Bonding and magnetism in transition metal sandwich structures with the aromatic hydrocarbon coronene C24H12 outer layers

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Chemical Physics 342 (2007) 223–235 www.elsevier.com/locate/chemphys

Bonding and magnetism in transition metal sandwich structures with the aromatic hydrocarbon coronene C24H12 outer layers Michael R. Philpott a

a,b,*

, Yoshiyuki Kawazoe

a

Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Sendai 980-8577, Japan b 1631 Castro Street, San Francisco, CA 94114, USA Received 6 August 2007; accepted 26 September 2007 Available online 13 October 2007

Abstract Plane wave based ab initio density functional theory has been used to study the chemical bonding and magnetism of transition metal atoms between coronene molecules in sandwich structures Mn(C24H12)2 where n = 7 and M = Cr, Fe, Pd. Symmetry conditions permit the metal atoms to occupy either a central site with g6-coordination as in the metal bis-benzene molecules M1(C6H6)2 or a lower symmetry edge site with g2- or g3-coordination. In some cases at the edge sites the metal atoms crimped the edges of the sandwich towards the smaller separations of the bis-benzene molecules. However, since this effect also depended on local metal atom spin, the sandwich cross-sections could be concave in one symmetry plane and convex in an orthogonal plane. The lowest energy states of the sandwiches had spin S = 5 (Cr), 6 (Fe) and 0 (Pd). The high spin systems occurred with a larger metal–ring spacing so that a concomitantly weaker electric field crossed the metal atom compared to the bis-benzene molecules which have S = 0 (Cr), 2 (Fe) and 0 (Pd) in the ground electronic state. In the spin polarized ground states the unpaired electrons resided exclusively on the metal atoms. In the Pd sandwich the excited states with spin S = 1 and S = 2 had qualitatively similar spin distributions to the Fe and Cr structures, with the difference that there was a much greater leakage of spin density onto the nearby carbon atoms. In all the sandwiches the spin density was not evenly distributed amongst metal atoms, and depended on the environment of the metal as gauged for example by the metal–nearest ring separation.  2007 Elsevier B.V. All rights reserved. Keywords: Sandwich molecules; DFT; Density functional theory; Coronene; Chromium; Iron; Palladium; Aromatic hydrocarbon; Magnetism; Chemical bonding; Organometallic molecules; Kohn–Sham levels; ELF

1. Introduction In this paper, we report plane wave based ab initio density functional theory (DFT) calculations of the structure and magnetism of transition metal (M = Cr, Fe, Pd) atom arrays sandwiched between coronene molecules. The metal atoms chosen span the first and second transition metal rows and encompass an interesting range of chemical bonding and magnetic properties. The molecule coronene (C24H12), a D6h symmetric peri-condensed aromatic hydro-

*

Corresponding author. Address: 1631 Castro Street, San Francisco, CA 94114, USA. Tel.: +1 415 824 7557. E-mail address: [email protected] (M.R. Philpott). 0301-0104/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2007.09.061

carbon with seven rings [1], was selected because it was large, has a compact skeleton with many internal C–C sigma bonds which act to reinforce its shape, and has a central ring resembling graphite in bond uniformity in contrast to its perimeter which has neither uniformity nor complete bond alternation. This hydrocarbon constitutes an important extension beyond the previous components of sandwich structures which were based on the molecules pyrene C16H10 and tetracene C18H12 [2,3]. We contrast the coronene results with those from the bis-benzene compounds M1(C6H6)2, calculated under identical conditions. The latter provide a useful yardstick for gauging and interpreting how some of the calculated properties of the sandwiches vary with the metal and the effect of extra rings. The ground state properties of the following structures MnR2

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are reported here: briefly as reference molecules M1(C6H6)2 for M = Cr (spin S = 0), Fe (S = 2) and Pd (S = 0); M7(C24H12)2 for M = Cr (S = 5), Fe (S = 6) and Pd (S = 0). We also summarily report on other spin states to confirm the minimum and in the case of Pd (S = 1, 2) to provide comparisons with the non-zero spin distributions in the Cr and Fe sandwiches. Motivation for this study of hypothetical structures comes primarily from the recent synthetic work on organo-metallic palladium (n = 3, 5) complexes by Murahashi, Kurosawa et al. [4], and from frontier areas such as molecular nano-electronics [5], astrophysics [6,7], organo-metallics in the gas phase [8], graphite intercalation [9] and possibilities for new synthetic structures based on advances in graphene research [10–12]. In their recent work the Murahashi–Kurosawa group [4] reported the synthesis of two sandwich structured molecular ions [Pd3Cl3(C7H7)2]2+ and [Pd5(C18H12)2 C6H5CH3]2. In this work the Pd5 complex ion contained a planar array of palladium and the principal geometric feature was g2- and g3-coordination of the metal atoms to edge carbon atoms of the tetracene (C18H12) moieties. It was proposed by Murahashi et al. [4] that ‘‘metal monolayer sandwich compounds containing different sizes and shapes of metal sheet can be synthesized using different extended pp-conjugated carbon frameworks’’ with the aid of their template effect [4]. Alternatively one could imagine creative assembly using atomic beams and graphene sheets sloughed off macrographite samples [12] manipulated by AFM probes and diced by STM probes. Extended organo-metallic sandwich structures with various metals could provide nano-scale electronic devices with a variety of useful properties. From our perspective the theoretical studies described in this report and elsewhere [2,3] could be used as the basis of models for studying edge effects in nano-wide graphene electronic circuitry and overpotential effects in thin batteries. Regarding the choice of metal atoms we note that chromium between C6-aromatic rings satisfies the 18 electron rule (6 + 6 + 6) implying a possible energetic preference for central sites between rings. In chromium bis-benzene the ground state is a singlet (S = 0), with an inter-plane spacing (322 pm) that is less than that in graphite (335 pm). In bulk (bcc) chromium metal the nearest neighbour spacing 249 pm almost matches the basal plane graphite ring spacing 245.6 pm suggesting that in small chromium arrays a limited amount of registration might accommodated. Iron has a (bcc) bulk metal nearest neighbour spacing almost the same as chromium. Iron forms many ground state spin polarized organo-metallic complexes. Palladium which belongs to the second row transition metals, has enough electrons to fill the 4d-shell and a nearest neighbour (fcc) bulk metal separation 275 pm that unlike chromium and iron exceeds the graphite ring spacing. We show that the metal atoms have sandwiches with some geometric similarities arising from the robustness of the coronene carbon skeleton. However the spin manifolds are different: in chromium compounds the spin states are

