Bonding in the Extended Metal Chain Compound La<sub>4</sub>Cl<sub>5</sub>C<sub>2</sub>
Bonding in the Extended Metal Chain Compound La4Cl5C2
Bulletin of the Korean Chemical Society. 2014. Jun, 35(6): 1897-1900
Copyright © 2014, Korea Chemical Society
  • Received : January 18, 2014
  • Accepted : February 27, 2014
  • Published : June 20, 2014
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Dae-Bok Kang

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Results and Discussion
An understanding of the chemical bonding in La 4 C l5 C 2 needs simpler structure. Let us focus on a La 6 Cl 14 C 2 cluster taken out from the La 4 Cl 5 C 2 lattice. Molecular orbital calcu-lations are performed on the C 2 -centered La 6 octahedral cluster system as well as the C 2 -free structure in order to judge the effect of the interstitial C 2 on the stabilization of clusters. The C 2 interstitial exists as C 2 5− , similar to other compounds such as Gd 12 (C 2 ) 3 I 17 [14] and Dy 12 (C 2 ) 3 I 17 , 15 with the C-C distance (1.44 Å) comparable with those in these compounds. This bond distance corresponds to the shortened C-C single bonds, thus suggesting the simple electron partitioning of (La 3+ ) 4 (Cl ) 5 (C 2 5− )·2e with two excess electrons per formula unit. With Cl and (C 2 ) 5− lanthanum has the oxidation state of +2.5. This leaves three excess electrons per La 6 Cl 14 C 2 cluster, i.e., (La 6 Cl 14 C 2 ) 4− . These electrons are responsible for La-La bonding inter-actions which are covalent in character.
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(a) Orbital interaction diagram of the La6Cl14C2 4− cluster observed in La4Cl5C2. (b) Plot of the highest occupied x 2 -y 2 orbitals of La6Cl14C2 4−.
In order to clarify more localized bonding interactions, fragment molecular orbital (FMO) analysis is made of the distinct La 6 Cl 14 C 2 4− cluster. Figure 3(a) shows an interaction diagram between La 6 Cl 14 states and C 2 orbitals. The result-ing molecular orbital levels are shown schematically in Figure 3(a) . These levels will correlate directly with the states in the infinite chains. A closer inspection of the frontier orbitals of this cluster reveals that the highest occupied (HO) La-La σ( x 2 -y 2 ) bonding orbital ( Figure 3(b) ) exists right above the C 2 g orbitals. Just above the HOMO level three t 2g ( xy, xz, and yz orbitals) bonding levels are found, with the shared La-La edges. All these levels are also of weakly La- Cl antibonding character. Thus the filling of these levels with some additional electrons will stabilize the structure slightly. This may be achieved by intercalation of cations into the structure.
Once C 2 (C-C distance: 1.44 Å) is present as an interstitial in the La 6 Cl 14 C 2 4− cluster, its molecular orbital levels will become different from the isolated one. The order of increasing energies of the molecular orbitals for an isolated C 2 is 1σ g , 1σ u , 1π u , 2σ g , and 1π g . This is shown at left in Figure 3(a). All the metal-metal bonding “acceptor” orbitals, except for the x 2 - y 2 , can interact with the lower lying C 2 “donor” orbitals to form metal-carbon bonding (occupied) and antibonding (unoccupied) combinations. Orbital inter-actions of filled 1π g with the empty La dπ states yield La-C(1π g ) bonding combinations around −10.1 eV. Backbond-ing from filled 1π g orbitals of the C 2 unit into empty d states of the La atoms obviously leads to a certain degree of elect-ron delocalization. The 1πg orbitals are stabilized greatly in the C 2 -to-metal π backbonding process. This type of bonding removes electron density from the C 2 . Therefore, C 2 is form-ally present as C 2 5− and enhanced La-La bonding always occurs together with La-C bonding in La 4 Cl 5 C 2 . It may be noted that the bonding La-C(1π g ) combination contains more carbon contribution than lanthanum. The 1σ u and 2σ g orbitals interact with z 2 orbitals of the two axial La neighbors to form La-C bonding combinations (near −18.4 and −12.8 eV). One can see that they have been considerably stabilized by mixing with the lanthanum orbitals. A stabilization of the La 6 Cl1 4 C 2 cluster structure on inclusion of C 2 is evident.
A better theoretical picture can be extract from band structure calculations. These calculations were performed for La 4 Cl 6 C 2 chains. Figure 4(a) shows the DOS plot calcu-lated for the chain system. The density of states can be divided into several distinctive regions. Contributions of chloride p-block states to the total DOS are shown in the energy region between −13.5 and −15.5 eV, followed by three main peaks stemming predominantly from C 2 mole-cular orbitals. At higher energies the lanthanum d bands are only partially occupied. These valence bands are made up predominantly of lanthanum x 2 - y 2 states. Contributions of most La d states to the total DOS are found, with dominant portions above the Fermi level.
