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Aug 23, 2008 - Most often the sites of electrophilically susceptible areas correspond to the mapping of f- function, electrostatic potential, and high...
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J. Phys. Chem. C 2008, 112, 14367–14376

14367

Origin of the Reactivity on the Nonterminated (100), (110), and (111) Diamond Surfaces: An Electronic Structure DFT Study D. Petrini and K. Larsson* Department of Materials Chemistry, Angstrom Laboratory, Uppsala UniVersity Box 538, SE-751 21 Uppsala, Sweden ReceiVed: NoVember 26, 2007; ReVised Manuscript ReceiVed: March 26, 2008

The reactivity of nonterminated diamond low-index surfaces has been evaluated using density functional theory (DFT). The intrinsic electronic structures of the topmost carbon atoms of diamond (100)-1 × 1, (100)-2 × 1, (110)-1 × 1, (111)-1 × 1, and (111)-2 × 1 surfaces have been calculated and analyzed using highly accurate numerical basis set first-principle techniques. The following reactivity indicators have been utilized: Fukui functions, electrostatic potential, and Kohn-Sham orbitals (highest occupied and lowest unoccupied). Their spatial representations have been mapped onto a charge density isosurface whereby plausible reactive sites were identified and related. Specifically, the change in chemically reactivity induced by a 1 × 1 to 2 × 1 surface reconstruction has been discussed. In addition, density of states and the deformation density of the topmost carbon atoms have been included. Most often the sites of electrophilically susceptible areas correspond to the mapping of f- function, electrostatic potential, and highest occupied molecular orbital. Conversely, nucleophilic sites correspond to the f+-function and the lowest unoccupied molecular orbital. However, some discrepancies are found, and it seems that the Fukui functions yield more accurate results due to orbital relaxation effects taken into account. The results herein were furthermore compared to adsorption studies of H-, O-, and OH-terminated diamond (100) and (111) surfaces, respectively. It was concluded that the reactivity of diamond surfaces can be evaluated by using DFT techniques, which will thereby make it possible to increase the knowledge about thin film growth mechanisms, surface functionalization, and reconstructions. 1. Introduction Diamond is the hardest material known and surfaces of diamond show very desirable properties that have been utilized in the areas of, e.g., optics, electrochemistry, and electronics. These properties include thermal conductivity in room temperature (highest known), output power capability, breakdown field, frequency bandwidth, large electrochemical potential window, and transparency of photon wavelength greater than 220 nm. Thus, diamond is well-suited to be used as vacuum ultraviolet sensors,1 mirrors,2 field effect transistors,3,4 and electrodes.5 When adding also chemical inertness, radiation hardness, and high degree of biocompatibility to the list of desirable diamond properties, diamond surfaces have been shown to perform as sensors capable of detecting, e.g., radiation in very harsh environments,6 pH,7,8 ions,9,10 and certain neurotransmitters.11 The relative ease and economics aspects of chemical vapor deposition (CVD) manufacturing are also of major importance for exploitation of diamond in various applications. Nonterminated, bulklike diamond surfaces are very reactive due to the unsaturated topmost carbon atoms and will readily reconstruct or adsorb hydrogen, oxygen, fluorine, and other carbonic species. The as-deposited diamond surfaces are, due to the inert character of the C-H bond, hydrogen-terminated and chemically stable at intermediate temperatures. It has been shown that a strong presence of chemisorbed hydrogen atoms on the surface is a prerequisite for the high surface conductivity of diamond.12 However, oxygen-terminated surfaces show a pronounced importance due to their specific optical13 and electrical properties,9 and a deeper understanding of various oxygen-termination * To whom correspondence [email protected]

should

be

addressed.

E-mail:

reactions at diamond surfaces are therefore of major importance to achieve. Also other properties (e.g., electron affinity (EA),14–16 wetting capabilities17) change whether the diamond surface is hydrogen- or oxygen-terminated. The chemisorbed hydrogen or fluorine species upholds the sp3 hybridization of the topmost carbon radicals and, thus, protects the surface from becoming reconstructed or sp2-hybridized (i.e., graphitized). The chemisorption of oxygen has also been shown to yield better film quality and growth rates due to the removal of sp2-hybridized carbon by CO desorption.18,19 Reactivity studies of nonterminated diamond surfaces by using theoretical methods have the potential of predicting and explaining experimental results regarding, e.g., growth mechanisms and surface functionalization. The dominating surface planes obtained during vapor-phase deposition of diamond are the low-index (111), (100), and (110) planes, which thereby are the most interesting ones when studying the reaction tendency for diamond surfaces. A number of techniques available in computational chemistry have been used to understand plausible reaction mechanisms at the atomic level. The electrostatic potential has been very successful20–25 in predicting sites of electrophilic attack, i.e., reactive toward species that are an electron acceptor. In equilibrium reactions these species are denoted as a Lewis acid. The electrostatic potential is described as

V(r) )

Z

∑ |RA -A r| - ∫ |r′F(r′) - r|

(1)

A

where the potential at position r depends on the nuclear charge of atom A (ZA) located at position RA, and the charge density in the vicinity of r. It is numerically equal to the interaction energy of a positive test charge of 1.0 electron units. Thus, the electrostatic potential mapped onto a charge density isosurface

10.1021/jp711190r CCC: $40.75  2008 American Chemical Society Published on Web 08/23/2008

