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Fig. 3.6 Bonding and antibonding orbitals of the hydrogen molecule (a), notations of the
distances between nuclei and electrons (b), and scheme of molecular orbitals (c) in the H
2
molecule
the wave function must be chosen. Practice shows that this can be done based on a
simplified Schr
¨
dinger equation, where the interaction between electrons is
neglected:
ðÞ
! H
ðÞ
1
ðÞ
¼
H
ðÞ
þ H
ðÞ
,
H
1
;
;
H
ðÞ
1
ðÞ
1
ðÞ
¼
E
ðÞ
ðÞ
1
ð Ψ
;
;
Ψ
ð :
;
It can be shown that this simplified equation can be partitioned into two ordinary
differential equations:
H ðÞˆ
1
ðÞ
¼
ʵ
1
ˆ
1
ðÞ
,
H ðÞˆ
2
ðÞ
¼
ʵ
2
ˆ
2
ðÞ
,
ðÞ
1
Ψ
ðÞ
¼
ˆ
1
ðÞˆ
2
ðÞ
,
E
¼
ʵ
1
þ ʵ
2
:
;
Consider solutions
H
(1) when the distance between the first electron and the
nucleus “
a
” is small and therefore
r
a
1
r
b
1
. In this case in
H
(1) the term
Ze
2
/
r
b
1
can