Pt and Cu(111) surfaces. Various adsorption sites, i.e., the fcc, hcp, bridge and top sites, are studied, and the top site adsorption is correctly predicted, which is consistent with experimental observation. Furthermore, for CO/Pt(111), the bridge site adsorption is more stable than both the fcc and hcp hollow sites, which is in accordance with the experimental results.

monolayer), which corresponds to single CO adsorption on a √3 × √3 lateral supercell with (1/2, 1/2, 0) shifted (2 × 2 × 1) k-point mesh in the DFT calculations. The adsorption structures were fully relaxed within DFT where the top two layers and the adsorbed molecule was allowed to relax. The DFT calculations were performed with a plane-wave basis set, as implemented in the CASTEP plane-wave code.38 The kinetic cutoff energy was 2000 eV and we used Perdew− Burke−Ernzerhof (PBE)32 for the exchange-correlation functional. We used the LDA/PBE optimized bulk lattice constants for the calculation of CO on Rh, Ir, Pt, and Cu(111) surfaces. Values predicted by PBE are closed to the experimental ones. The deviations are smaller than 0.6% for Pt, Ir, and Rh, while for Cu the deviation is close to 1.35%. The norm-conserving pseudopotentials (PP) generated by the OPIUM code39 were used for C, O, Pt, Cu, Ir, and Rh. The scalar relativistic effect was incorporated in the generation of these PPs. The pseudopotential input parameters for different elements are listed in Table 1. In comparison with the DFT adsorption Table 1. Input Parameters of Different Elements Used in the Generation of Pseudopotentiala Ve rcut lmax lloc

C

O

Pt

Cu

Ir

Rh

4 2s, 2p 1.1 d d

4 2s, 2p 1.1 d d

10 5d, 6s 2.2 d s

11 3d, 4s 2.15 d s

9 5d, 6s 2.0 d s

17 4s, 4p, 5s/4d 1.5/1.7 d s

a

Ve is the number of valence electrons, and rcut is the cut-off radius (in Bohr radius).

calculations using the projector augmented wave method, the DFT adsorption energies employing our generated PPs for the various adsorption sites differ by a constant energy shift of a few tens of millielectronvolts, except for the CO/Pt(111) whose constant energy shift is around 200 meV. However, all the relative energy orders remain the same. In QMC calculations, we used the fixed-node diffusion quantum Monte Carlo (DMC) method, as implemented in the CASINO code40 and the same pseudopotentials as in the CASTEP calculations. In DMC calculations, two approximation methods are frequently used to treat the nonlocal pseudopotentials, i.e., the locality approximation41 and the Tmove scheme.42 In the present DMC calculation, we have used the T-move scheme, in which the nonlocal potential is not fully localized. Doblhoff-Dier et al.43 have demonstrated that the Tmoves scheme would help to reduce errors in the relative energies originating from the approximation procedure of the nonlocal potential in DMC calculations. The trial wave functions were in a standard Slater−Jastrow (SJ) form, ΨSJ(R) = D↑(R↑)D↓(R↓) exp[J(R)], where D↑ and D↓ are Slater determinants of up- and down-spin single-particle orbitals, respectively. The single-particle orbitals were constructed from the DFT-PBE orbitals generated by CASTEP and the nodal surface of the trial wave function is constrained to that of the Slater determinant. The DFT-generated orbitals are represented numerically using a real-space splines grid in order to improve the system-size scaling of the QMC calculations.44 The Jastrow factor consists of isotropic electron−electron (μ), electron−ions (χ), and electron− electron−ions (f) terms45

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COMPUTATIONAL METHOD For QMC calculations of an extended system, one needs to consider a finite number of electrons in one large supercell with one single k-point. One solution to reduce the finite-size error and to obtain reasonably accurate energy using the finite supercell is to construct the many-body wave function from one-particle orbitals associated with a special single k-point in the new Brillouin zone (BZ) of this supercell.37 We have found the point (1/2, 1/2, 0) at the zone boundary of the supercell BZ to be a good choice for the special k-point in this fcc(111) surface system. To make QMC calculations feasible, the fcc(111) surface was modeled by a 2√3 × 2√3 supercell, using three atomic-layers with a vacuum region of ∼15 Å. For adsorption, there are four CO molecules adsorbed on the symmetry equivalent sites (i.e., the adsorption coverage is 1/3 15660

