The role of surface and subsurface point defects for chemical model studies on TiO2: a first-principles theoretical study of formaldehyde bonding on rutile TiO2(110)

We report a systematic investigation of the effects of different surface and subsurface point defects on the adsorption of formaldehyde on rutile TiO(2)(110) surfaces using density functional theory (DFT). All point defects investigated--including surface bridging oxygen vacancies, titanium interstitials, and subsurface oxygen vacancies--stabilize the adsorption significantly by up to 56 kJ mol(-1) at a coverage of 0.1 monolayer (ML). The stabilization is due to a decrease of the coordination (covalent saturation) of the surface Ti adsorption sites adjacent to the defects, which leads to a stronger molecule-surface interaction. This change in the Ti is caused by the removal of a neighboring atom (oxygen vacancies) or substantial lattice relaxations induced by the subsurface defects. On the stoichiometric reference surface, the most stable adsorption geometry of formaldehyde is a tilted η(2)-dioxymethylene (with an adsorption energy E(ads)=-125 kJ mol(-1)), in which a bond forms to a nearby bridging O atom and the carbonyl-O atom in the formaldehyde binds to a Ti atom in the adjacent fivefold coordinated lattice site. The η(1)-top configuration on five-coordinate Ti(4+) is much less favorable (E(ads)=-69 kJ mol(-1)). The largest stabilization is exerted by subsurface Ti interstitials between the first and second layers. These defects stabilize the η(2)-dioxymethylene structure by nearly 40 kJ mol(-1) to an adsorption energy of -164 kJ mol(-1). Contrary to popular belief, adsorption in a bridging oxygen vacancy (E(ads)=-86 kJ mol(-1)) is much less favorable for formaldehyde compared to the η(2)-dioxymethylene structures. From these results we conclude that formaldehyde will bind in the η(2)-dioxymethylene structure on the stoichiometric surface as well as in the presence of Ti interstitials and bridging oxygen vacancies. In the light of these substantial effects, we conclude that it is essential to include all the types of point defects present in typical, reduced rutile samples used for model studies, at realistic concentrations to obtain correct adsorption sites, structures, energetic, and chemi-physical properties.     

Theoretical study of adsorption of O((3)P) and H(2)O on the rutile TiO(2)(110) surface

The adsorption of oxygen atoms O(3P) on both ideal and hydrated rutile TiO(2)(110) surfaces is investigated by periodic density functional theory (DFT) calculations within the revised Perdew-Burke-Ernzerhof (RPBE) generalized gradient approximation and a four Ti-layer slab, with (2 x 1) and (3 x 1) surface unit cells. It is shown that upon adsorption on the TiO(2) surface the spin of the O atom is completely lost, leading to stable surface peroxide species on both in-plane and bridging oxygen sites with O-binding energies of about 1.0-1.5 eV, rather than to the kinetically unstable terminal Ti-O and terminal O-O species with smaller binding energies of 0.1-0.7 eV. Changes in O-atom coverage ratios between 1/3 and 1 molecular layer (ML) and coadsorption of H(2)O have only minor effects on the O-binding energies of the stable peroxide configurations. High O-atom diffusion barriers of about 1 eV are found, suggesting a slow recombination rate of adsorbed O atoms on TiO(2)(110). Our results suggest that the TiOOTi peroxide intermediate experimentally observed in photoelectrolysis of water should be interpreted as a single spinless O adatom on TiO(2) surface rather than as two Ti-O* radicals coupled together.     

NO adsorption on the stoichiometric and reduced SnO2(110) surface

The adsorption of NO molecules on the perfect and defective (110) surfaces of SnO₂ was studied with first-principles methods at the density-functional theory level. It was found that NO mainly interacts via the nitrogen atom with the bridging oxygens of the stoichiometric surface while the coordinatively unsaturated surface Sn atoms are less reactive. On the oxygen-deficient surface, NO is preferentially adsorbed at the vacancy positions, with the nitrogen atom close to the former surface oxygen site. Regardless of the adsorption site, the unpaired electron is located mainly on the NO molecule and only partly on surface Sn atoms. The results for the SnO₂ surface are compared to literature results on the isostructural TiO₂ rutile (110) surface. Dedicated to Professor Karl Jug on the occasion of his 65th birthday     

