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C: Surfaces, Interfaces, Porous Materials, and Catalysis
Multicenter Bonding Effects in Oxygen Vacancy in the Bulk and on the Surface of MgO Ivan A. Popov, Elisa Jimenez-Izal, Anastassia N. Alexandrova, and Alexander I. Boldyrev J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03118 • Publication Date (Web): 11 May 2018 Downloaded from http://pubs.acs.org on May 16, 2018
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The Journal of Physical Chemistry
Multicenter Bonding Effects in Oxygen Vacancy in the Bulk and on the Surface of MgO Ivan A. Popov,a,† Elisa Jimenez-Izal,b,c,† Anastassia N. Alexandrova,b,d,* Alexander I. Boldyreva,* a
Department of Chemistry and Biochemistry, Utah State University, 0300 Old Main
Hill, Logan, Utah, 84322-0300, United States b
Department of Chemistry and Biochemistry, University of California, Los Angeles,
607 Charles E. Young Drive, Los Angeles, California 90095-1569, United States c
Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), and Donostia
International Physics Center (DIPC), P. K. 1072, 20080 Donostia, Euskadi, Spain d
California NanoSystems Institute, Los Angeles, California, 90095, United States
†
These authors contributed equally.
*(A.N.A.)
[email protected]; (A.I.B.)
[email protected] 1
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Abstract We have studied the electronic structure of F-centers in the bulk and on the (100) of the MgO crystal. Chemical bonding analysis was performed using the Natural Bond Orbital (NBO) analysis with periodic boundary conditions and the Solid State Adaptive Natural Density Partitioning (SSAdNDP) method. The bonding in the pristine MgO was found to be very ionic, i.e. there are four lone pairs (s-, px-, py- and pz-type) on every oxygen atom with the occupation numbers (ONs) in the range of 1.76−1.86 |e|. Within the O vacancy (Ov) located in the bulk of MgO we found a pair of electrons in the place of the missing oxygen atom that is revealed by SSAdNDP as a six-center twoelectron (6c−2e) σ bond delocalized over six Mg atoms with ON=1.87 |e|. In the other defected MgO system featuring the Ov on the (100) surface we also found a pair of electrons in the place of the missing oxygen atom that is revealed as a 5c−2e σ bond with ON=1.84 |e|. Inclusion of the four closest Mg atoms of the second layer increases the ON value of this bond to 1.91 |e|. We believe that the SSAdNDP method has a great potential for the analysis of chemical bonding of surface atoms, bulk and surface defects, ad-atoms as well as at interfaces.
Keywords: Magnesium Oxide; Oxygen Vacancy; Multicenter Bonding; SSAdNDP
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Introduction Magnesium oxide is known to be an important catalyst,1−10 and also supporting surface for catalytic nanoparticle and clusters,11−17 for many reactions. Most of the chemistry at the surface of metal oxides is due to the presence of highly reactive defect sites.18 These sites can be morphological defects such as kinks, steps, terraces, and edges, or they can be anionic or cationic vacancies. Such vacancies are classified as Fcenters, when an oxygen atom is missing, or V-centers, when a magnesium atom is removed.19 While both F and V centers are naturally present on the surface and in the bulk of MgO crystal, the former are prevalent. In the case of surface-supported nanoparticle catalysts, F-centers play a major role as nucleophilic binding sites for the particles. The excess electrons present in the Ov site can be transferred to the particle and then participate in the activation of the bound substrate molecules. Hence, the importance of the Ov sites in catalysis can hardly be underestimated. The concentration of vacancies can be increased by γ-ray or neutron irradiation.19−21 F-centers also easily heal and reform in reaction conditions in catalysis. The theoretical studies of the electronic structure and chemical reactivity of F-centers are plentiful (see References,22−26 just to name a few). Yet, the electronic structure of vacancies is not completely understood, in the sense of knowing the precise preferred location of electrons left behind upon the formation of an Ov, as well as how this picture changes from one oxide to another. It is worthy to mention that F-centers on different oxides have markedly different reactivities, indicating strong alterations of their electronic structures. In this work, we undertook the electronic structure analysis for F centers in magnesia, in the bulk, and on the (100) surface, which is the most stable27 and most often used surface in catalysis. MgO is perhaps the best understood oxide in catalysis, and its modeling poses the fewest problems, such as poor representation of electron localization in density functional theory (DFT) (e.g. in TiO228,29), amorphous structure (e.g. in alumina and silica), or relativistic and multireference effects (e.g. in CeO2). Hence, the studied materials serve as a convenient show-case for the method, which we use to analyze electronic structure and chemical bonding of important defects in solids and on surfaces. The method can be applied to other pristine and defected materials, 3
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with a potential link to their reactivity. In particular, we believe that the analysis of chemical bonding in terms of localized/delocalized bonds may help better understand the correlation between catalytic activity and the presence of delocalized bonding in the materials exhibiting defect sites.
Computational Details Geometry optimization of the stoichiometric MgO and MgO with an Ov was performed within the context of DFT using the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE)30 exchange-correlation functional and the projected augmented wave (PAW)31 approach, as implemented in the Vienna abinitio simulation package (VASP).32 Pristine MgO was modeled with the lattice constants taken from experimental crystallographic data, i.e. a = b = c = 4.21 Å.33 For the non-stoichiometric MgO system with an Ov, we used a 3x3x3 supercell and for the MgO slab we added a vacuum gap of 14.3 Å in the z direction in order to minimize spurious effects between periodic cells. In this case, the lattice parameters were a = b = 12.63, and c = 25 Å. The surface orientation was chosen to be the (001), which is the most stable one. Among the six layers along the z direction, only two bottom layers were fixed. Large kinetic energy cutoffs of 450.0 eV and convergence criteria of 10–5 (10–6) eV for geometric (electronic) relaxation were employed. The Brillouin zone was sampled with a 1x1x1 Γ-centered Monkhorst–Pack34 k-point grid. Since pure DFT functionals are known to overly-delocalize electrons,35 we additionally ran single point calculations for the stoichiometric and non-stoichiometric MgO surface using the hybrid HSE06 functional.36 The same parameters were used for the periodic NBO37 and SSAdNDP38 calculations as for the VASP calculations. Similar to the standard NBO code,39−41 periodic NBO allows identification of Lewis elements of localized bonding, such as 1c−2e bonds (lone pairs, LPs) and 2c−2e bonds (two-center two-electron bonds). SSAdNDP, which is an extension of the molecular AdNDP42 method for the periodically extended systems, additionally enables the search for the delocalized bonding elements (nc−2e bonds, n > 2). The figure of merit of both NBO and 4
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SSAdNDP is the occupation number, ON, which is the number of electrons occupying a particular identified localized state. The closer this number is to 2 electrons, the more reliable the localization scheme is. The SSAdNDP projection algorithm was used to obtain a representation of the delocalized plane wave DFT results in a localized atomic orbital basis. Previously, the AdNDP program (parent to SSAdNDP used for finite molecular systems) was shown to produce results that are insensitive to the level of theory or basis set in use.43 As long as an appropriate atomic orbital basis set is chosen (it is usually trimmed of any functions with angular momentum l ≥ 4 as well as diffuse functions with exponents