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could provide valuable information about electrophilic reactive, and nonreactive, sites. In particular, a negative value indicates a region where an electrophilic species would attack. Another indication for reactivity is the polarizability of a molecular species. Pearson introduced his hard-soft acid-base principle in 1963, which states that “hard” species are often hard to polarize, and vice versa for “soft” species.26 The concept of reactivity is thereby defined as “hard reacts more strongly with hard species and soft species react more strongly with soft species”. It has been used with success within areas like organic chemistry and catalysis. However, it is often useful to estimate local reactivity by using Fukui functions. Fukui introduced his frontier orbital reactivity concept in 1952 (and earned the Nobel Prize 30 years later).27,28 Parr and Yang29,30 transferred this concept into the Fukui function (FF):

f(r) )

( δF(r) δN )

V

(2)

where N is the number of electrons, and F(r) is the electron density at a fixed external potential, V. By using eq 2, three specific Fukui functions may be defined (f-, f+, and f0), corresponding to the sensitivity toward a nucleophilic, electrophilic, and radical attack, respectively. The regional selectivity of Fukui functions has earlier successfully predicted nucleophilic and electrophilic reactions.31–34 In addition, since the Fucui functions also include the relaxation of the charge density, they are a good complement to two other common measures of chemical reactivity: (i) the highes occupied molecular orbita/ lowest unoccupied molecular orbital (HOMO/LUMO) concept and (ii) the change in electrostatic potential35 Condensed Fukui indices (i.e., the Fukui function centered on one atom in an attempt to quantify the ability of the atom to stabilize additional, or fewer, electrons) may also help in the investigation of reactive sites.36 The purpose with the present work has been to investigate the chemical reactivity of nonterminated diamond (111)-1 × 1, (111)-2 × 1, (110)-1 × 1, (100)-1 × 1, and (100)-2 × 1 surfaces, using the electron density, electrostatic potential, Fukui function, HOMO/LUMO orbitals, and partial density of states graphs using periodic density functional theory (DFT). Hence, this information may be able to assess a priori the surface reactivity using the electronic structure of the carbon atoms. The results herein can provide additional knowledge regarding plausible growth precursors, site of adsorption, and degree of reactivity. The methods used are common and reliable within the DFT framework. The highly accurate (local) numerical basis set used further strengthens the results. 2. Theoretical Approach 2.1. Methods. A DFT37,38 method, available within the program Dmol3,39,40 was used for the energy and geometry calculations. A local numerical orbital basis set was generated as values on an atomic-cetered spherical polar mesh, with a specific orbital cutoff of 4.0 Å (for a very accurate integration). A doubling of the number of functions, in addition to an introduction of polarization p- (for hydrogen atoms) and d-functions (for non-hydrogen atoms), was used to get a more flexible basis set. The quality of the basis set is imperative for a good description of the system, especially when weaker bonds are present.39 To study the periodicity of the surfaces, the Bloch theorem was used under symmetry unique Monkhorst-Pack41 generated k-points with a precise setting of 0.04 Å/k-point spacing), resulting in a total of five and six k-points for the diamond surface models, respectively. The exchange and

correlation parts of the Hamiltonian were approximated using the Perdew-Wang (PW91) generalized gradient approximation (GGA). This will, in contrast to the local density approximation (LDA), give a much better energy evaluation.42–45 The LDA method tends to overbind electrons in a molecule (or solid). Moreover, systems containing unpaired electrons will require spin-unrestricted theoretical methods, and the here-presented work is therefore largely based on spin-polarized calculations. The Columbic (electrostatic) potential was evaluated by solving the Poisson equation for the charge density, rather than an integration procedure, which provides better numerical precision.39 The Fukui function used to derive local reactivity was based on the finite difference approximation of the whole charge density, not just the frontier orbitals. Furthermore, a fraction of charge (0.1) was removed to better approach the infinitesimal change required for no approximation. The Fukui functions measure the sensitivities of the charge density due to gain or loss of electrons and are, hence, more flexible than, e.g., the HOMO-LUMO concept or the electrostatic potential. Fukui indices have also been computed using the Hirshfeld analysis scheme (the most appropriate and also the partitioning scheme with the best formal mathematical properties other than Baders).46 Test calculation of the Fukui index of four organic molecules has been compared versus another study,36 and the results are vary similar. Although the shortcomings of DFT prohibit estimating ionization potentials and band gaps, DFT may be used to derive conclusions about the Kohn-Sham orbitals.47–49 Fukui functions, electron density surfaces, the HOMO-LUMO orbitals, and electrostatic potential calculations could only be modeled at the γ point (i.e., one k-point). However, all of the geometry optimizations and the partial density of states were conducted at multiple k-point representation. The convergence criterion for the self-consistent field (SCF) energy, geometry optimization energy, and displacement were set to 1 × 10-6 Ha, 1 × 10-5 Ha, and 5 × 10-3 Å, respectively. 2.2. Diamond Surface Model. The diamond surfaces used throughout the electron structure calculations are shown in Figure 1. The diamond (100) and (111) surfaces consist of the 16 topmost carbon atoms, whereas the (110) surface has 18. In addition, six carbon layers were used for all models with the purpose being to properly simulate a surface with its electronic structure. In addition, the lower parts of the surface slabs were terminated with hydrogen atoms to simulate the sp3 hybridization of bulk diamond. Only the lowest positioned carbon layers (with their terminating H atoms) were held fixed during the geometry optimization process. The vacuum layer was set to 20 Å, something that the authors have found adequate in previous diamond surface calculations.7,50,51 3. Results The intrinsic electronic structure of the atoms constituting a surface may lead to accurate predictions regarding the surface reactivity. There exist different indictors for surface reactivity, which have been shown to be highly valuable in verifying and predicting both theoretical and experimental results. In short, these indicators have the capacity to increase the atomic-level knowledge within the area of diamond surface science and technology. The distribution and extent of reactivity of a nonterminated diamond surface is most important for surface chemical processes such as diamond growth, surface functionalization, and reconstruction. The reactivities of nonterminated diamond (100)-1 × 1, (100)-2 × 1, (110)-1 × 1, (111)-1 × 1, and (111)-2 × 1 surfaces have in the present study been evaluated using reactivity indicators such as electron densities,