Density functional study of the interaction between small Au clusters, Au(n) (n=1-7) and the rutile TiO2 surface. II. Adsorption on a partially reduced surface

We use density functional theory to examine the electronic structure of small Au(n) (n=1-7) clusters, supported on a rutile TiO(2)(110) surface having oxygen vacancies on the surface (a partially reduced surface). Except for the monomer, the binding energy of all Au clusters to the partially reduced surface is larger by approximately 0.25 eV than the binding energy to a stoichiometric surface. The bonding site and the orientation of the cluster are controlled by the shape of the highest occupied molecular orbitals (HOMOs) of the free cluster (free cluster means a gas-phase cluster with the same geometry as the supported one). The bond is strong when the lobes of the HOMOs overlap with those of the high-energy states of the clean oxide surface (i.e., with no gold) that have lobes on the bridging and the in-plane oxygen atoms. In other words, the cluster takes a shape and a location that optimizes the contact of its HOMOs with the oxygen atoms. Fivefold coordinated Ti atoms located at a defect site (5c-Ti(*)) participate in the binding only when a protruding lobe of the singly occupied molecular orbital (for odd n) or the lowest unoccupied molecular orbital (for even n) of the free Au(n) cluster points toward a 5c-Ti(*) atom. The oxygen vacancy influences the binding energy of the clusters (except for Au(1)) only when they are in direct contact with the defect. The desorption energy and the total charge on clusters that are close to, but do not overlap with, the vacancy differ little from the values they have when the cluster is adsorbed on a stoichiometric surface. The behavior of Au(1) is rather remarkable. The atom prefers to bind directly to the vacancy site with a binding energy of 1.81 eV. However, it also makes a strong bond (1.21 eV) with any 5c-Ti atom even if that atom is far from the vacancy site. In contrast, the binding of a Au monomer to the 5c-Ti atom of a surface without vacancies is weak (0.45 eV). The presence of the vacancy activates the 5c-Ti atoms by populating states at the bottom of the conduction band. These states are delocalized and have lobes protruding out of the surface at the location of the 5c-Ti atoms. It is the overlap of these lobes with the highest orbital of the Au atom that is the major reason for the bonding to the 5c-Ti atom, no matter how far the latter is from the vacancy. The energy for breaking an adsorbed cluster into two adsorbed fragments is smaller than the kinetic energy of the mass-selected clusters deposited on the surface in experiments. However, this is not sufficient for breaking the cluster upon impact with the surface, since only a fraction of the available energy will go into the reaction coordinate for breakup.     

CO在CeO2(111)表面的吸附与氧化

采用密度泛函理论计算了CO在CeO2(111)表面的吸附与氧化反应行为. 结果表明, O2在洁净的CeO2(111)表面为弱物理吸附, 而在氧空位表面是强化学吸附, 且O2分子活化程度较大, O—O键长为0.143 nm. CO在CeO2(111)表面吸附行为的研究表明, CO在洁净表面及氧空位表面上为物理吸附, 吸附能均小于0.42 eV; 当表面氧空位吸附O2后, CO可吸附生成二齿碳酸盐中间体或直接生成CO2, 与原位红外光谱结果相一致. 表面碳酸盐物种脱附生成CO2的能垒仅为0.28 eV. 计算结果表明, 当CeO2表面存在氧空位时, Hubbard参数U对CO吸附能有一定的影响. CeO2载体在氧化反应中可能的催化作用为, 在氧气氛下, CeO2表面氧空位吸附O2分子, 形成活性氧物种, 参与CO催化氧化反应.     

Identification of defect sites on MgO(100) thin films by decoration with Pd atoms and studying CO adsorption properties.

CO adsorption on Pd atoms deposited on MgO(100) thin films has been studied by means of thermal desorption (TDS) and Fourier transform infrared (FTIR) spectroscopies. CO desorbs from the adsorbed Pd atoms at a temperature of about 250 K, which corresponds to a binding energy, E(b), of about 0.7 +/- 0.1 eV. FTIR spectra suggest that at saturation two different sites for CO adsorption exist on a single Pd atom. The vibrational frequency of the most stable, singly adsorbed CO molecule is 2055 cm(-)(1). Density functional cluster model calculations have been used to model possible defect sites at the MgO surface where the Pd atoms are likely to be adsorbed. CO/Pd complexes located at regular or low-coordinated O anions of the surface exhibit considerably stronger binding energies, E(b) = 2-2.5 eV, and larger vibrational shifts than were observed in the experiment. CO/Pd complexes located at oxygen vacancies (F or F(+) centers) are characterized by much smaller binding energies, E(b) = 0.5 +/- 0.2 or 0.7 +/- 0.2 eV, which are in agreement with the experimental value. CO/Pd complexes located at the paramagnetic F(+) centers show vibrational frequencies in closest agreement with the experimental data. These comparisons therefore suggest that the Pd atoms are mainly adsorbed at oxygen vacancies.     

