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Physical Review B, 55(23), 15868-73.","mass_i":1515011812,"publisher_t":"American Physical Society","description_t":"First-principles calculations on the geometry and stability of AlnBm clusters have been carried out to examine the effect of size, composition, and electronic-shell filling on their relative stability. It is shown that although Al and B are both trivalent, a BAl12 cluster is more stable than an Al13 by 3.4 eV. The enhanced stability is shown to arise due to the relaxation of surface strain in the Al cage when the central Al is replaced by a smaller B atom. Replacement of an additional Al by B to produce B2Al11 results in deformation of the icosahedral BAl12 cage and reduces the stability. The possibility of forming crystals using BAl12 and Cs is examined via total-energy calculations. It is shown that a solid with icosahedral or cuboctahedral BAl12 and Cs and having the CsCl structure is metastable and could be synthesized.","first_page_t":"15868","rights_management_t":"(c) American Physical Society http://dx.doi.org/10.1103/PhysRevB.55.15868","title_t":"(BAl12)Cs: a cluster-assembled solid","journal_title_t":"Physical Review B","id":704735,"publication_type_t":"Journal Article","parent_i":0,"type_t":"Text","subject_lcsh_t":"Microclusters","thumb_s":"/72/f4/72f43b71e39f51649ae32631614bc18289156d94.jpg","last_page_t":"15873","oldid_t":"uspace 2557","metadata_cataloger_t":"CLR; car","format_t":"application/pdf","modified_tdt":"2012-07-11T00:00:00Z","school_or_college_t":"College of Engineering","language_t":"eng","issue_t":"23","file_s":"/8f/8f/8f8f751e2ad816e3c58e02b7ab9d8d5fb0d15c30.pdf","format_extent_t":"139,787 bytes","citatation_issn_t":"0163-1829","other_author_t":"Ashman, C.; Khanna, S. N.; Jena, P.; Kaplan, T.; Mostoller, M.","created_tdt":"2012-06-13T00:00:00Z","_version_":1664094464819331072,"ocr_t":"PHYSICAL REVIEW B VOLUME 55, NUMBER 23 15 JUNE 1997-I (BA112)Cs: A cluster-assembled solid C. Ashman and S. N. Khanna Physics Department, Virginia Commonwealth University, Richmond, Virginia 23284-2000 Feng Liu Material Research Group ERB 729, University of Wisconsin, 1500 Engineering Drive, Madison, Wisconsin 53760 P. Jena Physics Department, Virginia Commonwealth University, Richmond, Virginia 23284-2000 T. Kaplan and M. Mostoller Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (Received 9 January 1997) First-principles calculations on the geometry and stability of AlnBm clusters have been carried out to examine the effect of size, composition, and electronic-shell filling on their relative stability. It is shown that although Al and B are both trivalent, a BAl12 cluster is more stable than an Al13 by 3.4 eV. The enhanced stability is shown to arise due to the relaxation of surface strain in the Al cage when the central Al is replaced by a smaller B atom. Replacement of an additional Al by B to produce B2Al11 results in deformation of the icosahedral BAl12 cage and reduces the stability. The possibility of forming crystals using BAl12 and Cs is examined via total-energy calculations. It is shown that a solid with icosahedral or cuboctahedral BAl12 and Cs and having the CsCl structure is metastable and could be synthesized. [S0163-1829(97)03124-X] i. introduction An extensive body of work on atomic clusters indicates that they display a variety of novel electronic, magnetic, thermal, and chemical properties.1 The properties vary strongly with size and/or composition. The possibility of producing clusters of a given size and composition2 and with tailored properties provides hope that a new class of materials with clusters as building blocks3 could be synthesized. The major difficulty in this process arises due to the fact that clusters are metastable and have a tendency to coalesce when assembled. This can be prevented in one of two ways- either by isolating these clusters in matrices or by coating them with surfactants. An alternative route is to find clusters that are so stable that the intracluster interaction is stronger than the intercluster interaction. Thus these clusters upon assembling will tend to keep their individual identity intact. Even though such a cluster-assembled material would be metastable against dissociation into their bulk phases, an energy barrier against such dissociation can make the synthesis possible. Solids made out of C60 clusters4,5 are examples of such cluster-assembled materials. In a recent paper, two of the present authors proposed3 that it may be possible to synthesize a new class of