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Partial Oxidation of Methanol on the FeO(111) Surface Studied by Density Functional Theory Xiaoke Li, and Joachim Paier J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10557 • Publication Date (Web): 07 Jan 2019 Downloaded from http://pubs.acs.org on January 11, 2019

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The Journal of Physical Chemistry

Partial Oxidation of Methanol on the Fe3O4(111) Surface Studied by Density Functional Theory Xiaoke Li and Joachim Paier* Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany

ABSTRACT: To understand recent temperature-programmed desorption (TPD) experiments carried out for methanol adsorbed on a Fe3O4(111) single crystal surface by Batista and coworkers, we accomplished a systematic density functional theory study on the various dehydrogenation pathways of methoxy species on that surface. For a mass/charge ratio of 30, these experiments detected two desorption peaks, one centered at ca. 330 and the second one at ca. 630 K indicating that methoxide is partially oxidized to formaldehyde. Yet the origin of these two peaks has not been fully understood. Based on computed activation barriers for the H-transfer from methoxy species to the symmetrically distinct surface oxygen ions using the PBE+U approach and the HSE hybrid functional corrected for dispersion effects, we simulated the corresponding TPD peaks by numerical solution of a Polanyi-Wigner rate equation of first order. The simulated spectra using HSE suggest that the observed peaks are caused by the two inequivalent oxygen ions in the Fe3O4(111) surface. They have comparable activities in the protonation step upon adsorption of methanol but feature distinct reactivities towards the redox or H-transfer step causing significantly different activation barriers.

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1.

INTRODUCTION

The conversion of methanol on oxide surfaces to other compounds is crucial in energy-related techniques. Especially methanol, the smallest alcohol, is used in applications related to H2 production and may be directly employed in fuel cells, which can work at relatively low temperatures.1-2 Besides these technological applications, adsorbing and converting methanol is considered to be an important probe in more fundamental studies within the realm of surface science providing insight into density and nature of active sites on metal oxide surfaces.3-4 Our interest in the partial oxidation of methanol on reducible iron oxide surfaces finds its origin in catalysis science. In previous studies, the groups of Sauer and Freund elucidated atomiclevel details of the oxidative dehydrogenation (ODH) of methanol on vanadium oxide agglomerations supported on well-defined films exposing the (111) surface of the rare earth oxide ceria (CeO2).5-6 A low barrier pathway described by density functional theory (DFT) explains the observed  peak in temperature-programmed desorption (TPD) experiments.6-8 It turned out that so-called pseudo-oxygen vacancies, formed upon creation of VO2 monomers or linear (VO2)n oligomers on the CeO2(111) surface, serve as thermodynamically very favorable adsorption sites for methanol.7, 9 The latter adsorbs dissociatively in the pseudo-oxygen vacancy as a methoxide species and a proton forming a surface OH group. Subsequently, a C-H bond gets broken and the corresponding H atom is transferred to a V-O-Ce interphase bond. It is more precise to think in terms of a proton coupled electron transfer (PCET) in this case, as the proton binds to the aforementioned interphase O ion and the electron localizes in more distant Ce 4f orbitals creating surface Ce3+ ions. Note that during the ODH reaction formally an H ion is transferred. DFT structure optimizations helped in understanding the atomic-level details in the oxidation of methanol on that system, especially with respect to revealing the pseudo-O vacancy at the VO2/CeO2 phase boundary.9-11 Recently the adsorption and reactions of methanol on magnetite Fe3O4 surfaces attracted much interest. Parkinson and coworkers studied methanol adsorption on the single crystal Fe3O4(001) surface by virtue of X-ray photoelectron spectroscopy, scanning tunneling spectroscopy, as well as TPD.12-14 In TPD, recombinative desorption was observed at around 300 K, and a disproportionation reaction to methanol and formaldehyde occurred at 470 K. They concluded that defects like steps may strongly affect the surface reactivity towards methanol. Regarding the oxidation of methanol on the Fe3O4(111) surface, Freund and coworkers studied its reactivity towards methanol adsorption in the context of variously supported Pd catalysts.15 They carried out infra-red vibrational spectroscopy experiments for the clean Fe3O4(111) exposed to (deuterated) methanol. Both, weakly bound CD3OD with a CD3 stretching frequency of ACS Paragon Plus Environment