DOI: 10.1021/acs.jpcc.9b03780 J. Phys. Chem. C 2019, 123, 15659−15664

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The Journal of Physical Chemistry C Ne − 1

J({ri}, {rI}) =

Ne

∑ ∑

Nion Ne

μ(rij) +

i=1 j=i+1 Nion Ne − 1

+

results obtained from DFT-LDA, DFT-PBE, and DMC calculations are summarized in Table 2 and plotted in Figure

∑ ∑ χI (riI ) I=1 i=1

Ne

∑∑ ∑

Table 2. Adsorption Energy (in eV) of CO on fcc(111) Surfaces at Various Sites That Were Obtained by DMC and DFT Calculations with LDA and PBEa

fI (riI , rjI , rij)

I=1 i=1 j=i+1

where Ne and Nion are the numbers of electrons and ions, respectively, and rij and riI denote the distances between electrons i and j and between electron i and ion I respectively. The μ, χ, and f terms are power expansions containing variational parameters with spin dependence. We used a polynomial expansion of degree N = 6, 6, and 2 for the μ, χ and f terms, respectively. All the variational parameters were first optimized by minimizing the variance and then by minimizing the energy using variational quantum Monte Carlo method. In both minimization processes, 30000 configurations and four optimization cycles were used. Then, the optimized wave functions are subsequently used to generate the initial ensemble of electronic configurations for the DMC calculation through which the ensemble is propagated by the imaginarytime Schrödinger equation toward the ground state with a finite time step. The number of walkers is 1536 with a time step of 0.005 au for all of the DMC calculations. After the equilibration length of 10000 steps, the DMC data is accumulated for statistical analysis. For CO/Pt(111), as the adsorption energy differences between different adsorption sites are all larger than 200 meV, we use 60000 steps in the DMC calculations and the DMC error bar is about 65 meV. We use 90000 steps for CO/Ir(111) and CO/Rh(111) and 140000 steps for CO/Cu(111) in order to achieve a DMC error bar of 40 meV. The model periodic Coulomb interaction is used to increase the computational speed in the calculation of the energy.46−48 All of the DMC results presented in the manuscript were performed only with MPC interaction, in which the propagation of the walkers was according to the potential computed from the MPC but not the Ewald interaction. For the CO/Cu(111) system, we have used, alternatively, the Ewald (for moving the walkers) + MPC interaction to determine the effect on the adsorption energy. We found that the values were changed by a few tens of millielectonvolts, which were within the DMC error bars. For 2D systems, the long-range error was suggested to scale as O(N−5/4) where N is the system size.49 It has been studied in a previous QMC paper for the hydrogen dissociation on Mg(0001) surface to estimate the long-range error and they found the DMC energy difference between the initial and the final state is almost zero change when going from a 3 × 3 surface supercell to a 4 × 4 supercell.35 Accordingly, since we only considered the adsorption energies, it is conceivable that the overall conclusion stated in this paper should hold.

Rh

Ir

Pt

Cu

DMC PBE LDA DMC PBE LDA DMC PBE LDA DMC PBE LDA

top

bridge

fcc

hcp

−1.97 −1.93 −2.62 −2.06 −2.06 −2.66 −1.88 −1.70 −2.26 −0.65 −0.61 −1.16

−1.40 −1.79 −2.57 −1.00 −1.66 −2.43 −1.50 −1.81 −2.50 −0.19 −0.65 −1.36

−1.38 −1.82 −2.63 −0.70 −1.62 −2.42 −1.12 −1.83 −2.58 −0.25 −0.71 −1.47

−1.51 −1.88 −2.72 −0.73 −1.68 −2.53 −0.93 −1.81 −2.56 −0.25 −0.72 −1.47

a

The error bar of the DMC results is about 40 meV for Rh, Ir, and Cu, and is about 65 meV for Pt.