Reduction of the (001) surface of gamma-V2O5 compared to alpha-V2O5

The defect-free gamma-V(2)O(5)(001) surface and ordered structures of oxygen vacancies have been studied for a wide range of defect concentrations, Theta ((1)/(6) monolayer (ML) < or = Theta < or = 1 ML), combining density functional theory and statistical thermodynamics. The gamma polymorph of V(2)O(5) is characterized by two structurally different vanadium sites, V(A) and V(B). The V(A) sites having a weaker bond to an adjacent crystal layer are easier to reduce. Up to (1)/(2) ML, the V(A) defect structures with defects aligned along the [010] direction are increasingly more stable as in alpha-V(2)O(5)(001). At higher defect concentrations, the different coordination of the V(B) vanadium atoms at the gamma-V(2)O(5) surface causes an increase in the vacancy formation energy of approximately 0.8 eV/atom at Theta = 1.0 compared to Theta = (1)/(2). For alpha-V(2)O(5), this increase amounts to 0.2 eV/atom only. Under conditions (low oxygen partial pressures and high temperatures) at which the alpha-V(2)O(5)(001) surface would be fully reduced, the gamma-V(2)O(5)(001) surface is only partially reduced. The presence of surface vanadyl oxygen groups at V(B) sites may change the surface reactivity compared to that of alpha-V(2)O(5)(001).     

Adsorption of atomic and molecular oxygen on the LaMnO3(001) surface: ab initio supercell calculations and thermodynamics

We present and discuss the results of ab initio DFT plane-wave supercell calculations of the atomic and molecular oxygen adsorption and diffusion on the LaMnO(3) (001) surface which serves as a model material for a cathode of solid oxide fuel cells. The dissociative adsorption of O(2) molecules from the gas phase is energetically favorable on surface Mn ions even on a defect-free surface. The surface migration energy for adsorbed O ions is found to be quite high, 2.0 eV. We predict that the adsorbed O atoms could penetrate the electrode first plane when much more mobile surface oxygen vacancies (migration energy of 0.69 eV) approach the O ions strongly bound to the surface Mn ions. The formation of the O vacancy near the O atom adsorbed atop surface Mn ion leads to an increase of the O-Mn binding energy by 0.74 eV whereas the drop of this adsorbed O atom into a vacancy possesses no energy barrier. Ab initio thermodynamics predicts that at typical SOFC operation temperatures (approximately 1200 K) the MnO(2) (001) surface with adsorbed O atoms is the most stable in a very wide range of oxygen gas pressures (above 10(-2) atm).     

Oxygen adsorption on Al (111) surface interstitial site calculated by density functional theory

The adsorption possibilities of oxygen atoms at Al (111) surface for different oxygen atom coverages (Θ) from 0.25 to 1 ml have been studied using first principles based on density functional theory with generalized gradient approximation. The results show that the interstitial sites on Al (111) surface are relatively stable, in which binding energies are 0.6 ～ 1 eV/atom lower than those on surface face centered cubic (fcc) sites for the different coverages. The binding energy and work function of the oxygen‐adsorbed surface increase with the oxygen atom coverage. Moreover, the oxygen atom at one tetrahedral site of Al (111) subsurface becomes more and more unstable with the decrease of the coverage, and it moves up to the Al (111) surface hexagonal close packed (hcp) site at Θ = 0.25. All the octahedral absorption sites are also unstable in relatively lower coverages (Θ = 0.5 and 0.25). The bond length and overlap population between Al and O, including the relaxation effects on the oxygen atom coverage are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Interaction of Pt clusters with the anatase TiO(2)(101) surface: a first principles study