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3 2076 cm-1 desorbing below 300 K, as well as more strongly bound species (2064 to 2043 cm-1) were identified. Also with respect to the (111) surface of the same material, Batista and coworkers carried out a series of TPD experiments combined with DFT calculations.16 They detected two desorption peaks, the first one at 330 K and the second one located at 630 K. For both temperatures, the characteristic m/z = 30 and 32 signals were observed indicating that formaldehyde can be formed via at least two different pathways. The authors state that errors incurred by the employed density functional approximation, i.e. PBE+U, may be as large as several hundred meV ( tens of kJ/mol). This raises the question whether supposedly more accurate DFT approximations involving the orbital-dependent Fock exchange, i.e. hybrid functionals, outperform DFT+U applied to this complex system. Previous studies on methanol oxidation on ceria showed that the HSE hybrid combined with a correction for dispersion effects indeed predicts activation barriers in excellent agreement with observed values obtained using the Redhead equation.7, 17 The present contribution discusses novel results on the partial oxidation of methanol on Fe3O4(111) surfaces using the PBE+U approach and the HSE hybrid functional augmented by Grimme’s correction for dispersion effects. Importantly, the two symmetrically distinct oxygen ions in the surface play a crucial role. Recall that one type of these oxygen ions is bound to the terminating Fe ion (further called Oa), and the other one does not coordinate to Fe (Ob, for the nomenclature see also ref 18). Upon dissociative adsorption of methanol, which is thermodynamically favored compared to molecular adsorption, these two different oxygens may be protonated resulting in two different adsorption configurations regarding the position of the thereby formed surface OH group with respect to the methoxy moiety bound to Fe. Depending on the approach used, calculated activation barriers for proton diffusion (at a methanol coverage of 0.5 ML) are high and range between 120 and 160 kJ/mol, which hinders proton hopping at room temperature and slightly beyond. Although, thermodynamic stabilities of these two adsorption complexes are comparable, subsequent H-transfer or redox steps come with different activation barriers. Using the HSE hybrid functional, the simulated TPD spectrum for the pristine Fe3O4(111) surface shows two distinct groups of formaldehyde desorption peaks as indeed observed.16 Moreover, the calculated shift in CH (CD) stretching wavenumbers of the two distinct methoxy species, being respective precursors for the low- and high temperature pathways, agree with recent IRAS results reported by Freund and coworkers.15



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2.

COMPUTATIONAL DETAILS

2.1. Methods. PBE+U Electronic and Ionic Structure Calculations. Results discussed in this work were generated using the Vienna ab initio simulation package (VASP).19-20 The employed projector augmented wave method21-22 describes the electron-ion interaction by virtue of partial waves and projector functions supported on a radial grid within the augmentation region around the ionic cores. The interstitial region is described by a regular plane wave grid consisting of plane waves with a kinetic energy of up to 800 eV. Calculations use spin-polarization and the Perdew, Burke, and Ernzerhof (PBE)23 generalized-gradient approximation (GGA) to describe exchangecorrelation effects. In addition, PBE calculations use a Hubbard-type effective U parameter of 3.8 eV applied to the 3d orbitals of the Fe ions. This value of U has been successfully applied within previous work on Fe3O424-27 and our calculations confirm that local magnetic moments of Fe ions, the lattice parameter of the cubic Fe3O4 inverse spinel, as well as its bulk modulus are reasonably accurately described using PBE+U(3.8).8,

28

The implementation of the employed

DFT+U method follows Dudarev et al.29-30 We use PAW pseudo-potentials as released with VASP 5.2. The potential used for Fe describes 14 valence electrons with a ground state configuration of [Mg] 3p6 3d7 4s1, the potential for oxygen involves 6 valence electrons, [He] 2s2 2p4, the potential for carbon involves 4 valence electrons, [He] 2s2 2p2, and hydrogen features one valence electron. Electronic and ionic optimizations were performed using a self-consistent field (SCF) energy break criterion of 10-5 eV and a maximum force criterion of 0.02 eV/Å. The so-called Gaussian smearing method together with a broadening of 0.1 eV was applied. Since a p(21) supercell was used (see below), a (35) Monkhorst-Pack31 k mesh ensured converged total energies (see also refs 32 and 33). The so-called vacuum layer of the surface unit cell was set to ca. 10 Å. Adsorption complexes and reaction intermediates have been verified to be local minima on the potential energy surface by virtue of frequency calculations described below (all positive frequencies). The same applies to the characterization of transition structures (one imaginary frequency). HSE Electronic and Ionic Structure Calculations. We employ the HSE range-separated hybrid functional34-35 to assess PBE+U results. This functional uses 25% of orbital-dependent Fock exchange together with a screening parameter of 0.207 Å-1.35 Total energies of spin-polarized calculations are converged using a break criterion of 10-4 eV and forces are converged to better than 0.05 eV·Å-1. Ionic structure optimizations use the “PRECFOCK=normal” keyword to determine the Fourier grid involved in Fock exchange calculations. Employing a (24) -centered Monkhorst-Pack k mesh ensured converged energy differences. HSE calculations use a vacuum distance of ca. 7 Å.


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5 Harmonic Wavenumbers and Zero-Point-Vibrational Energies (ZPVE). Wavenumbers of normal modes were obtained via diagonalizing a partial, mass-weighted Hessian matrix, i.e. the matrix of second derivatives of the PBE+U total energy with respect to each of the Cartesian degrees of freedom per atom. To compute second derivatives, we employed the method of central differences to gradients obtained via the Hellmann-Feynman theorem22 using 0.015 Å as a displacement along each Cartesian component. These partial Hessian calculations involve a minimal number of atoms in the surfaces (methoxy plus four to five surface atoms) to restrict the computational workload. Transition Structure Optimizations. These calculations use the nudged-elastic band method in its climbing-image variant (CI-NEB).36 In few cases, these structures were taken as a starting point for refining optimizations using the improved dimer method.37-38 Based on our experience, we confirm conclusions of Klimeš et al. that, case specific, a combination of methods may be needed to obtain converged transition structures.39 We used three images when employing the climbingimage method. We found favorable convergence in improved dimer runs when using a tighter SCF criterion of 10-6 eV and the central differences method (FINDIFF=2) to determine the curvature along the dimer direction. A detailed description of the HSE+D calculations to determine selected transition structures is given in the Supporting Information. Dispersion Corrections. We employ Grimme’s semiempirical correction40-42 to approximately describe dispersion effects in calculations of total energies and gradients or forces (“DFT+D2”). The so-called global scaling parameter s6 is set to 0.75 in PBE(+U) and to 0.6 in HSE calculations. These are fitted parameters for the PBE and PBE0 functionals as published in refs 40 and 43, respectively. The C6 and R0 parameters obtained by Grimme et al. are used in this work and are summarized in Table 1. Dispersion effects are indicated by a “+D” throughout this work. According to previous experience (see refs 7 and 17) results on geometric structure using PBE+U are only minorly affected by dispersion effects, hence these corrections are obtained as single point calculations on top of relaxed PBE+U structures, i.e. PBE+U+D//PBE+U. Hybrid functional calculations use dispersion corrections in structure optimizations, i.e. HSE+D//HSE+D. We have chosen this approach because hybrid functionals may benefit from dispersion, while PBE+U+D appears to sometimes overestimate dispersion effects, as for instance shown in refs 44-46. In other words, whenever PBE+U+D results are discussed in the present work, they refer to PBE+U+D//PBE+U single point calculations.