1. The DMC calculations51 are performed using structures optimized by the DFT-PBE with CASTEP package, while the structures in DFT calculations are optimized individually. The DFT calculations were carried out using √3 × √3 supercell and six atomic layers, and the Brillouin Zone is sampled by a (8 × 8 × 1) k-point mesh. As described above, the initial trial wave function for the QMC calculations was obtained from CASTEP calculations with norm-conserving pseudopotentials. Therefore, the accuracy (within the DFT level) of the CASTEP calculation with respect to various (1/2, 1/2, 0) shifted k-point meshes has been checked carefully. We found that, for the DFT calculations using three atomic layers, the most stable adsorption site within DFT-PBE has already been established with (2 × 2 × 1) k-point mesh (the calculated adsorption energies using different k-point mesh and atomic layers in DFT level are shown and discussed in the Supporting Information). As shown in Table 2, for the adsorption energies of CO on these fcc(111) surfaces, LDA overestimates the adsorption energies to a much larger extent than the PBE. For CO/ Cu(111) and CO/Pt(111), the hollow sites are preferred over the top sites in the DFT-PBE calculations while for CO/ Ir(111) and CO/Rh(111), the most stable adsorption site is predicted as the top site. Our results for the adsorption energies and relative stability within the DFT level are similar to those previous standard DFT calculations.2−4,17 However, experimentally, the most stable adsorption site for CO on the Cu(111), Rh(111), Ir(111), and Pt(111) surfaces are all found to be the top site. That is, among these four systems, the CO/Ir(111) is the only case that the adsorbed (top) site is predicted correctly without ambiguity at the DFT level (for both LDA and PBE) and inconsistent with experiments. For CO/Rh(111), an ambiguity exists between the LDA and PBE results whereas LDA predicts hcp adsorption while PBE prefers top site adsorption. For the rest two cases, the hollow sites are preferred over the top site, in contradiction to the experimental results. Nevertheless, it is obvious from Table 2 that the most stable adsorption sites predicted by DMC are all on the top sites for the four fcc(111) surfaces, fully in agreement with experiments.

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RESULTS AND DISCUSSION The adsorption energies of CO on various adsorption sites of fcc(111) surface are evaluated as Eads = Efcc(111) + CO − Efcc(111)_VAC_CO

where Efcc(111)+CO is the energy of the system with CO at the adsorption position and Efcc(111)_VAC_CO is the energy of the system in which CO interacts with the slab at an asymptotic distance from the surface (around 7 Å). This definition of adsorption energy provides a better error cancellation in the calculation of adsorption energy using QMC methods.50 The 15661

DOI: 10.1021/acs.jpcc.9b03780 J. Phys. Chem. C 2019, 123, 15659−15664

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The Journal of Physical Chemistry C

Figure 1. CO adsorption energy on fcc(111) surfaces.

consequence due to neglecting the nonlocal exchangecorrelation contribution. That is, these higher coordinated adsorption sites would be destabilized when the nonlocal exchange-correlation contribution is properly taken into account. This is the reason why the previous standard DFT calculations with local or semilocal exchange-correlation functionals fail to predict the correct site preference.