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Figure 1. Optimized periodic models of the diamond (111)-1 × 1 (a), (111)-2 × 1 (b), (110)-1 × 1 (c), (100)-1 × 1 (d), and (100)-2 × 1 (e) surfaces. The upper row shows a side view of the different models, and the lower row shows on-top orientations. The topmost C atoms are shown with a whiter shade.

mapping of electrostatic potentials, frontier orbitals, and Fukui functions. The charge density isosurface represents the boundary for the electron distribution. Incoming (toward the surface) gaseous species will experience interactions with the surface, which totally depends on the distance to the surface and to the distribution of electron density. The variation and degree of interaction is thereby a valuable tool to obtain information about surface reactivity. In addition, partial density of states (pDOS) have also been included to study the distribution of electronic states for the topmost carbon atoms. The electrostatic potential estimates the amount of electronic charge surrounding a point in space. Hence, a negative value of the electrostatic potential will indicate a surface position with a susceptibility toward an electrophilic (electron withdrawing) attack from the surroundings. This closely resembles the electrophilic Fukui function, but the Fukui function also measures the response of the charge density as a result of density change. Hence, a high value of the Fukui function corresponds to an area where the charge density is changed a lot due to adding or withdrawal of electrons. The Fukui functions are more flexible than the electrostatic potential, but they often coincide spatially; i.e., they predict the same area to be reactive. Frontier orbitals, often the HOMO and the LUMO, are often involved in chemical reactions since they are most accessible for bonding and electron transfer. Mapping of the orbital spatial occupancy onto the charge density isosurface gives an indication of orbital contribution to the charge density. A plane intersecting two orbital areas of different sign is denoted a nodal plane, and many nodal planes yield a more antibonding orbital. The distribution of the HOMO on the density isosurface should correspond to the electrophilic attack reactivity as predicted by the electrostatic potential and Fukui function, whereas the LUMO and the nucleophilic Fukui function are related in a similar way. In addition, a large peak around the Fermi level of the DOS indicates strong electron-electron interactions and a small HOMO-LUMO separation. Many nodal planes of the LUMO, and fewer planes for the HOMO,

may render the gap (i.e., energy separation) between the HOMO-LUMO rather large and indicate a more nonreactive surface. 3.1. Electron Deformation Density. Information about the location of covalent bonds in a material can be obtained by subtracting the atomic densities from the total density of the solid. The hereby formed “electron deformation density” can be visualized in three-dimensional space or in two dimensions as slices through the density. Figure 2 demonstrates the deformation density within the planes parallel to the diamond surface and through the topmost carbon atoms: (a) (111)-1 × 1, (b) (111)-2 × 1, (c) (110)-1 × 1, (d) (100)-1 × 1, and (e) (100)-2 × 1 surfaces, respectively. Grayish and white areas indicate positive values in deformation density and, hence, the existence of a covalent bond, whereas the darker, more black, color indicates loss of electrons (i.e., negative values). The topmost 16 carbon atoms are shown as white balls, whereas the black balls denote the 16 atoms that are bonded to the topmost atoms, but lay deeper within the diamond surface. As can be seen in Figure 2, the 2 × 1 reconstructed surfaces of (111) and (100), as well as the (110)-1 × 1 surface, show large reallocation of the electronic density toward the region between carbon atoms within the same atomic layer. On the contrary, the (111)-1 × 1 and (100)-1 × 1 surfaces indicate less carbon-carbon electron densities. The overall largest C-C electron deformation density is calculated for diamond (100)-2 × 1, followed by (110)-1 × 1 and (111)-2 × 1 (0.51, 0.45, and 0.39 electrons, respectively). Hence, since the surface electrons are involved in C-C bonds, the electrons accessible for covalent bonding with gaseous species are quite few. Smaller adsorption energies for the reconstructed (100) and (111) surfaces, as well as for the (110)-1 × 1 surface, are expected. The feature of the 2 × 1 reconstruction of the (100) surface is of more typical C-C double bond character (i.e., two electrons per carbon atom), whereas for the (110)-1 × 1 and (111)-2 × 1 surfaces the unsaturated electrons are shared along the carbon chains (with a resulting delocalization of electrons).

