2 Quantum Chemistry in Perovskite Fluoride and Hydride: Nanoscale. . .
47
Fig. 2.18 The shapes of
selected molecular orbitals
related to hydrogen 1s
orbitals at (a) lattice position
(d = 0.0 Å), local minimum
(d = 0.6 Å) and local
maximum (d = 1.4 Å) in
KMg 4 H 3 model. The site
numbers of hydride ions are
also shown. Note that orbital
energy is given in parenthesis
Orbital Energy
(a)
(b)
MO30
(-1.3110)
MO31
(-1.2865)
MO32
(-1.2325)
(c)
MO30
(-1.3193)
MO31
(-1.2875)
MO32
(-1.2419)
MO30
(-1.3271)
MO31
(-1.2849)
MO32
(-1.2472)
H1
H2
H3
H1
H3
H1
H2
H3
H1
H2
H3
H1
H2
H3
H2
H3
H1
H2
H3
H1
H2
H3
H1
H2
H3
Figure 2.18 depicts the shapes of selected MOs related to hydrogen 1s orbitals
in KMg 4 H 3 model. In MO31s and MO32s, hydrogen 1s orbitals are overlapped as
same as MO40s and MO41s of K 2 Mg 4 H 3 model. From chemical bonding rule, it is
found that covalent bonding is formed between hydride ions. The wave functions of
MO30s are expressed as
MO30 (Lattice) = 0.11φ K1 (3pz)
+0.18φ H1
1s
+0.29φ H1
1s
+0.13φ H2
1s
+0.19φ H2
1s
+0.18φ H3
1s
+ 0.29φ H3
1s
+0.14φ Mg1
3s
+0.14φ Mg2
3s
+0.14φ Mg3
3s
+0.14φ Mg4
3s
(2.14)