cluster materials by assembling compound metallic clusters provided the clusters are designed to satisfy certain geometric and electronic-shell structures. Their arguments were based on the observation that the mass spectra of simple metal clusters generated in beams show pronounced peaks at ‘‘magic numbers'' corresponding to closing of the electronic shells.6 This can be understood within a simple picture in which the cluster is regarded as a jellium sphere with a uniform distribution of positive charge. The ‘‘magic numbers'' correspond to the cases where the electrons fill the electronic shells of this super atom, i.e., clusters containing 2, 8, 18, 20, 40,... electrons. The electronic effects are particularly dominant at small sizes, whereas at larger sizes, the most stable clusters correspond to filled geometric shells7 such as filled icosahedral shells. Khanna and Jena8 proposed that if a metallic cluster could be designed in such a manner that it has a compact geometry as well as a filled electronic shell, it will be stable as well as chemically less active due to the filled electronic shell and hence may be a likely candidate for forming cluster solids. They proposed CAl12, which has a compact icosahedral structure and 40 valence electrons, as a likely candidate. Indeed, the CAl12 cluster was found to be more stable than Al13 by 4.4 eV. It is also interesting to note that the chemistry of the Al13 cluster resembles that of a halogen atom since its electron affinity of 3.7 eV is close to that of Cl. Motivated by this, Khanna and Jena9 proposed forming a new class of solids analogous to the ionic solid KCl, but replacing Cl with Al13 as the new building block. To examine this possibility, Liu et al.10 carried out ab initio total-energy calculations on a proposed Al13K solid assuming a CsCl structure shown in Fig. 1. They found that while the icosahedral structure for Al13 was preferred for large lattice spacings, reduction of the lattice spacing to minimize the energy led to a change in the geometry of Al13 to cuboctahedral in the minimum-energy structure. The resulting solid, although metastable, resembled fcc Al with K chains in which Al13 units in different cages formed metallic bonds. In this paper we examine the possibility of designing a new solid. We propose BAl12 and Cs as the building blocks of the new solid. The choice of BAl12 is motivated by the fact that in an Al13 icosahedral cluster, the surface Al-Al 0163-1829/97/55(23)/15868(6)/$10.00 55 15 868 © 1997 The American Physical Society 55 (BAl12)Cs: A CLUSTER-ASSEMBLED SOLID 15 869 FIG. 1. Schematic picture of a prototype CsCl solid formed out of Al13 (cuboctahedral or icosahedral) and K atoms. bonds are about 5% longer than the radial bonds. Replacing the central Al by a smaller B atom is expected to relax the surface strain and lead to a more stable BAl12 cluster. In addition the binding energy of the AlB dimer is 0.85 eV larger than that of Al2. Thus BAl12 stands to gain more stability than Al13 from the electronic interaction as well. Since Al and B are both trivalent, we expect Al13 and BAl12 to have the same chemistry, i.e., they should resemble the chemistry of a halogen atom. In forming the solid made of K and Al13 units, we note that the K atom is much smaller in size than an Al13 cluster. In a crystal of KAl13, the space is optimally filled and the Al13 clusters interact strongly. Thus we study a crystal containing BAl12 clusters and Cs atoms since Cs is much larger than K. The chemistry of the building blocks is, however, unchanged since BAl12 is expected to be electronegative and Cs is electropositive. The bonding between BAl12 and Cs is therefore expected to be ionic. We, indeed, show that a combination of these features leads to a BAl12Cs crystal in which the BAl12 may maintain their icosa- hedral structure because of a barrier even though cuboctahe- dral symmetry is energetically preferable by a small margin. We first present a study of the electronic and geometric effects on the stability of individual clusters by studying 13- atom icosahedral BxAly clusters containing one or two B atoms. Both B and Al are trivalent but differ in size. We show that BAl12 has a perfect icosahedral geometry and is 3.43 eV more bound than Al13. The replacement of two Al by two B atoms, although it leaves the number of valence electrons unchanged, places at least one B in the outer shell. The icosahedron thus undergoes deformation and this leads to a reduced stability of B2Al11 compared to BAl12 in agreement with the observed mass