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Figure 2. Electron deformation density slices through the upper carbon layer of the (a) (111)-1 × 1, (b) (111)-2 × 1, (c) (110)-1 × 1, (d) (100)-2 × 1, and (e) (100)-1 × 1 surfaces of diamond (where, for example, 3.700e-1 represents 3.700 × 10-1). White circles represent the topmost 16 atoms, and 16 atoms within the second atomic layer are represented as gray circles.

3.2. Electrostatic Potential Contour Maps. The (columbic) electrostatic potential has been mapped onto the charge density of the studied diamond surfaces to evaluate possible electrophilic surface sites. The resulting figures display the potential of a (positive) test charge at a certain position on the isosurface; i.e., more positive values indicate electron-rich areas. As can be seen in Figure 3, the unreconstructed (100)-1 × 1 surface shows only negative potentials within the potential range from -8.73 × 10-2 to -2.20 × 10-2 Ha, which reflects the high concentration of dangling bonds on the topmost carbon atoms. Electrons are accumulated between the carbon atoms in the area that is not above the second topmost carbon atoms. This explains the spontaneous formation of the C-C dimer as can be seen as a (100)-2 × 1 reconstruction. In contrast, the monovalent dangling bonds are located directly above the surface carbon atoms on the diamond (111)-1 × 1 surface. The positive potential areas are located between the carbon atoms, and closer inspection to Figure 1 reveals that the most positive area is not located above the second topmost carbon atom but above the third topmost atoms. Hence, the (111)-1 × 1 surface should not have any tendency for bridge bonding by, e.g., oxygen atoms. Both the (111)-2 × 1 and (100)-2 × 1 reconstructions show positive electrostatic potentials and ranges from -1.76 × 10-2 to 2.75 × 10-2 vs from -5.27 × 10-2 to 2.30 × 10-2 Ha (as demonstrated in Figure 3b,e). Compared to their 1 × 1 reconstruction counterparts, the (100) and (111) surfaces show overall a more positive electrostatic potential. More electrons are involved in C-C bonds where the charge is distributed between the topmost atoms and deeper inside the isosurface. As expected, the location of the negative values are located along the Pandey chain and the C-C dimer of the (111) and (100)

surface, respectively, an observation that correlates well with the deformation densities discussed in section 3.1. Positive areas are located adjacent to the Pandey chain and C-C dimer of the (111) and (100) surfaces, respectively. Hence, a positive species would experience unfavorable interaction energy at those locations. The (110)-1 × 1 surface displays a large negative columbic potential along the chain formation with alternating double bonds, with a potential range from -2.69 × 10-2 to +5.00 × 10-3 Ha. The (110)-1 × 1 surface has a more negative electrostatic potential compared to the Pandey chain, although the surface geometries of the (110)-1 × 1 and (111)-2 × 1 surfaces are somewhat similar. As will be shown later, the frontier orbital (HOMO) is located along the chain for the (110)-1 × 1 surface, whereas it is located perpendicular to the chain on the (111)-2 × 1 surface. 3.3. Density of States. Partial density of state calculations have been conducted for the topmost 16 atoms of the five diamond surfaces, as shown in Figures 4–6. The pronounced reactivity of the unreconstructed (111) and (100) surfaces is evident by the large representation of energy levels (i.e., the large magnitude in the DOS) around the Fermi level (i.e., frontier orbitals). In particular, the diamond (111)-1 × 1 surface shows a large peak at the Fermi level that mainly originates from the 2p orbitals of C and which reflects the radical and reactive character of the carbon dangling bonds. There is an energy gap just below the Fermi level (from -2.5 to -0.5 eV). This gap originates from the energy difference of the (lower energy) C-C bonds and the (higher energy) dangling bond and is not observed for the 2 × 1 reconstruction. The many peaks close to the Fermi level are probably originating from the delocalized electrons of the Pandey chain, i.e. by overlap of localized C orbitals. In

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Figure 3. Electrostatic potential mapped onto the charge density of the (a) (111)-1 × 1, (b) (111)-2 × 1, (c) (110)-1 × 1, (d) (100)-2 × 1, and (e) (100)-1 × 1 surfaces of diamond (where, for example, 7.000e-3 represents 7.000 × 10-3). White areas indicate the more positive potential areas, whereas the dark areas denote the more negative potential areas.

Figure 4. Partial density of states for the topmost carbon atoms of the diamond (111)-1 × 1 and -2 × 1 surfaces.

addition, the (100)-1 × 1 surface also resembles a -2.5 to -0.5 eV energy gap similar to that of the (111)-1 × 1 surface, but the two dangling bonds increase the peak at the Fermi level and furthermore, there is some overlapping between the two C-C bonds and the two dangling bonds delocalizing some electrons to these states. The DOS profile of the (110) surface reveals a quite reactive surface, with a large density of states (i.e., a high peak) around the Fermi level. Whereas the (111)-1 × 1 and (100)-1 × 1 surfaces each have a reconstruction to convert into (and thereby

Figure 5. Partial density of states for the topmost carbon atoms of the diamond (110)-1 × 1 surface.

lower surface energies, as well as yielding a less reactive surface), the (110) surface shows no apparent reconstruction and should therefore have many accessible frontier orbitals available for chemical reactions. The energy gain obtained when undergoing a surface reconstruction from (100)-1 × 1 to (100)-2 × 1 is evident from the pDOS profile of the topmost carbon atoms, as can be seen in Figure 6. The many occupied levels just below the Fermi level (i.e., the peak with the large amplitude) are shifted toward more negative (i.e., more energetically favorable) levels. Especially, there is a large increase in