about 0.1 eV apart, in iron about 0.5 eV and in palladium almost 1 eV apart. Our current program with regard to organo-metallic sandwich structures has limited goals, namely to explore their properties by varying hydrocarbon size and shape, metal type and metal atom number. In this paper, we concentrate on metal type. In previous studies we have briefly reported preliminary results of the structure of sandwiches of palladium between hydrocarbons of varying sizes up to circumcoronene [2] and in more detail the geometry and electronic structure, including palladium metal–metal bonds between eclipsed pyrene and tetracene pairs [3]. This earlier work did not include an account of spin polarized states or include work or comparisons with chromium and iron as is provided here. This paper is organized as follows: next, a brief description of the computational methodology; followed by a summary of results for M1(C6H6)2 where M = Cr, Fe, Pd; then we describe in separate sections results for Cr7(C24H12)2, Fe7(C24H12)2 and Pd7(C24H12)2. The report ends with a Summary and discussion section in which the three metal sandwich structures are compared and main results briefly summarized. 2. Method of calculation All calculations were performed using the vienna ab initio simulation package Vasp [13–16]. The plane wave based calculations used PAW pseudo-potentials [17,18] and the spin polarized generalized gradient approximation for the exchange-correlation energy functional (PW91) parameterized by Perdew et al. [19,20]. Valence electrons were assigned as follows: Cr (6), Fe (8), Pd (10), C (4), and H (1). Note that the valence shell of palladium was treated as a 10 electron system (4d10). All calculations were performed using periodic boundaries with a cubic cell, edge lengths in the range 0.75–2.50 nm, so the molecules were at least 0.9–1.0 nm apart. All Brillouin zone integrations were done at the gamma point. The geometry optimizations were carried out using the conjugate gradient method usually until the forces acting on each atom were approximately 66 leV/pm (or 0.05 cm1/pm). We routinely calculated geometry, total energy for given total spin, isometric surfaces of total charge and Kohn–Sham partial charges, spin density and occasionally the electron localization function ELF [21,22]. Harmonic analysis of the wave function inside spheres with centers on individual atoms also assisted the analysis of charge density of the chemical bonds. The starting geometries were aromatic hydrocarbons with standard bond lengths. In the sandwiches the hydrocarbons were eclipsed and metal atoms were initially located in the middle above the ring centers. The total energy Et calculated by Vasp was referenced to the sum of separated metal atoms and separated planar hydrocarbon molecules. It appears in the following tables as DEf. All of the chromium and iron calculations were spin polarized and some of the palladium calculations too. The use of

M.R. Philpott, Y. Kawazoe / Chemical Physics 342 (2007) 223–235

a single determinant to represent the spin properties of open shell systems has been widely investigated in recent years [23,24]. Our interest in this study was energy, geometry and basic electronic structure, and not in pursuing a refined study of spin and magnet properties as done in the study of molecular magnetism. Current knowledge of the sandwich structures of the type studied here does not yet warrant such a detailed investigation. In the calculations the following conditions held: All systems were electrically neutral; all calculations were done with unrestricted spin; the symmetry of the sandwich structures was constrained to D2h or C2v symmetry unless otherwise stated; all energies in eV, all distances are in pm unless otherwise specified. In this symmetry the hydrocarbon layers stayed eclipsed and the metal atoms remained in their starting plane. The impact of the lower symmetry on the D6h symmetric bis-benzene compounds was observed to be very small in energy and geometry because of the large box size and in the case of the chromium compound its large binding energy. 3. Summary for M1(C6H6)2 Table 1 summarizes calculations of properties of the molecules M1(C6H6)2 for M = Cr (S = 0), Fe (S = 2) and Pd (S = 0), used in understanding the properties of the coronene sandwiches in the following sections. In this and other tables the notations are: M–ring, the distance from metal M to the plane of the nearest ring; M–C, metal–carbon distance; C–C ring carbon bond length; C–H carbon–hydrogen bond distance; C–C 0 (or H–H 0 ) the distance between C(or H) atoms on opposing eclipsed rings. The Vasp DFT total energies, calculated with PAW potentials, for benzene and metal atoms were: Etot(C6H6) = 76.238 eV; Cr atom (S = 2, configuration d5s1), Eatom = 5.445 eV; Fe atom (S = 1, configuration d6s2), Eatom = 3.194 eV; Pd atom (S = 0, configuration d10s0), Eatom = 1.496 eV. The energy of formation was defined by DEf ¼ fEtot ½M1 ðC6 H6 Þ2   2  Etot ðC6 H6 Þ  Eatom ðMÞg ðeVÞ ð1Þ

For an isolated benzene molecule the calculated C–C and C–H bond distances were 140 and 109 pm, these are Table 1 Properties of the molecules M1(C6H6)2 for M = Cr, Fe, Pd DEf

M–ring

M–C

C–C/C–H

C–C 0

H–H 0

Cr1(R)2 0 161.147 Expta. –

3.226 –

161 161

214 215

142/108 142/–

322 –

311 –

Fe1(R)2 1

158.576

2.906

173

223

141/108

346

344

Pd1(R)2 0 155.000

1.028

228

268

141/108

456

457

System Spin S

a

Etot

Electron diffraction experiments [25].