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Table 1. C6 Parameters (J nm6 mol-1) and van der Waals Radii, R0 (pm), Used in This Work (As Provided by Grimme40)

C6

R0

Fe

10.80

156.2

O

0.700

134.2

C

1.750

145.2

H

0.140

100.1

2.2. Models and Reaction Pathways. We use the same strategy to create slab models of the Fe3O4(111) surface as described in ref 28. The only difference is that we employ a (21) instead of a (11) cell to allow for enough relaxation of the atoms upon dissociative adsorption and dehydrogenation of methanol. Besides terminating Fe ions, the surface consists of two symmetrically distinct oxygen ions. We label them with subscript a, when they are coordinated to the Fe ion and label them with subscript b otherwise (see Figure 1). These slab models employed throughout this work contain eight Fe3O4 formula units, i.e. they consist of 12 ionic layers with the bottommost four layers fixed in bulk positions during ionic relaxations. Spurious dipole-dipole interactions between periodic images along the z-direction (i.e., along the surface normal) are corrected following the approach suggested by Makov and Payne47 as implemented in VASP. However, these corrections are small (few tens of meV or few kJ/mol for entire cells).

Figure 1. Top view on the p(21) surface unit cell of the Fetet1 terminated Fe3O4(111) surface employed in this work. The Fe ions are light blue, the oxygen Oa is light red, and the oxygen ion Ob (not bound to Fe) is dark red. Figures in the present work are created using the VESTA program.48


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7 Dissociative adsorption as well as the dehydrogenation steps of methanol may involve different oxygen ions in the surface. Formally, in total four distinct reaction pathways exist with the restriction to pathways involving one methanol molecule (or methoxy species) per (21) surface unit cell (1/2 ML coverage). When we classify these pathways according to i) the oxygen ion, which receives the “Brønsted acidic” proton of methanol upon adsorption, and to ii) the oxygen ion, which binds the H atom stemming from the methyl group in course of the oxidative dehydrogenation, we may write the resulting four pathways as (Oa; Oa), (Oa; Ob), (Ob; Oa), and (Ob; Ob). This means that in the first pathway, two Oa ions are (in total) hydrogenated, in the second pathway Oa is protonated first and Ob receives the H atom from the dehydrogenation step (involving a twoelectron transfer, i.e. formally H- is transferred), in the third pathway, this sequence is reversed, and in the fourth pathway two Ob ions are hydrogenated. A schematic representation to illustrate this notation is displayed in Figure 2. We maintain this notation throughout this work. Whenever an acronym for a structure has a double index (as for instance in transition structures, see Figure 3), the first index indicates the proton accepting oxygen ion and the second index refers to the oxygen ion, which binds the H atom originating from the methyl group.

Figure 2. Scheme to illustrate notations for the ODH reaction pathways studied in this work.



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3.

RESULTS

3.1

Dehydrogenation on the Pristine Surface. This work discusses three adsorption

pathways for methanol on the pristine Fe3O4(111) surface, i.e. the molecular adsorption and two dissociative pathways involving protonation of Oa as well as Ob ions. The structures involving dissociative adsorption are shown in Figure 3, and the molecularly adsorbed methanol (structure M) is displayed in the Supporting Information. Selected bond distances and angles obtained using PBE+U and HSE+D are summarized in Tables 2 and 3, respectively.

Figure 3. Dissociative adsorption structures Da and Db, transition structures TSaa, TSab, TSba, and reaction products Paa and Pab on the Fe-terminated Fe3O4(111) surface. Selected bond distances (PBE+U) are given in pm. The figure displays cutouts of the p(21) supercell. Surface oxygen is light red, oxygen of the methoxy species is red, iron is blue, carbon is black, and hydrogen is light yellow. Figures were created using the VESTA program.48

Transition structures obtained using PBE+U have been characterized by frequency calculations as described in Section 2.1. Structure TSaa features one imaginary frequency with 1608 cm-1, the imaginary frequency of structure TSab is 1567 cm-1, and structure TSba is characterized with 1605 cm-1. Structure TSbb (not shown in Figure 3) is discussed in Section 4 but has not been ACS Paragon Plus Environment

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9 explicitly optimized e.g. via a CI-NEB run. It was obtained by translating the proton of the surface OaH group in structure TSab to the Ob ion and subsequent optimization of the surface ions by preserving the atomic positions of the methoxy group involved in the H-transfer (including the H receiving surface Ob ion). Computed frequencies of structure TSbb featured only one imaginary mode with 1591 cm-1. Therefore, also structure TSbb is characterized as a transition structure.