spectrum11 of BxAly clusters. Having established the stability of the BAl12 cluster, we show that it has an electron affinity comparable to Al13 and resembles a halogen atom. To further support this observation, we present a calculation of a BAl12 K and show that the alkali-metal atom loses its charge to BAl12. We then examine the possibility of forming a crystalline solid using BAl12 and alkali-metal atoms. In a recent paper12 we had examined such a possibility for Al13 and K and assuming a CsCl structure. To further ensure that this is indeed the structure, in this work, we also present the corresponding results for the NaCl structure and show it to be far less stable than the CsCl structure. The Al13 clusters in a CsCl structure occupy central sites in cubes formed out of alkali-metal atoms. To minimize interaction between clusters, it is desirable to use larger alkali-metal ions. With this in mind we carry out electronic structure calculations on a (BAl12)Cs solid by assuming a CsCl structure and minimizing the total energy as a function of the lattice spacing. It will be shown that starting from large spacing, the energy of the solid with icosahedral- like BAl12 units goes through a minimum as the volume is decreased. Upon further compression, a second minimum corresponding to cuboctahedral BAl12 is obtained which is slightly more stable. The barrier height between the two minima is, however, significant, and it is possible that the material assembled by collecting individual BAl12 units and Cs will settle into either structure depending on the method of synthesis. In Sec. II we describe our methods and results for BxAly clusters. Section III contains details of the calculations and results on the solid phase. Section IV gives a summary of our findings. ii. electronic structure and stability of b*aiy clusters The electronic structure calculations on clusters were carried out using a linear combination of atomic orbitals molecular-orbital approach within the density-functional scheme.12 The particular version we have used is based on a representation of molecular orbitals in terms of Gaussian functions centered at the atomic sites.13 The Hamiltonian matrix elements are calculated by representing the charge density and the exchange-correlation potential in terms of auxiliary Gaussians centered at the atomic sites and in between atoms. To simplify the computations, the atomic cores have been replaced by norm conserving nonlocal pseudopotentials.14 In this work we have used the form proposed by Bachelet, Hamann, and Schluter14 along with the spin-polarized [local spin density approximation (LSDA)]15 870 C. ASHMAN et al. 55 TABLE I. Geometrical parameters and binding energies of Al13, BAl12, BAl12-, and (BAl12) K clusters. Cluster Radial distance of icosahedron (a0) Binding energy/atom (eV) Al13 5.06 2.82 BAl12 4.76 3.09 BAl-2 4.81 3.36 BAl12K 4.80 3.66 Ceperley-Alder form for exchange and correlation.15 The computations involve first solving the Kohn-Sham equations16 on a radial mesh of points for the isolated atoms. The numerical atomic orbitals are then fitted by Gaussians whose exponents are varied to optimize the fit. The Gaussian exponents serve to form the basis set. The molecular orbitals are the linear sum of Gaussians with coefficients determined by a self-consistent solution of the molecular Kohn-Sham equations. The details of the method are described in earlier 13 papers.13 Before we present our results on bigger clusters, it is useful to look at the quality of our basis functions. For B, the basis function had 5 s and 4p Gaussians. The calculated atomic ionization potential was 8.41 eV compared to the experimental value of 8.3 eV. For B2 we calculate a bond length of 3.06a0 and a binding energy of 3.68 eV compared to the corresponding experimental values of 3.0a0 and 3.08 eV, respectively. For Al, the basis functions had 5 s and 4p Gaussians. For Al2 we obtain a triplet ground state with a bond length of 4.75a 0 and a binding energy of 1.78 eV compared to experimental values of 4.84a 0 and 1.93 eV, respectively. These comparisons show that the basis functions and the approach are reasonably accurate. We begin with the BAl12 cluster. First we consider the effect of replacing an Al atom in Al13 by a B atom. The hetero atom can occupy a surface site or a central site depending on the energetics. We first calculated an AlB dimer. It has a binding energy of 2.63 eV compared to 1.78 of Al2, indicating that BAl bonds are stronger. Further, the surface bonds in the Al13 icosahedron are 5% longer