225

slightly smaller than the C–C distances calculated for benzene in the bis-benzene compounds. In the Cr1(C6H6)2 molecule the calculated metal and carbon geometry is in good agreement with the electron diffraction [25] result. However, we note that the calculated inter-ring H–H 0 distance is smaller than the C–C 0 distance. In the other bis-benzenes the difference is negligible. Previous theoretical studies [26,27] have focused almost entirely on chromium. Although a variety of metal bis-aromatic hydrocarbon compounds have been detected in the gas phase [6–8], there are no experimental geometries for the iron and palladium molecules. However in passing it is worth noting that Zenneck [28] has described the ‘‘18 (8 + 6 + 4) electron rule’’ crystalline compound Fe1(g6C6(CH3)6)(g4-C10H8). Singlet ground states occur for chromium (small Cr–ring separation, high field) and palladium (filled 4d10-subshell) bis-benzene. In contrast the iron compound is magnetic due to two (S = 1) unpaired electrons mainly in Kohn– Sham levels KS 34–35 with strong dzx- and dyz-function. The metal ring spacing M–ring is one half the C–C 0 spacing where C and C 0 are an eclipsed pair of carbon atoms on the opposing rings. The column H–H 0 gives the separation of the eclipsed H atoms. The hydrogen separations are not all greater than the C–C 0 spacing, the chromium compound being a case in point. The inter-plane spacing in graphite has c = 334.7 pm, 1/2c = 167.35 pm. Chromium bis-benzene has a significantly shorter ring separation 161 pm than graphite and a longer C–C ring bond signaling the quality of the chemical bonding in this molecule. The other two compounds 173 pm (Fe) and 228 pm (Pd) have progressively larger spacing consistent with d-shell filling and in the case of Pd larger principle quantum number. The shortness of the inter-plane spacing in chromium bis-benzene seems to exemplify a strong interaction with aromatic C6rings. This is consistent with the notion of a d-bond from chromium to the benzene p-system [26]. 4. General comments on results for M7(C24H12)2 sandwich structures In this and following sections we describe results for the sandwiches M7(C24H12)2. We begin with a brief overview of common results and then in separate sections describe aspects that distinguish the three metal sandwiches from one another. The starting geometry had one metal atom assigned to the center of each pair of rings of the coronene molecules. The experimental compounds of Murahashi et al. [4] and previous calculations [2,3] indicate that metal bonding to edge sites lowers symmetry. Accordingly, the symmetry D2h used in these calculations permitted the system some freedom to accommodate the movement of metal atoms, without an excessive increase in computer time. Nevertheless in D2h symmetry, the hydrocarbon moieties remained in an eclipsed configuration during the geometry optimization. We return to the effect of symmetry restrictions in the Discussion. The main feature of the sandwich

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pounds as the iron binding energy in small iron clusters is quite high around 6 eV (Philpott–Kawazoe, unpublished calculations). Further comments on issues linked to stability are postponed to the Discussion. Table 2 summarizes results for energy and basic electronic properties of sandwiches with seven metal atoms between coronene molecules. The total energy Etot is relative to unpolarized vacuum atoms, DEf is the energy relative to separate intact coronene molecules and metal atoms, BG1 (BG2) is the spin 1 (spin 2) homo–lumo single particle gap. The energy DEf is defined analogous to Eq. (1):

structures was the geometry of metal sites and so this is the focus of the information listed in the tables describing the geometry of the sandwich molecules. We do not list all the separate atomic coordinates. In the geometry optimizations it was necessary to calculate the energy of states over a range of spins to find the lowest energy spin state. In the case of chromium the unrestricted spin calculation of energy first converged to a local minimum corresponding to S = 10. However checking for the global minimum we found the lowest energy at spin S = 5. Note that the central metal–ring gap decreases with spin consistent with requiring a higher field to pair electrons or create anti-ferromagnetic coupling in the case of iron. For S < 4 the spin distribution in iron compounds is anti-ferromagnetic rather than electron pairing. This is discussed at greater length below. The calculated energies of the chromium sandwich in Table 2 are closer than for the other sandwiches. The total spin decreases with M–ring distance, consistent with an increase in field across the chromium centers and a concomitant increase in electron pairing. However it is as well to recall the comment in Section 2 (computation methodology) that a detailed understanding of magnetism is not available at the level of theory used here [22,23]. The physical stability of the sandwiches with the given geometry is not guaranteed in the case of the iron com-

DEf ðMÞ ¼ fEtot ½Mn ðC24 H12 Þ2   DEref ðMÞg ðeVÞ

ð2Þ

DEref ðMÞ ¼ f2  Etot ðC24 H12 Þ þ nEatom ðMÞg ðeVÞ

ð3Þ

Here Etot(C24H12) = 260.509 eV for the coronene singlet ground state (S = 0). For completeness we give here the coronene singlet S = 0 state, homo–lumo single particle band gap BG0 = 2.87 eV, and for the triplet the corresponding numbers were: Etot(S = 1) = 262.980 eV and homo–lumo gaps BG1 = 0.44 eV (spin 1) and BG2 = 0.42 eV (spin 2). Table 2 also includes very basic geometry for the central metal atom site namely: M–C the metal–carbon distance and the perpendicular M–ring distance. These are included

Table 2 DFT energies (eV) of the sandwich structures M7(C24H12)2 for M = Cr, Fe, Pd System Spin S

DEf(M)

DEf(M)/7

BG1

BG2

M–C/pm

M–ring/pm

Cr7(R)2 /11 /10 /9 /8 /7 /6 /5 /4 /3 /2 /1 /0

11.023 11.427 11.426 11.196 11.187 11.218 13.957 13.904 13.762 13.690 13.618 13.601

1.58 – – – – – 1.99 – – – – 1.94

0.55 0.53 0.21 0.21 0.07 0.25 0.10 0.18 0.33 0.16 0.28 0.38

0.27 0.32 0.31 0.11 0.32 0.18 0.50 0.32 0.25 0.45 0.50 0.17

206 212 213 213 202 202 202 202 200 196 195 192

175 171 171 171 161 158 157 156 156 159 159 160

Fe7(R)2 /6 /5 /4 /3 /2 /1 /0

19.832 19.321 19.722 19.538 19.089 18.816 18.750

2.83 – – – – – –

0.97 0.31 0.52 0.33 0.15 0.10 0.07

0.15 0.19 0.26 0.23 0.15 0.14 0.07

206 195 196 206 199 199 199

163 162 164a 160 159 155 155b

Pd7(R)2 /2 /1 /0

14.534 15.665 16.702

– – 2.39

0.36 0.13 1.14

0.07 0.13 1.14

225 222 226

203 202 201

Using the table DEf(M) energy values (eV), the sandwich total energy Etot(M) = Eref(M)  DEf(M): chromium sandwich Eref(Cr) = 564.076 eV; iron sandwich Eref(Fe) = 508.304 eV; palladium sandwich Eref(Pd) = 536.431 eV. a Begin anti-ferromagnetic coupling relative to central Fe atom. b Some forces on atoms oscillating but energy differences very small in D2h symmetry.