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Figure 6. Partial density of states for the topmost carbon atoms of the diamond (100)-1 × 1 and -2 × 1 surfaces.

the state density at -20 eV, which is a direct consequence of the C-C double bond. Chemical reactions will generally involve the frontier orbital electrons at, or nearby, the Fermi level, where electrons are more susceptible to interactions compared to deeper energy levels (sorbitals). Analysis of frontier orbitals may provide further important information about surface reactivity, and this will be described in section 3.4 in terms of HOMO/LUMO orbital mapping. 3.4. HOMO and LUMO Orbitals. The mapping of the HOMO and LUMO onto the charge density have also been performed in the present investigation and is shown in Figure 5 as the contribution of these orbitals to the total electron density. For all surfaces studied, the black color indicates a negative value and white color indicates a positive value. A borderline between black and white areas denotes a nodal surface where destructive interference minimizes the electron density from the orbitals. Hence, many adjacent black and white areas are signs of antibonding character of the orbitals studied. Basic molecular orbital (MO) theory of polyatomic molecules states that the most bonding MOs are obtained for a large overlap of atomic orbitals with similar energies and without any nodes in the bonds. The results for the (111)-1 × 1 surface show that the mapping of electron densities is not centered around any surface atom, and hence, it is hard to draw any conclusion about surface reactivity from those corresponding orbitals. In addition, as can be seen in Figure 4, the (111)-1 × 1 surface shows a large DOS peak around the Fermi level. A sharp peak around the Fermi level is an indication of delocalization of electrons and, consequently, a high degree of electron-electron interaction. Conversely, the (111)-2 × 1 Pandey chain (Figure 7b) shows two interesting features. At first, the large HOMO and LUMO contributions to the isodensity coincide perfectly with the locations of the topmost carbon atoms (i.e., those within the Pandey chain) and the most probable chemisorption site.52 Second, the (111)-2 × 1 reconstruction should broaden the energy levels close to the Fermi level due to the many nodal planes between the HOMO and LUMO of the Pandey chain, and this is also the situation as can be seen when studying the density of states within Figure 4. The large peak at the Fermi level for the (111)-1 × 1 surface is divided into smaller peaks around E ) 0 when the surface has reconstructed to the 2 × 1 configuration. In addition, the energy separation of the HOMO and LUMO for the diamond (111)-2 × 1 surface, and in particular the evidence for the lower-lying HOMO level, is

Petrini and Larsson evident from Figure 5a; there are more nodal planes of the LUMO. Moreover, the LUMO of the (110)-1 × 1 surface is highly unsymmetrical, whereas the HOMO is mainly of bonding character. The orbital energy levels show that the energy separation between the HOMO and LUMO is rather large: 1.53 eV. However there are six orbitals higher than the Fermi levels that lie at the same energy, i.e., they are degenerate, and explains to some extent the reactivity of the (110) surface. The diamond (100)-1 × 1 surface has a HOMO of largely antibonding character, as can be seen in Figure 7d. Atomic orbitals from each surface atom contribute to the orbital (HOMO). However, all of the neighbor contributions are of opposite sign and, hence, antibonding. Non-nearest contributions are of identical sign, and their constructive interference is intrinsically weak. However, the reconstruction toward diamond (100)-2 × 1 yields a HOMO that is much more bonding. In fact, the here-presented calculations show a very favorable reconstruction energy of -1.85 eV per surface atom.. Furthermore, the reconstruction from 1 × 1 to 2 × 1 was found to be spontaneous, i.e. without any energy barrier. The HOMO contribution to the electron density is largest for the bond within the C-C dimer (despite the fact that there is a large accumulation of electrons near the C-C bond): the orbital of the C-C dimer bond is not a frontier orbital due to the lower energy level. The rather strong double bond (see Figure 2e) lowers the energy of those orbitals, and they are no longer the highest occupied orbital. The LUMO of the diamond (100)-1 × 1 surface has no nodal plane mapped on the isodensity and should therefore be of rather bonding character. However, the reconstruction of the (100) surface to the 2 × 1 configuration results in many nodal planes for the LUMO density. Thus, the reconstruction of the diamond (100) surface would separate the HOMO and LUMO, whereby the lowering of the HOMO-level accounts for the large reconstruction energy. This HOMO-LUMO energy separation is indeed observed, as presented in Figure 6. There is a bandgap between the energy levels just below and above the Fermi level, which increases by 1.03 eV when the (100)-1 × 1 surface reconstructs to the 2 × 1 configuration. The rather wide distribution of energy states around the Fermi level for the (100)-1 × 1 surface is manifested by the small orbital overlaps within the HOMO (in the otherwise very unfavorable configuration of many nodal planes). 3.5. Fukui Functions. One of the most successful ways to determine chemical reactivity of a molecule (or periodic surface) is by analyzing the frontier orbitals originally formulated by Fukui function, and further developed by Yang and Parr.25,29 Three types of FFs have in this study been analyzed; the f-, f+, and f0 which correspond to the reactivity toward electrophilic, nucleophilic, and radical attack (the latter being the average of the first two functions). To predict reactive sites, the FF orbitals are mapped onto an isosurface charge density. The FF values have been assigned to the charge density and are color-coded that range from white (the largest value, most susceptible to the specific attack) to black (the smallest value, least susceptible to the specific attack). As can be seen in Figure 8, both the electrophilic and nucleophilic reactive sites of the diamond (111)-1 × 1 surface are centered above the topmost carbon atoms, and, hence, the sites for the radical attack are also positioned above these atoms. This is reasonable since a carbon atom that has one unpaired electron, as the topmost carbon atoms of the (111)-1 × 1 surface have, should be very reactive, and thereby react strongly toward both electrophilic and nucleophilic attacks. As expected, the FF values decrease considerably around the topmost carbon atoms and reach the minimum value at the positions of the carbon atoms in the second atomic layer (the

