Appendix A
Effect of the ˆ l Operator and the Matrix
Elements of the p and d Orbitals
ψ
ˆ l x |ψ
ˆ l y |ψ
ˆ l z |ψ
p x
0
−ip z
ip y
p y
ip z
0
−ip x
p z
−ip y
ip x
0
d z 2
−i
√
3d yz
i
√
3d xz
0
d x 2 −y 2
−id yz
−id xz
2id xy
d xy
id xz
−id yz
−2id x 2 −y 2
d yz
id x 2 −y 2 + i
√
3d z 2
id xy
−id xz
d xz
−id xy
−i
√
3d z 2 + id x 2 −y 2
id yz
ˆ l
p x
p y
p z
p x
0
−i
1
p y
i
01
p z
110
ˆ l
d z 2
d x 2 −y 2
d xy
d yz
d xz
d z 2
000
i
√
3
−i
√
3
d x 2 −y 2
00
−2ii
i
d xy
02 i
0
i
−i
d yz
−i
√
3
−i
−i
0
i
d xz
i
√
3
−ii−i
0
© Springer International Publishing Switzerland 2016
C. Graaf and R. Broer, Magnetic Interactions in Molecules and Solids,
Theoretical Chemistry and Computational Modelling,
DOI 10.1007/978-3-319-22951-5
213