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for easy comparison with the metal bis-benzene compounds listed in Table 1. Pertinent results for metal atoms on edge sites are given later. Fig. 1 shows the scheme of labeling carbon atoms in order to simplify the geometry of the three metal sites (1, 2, 3) in hydrocarbon sandwiches. In these idealized geometries, the central metal site 1 (see panel 1) has maximally g6-coordination, site 2 (A-site with g2-coordination, see panel 2) occurs at the edge of the sandwich with two carbon atoms above and below, and edge site 3 (site B with g3-coordination, see panel 3) has three C atoms above and below. An orthogonal set of axes L, M, N (long, medium, normal) is useful to describe directions and planes of the sandwich. Fig. 1 (panel 4) shows a more elaborate scheme for labeling carbon atoms on site M3 site of chromium compounds when the metal atom is close to the ring center. Fig. 2 shows the DFT geometry of the three metal systems in their ground electronic state, viewed down the Naxis and a side view along the M-axis. The top view shows the central metal site and the edge bonding motif adopted

2

1

C1

2

A-site C2

3

1 M

C2'

C1'

L M

4

2

1

3 1

6'

C2

2

M2 6

M1

B-site C3

3

M3 5

C1

4

M C1 '

C3 ' C2 '

Fig. 1. Scheme for labeling carbon atoms in metal bonding sites used to simplify the characterization of the geometry surrounding the metal sites M(1, 2, 3). The central metal site 1 (see panel 1) has maximally g6coordination, site 2 (A-site with g2-coordination, see panel 2) occurs at the edge of the sandwich with two carbon atoms above and below, and edge site 3 (B-site with g3-coordination, see panel 3) has three C atoms above and below. An orthogonal set of axes L, M, N (long, medium, normal) is useful to describe directions and planes of the sandwich. Panel 4 shows a more elaborate scheme for labeling carbon atoms on site M3 site of chromium sandwiches when the metal atom is close to the ring center.

227

by the other metal atoms. The side views show the differences in cross-section which arise because of differences in spin and chemical bonding. In the chromium complex (Fig. 2, left side) the structure is concave along the L-axis (coaxial with M1 and M2) and convex along the M-axis. In the iron complex spin S = 6 (Fig. 2, middle) the central iron has the highest spin and a higher separation giving the structure a convex appearance. In the palladium containing structure spin S = 0 (Fig. 2, right side) the ground state has zero spin on every metal and the overall geometry is flatter as a result. 5. Results for Cr7(C24H12)2 in spin state S = 0, 1, . . ., 11 5.1. Summary for different spin states Table 2 shows the manifold of states S = 0, 1, . . ., 11 (22 unpaired electrons) due to different spin arrangements on the seven metal atoms. The energy spacing, mostly in the range 0.1–0.3 eV, are the smallest of the three metals. The spin density is confined to the chromium atoms. The charge and spin on each metal site inside a sphere radius 150 pm is given in the table. The ground state was identified as S = 5 (10 unpaired electrons). States with higher spin have larger metal–ring gaps or equivalently longer M–C bonds. The weaker field across the Cr atoms allows more degeneracy in the 3d-levels and by Hunds rule a higher spin. Two effects can yield low spin structures, for example when the metal spins couple anti-ferromagnetically or the chemical attraction for the hydrocarbons ‘‘squeezes’’ the metal atom and the resulting high field reduces degeneracy. The primary change in geometry with spin is metal–ring distance at the three sites. Spill over of magnetic polarization onto the C atoms is a minor effect in this system. In all states the Cr–Cr distances are long compared to the bulk metal (bcc, a0 = 288 pm) where the Cr–Cr nearest neighbour distance is 249.4 pm. Fig. 3 shows the spin density distribution for spins S = 11, 5 and 0. In the high spin state the spins are aligned parallel (Fig. 3, top left, S = 11). In the ground state (Fig. 3, top right, S = 5) the spins are parallel and concentrated on the L-axis atoms (A-sites). In the spin S = 0 state the spins are aligned anti-ferromagnetically with the A-sites on the L-axis in one direction (Fig. 3, bottom left, S = 0) and the four B-sites and central site polarized in the opposite direction (Fig. 3, bottom right, S = 0). The stick-andballs in Fig. 3 also show that the geometrical cross-sections depend on spin. In the MN-plane the structure is weakly convex for S = 11 and more strongly convex for S = 5 and S = 0. In the LN-plane the cross-section is concave for S = 11 and S = 5 (see Fig. 3, left panel) and convex for S = 0. Fig. 4 shows main features of the equilibrium geometries in the LM-plane viewed along the N-axis. At high spin S = 11, with the exception of the central atom, all the atoms are located on the perimeter in A- or B-sites. The A-site metal atoms lie outside the molecular skeleton. At

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Fig. 2. Geometry of the chromium, iron and palladium sandwiches in their ground electronic states, viewed down the N-axis (top) and viewed along the M-axis (bottom). In the top view the edge bonding motif comprising A-sites and B-sites is evident for all three metals. The side views show the differences in cross-section which arise because of differences in spin and chemical bonding. In the chromium complex (left) the structure is concave along the L-axis (coaxial with M1 and M2) and convex along the M-axis. In the iron complex spin S = 6 (middle) the central iron has the highest spin and a higher separation giving the structure a convex appearance. In the palladium containing structure spin S = 0 (right) the ground state has zero spin on every metal and the overall geometry of the sandwich is flat.