The adsorption of Pt(n)() (n = 1-3) clusters on the defect-free anatase TiO(2)(101) surface has been studied using total energy pseudopotential calculations based on density functional theory. The defect-free anatase TiO(2)(101) surface has a stepped structure with a step width of two O-Ti bond distances in the (100) plane along the [10] direction and the edge of the step is formed by 2-fold-coordinated oxygen atoms along the [010] direction. For a single Pt adatom, three adsorption sites were found to be stable. Energetically, the Pt adatom prefers the bridge site formed by 2 2-fold-coordinated oxygen atoms with an adsorption energy of 2.84 eV. Electronic structure analysis showed that the Pt-O bonds formed upon Pt adsorption are covalent. Among six stable Pt(2) adsorption configurations examined, Pt(2) was found to energetically favor the O-O bridge sites on the step edge along [010] with the Pt-Pt bond axis perpendicular to [010]. In these configurations, one of the Pt atoms occupies the same O-O bridge site as for a single Pt adatom and the other one either binds a different 2-fold-coordinated oxygen atom on the upper step or a 5-fold-coordinated Ti atom on the lower terrace. Three triangular and three open Pt(3) structures were determined as minima for Pt(3) adsorption on the surface. Platinum trimers adsorbed in triangular structures are more stable than in open structures. In the most stable configuration, Pt(3) occupies the edge O-O site with the Pt(3) plane being upright and almost perpendicular to the [001] terrace. The preference of Pt(n)() to the coordinately unsaturated 2-fold-coordinated oxygen sites indicates that these sites may serve as nucleation centers for the growth of metal clusters on the oxide surface. The increase in clustering energy with increasing size of the adsorbed Pt clusters indicates that the growth of Pt on this surface will lead to the formation of three-dimensional particles.     

Vanadium oxides on aluminum oxide supports. 2. Structure, vibrational properties, and reducibility of V2O5 clusters on alpha-Al2O3(0001)

The structure, stability, and vibrational properties of isolated V2O5 clusters on the Al2O3(0001) surface have been studied by density functional theory and statistical thermodynamics. The most stable structure does not possess vanadyl oxygen atoms. The positions of the oxygen atoms are in registry with those of the alumina support, and both vanadium atoms occupy octahedral sites. Another structure with one vanadyl oxygen atom is only 0.12 eV less stable. Infrared spectra are calculated for the two structures. The highest frequency at 922 cm(-1) belongs to a V-O stretch in the V-O-Al interface bonds, which supports the assignment of such a mode to the band observed around 941 cm(-1) for vanadia particles on alumina. Removal of a bridging oxygen atom from the most stable cluster at the V-O-Al interface bond costs 2.79 eV. Removal of a (vanadyl) oxygen atom from a thin vanadia film on alpha-Al2O3 costs 1.3 eV more, but removal from a V2O5(001) single-crystal surface costs 0.9 eV less. Similar to the V2O5(001) surface, the facile reduction is due to substantial structure relaxations that involve formation of an additional V-O-V bond and yield a pair of V(IV)(d1) sites instead of a V(III)(d2)/V(V)(d0) pair.     

甲硫醇在Cu(111)表面的解离吸附: 密度泛函理论研究

采用基于密度泛函理论的第一性原理方法和平板模型研究了CH₃SH分子在Cu(111)表面的吸附反应.系统地计算了S原子在不同位置以不同方式吸附的一系列构型, 第一次得到未解离的CH₃SH分子在Cu(111)表面顶位上的稳定吸附构型,该构型吸附属于弱的化学吸附, 吸附能为0.39 eV. 计算同时发现在热力学上解离结构比未解离结构更加稳定. 解离的CH₃S吸附在桥位和中空位之间, 吸附能为0.75-0.77 eV. 计算分析了未解离吸附到解离吸附的两条反应路径, 最小能量路径的能垒为0.57 eV. 计算结果还表明S―H键断裂后的H原子并不是以H₂分子的形式从表面解吸附而是以与表面成键的形式存在. 通过比较S原子在独立的CH₃SH分子和吸附状态下的局域态密度, 发现S―H键断裂后S原子和表面的键合强于未断裂时S原子和表面的键合.     

