VrsðH; 1 Þ¼
Z
fr
ZH
rH 1
fsdv ð 5 : 102 Þ
and
VrsðHe; 1 Þ¼
Z
fr
ZHe
rHe1
fsdv ð 5 : 103 Þ
In Eq.5.102the variable is the distance of the electron (“electron 1” – see the
discussion in connection with Eqs.5.18and5.19) from the hydrogen nucleus, and
eV (1 eV particle–1 = 96.5 kJ mol–1)
20
10
0
–10
–20
–30
–500
- 40
–50
H 2 O
neutral, singlet
H 2 O
neutral, triplet
H 2 O
radical cation, doublet
0 unpaired electrons,
S = 0
multiplicity = 2S + 1 = 1
2 unpaired electrons,
S = 1 / 2 + 1 / 2 = 1
multiplicity = 2S + 1 = 3
i.e. H 2 O .+
1 unpaired electron,
S = 1 / 2
multiplicity = 2S + 1 = 2
Fig. 5.9 Some examples of the results of specification of charge and multiplicity. The calculations
used the STO-3G basis set (Section 5.3) which has seven basis functions, and so creates seven
MOs. All calculations were at the HF/STO-3G geometry of the neutral singlet
5.2 The Basic Principles of the ab initio Method 217