Bonding in the Extended Metal Chain Compound La₄Cl₅C₂

Results and Discussion

An understanding of the chemical bonding in La4Cl5C2 needs simpler structure. Let us focus on a La6Cl14C2 cluster taken out from the La4Cl5C2 lattice. Molecular orbital calcu-lations are performed on the C2-centered La6 octahedral cluster system as well as the C2-free structure in order to judge the effect of the interstitial C2 on the stabilization of clusters. The C2 interstitial exists as C25−, similar to other compounds such as Gd12(C2)3I17 [14] and Dy12(C2)3I17,15 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 (La3+)4(Cl−)5(C2 5−)·2e− with two excess electrons per formula unit. With Cl− and (C2)5− lanthanum has the oxidation state of +2.5. This leaves three excess electrons per La6Cl14C2 cluster, i.e., (La6Cl14C2)4−. These electrons are responsible for La-La bonding inter-actions which are covalent in character.

Figure 3.(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 La6Cl14C2 4− cluster. Figure 3(a) shows an interaction diagram between La6Cl14 states and C2 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(x2-y2) bonding orbital (Figure 3(b)) exists right above the C2 1πg orbitals. Just above the HOMO level three t2g (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 C2 (C-C distance: 1.44 Å) is present as an interstitial in the La6Cl14C2 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 C2 is 1σg, 1σu, 1πu, 2σg, and 1πg. This is shown at left in Figure 3(a). All the metal-metal bonding “acceptor” orbitals, except for the x2-y2, can interact with the lower lying C2 “donor” orbitals to form metal-carbon bonding (occupied) and antibonding (unoccupied) combinations. Orbital inter-actions of filled 1πg with the empty La dπ states yield La-C(1πg) bonding combinations around −10.1 eV. Backbond-ing from filled 1πg orbitals of the C2 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 C2-to-metal π backbonding process. This type of bonding removes electron density from the C2. Therefore, C2 is form-ally present as C25− and enhanced La-La bonding always occurs together with La-C bonding in La4Cl5C2. It may be noted that the bonding La-C(1πg) combination contains more carbon contribution than lanthanum. The 1σu and 2σg orbitals interact with z2 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 La6Cl14C2 cluster structure on inclusion of C2 is evident.

A better theoretical picture can be extract from band structure calculations. These calculations were performed for La4Cl6C2 − 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 C2 mole-cular orbitals. At higher energies the lanthanum d bands are only partially occupied. These valence bands are made up predominantly of lanthanum x2-y2 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 C2 1πg. The 1πg states (ca. −9.5 to −10.8 eV) are La-C bonding and C-C antibonding. The 2σg and 1πu states fall just above the energy block of the chloride p states. The 2σg and 1πu states (ca. −12.5 to −13.5 eV) are not only C-C bonding but also La-C bonding. Finally, the 1σu 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 C2 states have five peaks below the Fermi level which are derived from the 1σg, 1σu, 1πu, 2σg, and 1πg orbitals. This implies that the number of C2 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 La4Cl5C2 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 La4Cl6C2 − 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 C2 2σg and 1πg 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.

Figure 4.(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 La6 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 x2-y2. 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 (La3+)4(Cl−)5(C2 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.

Table 2.Overlap populations (OP) for a pair of atoms in La4Cl5C2

 

Conclusion

In summary, the bonding in La4Cl5C2 is dominated by strong covalent La-C with lesser La-Cl and La-La inter-actions. Interstitial C2 units are essential to the stability of the compound; formally, they provide electrons to the La6 cage and engage in strong La-C bonding that is much stronger than the La-La bonding. The band structure calcu-lations for a La4Cl6C2− chain reveal that 2σg and 1πg levels of C2 are substantially stabilized. All La-C and La-Cl bonding states are occupied and La x2-y2 orbitals combine to form the highest occupied x2-y2 bonding band. The shortened C-C single bond may be understood by π*-backbonding from the occupied C2 1πg orbitals into the empty La dπ states, in agreement with the formal charge distribution of (La3+)4-(Cl−)5(C2 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 La6C2 octahedra within the chain.