Fig. 3. Chromium sandwich isometric surfaces of spin density for S = 11, 5, 0. In the high spin state (S = 11, top left) the spins are aligned parallel. In the ground state (S = 5, top right) the spin is on atoms lying on the L-axis. In the low spin S = 0 state (bottom left, diso = 1000; bottom right, diso = 1000) the spins are aligned anti-ferromagnetically with the A-sites on the L-axis with positive spin density and the four B-sites and central site polarized in the opposite direction (bottom right, S = 0). The stick-and-ball models show the dependence of geometry on the spin. In the MN-plane the structures are weakly convex for S = 11 and more strongly convex for S = 5 and S = 0. In the LN-plane the cross-section is concave for S = 11 and S = 5. For S = 0 the carbon frame is convex.

spin S = 5 the B-sites have moved towards ring center. At spin S = 0 the A-sites metals have also moved

past the perimeter C–C bond and are inside the carbon ring. For S = 5 and S = 0 the metal–carbon bonds are

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229

Fig. 4. Chromium sandwich geometry viewed along the N-axis for spin S = 11, 5 and 0. Metal carbon bonds are shown for emphasis in the case of S = 5 and S = 0 to emphasize the shift towards ring centers. At high spin, with the exception of the central atom, all the atoms are located on the perimeter in A- or B-sites. In particular at S = 11 the A-site metal atoms are outside the coronene foot print. At spin S = 5 the B-sites have moved towards ring center. At spin S = 0 the A-sites are under the hydrocarbon umbrella and all metal atoms are more central in their assigned rings.

drawn to emphasize the close to central position as appropriate. 5.2. Comments for the high spin state S = 11 The main geometry results for the S = 11 state of Cr7(C24H12)2 are summarized in Table 3. The atom labels used in all the tables are shown in Fig. 1. In the tables: the symbol M stands for a generic metal site M1, M2 or M3; C1–2 is short for C1–C2 the bond distance between carbons C1 and C2 in A- or B-sites; C and C 0 are pairs of eclipsed carbon atoms on hydrocarbons on opposite sides of the sandwich. We remind the reader that we do not list all the co-ordinates, just relative positions for each symmetry unique site (edge sites A- and B- and the central site).

All metal–metal distances far exceed the chromium metal nearest neighbour distance 249.4 pm. The metal–ring distance is an approximate measure of separation since the M–C bonds differ around the nearest ring. Note that the central metal Cr1 has the smallest M–ring separation ca. 188 pm, consistent with smallest electronic charge and spin density inside a sphere of radius 150 pm. The M1–C bonds are all similar (average 237 pm) with deviation of about 1 pm. The M2–C1 bonds are short because the metal atom lies almost directly under the pair C1 and C2. This proximity increases the M1–ring separation. Similar considerations apply to the B-site where the metal atom lies almost beneath the C2 atom. The total charge density is devoid of evidence for metal– metal bonds. The isometric surfaces at values for electron charge density values below that for M–C bonds show no

Table 3 Geometry of molecule Cr7(C24H12)2 in spin state S = 11 Cr–Cr distances Center metal atom to perimeter atoms Cr1–Cr2 = 392 pm (kL-axis); Cr1–Cr3 = 308 pm; Perimeter distances Cr2–Cr3 = 299 pm; Cr3–Cr3 0 = 405 pm. The Cr3 0 atom is obtained from site Cr3 by a 2-fold rotation around the M-axis. Cr1 site/central site/spin 1.41 M–C1 Cr1–ringa 187.7 236.5

C1–C2 144.5

C1–C1 0 375.3

H–H 0 na

\C1–M–C2 35.6

Cr2 site/symmetrical A-site/spin 3.63 M–C1 Cr2–ringb 206 218

C1–C2 142

C1–C1 0 412

H–H 0 471

\C1–M–C2 38.11

Cr3 site/unsymmetrical B-site/spin 2.99 Cr3–ringc M–C1 200 224

M–C2 212

M–C3 223

C1–2/C2–3 142/142

\C1–M–C2 38.01

C1–C1 0 344

C3–C3 0 401

H1–H 0 336

H2–H 0 434

a b c

C2–C2 0 399

Cr1–ring = 0.5 · (C1–C1 0 ) distance. Cr2–ring = 0.5 · (C1–C1 0 ) distance. Cr3–ring = 0.5 · (C2–C2 0 ) distance.

\C2–M–C3 37.92

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surfaces that are directed between metal atoms. As the density value is reduced the isometric total charge surfaces for regions directly between metal atoms gradually fill in the hole, there is no directed axial charge as seen for chemical bonds between first and second row atoms. The charge at the mid point of a metal–metal axis is about 900 units (about 5%, compared to dmax = 23,378), diso = 11,771 between bonded C atoms, diso = 2800 between Cr–C in a B-site and diso = 2480 between Cr–C in an A site and diso = 1700 at the mid point of the Cr–C axis in a central H site. All the metal atoms have approximately the same spin density. The central site Cr1 has the lowest spin and this is consistent is the idea from the metal bis-benzenes that the smaller the metal–ring spacing the lower the spin density. In chromium bis-benzene the Cr atom has spin zero, and we assume this value obtains to chromium atoms sandwiched between rings separated by about 320 nm. For spin S = 11, isometric surfaces are shown in Fig. 3 (top, left side). Analysis of orbital spin contributions showed this to come almost entirely (99%) from 3d-functions. There is effectively no spin on the carbon or hydrogen atoms of this complex as even isometric surfaces at diso = 250 (about 1%) shows only very small spin on carbon atoms on the Maxis.

state of Cr7(C24H12)2 are summarized in Table 4. As mentioned earlier the cross-sections can be rationalized from the spin (given in the tables) on each metal atom. Simply put, high spin means larger metal–ring spacing and low spin (e.g., S = 0 in chromium bis-benzene) requires small gaps.

5.3. Comments for the ground state S = 5

Table 5 summarizes the main geometrical features of the iron structure in the ground state. The metals are too far apart for metal–metal bonds. In bulk bcc iron (a0 = 287 pm) the nearest neighbour distance is a(NN) = 248.5 pm. Fig. 2 (center panels) shows the position of iron atoms between the coronene layers for the ground state spin S = 6. Atom Fe1 is central, and the metal sites Fe2 and Fe3 are examples of a high symmetry A-site and B-site

The overall geometry in Fig. 3 (top left panel) shows that the sandwich has two A-sites with the metal just inside the coronene and four B-type sites where the atom is closer to ring center than in the high spin structure. The cross-sections visible in Fig. 3 (top right) are convex in the MN-plane in the LN-plane. The main geometry results for the S = 5

5.4. Comments for the low spin S = 0 state The key geometry results for the low spin state are listed in Table 5. This metal atom spins are arranged anti-ferromagnetically. The sites with highest spin have the larger separations. The structure is the flattest of the group, being convex in the LN-plane and mildly convex in the MNplane cross-section. In this state the spins are in a net anti-parallel arrangement. From Table 5 we note that the spins on the M2 (A-sites) are opposed by the spins on the central M1 and M3 (B-sites). The result is an anti-ferromagnetically aligned spin array with total spin S = 0. In this structure the larger spin on a site correlates with larger metal–ring separation. The metal–ring separations are also the smallest in the entire manifold of chromium spin states given in Table 2. 5.5. Geometry, charge and spin density of Fe7(C24H12)2 in the ground state S = 6