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Figure 7. Mapping of HOMO and LUMO orbitals onto the charge density isosurface of a diamond (111)-1 × 1 (a), (111)-2 × 1 (b), (110)-1 × 1 (c), (100)-1 × 1 (d), and (100)-2 × 1 (e) surface, respectively (where, for example, 3.348e-2 represents 3.348 × 10-2). The panels in the upper row show the HOMO densities, whereas the lower row shows the LUMO densities.

values ranges from +3.51 × 10-4 to +2.42 × 10-3, from +3.53 × 10-4 to +2.42 × 10-3, and from +3.52 × 10-4 to +2.38 × 10-3 for the f-, f+, and f0 functions, respectively). The mapping of the f- function is in perfect agreement with the electrostatic potential; see section 3.2 and Figure 3. The accumulation of electrons correlates well with the site for electrophilic attack. The FF values for the (111)-2 × 1 reconstruction (as seen in Figure 8b) show indications of a totally different behavior. The electrophilic and nucleophilic reactive sites are alternatively located above the topmost carbon atoms within the Pandey chain. This is conceivable since the HOMO (f+) and LUMO (f-) are strongly represented on alternating sides of the carbon atoms of the Pandey chain (see section 3.4). The radical FF contour map shows that the (whole) Pandey chain should be susceptible toward radical species. All of the mapped FFs indicate that carbon atoms that are located between the Pandey chain (dark circles) are very unreactive, as displayed by the dark shade. Neither nucleophilic or electrophils nor radicals should have any tendency to react at these sites. The FF values ranges from -2.06 × 10-4 to +3.27 × 10-3; hence, the Pandey chain shows a broader spectrum in the reactive-nonreactive areas than the unreconstructed 1 × 1 surface. The most probable chemisorption spot of species, as the Fukui functions indicate, on the diamond (110) surface is shown in Figure 6c). The position of these electrophilic and nucleophilic areas diverge somewhat compared to the location of the HOMO/LUMO and the mapping of the electrostatic potential. The Fukui function values are intermediates of those in the (111)-2 × 1, (100)-2 × 1 and (111)-1 × 1, (100)-1 × 1 surfaces (from +1.40 × 10-3 to +2.68 × 10-3, from +9.61 × 10-4 to +3.30 × 10-3, and from +1.30 × 10-3 to +2.95 × 10-3, for f-, f+, and f0, respectively). The areas of the (100)-2 × 1 surface that are susceptible to electrophilic and nucleophilic attack are located on the same position; to the left and right of the C-C dimer as shown in Figure 8e). However, the nucleophilic attack positions are remarkably strong (4.59 × 10-3) and are perfectly correlated with the location of the LUMO as shown in Figure 7e). Furthermore, since the HOMO of the (100)-2 × 1 surface shows strong contributions to the isodensity between the C-C

dimer rows, it is plausible to assume that the electrophilic attack (f-) sites are not directly above the C-C dimer: these bonds are strong and do not respond favorably to electron addition or removal. 4. Discussion The reactivity of nonterminated, diamond low-index surfaces may be studied using density functional theory and electronic structure calculations involving, e.g., the electrostatic potential, Kohn-Sham orbitals, density of state graphs, and Fukui functions. Both the site and the relative degree of reactivity may be deducted, and overall, the results correlate well with each other. Mapping electronic properties, onto a charge density isosurface is motivated since this surface is accessible for interaction by other species including growth species, functionalization groups, etc. The following conclusions may be drawn: (i) areas of high electrostatic potential are very similar to the ones represented by the HOMO and most susceptible to electrophilic attack determined by using Fukui functions; (ii) the site for nucleophilic attack (f+) and the site for electrophilic attack often show coherence (a plausible explanation is that the nonterminated diamond surfaces are rather reactive due to the topmost unsaturated carbon atoms and respond well to electron withdrawal or removal); (iii) the mapping of the frontier orbital (HOMO and LUMO) of the diamond surface on the charge density isosurface shows not only the contribution, but also the bonding character of those orbitals. Less nodal planes equal a more favorable (i.e., more bonding) orbital. Reconstruction of the diamond (111) and (100) surfaces to the 2 × 1 configuration yielded LUMOs of rather antibonding nature and HOMOs of a more bonding character. In particular, the (100)-1 × 1 HOMO is of significantly antibonding character, and reconstruction to the 2 × 1 surface widens the HOMO-LUMO energy gap by 1.0 eV. However, there are some discrepancies in the results, the HOMO and LUMO of the (111) surface in highly unsymmetrical, and no real conclusion may be drawn from those. Furthermore, the area of the largest electrostatic potential for the (100)-1 × 1 surface is located adjacent to two surface