Table 2. Selected PBE+U Bond Distances (pm) and Angles for Structures Shown in Figure 3

C-H

Ma

Da

Db

TSaa

TSab

TSba

Paa

Pba

109.6b

110.3

110.4

110.8

110.3

110.2

110.3

110.3

135.4

143.7

136.9

375.6

434.1

C-Hc C-O/C=O

145.8

140.9

141.3

134.2

134.4

134.4

124.4

125.1

CH3O-Fe

211.3

180.8

182.0

188.7

186.0

188.7

198.4

193.4

 C-O-Fe

119

136

130

118

121

118

142

157

305.8

393.1

319.2

378.5

445.6

334.3/ 296.5

322.6/ 362.6

CH3O···HOsd

Molecularly adsorbed CH3OH with OH bond length of 97.4 pm (see also Supporting Information). Average bond distance. c Distance to transferred H atom. d Subscript s indicates a surface O ion.

a

b

Table 3. Selected HSE+D Bond Distances (pm) and Angles for Structures Shown in Figure 3

C-H

Ma

Da

Db

TSba

Pba

109.0b

109.8

109.8

109.7

109.4

135.6

323.4

C-Hc C-O/C=O

144.1

139.7

140.1

133.8

125.0

CH3O-Fe

207.5

178.3

179.7

186.3

190.3

 C-O-Fe

118

136

130

118

145

300.7

385.7

440.9

411.9/ 274.0

CH3O···HOsd

Molecularly adsorbed CH3OH with OH bond length of 96.4 pm. Average bond distance. c Distance to transferred H atom. d Subscript s indicates a surface O ion.

a

b



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10 As expected, the C-O bond distance shortens significantly comparing the adsorbed methanol (structures M, Da, and Db) with transition as well as corresponding product structures, i.e. formaldehyde bound to the terminating Fe ion (structure Pba). This is due to the conversion of a C-O single bond into a double bond during the ODH reaction. Regarding aspects related to the performances of the employed DFT approaches, it is readily seen that bond distances obtained with the PBE(+U) approach are overall slightly larger than the ones obtained with the HSE hybrid functional (using the as defined Fock exchange mixing ratio of 25% and a screening parameter of 0.207 Å-1). Hence, HSE structure parameters usually agree better with observed values than PBE results. This is known and has been shown previously in publications related to the description of molecules35 as well as solids.34, 49

3.2

Proton Diffusion. Table 4 shows activation barriers obtained using PBE+U+D and

HSE+D for the interconversion of structure Da into Db as well as for the backward reaction. Similar to findings discussed by Dohnálek and coworkers for TiO250 and Besenbacher and coworkers discussing the adsorption of water on FeO51 surfaces, proton diffusion at lower coverages of protic agents like water or in the present case methanol, involves relatively high activation barriers. PBE+U+D predicts the barrier for conversion of structure Da into Db to be as large as 125 kJ/mol. The hybrid functional HSE+D predicts—as expected—a higher barrier of 156 kJ/mol. Therefore, proton mobility is estimated to be very low for room temperature and temperatures slightly beyond. This finding is relevant for the discussion in Section 4. Structural details on the transition structure involved in the Da  Db proton transfer are summarized in the Supporting Information.

Table 4. PBE+U+D and HSE+D Activation Barriers in kJ/mol (Zero-Point Vibrational Energy (ZPVE) Corrected) for Forward and Backward Diffusion of the Proton in Structures Da and Db

∆E0≠ (Da→Db)

∆E0≠ (Db→Da)

PBE+U+D

125.1

119.6

HSE+D

156.4

143.5


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11 Note that formation of structure Da is expected to be more likely upon adsorption of methanol. This is because of the three-fold symmetry at the Fe ion (see Figure 1). Nonetheless formation of structure Db is not impossible, however less likely given the 3:1 ratio of Oa and Ob ions and the geometric barrier induced by the larger distance between Fe and Ob (PBE+U: 356.3 pm; HSE+D: 347.1 pm) compared with the distance between Fe and Oa (PBE+U: 186.4 pm; HSE+D: 183.6 pm).

3.3

Dehydrogenation on the Defective Surface. Reactivity Descriptors. Before presenting

results on the dehydrogenation of methoxy on Fe3O4(111), it is educating to look at O-vacancy formation (Ed(1/2O2)) as well as hydrogenation (Eh(1/2H2)) energies. These quantities were shown to perform favorably when it comes to assessment of reactivities of solid oxide catalysts involved in Mars and van Krevelen-type of mechanisms.52-53 The present calculations use half of the total energy of an O2 or H2 molecule as a reference energy. Table 5 summarizes the (mono-) vacancy formation energies for Oa and Ob ions. In addition, hydrogenation energies for both types of oxygen ions are also presented, because they relate to the barrier of the (supposedly) ratedetermining redox step, i.e. the H transfer in the ODH reaction. We compare PBE+U and HSE values and additional contributions stemming from the dispersion correction are given in parenthesis. As shown in Table 5, oxygen vacancy formation energies are identical for Oa and Ob ions when relaxation effects are omitted. In this case Ed(1/2O2) is 3.98 eV using the PBE+U approach. Without surprise, the relaxation contribution to the defect formation energy is larger for the Ob ion, which is not bound to the terminating Fe ion (0.84 eV compared to 0.45 eV for Oa). Thus, creating Ob vacancies is thermodynamically more facile. Corresponding (relaxed) HSE results are 0.2 eV larger than PBE+U formation energies. This difference between PBE+U and HSE vacancy formation energies was found to be more pronounced for other reducible oxides like CeO2.54-55 While with respect to oxygen vacancy formation, PBE+U and HSE approaches give qualitatively the same picture, the trend in hydrogenation energies is different. PBE+U results are de facto identical for Oa and Ob ions; hence these results suggest similar reactivities for these oxygen ions. In contrast, the HSE hybrid functional predicts a more exothermic hydrogenation for Ob, which is thus expected to perform more actively in ODH reactions (lower barrier). The hydrogenation energy of the Oa ion is 0.14 eV less exothermic. Adding corrections for dispersion effects does not change these results qualitatively.