Table 4 Spin state S = 5 geometry of molecules Cr7(C24H12)2 Cr–Cr distances Center metal atom to perimeter atoms Cr1–Cr2 = 356 pm (kL-axis); Cr1–Cr3 = 256 pm; Perimeter distances Cr2–Cr3 = 295 pm; Cr3–Cr3 0 = 294 pm where Cr3 0 is given by reflection in the MN-plane; M3–M300 = 418 pm where M300 is given by reflection in the LN-plane; Cr1/central site/spin 2.21 M–C1 Cr1–ringa Av189 Av238

C1–C1 0 Av378

H–H 0 na

\C1–M–C2 –

Cr2 site/symmetrical A-site inside the coronene footprint/spin 3.04 M–C1 C1–C2 C1–C1 0 Cr2–ringb 202 214 142 403

H–H 0 447

\C1–M–C2 38.66

Cr3 site/distorted B-site/spin 0.03 M–C1 Cr3–ringc 171–177 223

M–C2 211

M–C3 215

C1–2/C2–3 142/141

\C1–M–C2 38.30

C1–C1 0 373

C3–C3 0 313

H1–H 0 –

H2–H 0 –

a b c

C2–C2 0 337

C1–C2 Av147

Cr1–ring = (2 · C16-C16 0 + C14-C14 0 )/6 = 188. Cr2–ring = 0.5 · (C1–C1 0 ). Cr3–ring = (C1–C1 0 + C2–C2 0 + C3–C3 0 )/6 = 171 pm.

\C2–M–C3 38.77

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Table 5 Geometry of structure Cr7(C24H12)2 in spin state S = 0 Cr–Cr distances Center metal atom to perimeter atoms Cr1–Cr2 = 288 pm (kL-axis); Cr1–Cr3 = 258 pm; Perimeter distances Cr2–Cr3 = 260 pm; Cr3–Cr3 0 = 283 pm where Cr3 0 is given by reflection in the MN-plane; Cr1/central site/spin-0.63 Cr1–ringa Av144

C1–C1 0 Av288

H–H 0 na

\C1–M–C2 Av35.22

Cr2 site/symmetrical A-site well inside the coronene carbon footprint/spin 0.94 M–C1 C1–C2 C1–C1 0 Cr2–ringb 174 207 142 348

H–H 0 353

\C1–M–C2 40.22

Cr3 site/distorted B-site near the ring center/spin-0.35 M–C1 Cr3–ringc 168–178 223

M–C2 208

M–C3 214

C1–2/C2–3 144/141

\C1–M–C2 –

C1–C1 0 362

C3–C3 0 319

H1–H 0 –

H2–H 0

a b c

M–C1 Av241

C2–C2 0 326

C1–C2 Av147

\C2–M–C3 –

Cr1–ring=(C1–C1 0 + C6–C6 0 + C5–C5 0 )/6 = 144. Cr2–ring = 0.5 · (C1–C1 0 ) = 174. Cr3–ring = (C1–C1 0 + C2–C2 0 + C3–C3 0 )/6 = 168.

respectively. Atom Fe3 is closer to two of the carbons (C1 and C2) out of three but not directly beneath C2 atom as compared to the corresponding palladium site (Fig. 2, right). In this iron structure, in contrast to the chromium one, the central portion of the molecule is thicker than at the edges. For example the four H atoms (two per hydro-

carbon) shown in Fig. 2 (middle, central bottom panel) have the shortest separations, Table 5 lists these separations as H1–H 0 = 292 pm closer than the distance separating their C atoms C1–C1 0 = 326 pm which are themselves narrowly separated because of the convex curvature of the MN-cross-section.

Fig. 5. Total electronic charge and spin density of the iron sandwich structure in the ground state spin S = 6. Top panel shows a high density isometric surface (diso/dmax = 11,660/52,817) for total charge density, revealing the bonding of the C–C skeleton around the iron sites. The background colours are the charge density plotted with a log colour scale (dmax = 52,817) on the plane through all the metal atoms. Bottom panel shows an isometric surface (diso = 3330) of interesting topological features for the bonding of iron to the C atoms. In the case of the A-site there are two oval funnels joining iron to the hydrocarbon surface. At lower isometric values these two funnels coalesce. In the case of the B-site there is one opening which is biased towards the C atom with an attached H atom. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)

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For the iron sandwich structure we found some useful features in the isometric surfaces of the total electronic charge. Fig. 5 shows two isometric surfaces of total charge density. Top panel is for high charge density revealing the bonding of the C–C skeleton at the iron sites. The C–C bonds pointing radially from the central hexagon have lower charge density than the bonds of the central hexagon and some but not all of the perimeter bonds. Bottom panel shows surface features indicated by the vertical arrows for the bonding of iron to the C atoms. In the case of the A-site there are two oval funnels joining iron to the hydrocarbon surface. At lower isometric values these two funnels coalesce. In the case of the B-site there is

one opening which is biased towards the C atom with an attached H atom. Analysis of the harmonic components of the charge density around the metal atoms reveals that in iron the s- and p-functions account for 10–20% of the total density with a radius of 150 pm around the atom. This is much higher than observed for chromium where s- and p-functions accounted for 1% and palladium where the ratio is less than 10%. In Fig. 6 we show that in the iron sandwich ground state (S = 6) the spin distribution resembles the high spin chromium with all ferromagnetic distribution of spins on the seven atoms. An isometric surface (diso = 5000, dmax = 25,600, dmin = 394) for the spin density of Fe7(C24H12)2 in spin state S = 6 is shown superimposed on the stick-ball molecular framework in Fig. 6. The coupling is ferromagnetic with the highest spin on the central atom. The relative spin scales inversely with the metal–ring gap according to: Fe1 (spin 2.7, 206 pm), Fe2 (spin 2.0, 195 pm), Fe3 (spin 183, 183 pm). The entire spin density comes from 3d-electrons (harmonic analysis) there was no spin on the carbon atoms. 6. Geometry, charge and spin density of Pd7(C24H12)2 for the ground state S = 0 and excited states S = 1 and S = 2

Fig. 6. The spin density around individual atoms of Fe7(C24H12)2 in spin state S = 6 is shown as an isometric surface (diso = 5000; dmin = 394; dmax = 25,601) superimposed on the molecular structure. The coupling is ferromagnetic with the highest spin on the central atom. The spin on a site scales inversely with the metal–ring gap according to: Fe1 (spin 2.7, 206 pm), Fe2 (spin 2.0, 195 pm), Fe3 (spin 1.6, 183 pm).