than the radial bonds. The B atom is smaller than an Al atom and if substituted at the central site, it can relax the surface stress. These considerations clearly suggest that the B atom will occupy the central site. We therefore optimized the geometry of an icosahedral cluster with a central B. The bond lengths and binding energy of BAl12 are given in Table I and compared with corresponding values of Al13. As expected, the radial bonds are shorter and the binding is 3.4 eV higher than in Al13. We believe that this is largely due to the relaxation of the surface bonds as well as due to enhanced bonding between Al and B. This enhanced stability is reflected in the mass spectrum. Nakajima et al.11 have generated BAlK clusters in beams and indeed find a magic peak at BAl12. While the new cluster is stabilized by the geometry, it has the same number of electrons (i.e., 39) as Al13. As mentioned before, Al13 has a large electron affinity of 3.7 eV which can be understood within the simple jellium picture as arising due to a hole in the electronic shell closing at 40 electrons. Does BAl12 share this electronic feature with Al13? To explore this possibility, we calculated the electron affinity by optimizing the geometry of the anionic cluster. The addition of an electron produces insignificant changes in the bond lengths but the cluster becomes significantly more stable (see Table I). BAl12 has an electron affinity of 3.6 eV which is close to that of Al13. This shows that the substitution of B for the central Al in Al13 does not affect the chemistry and one should be able to form ionically bound molecules by combining BAl12 with alkali-metal atoms. To investigate this possibility, we calculated the electronic structure and binding of a (BAl12) K cluster. A K atom was brought towards a BAl12 cluster along the on top, bridge, and hollow directions. In each case, the radius of the icosahedral cluster was optimized to minimize the energy. The hollow site was found to be most stable. The icosahedral bond length and the binding energy per atom of (BAl12) K are given in Table I. A Mulliken population analysis of the resulting charge indicates that the K atom loses its electron to BAl12. The bonding is therefore primarily ionic. Assuming complete charge transfer and a uniform sphericity of charge around BAl12, one can write the binding energy of K to the cluster as - e2/r where r is the distance of K from the center of the icosahedron. In our studies, the K atom is 9.037 a.u. from the center. This leads to an electrostatic energy of 3.01 eV. Our self-consistent calculation yields the binding energy of BAl12 with K to be 3.1 eV. This further illustrates that the K atom prefers the hollow site over other sites since at this configuration K can come closest to the center of the icosahedron. We now consider another example that displays the interplay between geometry and electronic effects in clusters by studying clusters containing two B atoms, i.e., replacing an additional Al in BAl12 by B. The additional B must occupy a surface site and since it is smaller than Al, one expects a deformation of the icosahedral geometry. To calculate its structure, note that the cluster still has fivefold symmetry around the axis containing two B atoms. We optimized various bond lengths keeping the fivefold symmetry. The resulting geometry is shown in Fig. 2. Note that the icosahedral cluster undergoes significant geometrical distortions. The BAl surface bonds are 4.21a0 compared to Al-Al bonds of 4.83a0-5.22a0. The cluster has an atomization energy of 3.28 eV per atom as compared to 3.09 eV/atom in BAl12. This is puzzling since experiments on BxAly clusters show that BAl12 is more abundant in the mass spectra than B2Al11. We believe that an analysis of the bonding may provide a clue. Note that whereas BAl12 is spherically symmetric, B2Al11 has large distortions because the B atom in the outer shell is pushed inward and the central B is pushed upward to optimize the B-B bond which is stronger and shorter than B-Al or Al-Al bonds. This generates considerable strain in the outer layer as seen from Fig. 2, which shows that the B-Al bonds involving the surface B to surrounding Al are reduced to 4.2 a.u. compared to all other B-Al bond lengths of around 4.8 a.u. in B2Al11 and in BAl12. This is also reflected in the energetics. The energy difference E ( B2Aln ) + E ( M 13) - 2 E (BM 12) 55 (BAl12)Cs: A CLUSTER-ASSEMBLED SOLID 15 871 B2AI11 B.E./Atom 3.28 eV B 2 Alii B.E./Atom 3.62 eV EA. 4.43 eV FIG. 2. The geometry of B2Al11 and B2Al11 