For CO/Pt(111), the adsorption energy of top site obtained by DMC is 1.88 eV which agrees reasonably well with the experimental values of about 1.43−1.71 eV,19,22 and lower in energy by 0.38, 0.76, and 0.95 eV than the bridge (which is the second most stable site), fcc, and hcp sites, respectively. These DMC results are in well agreement with the experimental fact that the top site is the most preferred site while the bridge site adsorption was also observed but never the hollow sites.18−22 Our DMC results have predicted the correct order of site preference that includes bridge site and shown that the hollow sites are much less stable than the top site for CO/Pt(111). When compared with the DMC results, the DFT-LDA calculations always overestimate the adsorption energy of CO at all the considered sites on all the four fcc(111) surfaces (Figure 1). The adsorption energy predicted by DFT-PBE calculations is closer to the DMC results than those predicted by DFT-LDA. However, the DFT-PBE calculations still overestimate the adsorption energy at the three-coordinated fcc and hcp sites, likewise at the two-coordinated bridge site. Most interestingly, for the single-coordinated top site, the DFT-PBE calculations predict similar adsorption energies as DMC does for all the four cases. This indicates that the exchange-correlation is already well described by the semilocal PBE functional for the top site adsorption. For the singlecoordinated adsorption, the bonding is much more localized between the molecule and top of the surface atom, and thus, the contribution from the nonlocal exchange-correlation could be neglected. For the hollow site and the bridge site adsorptions, the bonding might somehow more spread out between the molecule and the surface atoms, and the contribution from the nonlocal exchange-correlation could not be ignored for these high-coordinated sites. Although a similar argument about the effect of the nonlocal correlation within the bonding region has been proposed by Lazić et al.,9 it still fails to predict the correct adsoprtion site for CO/Pt(111) which is well-known as the most difficult system. This puzzle would only be resolved when both of the nonlocal exchange and correlation were addressed properly, as demonstrated from our DMC results. On the whole, the semilocal GGA functional fails to describe the adsorption behavior for the highcoordinated hollow and bridge sites and led to the overbinding

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CONCLUSION

In summary, we report the results of quantum Monte Carlo calculations as well as density functional calculations with both PBE and LDA exchange-correlation potentials for CO adsorptions on Rh, Ir, Pt, and Cu(111) surfaces. The top sites are the most stable adsorption sites on all these fcc(111) surfaces predicted by DMC, which are consistent with experiments. In particular, the order of site preference including the bridge site for CO/Pt(111) is correctly predicted without ambiguity by our DMC calculations as the most preferred top site, followed by the bridge site, and the much less favorable hollow sites. These results are in good agreement with the experiments. Compared to the DMC results, LDA was shown to overestimate the adsorption energies to a much larger extent at various sites. However, the adsorption energies on top sites predicted by PBE are similar to the DMC values, while the adsorption energies at the bridge and hollow sites are all overestimated. This explains why the top-site adsorption for CO on fcc(111) surfaces was not predicted correctly by the previous standard local or semilocal DFT calculations. That is, the contribution from the nonlocal exchange-correlation is small for the single-coordinated top site adsorption, while it is important and correctly including its effect in DMC will destabilize the adsorption on the hollow sites predicted by DFT. Furthermore, we have demonstrated that even though the LDA and PBE calculations predicted the correct adsorption site for CO on Ir(111), the adsorption energies at the bridge and hollow sites were still overestimated as compared to the DMC results. Thus, for the study of CO on the various fcc(111) surfaces, one needs to carefully work on the nonlocal exchange-correlation contribution for the highcorrelated sites. It would be interesting to extend the DMC study to other kinds of molecules in the future. 15662

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b03780. Detailed DFT calculation results using different k-point meshes (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*(C.-M.C.) E-mail: [email protected]. *(C.-M.W.) E-mail: [email protected]. ORCID

Ching-Ming Wei: 0000-0003-3984-4422 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Ministry of Science and Technology of Taiwan under Grant Nos. MOST 102-2112-M001-023-MY3, MOST 105-2112-M-001-007-MY3 (C.-R.H. and C.-M.W.), and MOST 106-2112-M-259-007 (C.-M.C.). Computing resources from the Academia Sinica Computing Center of Taiwan are acknowledged. We also thank the National Center for Theoretical Sciences (NCTS) for support through the Computational Material Research (CMR) focus group.

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REFERENCES

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DOI: 10.1021/acs.jpcc.9b03780 J. Phys. Chem. C 2019, 123, 15659−15664

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DOI: 10.1021/acs.jpcc.9b03780 J. Phys. Chem. C 2019, 123, 15659−15664