Table 2 lists the energy and related properties of three spin states S = 0 (ground state), 1 and 2. The ground state is state examined in most detail here. In contrast to the Cr (separations 0.1 eV) and Fe (separations 0.5 eV) structures, the palladium sandwiches have spin states separated by about 1 eV. In the excited states the spin density was confined mostly to the metal atoms in a manner analogous to the Cr and Fe molecules, however there is some small amount of spin on some carbons where in the Cr and Fe

Table 6 Geometry of molecules Fe7(C24H12)2 in spin state S = 6 Fe–Fe distances Center metal atom to perimeter atoms Fe1–Fe2 = 338.4 pm (kL-axis); Fe1–Fe3 = 292.7 pm; Distances between metal atoms on the perimeter Fe2–Fe3 = 255 pm; Fe3-Fe3 0 = 401 pm. The Fe3 0 atom is generated from Fe3 by a 2-fold rotation about the M-axis. Fe1 site/central/spin 2.7 Fe1–ringa 206

M–C1 250

C1–C2 143

C1–C1 0 411

H–H 0 na

Fe2 site/symmetrical A-site/spin 2.0 Fe2–ringb 195

M–C1 206

C1–C2 141

C1–C1 0 381

H–H 0 406

Fe3 site/perturbed B-site/spin 1.6 Fe3–ringc 183

M–C1 225

M–C2 202

M–C3 211

C1–2/C2–3 141/142

C1–C1 0 326

C2–C2 0 366

C3–C3 0 387

H1–H 0 292

H2–H 0 385

a b c

Fe1–ring = 0.5 · (C1–C1 0 ). Fe2–ring = 0.5 · (C1–C1 0 ). Fe3–ring = 0.5 · (C2–C2 0 ).

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Table 7 Geometry of molecule Pd7(C24H12)2 in spin state S = 0 Pd–Pd distances Central metal atom to perimeter atoms Pd1–Pd2 = 366 pm (kL-axis); Pd1–Pd3 = 375 pm; Distance between metal atoms on the perimeter Pd2–Pd3 = 326 pm; Pd3-Pd3 0 = 460 pm. The atom Pd3 0 is related Pd3 by a 2-fold rotation operation about the M-axis. Pd1 site/central site/spin 0 Pd1–ringa 224

M–C1 265

C1–C2 143

C1–C1 0 448

H–H 0 na

\C1–M–C2 31.3

Pd2 site/symmetrical A-site/spin 0 Pd2–ringb 215

M–C1 226

C1–C2 226

C1–C1 0 431

H–H 0 455

\C1–M–C2 35.05

Pd3 site/unsymmetrical B-site/spin 0 Pd3–ringc 214

M–C1 268

M–C2 214

M–C3 234

C1–2/C2–3 143/140

\C1–M–C2 32.21

C1–C1 0 439

C2–C2 0 427

C3–C3 0 402

H2–H 0 470

H3–H 0 414

Torsion ca. 2

\C2–M–C3 36.28

C1–2 is short notation for C1–C2. C and C 0 are eclipsed pairs of carbon atoms on hydrocarbons on opposite sides of the sandwich. a Pd1–ring = 0.5 · (C1–C1 0 ). b Pd2–ring = 0.5 · (C1–C1 0 ). c Pd3–ring = 0.5 · (C2–C2 0 ).

structures there was none. This is consistent with higher excitation energy and the ‘‘filled’’ subshell status of the Pd atoms. The second row transition metal palladium is a larger atom. In the bulk fcc metal the lattice constant and nearest neighbour distances are a0 = 389 pm and a(NN) = 275 pm. There are no metal–metal bonds in the palladium structures described here. The charge density of the spin S = 0 structure shows very little disruption of the coronene carbon skeleton compared to chromium and iron. Also since the S = 1 and S = 2 states have spin confined to the metal there is little net change in the total charge density function on the carbon skeleton. 6.1. Geometry of Pd7(C24H12)2 in spin state S = 0 The geometry of Pd7(C24H12)2 in spin state S = 0 is listed in Table 7. An overview of the geometry is given in Fig. 2 (right panels). The structure is the flattest of all those considered in this paper. The torsion angles for the central ring are about two degrees. Cross-sections are slightly convex in the MN-plane and slightly concave in the LN-plane. On the perimeter the A-sites are flat with the Pd2 atom lying almost in the middle of a plane bounded by atoms C1, C2, C1 0 and C2 0 . In the B-site atom Pd3 lies almost under the central C atom. Some specific geometric details are given listed in Table 6. In the excited states S = 1 and S = 2 the change in geometry involves essentially no movement of either the central metal or the metal on the A-site. For the B-site the metal atom in S = 2 state is displaced slightly inwards and at the same time assume a more symmetrical position in the B-site.

In both spin states there is no spin on the central atom. In state S = 1 the spin density is twice as high on A-sites as the B-sites. In state S = 2 there are roughly equal spins on all the perimeter sites. 7. Summary and discussion This report has described the properties of sandwich structures M7(C24H18)2 containing seven metal atoms M = Cr, Fe, Pd between coronene molecules and interpreted the results with the help of the metal bis-benzene compounds M1(C6H6)2 as reference systems. Coronene was selected because it is a stable compact pericondensed aromatic hydrocarbon with a simple perimeter. In the graphite crystal the C atoms are not eclipsed and interlayer spacing equals 335 pm. The eclipsed coronene pair separation provides a small repulsive potential for chromium to overcome [29]. The metals were selected to extend the range of previous studies that focused on palladium [2,3] and to include properties such as magnetism. In particular it was important to assess the influence of edge sites on magnetic properties. Magnetism in this paper is due solely to spin density located on the metal atoms. Since the ground state spin could be high in chromium and iron systems, additional checks are required that the ground state has indeed been found. Essentially no spin density occurs on the carbon atoms for chromium and iron. For the palladium system which is a singlet we have examined the lowest triplet and quintuplet states and find spin properties that fit the pattern set by chromium and iron, except that minor spin density is found on carbon atoms close to the palladium atoms. Changing the spin state in any of these transition metal systems did not result in any