A graphical interpretation of the COOP ( Figure 4(b) ) reveals that there are rather strong La-La bonding states right below the Fermi level. The vacant La dπ bonding states are also involved in bonding with C 2 g . The 1π g states ( ca . −9.5 to −10.8 eV) are La-C bonding and C-C antibonding. The 2σ g and 1πu states fall just above the energy block of the chloride p states. The 2σ g and 1π u states ( ca . −12.5 to −13.5 eV) are not only C-C bonding but also La-C bonding. Finally, the 1σ u state ( ca . −18.5 eV) is much less antibonding through the mixing with the 2σu orbital, but clearly La-C bonding. These may be compared with the interaction dia-gram in Figure 3(a) . It is interesting to note in Figure 4(a) that the C 2 states have five peaks below the Fermi level which are derived from the 1σ g , 1σ u , 1π u , 2σ g , and 1π g orbitals. This implies that the number of C 2 occupied states is close to that for a C-C single bond, giving a bond order of one. The integrated overlap population (OP) of 0.81 for the C-C bonds in La 4 Cl 5 C 2 is closer to the value of a C-C single bond than that of a C=C double bond (0.74 and 1.30 for ethane and ethylene calculated by EH method, respectively).
Figure 4(b) shows the COOP curves for some selected La-La, La-Cl, and La-C bonds as well as the C-C bond in the La 4 Cl 6 C 2 chain structure. The COOP curves emphasize the major bonding roles of La-C and La-Cl and the lesser La-La contributions. The La-C interactions are distributed over the entire energy region, in contrast to the polar La-Cl interactions. The axial La2-C bond is remarkably short, 2.303 Å, and evidently very strong (OP = 0.62). Note the highly bond-ing OP value of the La2-C bond. The shortest La-C contact distance observed can be understood from bonding effects from occupied C 2 g and 1π g orbitals into the vacant La d orbitals of appropriate symmetry. The La-Cl contacts ranging between 2.951 and 3.001 Å have average overlap populations of 0.29. These La-Cl interactions are responsible for the broad DOS peaks around −14.5 eV ( Figure 4(a) ). These La-Cl distances are within the normal range as in many other reduced rare earth chlorides. Thus, La-Cl bonding must be covalent.
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(a) Total DOS (black line) and the contributions of La d (red), Cl p (green), C pz (σ, blue), and C px,y (π, yellow) orbitals to it in La4Cl6C2 chains. (b) Crystal orbital overlap populations for La-La (3.399 Å, black), La-La (~3.95 Å, red), La-Cl (green), La-C (blue), and C-C (yellow) bonds in La4Cl6C2 chains. The Fermi level is indicated by the vertical dashed line.
A substantial difference appears in the OP values for La-La contacts. Comparisons of the refined distances with the OP values for each bond are listed in Table 2 . The largest contrasts lie between the three independent La-La distances, which vary from 3.399 to 3.983 Å, their overlap populations vary from 0.02 to 0.10. The small overlap populations pertain to La1-La1 and La1-La2 contacts, 3.921and 3.983 Å, in distinct contrast to the large overlap populations for the 3.399 Å separations of the shared edges, La1-La1. The La-La separations of shared edges within the La 6 octahedron are unusually short. This short La-La separation may be the result of relatively strong La-La bonding. Indeed, nearly all states just below the Fermi level have strong La-La σ bonding character and are clearly derived from x 2 - y 2 . A substantial fraction of the La 5d bonding states fall above the Fermi level, confirming the above FMO analysis. With an oxidation state of +2.5 for lanthanum, one electron can be allocated to each of the two short La-La bonds in the octahedron. The OP values reflect the strength of La-C, La-Cl, and La-La bonding interactions. The above argu-ments are consistent with the formal electron partition of (La 3+ ) 4 (Cl )5(C 2 5− )·2e for this compound, with the assump-tion that the excess electrons reside mainly in strong localized La-La bonds within the shared edges between the La6 octahedra which are considerably shorter than the remaining ones. On the other hand, little is known about the physical properties of this compound.
Overlap populations (OP) for a pair of atoms in La4Cl5C2
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Overlap populations (OP) for a pair of atoms in La4Cl5C2
In summary, the bonding in La 4 Cl 5 C 2 is dominated by strong covalent La-C with lesser La-Cl and La-La inter-actions. Interstitial C 2 units are essential to the stability of the compound; formally, they provide electrons to the La 6 cage and engage in strong La-C bonding that is much stronger than the La-La bonding. The band structure calcu-lations for a La 4 Cl 6 C 2 chain reveal that 2σ g and 1π g levels of C 2 are substantially stabilized. All La-C and La-Cl bonding states are occupied and La x 2 - y 2 orbitals combine to form the highest occupied x 2 - y 2 bonding band. The shortened C-C single bond may be understood by π*-backbonding from the occupied C 2 g orbitals into the empty La dπ states, in agreement with the formal charge distribution of (La 3+ ) 4 -(Cl ) 5 (C 2 5− )·2e . The two excess electrons are available for intra-cluster bonding and are likely to be localized in the shortened La-La bonds forming the shared edges between the La 6 C 2 octahedra within the chain.
This work was supported by the Kyungsung University Research Grant in 2014.
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