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Figure 8. Fukui functions mapped onto the charge density isosurfaces of diamond (111)-1 × 1 (a), (111)-2 × 1 (b), (110) (c), (100)-1 × 1 (d), and (100)-2 × 1 (e) and shows the susceptibility of electrophilic (left column), nucleophilic (middle column), and radical (right column) attack (where, for example, 2.424e-3 represents 2.424 × 10-3).

carbons, whereas the f- function locates this site directly above the atoms. The site predicted by the electrostatic potential calculations is only based upon the location of charge (i.e., of the electrons). Hence, areas of large electrostatic potential may

be nonreactive and rather inaccessible for chemical interactions. In addition, the position of the HOMO of the (110) and the (100)-2 × 1 surface does not match those of the Fukui functions. The inconsistency between the HOMO/LUMO and

Reactivity on Nonterminated Diamond Surfaces Fukui functions has been observed before and is ascribed to the more flexible Fukui functions that accounts for the charge density relaxation.25 A number of reflections of the results within this study, based on other theoretical adsorption studies, can be made. The present study could help to explain the tendency53 for oxygen to bind in the on-top rather than bridge position for the (111)-1 × 1 surface. The reactive sites (determined through Fukui functions and electrostatic potential) are located above the carbon atoms, and there is a rather long distance to the next reactive site (2.52 Å). One oxygen atom was found to be highly unstable relative to one on-top oxygen and one unsaturated carbon atom. Hydrogen, oxygen, and OH groups, chemisorbed on the (111)-1 × 1 surface, all formed covalent bonds in the position predicted in this study. Also, investigations have shown53,54 that the (111)-2 × 1 Pandey chain locates the adsorbed species not directly above the topmost carbon atoms, as may be predicted in this study. Rather, their positions are somewhat shifted away from the Pandey chain in a perpendicular direction. The location of the HOMO and LUMO on the (111)-2 × 1 is identical to the binding site for H and OH groups. Oxygen adsorbed in the bridge position on the (111)-2 × 1 surface is explained by the fact that the divalent oxygen radical may form a C-O-C bond by the readily available, in terms of geometry and the electronic structure, frontier orbitals. It has been shown50 that the final structure for a diamond (100)-1 × 1 surface fully covered with oxygen prefers the bridge position, in terms of adsorption energies, closely followed by the on-top position (-6.21 and -5.95 eV, respectively). The latter position is in this study determined by the electrostatic potential (see Figure 3) and the former by the susceptibility of electrophilic and radical attack (see Figure 6) as well as the location of the HOMO (see Figure 5). Hydrogen and OH groups adsorbed in the position predicted by the Fukui function and HOMO/LUMO: somewhat adjusted perpendicular to the C-C dimer direction. Oxygen was found to adsorb in the on-top position; however, as the surface coverage of oxygen increased it also induced a 2 × 1 to 1 × 1 reconstruction of the surface. Oxygen in the bridge position is unfavorable due to the replacement of two hydrogen atoms but is stable with respect to the on-top position. 5. Summary Electronic properties of the topmost carbon atoms of nonterminated, diamond (111)-1 × 1, (111)-2 × 1, (110), (100)-1 × 1, (100)-2 × 1 surfaces have been studied using density functional theory. These properties have been related to the surface reactivity, where positions susceptible to electrophilic, nucleophilic, and radical attack have been analyzed in detail. The following properties have been studied: electron deformation density, HOMO/LUMO orbital occupation, density of state graphs, electrostatic potential, and three types of Fukui functions. The results shows in general these indicators listed above do correlate well with each other; the site most probable to experience an electrophilic attack corresponds to the site of high electrostatic potential, large values of the electrophilic Fukui function, and the location of the HOMO. The sites susceptible to nucleophilic reactions determined by the Fukui function correspond to the location of the LUMO. Furthermore, HOMO/ LUMO orbital maps can be capable of displaying the bonding character of these frontier orbitals. Density of state graphs were used to study the distribution of energy states around the Fermi level, as well as in studying the energies for surface reconstruction. Delocalized electron from orbital overlapping exhibit many small peaks in the energy states of the DOS. Since the Fukui