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significant change in the bonding. The spin changes were confined to the metal sites. In Cr7(C24H18)2 though the spacing varies in the range 300–400 pm, it does approximately correlate with the chromium local spin density. One conclusion to be drawn from Table 2 is that spin and metal–ring spacing are strongly correlated for all the metals. The crystal field model describes this as an effect due to increasing electric field with decreasing gap, and in a complimentary way the MO theory describes this as chemical bond pair formation. The geometric range of chromium containing structures was the greatest of the three metals examined. Iron turned out to be an intermediate case. In the bisbenzene reference molecule the metal–ring spacing is slightly larger than half the layer spacing in graphite, so carbon–carbon interactions should be weaker than around low spin chromium centers. In terms of inert gas shell filling the structure is 22 electrons short. The Figures indicate a narrower range of geometric deviations from uniform structures than for example is the case for chromium. The 4d10-subshell of the palladium atom provides for weaker metal–hydrocarbon interactions. For the sandwich structure the electron count was eight short of an extended inert gas structure. The metal–carbon ring spacing was the largest in all of the reference bis-benzene molecules and in the sandwich structures. The S = 0 ground state and S = 1 and S = 2 excited states with energies higher by 1 eV are a result of the filled 4d10-subshell configuration. However in the excited states the spin distributions resembled the other metals, being a ferromagnetic array with spin changes confined to the palladium atoms. This study showed that the edge bonding motifs identified previously for palladium, extend to transition metals that are intrinsically magnetic and can more strongly interact with the p-electrons of aromatic hydrocarbons. On the basis of local geometry, total charge density isometric surface analysis and examination of individual KS-level contributions to the total charge density, the bonding at A-, B- and central-sites approximated g2-, g3-, g6-coordination. Generally it was found that the metal–carbon bonding at the B-site has higher electron density than at A-sites. No metal–metal bonding was observed under the imposed symmetry conditions and metal loadings (n = 7). The central metal atom cannot be regarded as an incipient core atom because the center-to-perimeter metal–metal distances were all greater than the crystal nearest neighbour separations. The magnetism of the structures included anti-ferromagnetic spin alignments in the case of chromium and iron at low spin. The chromium structure (unlike chromium bisbenzene) was not a ‘‘multiple 18 electron system’’ so that some type of ground state magnetism could have been anticipated. In the ground state the iron structure had a ferromagnetic spin array. The palladium system, a ground state singlet, showed ferromagnetic spin distribution in the excited S = 1 and S = 2 states. Smaller average metal–ring separations paralleled smaller spin on the metal atom.

The initial geometry of the sandwich structures had D6h symmetry. The environment in the simulation was lower D2h. This permitted the metal atoms some freedom of movement in finding local equilibrium positions, whilst confining all the metal atoms to the xy-plane and maintaining all C (and H) atoms to an eclipsed orientation with a atom on the opposite side of the sandwich. In the final configuration there was one central site with approximate hexagonal symmetry, two A-sites with local C2v symmetry and four B-sites with approximate C2v symmetry. Various combinations of these sites resulted in the variety of cross-sections found in these calculations. An investigation of sandwiches without symmetry restrictions was not part of the present agenda. As our knowledge of properties the higher symmetry structures expands, a study of systems without symmetry restrictions becomes worth while together with a study of sandwiches on substrates. Acknowledgments MRP thanks the Center for Computational Materials Science for warm hospitality and financial support. All calculations were performed on the Supercomputer Facility at IMR. The authors thank all the staff of the Supercomputer Facility, Institute of Materials Research, Tohoku University for their dedicated, enthusiastic and unflinching support. References [1] E. ClarPolycyclic Hydrocarbons, Vols. 1 and 2, Academic Press, London, 1964. [2] M.R. Philpott, Y. Kawazoe, Mater. Trans. (Japan) 48 (2007) 689. [3] M.R. Philpott, Y. Kawazoe, Chem. Phys. 337 (2007) 55. [4] T. Murahashi, M. Fujimoto, M. Oka, Y. Hashimoto, T. Uemura, Y. Tatsumi, Y. Nakao, A. Ikeda, S. Sakaki, H. Kurosawa, Science 313 (2006) 1104. [5] C. Joachim, M.A. Ratner, Proc. Nat. Acad. Sci. (US) 102 (2005) 8801. [6] J.L. Weisman, T.J. Lee, F. Salama, M. Head-Gordon, Astrophys. J. 587 (2003) 256. [7] P. Thaddeus, Philos. Trans. Roy. Soc. B 361 (2006) 1681. [8] N.R. Foster, G.A. Grieves, J.W. Buchanan, N.D. Flynn, M.A. Duncan, J. Phys. Chem. 104 (2000) 11055. [9] D. Savoia, C. Trombini, A. Umani-Ronchi, Pure Appl. Chem. 57 (1985) 1887; J.K. Burdett, E. Canadell, Organometallics 4 (1985) 805; M. Shirai, K. Igeta, M. Arai, Chem. Commun. 2000 (2000) 623; J. Walter, Adv. Mater. 12 (2000) 31. [10] K.S. Novoselov, D. Jiang, F. Schedlin, V.V. Khotkevich, S.V. Morozov, A.K. Giem, Proc. Nat. Acad. Sci. (US) 102 (2005) 10451. [11] Y. Zhang, J.W. Tan, H.L. Stormer, P. Kim, Nature 438 (2005) 201. [12] A.K. Geim, A.H. MacDonald, Phys. Today 60 (8) (2007) 35. [13] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 588. [14] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251. [15] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15. [16] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [17] P.E. Blo¨chl, Phys. Rev. B 50 (1994) 17953. [18] G. Kresse, J. Joubert, Phys. Rev. B 59 (1999) 1758. [19] J.P. Perdew, in: P. Ziesche, H. Eschrig (Eds.), Electronic Structure of Solids 1991, Akademie-Verlag, Berlin, 1991.

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