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12 Table 5. Oxygen Defect Formation and Hydrogenation Energies in eV. The Additional Contribution to Correct for Dispersion Effects is Given in Parenthesis

Ed(1/2 O2)

a

Eh(1/2 H2)

PBE+U

HSE

PBE+U

HSE

Oa

3.53a (0.14)

3.72 (0.13)

-0.73 (-0.11)

-0.65 (-0.06)

Ob

3.14a (0.11)

3.31 (0.12)

-0.69 (-0.14)

-0.79 (-0.11)

Value without relaxation amounts to 3.98 eV.

Figure 4. Adsorption structure (DV), transition structure (TSV), and product (PV) for the dehydrogenation of methanol in the Ob vacancy. Note that all displayed surface oxygen ions are of Oa-type. Color code as in Figure 3.

Adsorption and Dehydrogenation in the Ob Vacancy. Figure 4 shows relevant structures involved in the partial oxidation of methanol in the Ob vacancy of the Fe3O4(111) surface. Note that all surface oxygen ions surrounding the vacancy are of Oa-type. We chose the Ob defect to be a representative point defect, because it is thermodynamically more stable and hence easier to create than the Oa vacancy. These structures refer to a reduced, O-defective surface with a


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13 vacancy concentration of 1/8 ML (or 12.5%) with respect to the oxygen layer below the terminating Fe layer.56 Table 6 reports selected bond distances and angles obtained with the PBE+U and HSE+D approaches. Note that transition structure TSV has been optimized using the improved dimer method and the PBE+U approach (see Section 2.1). HSE+D calculations on TSV are described in detail in the Supporting Information and discussed in Sections 3.5 and 4.1.

Table 6. Selected Bond Distances (in pm) and Angles Obtained using PBE+U and HSE+D

DV

TSV

PV

PBE+U

HSE+D

PBE+U

PBE+U

HSE+D

C-Ha

109.9

109.4

109.6

109.2

108.5

C-Hb

-

-

167.0

313.4

304.7

O-H

97.6

96.6

97.6/109.7

97.7a

96.7

42

42

42/40

41a

42a

143.9

142.0

139.2

131.6

132.7

 OHc C-O

Average bond distance/angle. Distance to transferred H atom. c Tilting wrt surface normal. a b

3.4

Vibrational Characterization. Table 7 shows computed stretching wavenumbers

obtained using PBE+U of methanol (CH3OH as well as CD3OD) adsorbed molecularly (structure M) and dissociatively (structures Da and Db) on the Fe3O4(111) surface. In addition, methoxide adsorbed at the defect site of a missing Ob ion (structure DV, see Figure 4) was also calculated. Table 7. Harmonic, Unscaled PBE+U Wavenumbers (in cm-1) of Methanol Adsorbed on the Fe3O4(111) Surface

a

M

Da

Db

DV

CH3OH S(OH)

3725

3643

3754

3703

S(CH3

2989

2940

2918

2956

S(CO)

970

1098

1075

1008

CD3OD S(OD)

2703

2641

2723

2684

S(CD3)a

2132

2094

2079

2107

S(CO)

773

867

865

877

)a

Refers to the in-phase (symmetric) stretching mode. ACS Paragon Plus Environment


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3.5

Thermodynamic and Kinetic Properties. Table 8 summarizes adsorption energies,

activation barriers, reaction as well as desorption energies involving relevant structures introduced in previous sections obtained with PBE+U+D and HSE+D approaches. Note that these values include zero-point vibrational energies (ZPVEs). Transition structure TSba computed employing HSE+D has been optimized using the CINEB approach, while structures TSaa, TSab, and TSV are optimized using the HSE+D functional starting from rescaled PBE+U transition structures as described in the Supporting Information. The HSE+D activation barrier involving transition structure TSbb has been estimated by adding the average of the differences between PBE+U+D and HSE+D barriers of structures TSba and TSV to the respective PBE+U+D barrier. Hence, we approximate a correction for the effect on PBE+U+D barriers using HSE+D. This correction for the supposedly underestimated PBE+U+D barriers (see for instance ref 57 for benchmark calculations on molecular reactions) has been computed as 33 kJ/mol. This approach incurs uncertainties, which we estimate to 15 kJ/mol. Note that an equally large HSE correction was determined for activation barriers in the methanol oxidation at VO2/CeO2(111).7

Table 8. Adsorption Energy, Intrinsic Activation Barrier, Reaction Energy, and Desorption Energy (in kJ/mol) Corrected for Zero-Point Vibrational Effects. Calculated Pre-exponential Factors at Tdes (in 1013 s-1) and Peak Temperatures (Tdes in K) are Presented for all Pathways