clusters. The bond lengths are in are in atomic units. is 1.1 eV, indicating that the reaction where a B2Al11 and an Al13 combine to generate two BAl12 is energetically favorable. A calculation for the anionic cluster (B2Al11) leads to an electron affinity of 4.4 eV. iii. electronic structure of BA112 and Cs assembled crystal In this section we investigate the possibility of forming a crystalline solid using BAl12 and alkali-metal atoms as the building blocks. Our electronic structure calculations are first principles and have been carried out within the density- functional approximation using a combination of the ultra- soft pseudopotentials17 proposed by Vanderbilt with the preconditioned conjugate gradient algorithm.18 We used neutral 5s25p66s1 as the reference state to construct the cesium potential (the shallow 5 s and 5p core states are included to improve transferability). Nonlocal projectors are introduced for both s and p channels; the cutoff radii (rc) for the s and p valence functions are 2.3a 0 and 1.8a 0, respectively. Each channel is matched to the all-electron wave function at two construction energies (5 s and 6 s eigenvalues for the s channel and 6s and 5p eigenvalues for the p channel). For charge augmentation function, the cutoffs (rinner) are chosen to be 0.8 (l = 0), 1.0 (l = 1), and 1.2 (l = 2). The B potential is generated from a neutral 2s22p1 refer- ence configuration. The cutoff radius (rc) for both s and p wave functions is taken to be 1.7a0 with two construction energies at the s and p eigenvalues. The values for rinner are 0.75 (l = 0), 0.75 (l = 1), and 0.80 a.u. (l = 2). The details of the K and Al potentials have been published elsewhere.10 All the pseudopotentials have been tested by calculating the corresponding bulk and/or dimer structures. In general they agree with experiments within a few percent. In the solid-state calculation, the total-energy and force calculations are performed within the local-density approximation. The Ceperly-Alder form for the exchange- correlation potential15 is used. The electronic solution is obtained via a preconditioned conjugate gradient minimization scheme, with all the bands updated simultaneously. The atomic positions are optimized via a Newtonian damping procedure. A plane-wave cutoff of 20 Ry is used and the Brillouin zone was sampled with 24 special k points in the cubic cell for the Th group and 20 points for the Oh group. To account for the metallic nature, the one-electron Kohn- Sham eigenvalues are broadened with Gaussian functions with a width of 0.1 eV to determine the occupation numbers and the Fermi energy. As mentioned before, because of the dissimilarity in size between the cluster and the alkali-metal atom, the solid is expected to favor a CsCl structure. But one has to worry about a change in geometry of the BAl12 clusters from icosa- hedral to fcc-like (from icosahedron to cuboctahedron) as the solid is formed. To allow this freedom, we arranged the Cs atoms in a cubic structure and placed the BAl12 clusters at the center of the Cs cubes in a manner as shown in Fig. 1. The latter were relaxed within a Th point group using the two edges of the rectangle l1 and l2 as the characteristic lengths. Note that when 11 = 12, the BAl12 cluster becomes cubocta- hedral whereas 11 = 1.618l2 leads to an icosahedral cluster. 1 1 I I T 150 200 250 300 350 400 450 500 550 Volume (A3) FIG. 3. Cohesive energy as a function of volume for Al13K. The solid circles and hollow circles correspond to CsCl arrangement with cuboctatedral and icosahedral Al13 clusters, respectively. The squares are a NaCl arrangement with icosahedral Al13.15 872 C. ASHMAN et al. 55 150 200 250 300 350 400 450 500 550 Volume (A3) FIG. 4. Cohesive energy as a function of volume for BAl12Cs solid. The solid circles and hollow circles correspond to CsCl arrangement with cuboctatedral and icosahedral BAl12 clusters, respectively. In a previous paper we had examined the stability of the ionic solid formed from Al13 and K. In Fig. 3 we show the energies of Al13K in the CsCl structure as a function of volume with an icosahedral-like (hollow circles) and a cuboctahedral (filled circles) central Al13. We also show the energy of a possible NaCl structure (squares). One notices two things. First, as expected, the NaCl structure is far less stable than the CsCl structure. Second, while the solid favors icosa- hedral Al13 clusters at large volumes, the clusters change to the fcc form as one approaches the equilibrium configuration. The final solid thus resembles fcc