Density functional theory (DFT) investigation of the adsorption of the CH3OH/Au(100) system

The adsorption of methanol on flat Au (100) surface with different coverages (θ = 1.0, 0.5 and 0.25 monolayer (ML)) is studied using density functional theory. Among the three sites (top, bridge and hollow) and coverages investigated in the present work, no adsorption is stable for θ = 1.0 ML. The most energetically preferred site of adsorption for CH₃OH is found to be the hollow site for coverages of 0.25 ML and 0.50 ML. We also find that for all adsorption sites, an increase in CH₃OH coverage triggers a decrease in the adsorption energy. The geometric parameters, local density of states and work function changes are analysed in detail. The coadsorption of methoxy and hydrogen has also investigated. In addition, the dissociation of methanol on Au(100) has been studied, and an activation energy was found to be 1.72 eV. This result compare with existing data in the literature for Au(111) surface. Copyright © 2013 John Wiley & Sons, Ltd.     

Computational study of ethanol adsorption and reaction over rutile TiO(2) (110) surfaces

Studies of the modes of adsorption and the associated changes in electronic structures of renewable organic compounds are needed in order to understand the fundamentals behind surface reactions of catalysts for future energies. Using planewave density functional theory (DFT) calculations, the adsorption of ethanol on perfect and O-defected TiO(2) rutile (110) surfaces was examined. On both surfaces the dissociative adsorption mode on five-fold coordinated Ti cations (Ti(4+)(5c)) was found to be more favourable than the molecular adsorption mode. On the stoichiometric surface E(ads) was found to be equal to 0.85 eV for the ethoxide mode and equal to 0.76 eV for the molecular mode. These energies slightly increased when adsorption occurred on the Ti(4+)(5c) closest to the O-defected site. However, both considerably increased when adsorption occurred at the removed bridging surface O; interacting with Ti(3+) cations. In this case the dissociative adsorption becomes strongly favoured (E(ads) = 1.28 eV for molecular adsorption and 2.27 eV for dissociative adsorption). Geometry and electronic structures of adsorbed ethanol were analysed in detail on the stoichiometric surface. Ethanol does not undergo major changes in its structure upon adsorption with its C-O bond rotating nearly freely on the surface. Bonding to surface Ti atoms is a σ type transfer from the O2p of the ethanol-ethoxide species. Both ethanol and ethoxide present potential hole traps on O lone pairs. Charge density and work function analyses also suggest charge transfer from the adsorbate to the surface, in which the dissociative adsorptions show a larger charge transfer than the molecular adsorption mode.     

The Surface Chemistry of Water on Fe(100): A Density Functional Theory Study

The formation of water by hydrogenation of atomic oxygen is studied using density functional theory. Atomic oxygen preferentially adsorbs at the four‐fold hollow site, the hydroxyl group prefers the bridge site in a tilted configuration, and water is most stable when adsorbed at the top site with the two O? H bonds parallel to the Fe surface. Water formation by the hydrogenation of oxygen is a highly activated process on the Fe(100) surface, with similar activation energies, in the order of 1.1 eV, for the first and second hydrogen additions. A more favourable route for the addition of the second hydrogen atom involves the disproportionation of hydroxyl groups to form water and adsorbed oxygen. Dissociation of the OH is also likely since the activation energy is similar to that for disproportionation of 0.65 eV. Furthermore, the results show that the dissociation of water on Fe(100) is a non‐activated process: 0.16 eV for the zero‐coverage limit and 0.03 eV when surface oxygen is present. Herein, adsorption energies, structures and vibrational frequencies are presented for several adsorption states at 0.25 ML coverage, as well as the potential energy surface for water formation on Fe(100).     

Nitrogen/gold codoping of the TiO2(101) anatase surface. A theoretical study based on DFT calculations

The interaction between implanted nitrogen atoms, adsorbed gold atoms, and oxygen vacancies at the anatase TiO(2)(101) surface is investigated by means of periodic density functional theory calculations. Substitutional and interstitial configurations for the N-doping have been considered, as well as several adsorption sites for Au adatoms and different types of vacancies. Our total energy calculations suggest that a synergetic effect takes place between the nitrogen doping on one hand and the adsorption of gold and vacancy formation on the other hand. Thus, while pre-implanted nitrogen increases the adsorption energy for gold and decreases the energy required for the formation of an oxygen vacancy, pre-adsorbed gold or the presence of oxygen vacancies favors the nitrogen doping of anatase. The analysis of the electronic structure and electron densities shows that a charge transfer takes place between implanted-N, adsorbed Au and oxygen vacancies. Moreover, it is predicted that the creation of vacancies on the anatase surface modified with both implanted nitrogen and supported gold atoms produces migration of substitutional N impurities from bulk to surface sites. In any case, the most stable configurations are those where N, Au and vacancies are close to each other.     