PBE+U+D A

E0ads

E0

E0r

Tdes

HSE+D A

Tdes

M

-90.8

-90.9

Da

-123.4

-128.0

Db

-117.9

-133.2

DV

-265.0

-262.7

TSaa

1.6

480

127.9

2.7

650

180  10

TSab

54

310

91.8

157

430

132  10

TSba

3.2

400

111.0

7.4

570

162a

TSbb

24

290

83.5

100

390

116  15

TSV

13

650

187.6

15

700

203  10

Paa

23.1

Pbb

48.4

Pba/ab

13.6 ACS Paragon Plus Environment

59.7

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15

E0des

PV

88.1

Hab/ba

64.6

HV

110.5

110.8

a

Transition structure generated by a CI-NEB run using HSE+D (see text and SI).

It is noteworthy that besides discrepancies in PBE+U+D and HSE+D activation barriers, also slight differences in adsorption energies for structures Da and Db were obtained. This refers to the qualitative different picture obtained with these two approaches. While PBE+U+D predicts Da to be more strongly bound to the surface, HSE reverses the picture and predicts structure Db to be the slightly stronger bound species. Admittedly, these differences in adsorption energies of Da and Db are small and amount to ca. 5 kJ/mol only. It would be interesting to assess these values either with functionals on 5th rung of the Jacob’s ladder, like the random phase approximation (see, for instance, ref 8), or with post-HF wavefunction-based methods using embedding techniques or cluster models (see, e.g., refs 58 and 59). To calculate desorption temperatures and pre-exponential factors, we employed the PolanyiWigner equation of first order similarly to the work published in ref 7. The required ratio of the vibrational partition functions of respective transition structures and adsorption complexes used harmonic wavenumbers obtained with the PBE+U approach (see Section 2.1). Pre-factors are computed self-consistently by evaluating the desorption temperature, i.e. integrating the rate equation and calculating the temperature-dependent partition functions a few times. Integration of the rate equation used a heating rate of 2 K·s-1 as employed in experiment (see ref 16).



Page 16 of 34

16

4.

DISCUSSIONS

4.1

Simulation of TPD Experiments.

Figure 5. PBE+U+D (black) and HSE+D (blue) energy profiles (ZPVE-corrected, in kJ/mol) for the methanol oxidation on the pristine (a) and Ob-defective (b) Fe3O4(111) surfaces. The HSE+D pathway involving transition structure TSba in (a) corresponds to the desorption peak at ca. 570 K shown in Figure 6. Energy levels regarding “surface plus gas-phase molecule” are depicted with a “+” at the abscissa. Notation of structures as in Figure 3 (see also Table 8 and Supporting Information for profiles of remaining pathways).

According to Table 8, Figures 5a and 5b show reaction profiles obtained with PBE+U+D and HSE+D approaches. Figure 5a shows the dissociative adsorption of methanol on the clean surface via structure Db, i.e. protonation of an Ob ion not coordinated to the terminating Fe ion (see Figure 1). With respect to the H-transfer or redox step, an H atom of the methyl group is transferred to an Oa ion via transition structure TSba. Eventually, forward relaxation yields formaldehyde sitting on the Fe ion (structure Pba), which may desorb (structure Hba, see Supporting Information). As


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17 clearly shown, the HSE+D activation barrier and reaction energy are 51 and 46 kJ/mol higher than respective PBE+U+D results. Figure 5b shows the analogous reaction in the Ob point defect (Ob vacancy). In this case, the activation barrier as well as the reaction energy are substantially larger compared to the reaction in the pristine surface. For the ODH in the vacancy, the difference in HSE+D and PBE+U+D results is smaller (ca. 15-20 kJ/mol) compared with results for the ODH on the pristine surface (ca. 45-50 kJ/mol).

Figure 6. Upper panel: Experimental TPD spectrum (red dots refer to m/z=30 as shown in Figure 2 of ref 16) along with the simulated CH2O desorption peaks via structures TSbb, TSab, TSba, TSaa, and TSV using PBE+U+D activation barriers. Lower panel: Simulated TPD peaks based on HSE+D activation barriers.

To directly compare DFT results with observation, Figure 6 shows simulated TPD peaks obtained in the same way as in the work on the ODH of methanol on VO2/CeO2.7,

11

Regarding the

PBE+U+D results for the ODH on the pristine Fe3O4(111) surface (upper panel of Figure 6), the second observed peak centered at ca. 630 K could only be simulated by considering the reaction in the vacancy. In order to check this assignment, we compare our computed CD stretching wavenumbers (see Table 7) with recently published infra-red data.15 This reference reports IR ACS Paragon Plus Environment