J. Phys. Chem. C, Vol. 112, No. 37, 2008 14375 function takes into account the electron relaxation, i.e., the response of addition or removal of (partial) electrons, it should be one of the most reliable and robust method available. Finally, the results within the present study were compared to (theoretical) investigation of the adsorption of hydrogen and oxygen species onto these low-index diamond surfaces. Acknowledgment. This work was supported by the Swedish Research Council (VR). The results were generated using the program package Material Studio, developed by Accelrys Inc., San Diego. First-principle calculations were done with the Dmol3program within Material Studio 3.1.5. This work was also supported by the RTN-project DRIVE (MRTN-CT-2004512224) supported by the European Commission. References and Notes (1) Hayashi, K.; Tachibana, T.; Kawakami, N.; Yokota, Y.; Kobashi, K.; Ishihara, H.; Uchida, K.; Nippashi, K.; Matsuoka, M. Diamond Relat. Mater. 2006, 15, 792. (2) Pace, E.; Pini, A.; Corti, G.; Bogani, F.; Vinattieri, A.; Pickles, C. S. J.; Sussmann, R. CVD diamond optics for ultraViolet, Porto, Portugal, 2001. (3) Aleksov, A.; Kubovic, M.; Kaeb, N.; Spitzberg, U.; Bergmaier, A.; Dollinger, G.; Bauer, T.; Schreck, M.; Stritzker, B.; Kohn, E. Diamond Relat. Mater. 2003, 12, 391. (4) Kasu, M.; Ueda, K.; Ye, H.; Yamauchi, Y.; Sasaki, S.; Makimoto, T. Diamond Relat. Mater. 2006, 15, 783. (5) Xu, J. J.; Wei, Z.; Qing-Qing, Q.; Hong-Yuan, C. Biosens. Bioelectron. 2006, 22, 649. (6) Kagan, H.; Adam, W.; de Boer, W.; Borchi, E.; Bruzzi, M.; Colledani, C.; D’Angelo, P.; Dabrowski, V.; Dulinski, W.; van Eijk, B.; Eremin, V.; Fizzotti, F.; Frais-Kolbl, H.; Furetta, C.; Gan, K. K.; Gorisek, A.; Griesmayer, E.; Grigoriev, E.; Hartjes, F.; Hrubec, J.; Huegging, F.; Kaplon, J.; Kass, R.; Knopfle, K. T.; Krammer, M.; Lange, W.; Logiudice, A.; Manfredotti, C.; Mathes, M.; Menichelli, D.; Mishina, M.; Moroni, L.; Noomen, J.; Oh, A.; Pernegger, H.; Pernicka, M.; Potenza, R.; Riester, J. L.; Rudge, A.; Sala, S.; Schnetzer, S.; Sciortino, S.; Stone, R.; Sutera, C.; Trischuk, W.; Velthuis, J. J.; Vincenzo, B.; Weilhammer, P.; Weingarten, J.; Wermes, N.; Zeuner, W. Nucl. Instrum. Methods Phys. Res., Sect. A 2006, 565, 278. (7) Rezek, B.; Watanabe, H.; Shin, D.; Yamamoto, T.; Nebel, C. E. Diamond Relat. Mater. 2006, 15, 673. (8) Song, K.-S.; Nakamura, Y.; Sasaki, Y.; Degawa, M.; Yang, J.-H.; Kawarada, H. Anal. Chim. Acta 2006, 57, 3–574. (9) Kanazawa, H.; Kwang-Soup, S.; Sakai, T.; Nakamura, Y.; Umezawa, H.; Tachiki, M.; Kawarada, H. Diamond Relat. Mater. 2003, 12, 618. (10) Petrick, S.; Benndorf, C. Diamond Relat. Mater. 2001, 10, 519. (11) Park, J.; Quaiserova-Mocko, V.; Peckova, K.; Galligan, J. J.; Fink, G. D.; Swain, G. M. Diamond Relat. Mater. 2006, 15, 761. (12) Williams, O. A.; Jackman, R. B. Semicond. Sci. Technol. 2003, 18, 34. (13) Laikhtman, A.; Hoffman, A.; Kalish, R.; Avigal, Y.; Breskin, A.; Chechik, R.; Shefer, E.; Lifshitz, Y. Appl. Phys. Lett. 1998, 73, 1433. (14) van der Weide, J.; Zhang, Z.; Baumann, P. K.; Wensell, M. G.; Bernholc, J.; Nemanich, R. J. Phys. ReV. B: Condens. Matter Mater. Phys. 1994, 50, 5803. (15) Zhang, Z.; Wensell, M.; Bernholc, J. Phys. ReV. B: Condens. Matter Mater. Phys. 1995, 51, 5291. (16) Maier, F.; Ristein, J.; Ley, L. Phys. ReV. B: Condens. Matter Mater. Phys. 2001, 64, 165411. (17) Larsson, K.; Bjorkman, H.; Hjort, K. J. Appl. Phys. 2001, 90, 1026. (18) Hara, T.; Yoshitake, T.; Fukugawa, T.; Ling yun, Z.; Itakura, M.; Kuwano, N.; Tomokiyo, Y.; Nagayama, K. Diamond Relat. Mater. 2004, 13, 622. (19) Maki, T.; Miyake, H.; Sugahara, K.; Kobayashi, T. Diamond Films and Technology 1998, 8, 1. (20) Kornelak, P.; Michalak, A.; Najbar, M. Catal. Today 2005, 101, 175. (21) Halim, W. S. A.; Shalabi, A. S. Appl. Surf. Sci. 2004, 221, 53. (22) Hoffmann, M.; Rychlewski, J. J. Am. Chem. Soc. 2001, 123, 2308. (23) Koper, M. T. M.; van Santen, R. A.; Wasileski, S. A.; Weaver, M. J. J. Chem. Phys. 2000, 113, 4392. (24) Garcia-Ochoa, E.; Cruz, J.; Pandiyan, T. J. Electroanal. Chem. 2005, 583, 8. (25) Bartolotti, L. J.; Ayers, P. W. J. Phys. Chem. A 2005, 109, 1146. (26) Pearson, R. G. J. Am. Chem. Soc. 1963, 85, 3533. (27) Fukui, K.; Yonezawa, T.; Shingu, H. J. Chem. Phys. 1952, 20, 722. (28) Fukui, K. Science 1982, 218, 747.

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