Al. Can the enhanced stability of BAl12 force it to remain icosahedral? Figure 4 shows the energy as a function of the volume for a CsCl structure composed of BAl12 and Cs. In each case, the energy was minimized by varying the l 1 / l 2 ratio shown in Fig. 1. Starting at the large volume, as the volume is decreased, the crystal with icosahedral units goes through a minimum. The 11/12 ratio changes from 1.68 to 1.69, 1.70, 1.66, 1.72, and 1.53 for the six points shown by hollow circles in Fig. 4. It had a value of 1.72 for the minimum- energy configuration. As mentioned before, the l 1 /l 2 ratio is 1.618 for an icosahedral structure and 1.0 for the cuboctahe- dral structure. The minimum-energy structure in the graph of hollow circles is therefore primarily icosahedral. The energy rises as the volume is further reduced. A second minimum is found when the BAl12 cluster has cuboctahedral symmetry. 6 Energy (eV) FIG. 5. The density of electronic states in the solid composed of icosahedral BAl12 units and Cs. This configuration is marginally more stable than the previous structure. However, unlike the case of Al13, the minimum with icosahedral BAl12 units is separated from this more stable configuration by a barrier of about 0.3 eV. This indicates that it may be possible to form a cluster material with icosahedral subunits by assembling BAl12Cs clusters. To examine the electronic structure of the resulting solid, we calculated the electronic density of states. These are shown in Fig. 5 where the Fermi energy is chosen as the zero of energy. Note that there is an appreciable density of states at the Fermi energy, indicating that the solid is metallic. iv. summary To summarize, we have shown how the size, geometry, and composition can be used to control the stability and electronic structure of clusters. An Al13 cluster is icosahedral, and the replacement of the central Al by another trivalent B atom enhances the stability largely due to relaxation of the surface strain. If another Al in BAl12 is replaced by B to form B2Al11 the cluster undergoes significant geometrical distortions. All three clusters have high electron affinities, thus promising to be candidates to form ionically bound cluster compounds with alkali-metal atoms. For the case of Al13, however, the clusters undergo a transition to cubocta- hedral form as the Al13K solid is formed. A CsCl solid formed from Cs and BAl12 units has energy minima for both the icosahedral and cuboctahedral BAl12 clusters separated by an energy barrier of 0.3 eV. acknowledgment This work was funded by a grant from the Department of Energy (Grant No. DE-FG05-87ER45316). 1 Physics and Chemistry of Finite Systems: From Clusters to Crystals, edited by P. Jena, S. N. Khanna, and B. K. Rao (Kluwer, Dordrecht, 1992). 2 Proceedings of the Sixth International Conference on Small Particles and Inorganic Clusters [Z. Phys. D 26 (1993)]. 3S. N. Khanna and P. Jena, Phys. Rev. Lett. 69, 1664 (1992). 4 W. Kratschmer, L. D. Lamb, K. Fostiropoulos, and D. R. Huffman, Nature (London) 347, 354 (1990); H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl, and R. E. Smalley, ibid. 318, 162 (1985).55 (BAl12)Cs: A CLUSTER-ASSEMBLED SOLID 15 873 5A. F. Hebard, M. J. Rosseinsky, R. C. Haddon, D. W. Murphy, S. H. Glarum, T. T. M. Palstra, A. P. Ramirez, and A. R. Kortan, Nature (London) 350, 600 (1991). 6W. D. Knight, K. Clementer, W. A. de Heer, W. A. Saunders, M. Y. Chou, and M. L. Cohen, Phys. Rev. Lett. 52, 2141 (1984). 7 T. P. Martin, T. Bergmann, H. Gohlich, and T. Lange, Chem. Phys. Lett. 172, 209 (1990). 8S. N. Khanna and P. Jena, Phys. Rev. B 51, 13 705 (1995). 9S. N. Khanna and P. Jena, Chem. Phys. Lett. 219, 479 (1994). 10F. Liu, M. Mostoller, T. Kaplan, S. N. Khanna, and P. Jena, Chem. Phys. Lett. 248, 213 (1996). nA. Nakajima, T. Sugioka, T. Kishi, and K. Kaya, in Physics and Chemistry of Finite Systems: From Clusters to Crystals, edited by P. Jena, S. N. Khanna, and B. K. Rao (Kluwer, Dordrecht, 1992), p. 99. 12P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). 13 F. Reuse, S. N. Khanna, V. de Coulon, and J. Buttet, Phys. Rev. B 41, 11 743 (1990). 14 G. B. Bachelet, D. R. Hamann, and M. Schluter, Phys. Rev. B 26, 4199 (1982). 15D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980); J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981). 16W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). 17D. Vanderbilt, Phys. Rev. B 41, 7892 (1990). 18 M. P. Teter, M. C. Payne, and D. C. Allan, Phys. Rev. B 40, 12 255 (1989)."}]},"highlighting":{"704735":{"ocr_t":[]}}}