Fig. 1. (top) Nitrogen atom substitution into (a) planar graphene, (b) (7,0) CNT, and (c) (5,5) CNT. (bottom) The Fe–4N substitution sites for (f) graphene sheet and (d,e,g,h) (7,0) CNT clusters. Coordinations of Fe to pyridine-like and pyrrole-like configurations are shown in (d,g) and (e,h), respectively. The configurations are in axial (d,e) and helical orientations (g,h). Terminal hydrogen atoms are not shown.

Fig. 2. Nitrogen substitution energies Eq. (1) for the graphene and CNT clusters. On the horizontal axis, the configurations of the two N substitutions are shown for the zigzag/armchair nanotube clusters, as schematically represented by the six-membered carbon rings on the top (bottom) of the graph for the armchair (zigzag) nanotube clusters. The symmetry axis of the CNTs is oriented horizontally. In the flat graphene, the N configurations are double degenerate.

Fig. 3. Fe binding energies for the planar and curved clusters containing 2 N atoms. The structures are shown schematically on the graph by the six-membered carbon rings and the CNT axis is oriented horizontally.

Fig. 4. Carbon nanocones doped with Ni(II) and N atoms. Structures 1–6 are in the first group whereas 7 –11 are in the second group.

Fig. 5. Diagram of the dianionic ligand of complex 2.

Fig. 6. Schematic diagrams of the molecular orbitals that contain major Ni d_z2 and s atomic orbital contributions for the cones of the first group.

Fig. 7. Metal-doped carbon nanocapsules.

Fig. 8. Metal and nitrogen doping patterns for capsules 1 (left) and 2 –4 (right).

Fig. 9. Electron spin density (ESD) surface (±0.0004 e/bohr³) of capsules 5 (top left), 23 (top middle), 7 (top right) and and 24 (bottom left). Electrostatic potential (ESP) of capsule 24 in the interval (−0.04,+0.04) e mapped on the 0.0004 e/bohr³ total electron density surface (bottom right).

Fig. 10. Experimental (exp) and calculated (theory) EXAFS spectra of iron-phthalocyanine (FePc).

Fig. 11. Experimental and calculated absorption coefficient functions χ(k) for (a) flat graphene clusters and (b) bent clusters. (c) Linear combination of the Fe–2N and Fe–4N spectra for structures with the lowest substitution energy optimized to fit to the χ_exp(k). The resulting curve contains 22.26% and 77.74% contributions from the Fe–2N and Fe–4N configurations, respectively.

Fig. 12. (up left) Top view of the Ni-doped cone and (up right) (4,4) CNT. (down) Extended MOs of the Ni-doped cone with a large metallic content. (left to right) The MOs with large composition of the 5s Ni-orbital (E₂₀₃=2.64 eV), the 11 px Ni-orbital (E₁₉₃=1.06 eV) and the 6s Ni-orbital (E₁₈₆=0.24 eV). (last) The HOMO is more spread on the cone and less away from it (E₁₇₁=−5.55 eV).

Fig. 13. Dependence of the neutral Ni-doped nanocone MO energies on the strength of the electric field . The HOMO and the LUMO are shown by thick lines. The extended Ni-orbitals drop fast with . (inset) The HOMO at electric field of 15.4 V/nm that contains mostly Ni s orbital contribution.

Fig. 14. (Up left to right) Extraction of the electron density from the Ni-doped nanocone in the static electric field , 13.4 and 15.4 V/nm. (down) Extraction of the electron density from the Ni-doped (4,4) CNT in (left) and 20.6 V/nm (right). In all the structures, the electrostatic potential in the interval =(−5.4,+5.4) V is mapped on the surface of the constant electron density 0.0004 e/Bohr³.

Fig. 15. Dependence of the Ni atom Mulliken charge and the average Ni–N distance on the strength of the electric field for the Ni-doped nanocone. (inset) Dependence of the electric field needed for the filling of the extended states on the length of the nanocone (number of CNT’s elementary cells).

Fig. 16. Binding of the Cl⁻ and Na⁺ ions to the cone. (left) Extraction of Cl⁻ at  V/nm and Na⁺ in  V/nm. (right) The Ni–Cl and Ni–Na distances as a function of the field strength.

Fig. 17. (left) Frontier molecular orbitals HOMO-2, (middle) HOMO and (right) LUMO of a sandwich-like light-harvesting antenna.

Fig. 18. (Top) A nanomechanical system formed by two extended capsules coordinated to a bpm ligand. The system can be displaced from its equilibrium bent conformation by bending and twisting. (bottom) The relative energy of the nanomechanical system for twisting and bending. The E and E₀ are the total energies of the bent (twisted) and optimized structures, respectively.

Table 1.

(top) Nitrogen substitution energies , Fe binding energies (eV), and Fe–N bond lengths (Å) for the graphene and CNT clusters. The cluster curvature increases from left to right. Pyridine and pyrrole-like coordination sites are denoted as py and pr, respectively

Table 2.

Selected optimized N–N distances for anionic ligands (N–N(L)) and for cones (N–N(co)), Ni–N distances (Å), N–Ni–N angles (°), Mulliken Ni atom charges (q(Ni), e), Ni–N(ligand) total binding energies (E_b(co), eV), and HOMO–LUMO gaps (H–L, eV) for the cones in their ground electronic states (GS). The GS s, d, t, qr and qn are singlet, doublet, triplet, quartet and quintet, respectively. The HOMO–LUMO gaps of open-shell systems are determined relative to LUMOs of the same spin type as the HOMOs. The N–N distances for 1 –6 are for N atoms trans to the Ni atom. The N–N distances for 8 –11 are for N atoms that belong to the same tridentate ligand. The N–N distances for ligands are defined as in the corresponding cones. The N–Ni–N angles for 8 –11 involve N atoms that belong to the same ligand.

Table 3.

Selected optimized metal–N (M–N) and metal-metal (M–M) distances (Å), binding energy (E_b(ca), eV), HOMO–LUMO gaps (H–L, eV) and Mulliken metal atom charges (q, e) Mulliken metal atom spin densities (Spin(M), e) for the capsules in their ground electronic states (GS). The GS types s, t, qn, h, n and ed are singlet, triplet, quintet, heptet, nonet and endecet, respectively. The HOMO–LUMO gaps of open-shell systems are determined relative to LUMOs of the same spin type as the HOMOs. For capsules 10, 10’ and 12 –15, only the diametral M–M distances are listed.