Chapter 2 – Quantum Chemistry in Functional Inorganic Materials

Figure 2.1. The energy production system by the use of photocatalyst, fuel cell, and lithium ion battery. Solar and waste heat are utilized as energy resource.

Figure 2.2. The eight-nuclear KMn₈F₁₂ model for KMnF₃ perovskite.

Figure 2.3. The shapes and occupation numbers of the selected singly occupied natural orbitals (SONOs) for LS state of KMn₈F₁₂ model (UBHHLYP method).

Figure 2.4. The schematic pictures of the two types of the superexchange (SE) interactions (a) between manganese's 3d_{x² − y²} orbitals via fluorine's 2p orbital and (b) between manganese's 3d_{x² − y²} orbitals via fluorine's 2p orbital.

Figure 2.5. The crystal structure of K₂CuF₄ perovskite.

Figure 2.6. The two types of the normal vibration modes of the octahedral fluorine around copper: (a) Q₂ mode and (b) Q₃ mode.

Figure 2.7. The cluster models for K₂CuF₄ perovskite: (a) Cu₄F₄F₁₂ and (b) Cu₄F₄F₂₀ models.

Figure 2.8. The potential energy curve for Cu₄F₄F₁₂ model, changing the amplitude of the Jahn–Teller crystal distortion in Q₂ mode (q) (UB2LYP method).

Figure 2.9. The potential energy curve for Cu₄F₄F₁₆ model, changing the amplitude of the Jahn–Teller crystal distortion in Q₂ mode (q) (UB2LYP method).

Figure 2.10. The shapes and occupation numbers of the singly occupied natural orbital (SONO + 1) for (a) Cu₄F₄F₁₂ and (b) Cu₄F₄F₁₆ models, at q = 0.0, 0.15, and 0.5 Å (UB2LYP method).

Figure 2.11. (a) BaTi₈O₁₂ model for BaTiO₃ perovskite and (b) PbTi₈O₁₂ model for BaTiO₃ perovskite.

Figure 2.12. The orbital energy diagram in BaTi₈O₁₂ model (BHHLYP method).

Figure 2.13. The shapes of the selected molecular orbitals (MOs) in BaTi₈O₁₂ model (BHHLYP method).

Figure 2.14. The orbital energy diagram in PbTi₈O₁₂ model (BHHLYP method).

Figure 2.15. The shapes of the selected molecular orbitals (MOs) in PbTi₈O₁₂ model (BHHLYP method).

Figure 2.16. The schematic picture of lithium ion migration through A-site vacancy.

Figure 2.17. Onishi ionics model I: lithium ion for AMX₃-type perovskite (LiM₈X₁₂ model). Lithium ion is displaced along x-axis.

Figure 2.18. The obtained potential energy curve for La_{2/3 − x}Li_3xTiO₃ perovskite (LLT), displacing lithium ion along x-axis. d is the lithium ion conduction distance along x-axis (BHHLYP method).

Figure 2.19. The obtained potential energy curve for LaTiO₃ perovskite, displacing lithium ion along x-axis. d is the lithium ion conduction distance along x-axis (BHHLYP method).

Figure 2.20. The electron density map for Ti₄O₄ bottleneck: (a) La_{2/3 − x}Li_3xTiO₃ perovskite (LLT) and (b) LaTiO₃ perovskite (BHHLYP method).

Figure 2.21. The selected molecular orbitals (MOs) for La_{2/3 − x}Li_3xTiO₃ perovskite (LLT): (a) d = 0.0 Å and (b) d = 1.935 Å (bottleneck) (BHHLYP method).

Figure 2.22. The selected molecular orbitals (MOs) for LaTiO₃ perovskite: (a) d = 0.0 Å and (b) d = 1.979 Å (bottleneck) (BHHLYP method).

Figure 2.23. The obtained potential energy curve for K_xBa_{(1 − x)/2}MnF₃ perovskite, displacing lithium ion along x-axis. d is the lithium ion conduction distance along x-axis (BHHLYP method).

Figure 2.24. Onishi ionics models I for the oxygen-doped K_xBa_{(1 − x)/2}MnF₃ perovskite: (a) LiMn₈F₁₁O₁ model, (b) LiMn₈F₁₀O₂ (I) model, (c) LiMn₈F₁₀O₂ (II) model. Lithium ion is displaced along x-axis.

Figure 2.25. The obtained potential energy curves for LiMn₈F₁₁O₁ model, displacing lithium ion along x-axis. d is the lithium ion conduction distance along x-axis (BHHLYP method).

Figure 2.26. The obtained potential energy curves for LiMn₈F₁₀O₂ (I) model, displacing lithium ion along x-axis. d is the lithium ion conduction distance along x-axis (BHHLYP method).

Figure 2.27. The obtained potential energy curves for LiMn₈F₁₀O₂ (II) model, displacing lithium ion along x-axis. d is the lithium ion conduction distance along x-axis (BHHLYP method).

Figure 2.28. The two kinds of the oxide ion conduction paths on AlO₂ layer in AMO₃-type perovskite. The arrows show the oxide ion paths. In (a) and (b) paths, oxide ion migrates parallel and diagonally to AlOAl bond, respectively.

Figure 2.29. Onishi ionics model II: oxide ion for AMO₃-type perovskite (A₂M₄O₃ model). Oxide ion is displaced along the diagonal line ((b) path).

Figure 2.30. Onishi ionics models II for LaAlO₃ perovskite: (a) Al₄O₃ model, (b) La₂Al₄O₃ model, (c) LaSrAl₄O₃ model, and (d) Sr₂Al₄O₃ model.

Figure 2.31. The obtained potential energy curves for Al₄O₃ model, displacing oxide ion along the diagonal line. d is the oxide ion conduction distance along the diagonal line (BHHLYP method).

Figure 2.32. The obtained potential energy curves for La₂Al₄O₃ model, displacing oxide ion along the diagonal line. d is the oxide ion conduction distance along the diagonal line (BHHLYP method).

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