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18 wavenumbers of adsorbed species for a series of increasing temperatures starting from 190 K up to 600 K. Comparing the “low temperature wavenumber” with the one obtained for higher temperatures (see Figure 12 in ref 15), one realizes that the observed band at 2076 cm-1 recorded at 190 K vanishes upon increasing the temperature and a red-shifted band at 2064 cm-1 appears. This is a red shift of 12 cm-1. However, looking at Table 7 of the present work, the CD stretching wavenumber of DV is blue-shifted by 13 cm-1 with respect to Da and with respect to Db, it is blueshifted by even 28 cm-1. Thus, methoxide in the vacancy must be ruled out. In contrast to PBE+U+D results, simulated TPD peaks based on HSE+D activation barriers yield a different picture (see lower panel of Figure 6). It is readily seen that—with respect to the ODH on the clean surface—two groups of desorption peaks occur. The first group occurs at a desorption temperature centered at around 400 K and the second group is centered at around 600 K. Based on that, we assign the observed low-temperature (190 K) IR band at 2076 cm-1 to the CD stretching wavenumber of structure Da. The reason for this assignment is that according to our calculations, the low barrier pathway converting methoxy to formaldehyde occurs via transition structure TSab (see Figures 2 and 3). Thus, in course of the reaction almost all Da will be consumed. Therefore, at temperatures higher than 300 K, the band at 2076 cm-1 is expected to disappear and the band at 2064 cm-1 remains. The high activation barrier for proton diffusion at this methanol coverage (0.5 ML), which is estimated to fall into the interval ranging from 125 (PBE+U+D) to 156 kJ/mol (HSE+D) as discussed in Section 3.2, hinders interconversion of adsorption structures Da and Db. Overall, this leads to the above mentioned red-shift in IRAS of 12 cm-1. According to our computed wavenumbers a comparable red-shift is found when comparing S(CD3) of structure Da with the corresponding frequency of structure Db (15 cm-1). Reference 15 reports that at higher temperatures also the band at 2064 cm-1 vanishes. We interpret this vanishing of the band as the conversion of methoxy to formaldehyde. It is consistent with our analysis that the ODH pathway via structure TSba features a barrier of 162 kJ/mol (HSE+D) associated with a higher desorption temperature of 570 K. According to the computed proton diffusion barriers as well as to the observed IR results, a reaction pathway via TSaa is expected to be minority channel, since essentially all Da is supposed to be oxidized already at lower temperatures (via the TSab route). Similarly to studies devoted to the adsorption of water on Fe3O4(111),32 an observed “quite red” band at 2043 cm-1 persists up to 510 K. This band may be assigned to defects (see also Figures 3 and 4 in ref 32). The two experimental data sets underlying our discussion origin from different surface preparations. While Li et al.16 report on single crystal results, Bäumer et al.15 accomplished IRAS experiments employing a Fe3O4 film grown on Pt(111). Importantly, both experiments observe the above discussed bimodal desorption behavior. However, Bäumer at el. observe the second IR ACS Paragon Plus Environment

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19 band (2064 cm-1) to disappear already at 510 K. In context with theory, this means that the dehydrogenation pathway involving structure TSba sets in at that very temperature. Hence, it seems that in the experiments discussed in ref 15, the second desorption peak is expected to occur at a somewhat lower temperature than the one observed in ref 16. We reiterate that different preparation techniques and conditions may matter (see discussion in ref 56). A comment on isotope effects using CD3OD instead of CH3OH is required. Using deuterium will essentially affect ZPVE corrections, overall leading to increased activation barriers. We estimated these effects by re-computing desorption spectra using pre-exponential factors and ZPVE corrections based on deuterated structures (i.e., respective wavenumbers). This shifts the “low-T desorption peak” involving structure TSab by ca. 50 K and the “high-T peak” involving TSba by 20 K. Therefore, HSE+D results for the low temperature desorption do not agree well with observation upon inclusion of isotope effects. However, for the high temperature desorption (involving structure TSba) agreement is almost perfect (see lower panel in Figure 6). Conversely, the isotope shift in PBE+U+D results leads to better agreement with observation for the low temperature desorption peak (involving structure TSab, upper panel Figure 6). This reveals shortcomings in both approaches, PBE+U as well as HSE, when applied to the Fe3O4(111) surface.

4.2

Electronic Structure. When dealing with reactions involving electron transfer, it is always

justified to ask for electron localization effects. Thus, where do the transferred electrons in the ODH of methanol on Fe3O4(111) go? Certainly, electron localization effects are a material specific property. For instance, in case of the ODH of methoxy on ceria, DFT predicts the electrons to be localized in Ce 4f orbitals in the surface, thus Ce3+ ions (known as small polarons60) are formed upon surface reduction.6-7 The Fe3O4(111) magnetite surface, which derives from the cubic (inverse) spinel structure, shows a different behavior. Figures 7a and 7b display Fe 3d orbital projections of HSE electronic densities of states (pDOS) for the various Fe ions located in different layers of the slab model used. Figure 7a shows results on the pristine surface and Figure 7b shows results on the hydrogenated, hence reduced surface after the ODH of methoxy to formaldehyde. As mentioned earlier, this step involves a transfer of—in total—two electrons. We recall that the Fe3O4(111) surface inherits the antiferromagnetic order between tetrahedrally and octahedrally coordinated (high-spin) Fe ions from its parent bulk structure.13, 6162

Hence, an analysis in terms of the  or up-spin and  or down-spin pDOS is mandatory.