氢原子在Be(0001)表面吸附的密度泛函理论研究

采用第一性原理的密度泛函理论研究单个氢原子和多个氢原子在Be(0001)表面吸附性质.给出了氢吸附Be(0001)薄膜表面的原子结构、吸附能、饱和度、功函数、偶极修正等特性参数.同时也讨论了相关吸附性质与氢原子覆盖度(0.06-1.33ML)的关系.计算结果表明:氢原子的吸附位置与覆盖度之间有强烈的依赖关系,覆盖度低于0.67ML时,氢原子能量上易于占据fcc或hcp的中空位置;覆盖度为0.78ML时,中空位与桥位为氢原子的最佳吸附位;覆盖度在0.89到1.00ML时,桥位是氢原子吸附能量最有利的位置;以上覆盖度中Be(0001)表面最外层铍原子的结构均没有发生明显变化.当覆盖度为1.11-1.33ML,高覆盖度下Be(0001)表面的最外层铍原子部分发生膨胀,近邻氢原子渗入到铍表面次层,氢原子易于占据在hcp和桥位.吸附结构中的氢原子比氢分子中的原子稳定.当覆盖度大1.33ML时,计算结果没有发现相对于氢分子更稳定的吸氢结构.同时从分析偶极修正和氢原子吸附垂直高度随覆盖度的变化关系判断氢覆盖度为1.33ML时,在Be(0001)表面吸附达到饱和.     

The electronic structure of intrinsic defects at TiO2 (110) surfaces: An ab initio molecular orbital study

We report on an isolated cluster approach to determine local electronic structures of TiO₂ surfaces before and after formation of intrinsic defects, i.e., oxygen vacancies, at different crystallographic sites. In particular, isolated oxygen vacancies at bridging sites, isolated oxygen vacancies at in-plane sites and aggregated oxygen vacancies at bridging sites have been treated which lead to changes in the coordination of the adjacent Ti atoms. We find that electronic band gap states are only formed in the presence of fourfold coordinated Ti surface atoms. © 1996 John Wiley & Sons, Inc.     

First principles study of CO oxidation on TiO2(110): the role of surface oxygen vacancies

The reactivities of the stoichiometric and partially reduced rutile TiO2(110) surfaces towards oxygen adsorption and carbon monoxide oxidation have been studied by means of periodic density functional theory calculations within the Car-Parrinello approach. O2 adsorption as well as CO oxidation are found to take place only in the presence of surface oxygen vacancies (partially reduced surface). The oxidation of CO by molecularly adsorbed O2 at the O-vacancy site is found to have an activation energy of about 0.4 eV. When the adsorbed O2 is dissociated, the resulting adatoms can oxidize incoming gas-phase CO molecules with no barrier. In all studied cases, once CO is oxidized to form CO2, the resulting surface is defect-free and no catalytic cycle can be established.     

Density Functional Study of the C Atom Adsorption on the α-Fe2O3 （001） Surface

The adsorption of C atoms on the α-Fe2O3(001) surface was studied based on density function theory(DFT) ,in which the exchange-correlation potential was chosen as the PBE(Perdew,Burke and Ernzerhof) generalized gradient approximation(GGA) with a plane wave basis set. Upon the optimization on different adsorption sites with coverage of 1/20 and 1/5 ML,it was found that the adsorption of C atoms on the α-Fe2O3(001) surface was chemical adsorption. The coverage can affect the adsorption behavior greatly. Under low coverage,the most stable adsorption geometry lied on the bridged site with the adsorption energy of about 3.22 eV;however,under high coverage,it located at the top site with the energy change of 8.79 eV. Strong chemical reaction has occurred between the C and O atoms at this site. The density of states and population analysis showed that the s,p orbitals of C and p orbital of O give the most contribution to the adsorption bonding. During the adsorption process,O atom shares the electrons with C,and C can only affect the outermost and subsurface layers of α-Fe2O3;the third layer can not be affected obviously.