Computational Chemistry

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