However, a detailed analysis of the surface electronic structure, particularly with respect to different crystal field splitting and irreducible representations of orbitals is beyond the scope of the ACS Paragon Plus Environment


Page 20 of 34

20 present work. The point we want to make is, according to the HSE pDOS, that surface Fe ions will not be reduced upon electron transfer. Instead, predominantly (+2, +3) mixed-valent Feoct ions in subsurface positions will be reduced. The terminating threefold coordinated Fe ion of the (111) surface (see ref 56) is in the bulk phase fourfold coordinated and is shown in light blue in the inset of Figure 7a. The corresponding up- as well as down-spin projections of Fe 3d orbitals are shown in the same color. The surface Fe ion appears as a prominent light blue up-spin peak located at the Fermi level. The orange pDOS stems from deeper lying Fe ions located in the so-called mix-trigonal, i.e. Fetet plus Feoct layer63 (see orange Fe ions shown in the inset of Figure 7a and in the Supporting Information). Regarding the up-spin pDOS, HSE predicts a sizeable energy gap of ca. 1.5-2.0 eV. In this case the unoccupied 3d states (orange line) stem from subsurface layers. In contrast, the down-spin channel is predicted to be nearly “gapless”. This is usually referred to as the half-metallic property of magnetite.64 Hence, based on hand waving, the surface Fe ion features a more ionic character compared to the (predominantly) octahedrally coordinated, Fe2+ and Fe3+ ions located in subsurface layers. These Fe ions are shown in dark blue (subsurface Feoct or Kagomé layer63), orange (mix-trigonal Fe), and red (Feoct in 2nd Kagomé layer).65 Note that the energy gap within the up-spin 3d orbitals of the surface Fe ion is predicted to be ca. 4 eV. Displayed in Figure 7b, the pDOS analysis of the product (structure Pab, Figure 3), i.e. formaldehyde adsorbed on the surface Fe ion, shows that the transferred electrons predominantly occupy 3d orbitals of the subsurface Feoct layer (-pDOS, dark blue peak) but also orbitals of deeper lying Fe ions (orange peak). Note that the pDOS shown in red relating to Feoct ions of the 2nd Kagomé layer remains largely unmodified after reduction. The slight splitting of the light blue up-spin peak at the Fermi energy relating to the surface Fe ion is caused by the oxygen of formaldehyde bound to the Fe ion. These findings are distinct compared to redox reactions on CeO2(111) and will affect the reactivity of the Fe3O4(111) surface in reduction-oxidation reactions.


Page 21 of 34 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


21

Figure 7. Layer projected densities of Fe 3d orbitals (pDOS,  or up and  or down spin) obtained with HSE+D for (a) the clean Fe3O4(111) surface and (b) the formaldehyde (structure Pba) on the surface. The color code indicating the depth of the Fe layer(s) is explained by the inset in the upper panel. The surface Fe ion as well as the corresponding pDOS are shown in light blue. The vertical dashed line indicates the Fermi energy.

5.

CONCLUSIONS

The simulated TPD spectrum for the oxidative dehydrogenation of methoxy species to formaldehyde on the Fe3O4(111) surface based on HSE+D activation barriers is consistent with observed results obtained by Batista and coworkers16 featuring two desorption peaks centered at ca. 330 and 630 K. We attribute the origin of these peaks to pathways related to transition structure TSab (see Figure 3) featuring an activation barrier of ca. 132 kJ/mol and structure TSba with a barrier of 162 kJ/mol. Both transition structures evolve from dissociatively adsorbed methanol, which is thermodynamically more favorable compared to molecular adsorption. Formation of the low-barrier transition structure requires as a first step protonation of a so-called surface Oa ion (bound to the terminating Fe ion) and a subsequent H-transfer or redox step to a surface Ob ion (not bound to the Fe ion). In the high-barrier pathway, this sequence is reversed and consequently a surface Oa ion receives the H atom from the methyl group. We emphasize that the activation barrier depends on the nature of the O ion (Oa or Ob), which receives the H atom in the redox or dehydrogenation step. At lower methanol coverages, high activation barriers computed for proton ACS Paragon Plus Environment


Page 22 of 34

22 diffusion (ca. 125-156 kJ/mol) suggest that H mobility is low at room temperature. This is corroborated by an independent set of IRAS experiments of Freund and coworkers15 via comparison of computed CD3 stretching wavenumbers of the two distinct “precursor methoxy” species Da and Db with observed values. Distinct reactivities of the Oa and Ob oxygen ions in Marsvan Krevelen-type of reactions are also reflected in values for reactivity descriptors like the oxygen defect formation and the hydrogenation energies using the HSE hybrid functional. In contrast, descriptors and activation barriers obtained using the PBE+U approach cannot be interpreted as consistently as HSE results in context of the observation.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: xxx/acs.jpcc.xxxxxx Additional structures not shown in main text, Transition structure optimizations using HSE+D, Transition structure involved in proton diffusion, Reaction profiles for the methanol oxidation, Projected DOS including total DOS, Total energies and zeropoint vibrational energy contributions, Coordinates of structures obtained using PBE+U, Coordinates of structures obtained using HSE+D.

AUTHOR INFORMATION Corresponding Author *Phone +(49)-30-2093-7139; e-mail [email protected]. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This

work

has

been

supported

by

the

Deutsche

Forschungsgemeinschaft

within

Sonderforschungsbereich SFB 1109 (“Understanding of Metal Oxide/Water Systems at the Molecular Scale: Structural Evolution, Interfaces, and Dissolution”) and by generous grants for computing time at the high-performance computer center HLRN (North-German Supercomputing Alliance in Berlin and Hannover). We thank the reviewers for their useful comments, which helped to improve the manuscript.


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Figure 01 253x99mm (300 x 300 DPI)



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Figure 03 190x230mm (300 x 300 DPI)



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Figure 05 167x246mm (300 x 300 DPI)



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135x163mm (300 x 300 DPI)



TOC Graphic 82x43mm (300 x 300 DPI)


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Partial Oxidation of Methanol on the Fe3O4(111 ... - ACS Publications

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