# Predicting the Bond-Order of Diatomic Species

Bond-order usually predicted from the Molecular Orbital Theory1,2. Molecular Orbital Theory (MOT) was first proposed by Friedrich Hund and Robert Mulliken in 1933. They developed an approach to covalent bond formation which is based upon the effects of the various electron fields upon each other and which employs molecular orbital rather than atomic orbital. Each such orbital characterizing the molecule as a whole is described by a definite combination of quantum numbers and possesses relative energy value.

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## Classification

First of all we classify the molecules or ions into the following four sets based on total number of electrons present in them.

SET 1: Molecules and ions having total no of electrons within the range (1-2):

In such case Bond order = n/2; [Where n = Total no of electrons]

Eg. H2 (Total electrons = 2), Therefore B.O. = n/2 = 2/2 = 1

SET 2: Molecules and ions having total no of electrons within the range (2-6):

In such case Bond order = I 4- n I / 2 ;

where n = Total no of electrons, ‘I I’ indicates Mod function i.e. the value of bond order is always positive]

Eg. Li2+(5electrons) Therefore B.O. = I 4-5 I / 2 = 1/2 = 0.5.

SET 3: Molecules and ions having total no of electrons within the range (6-14):

In such case Bond order = I 8-n I / 2

Eg: CO (Total electrons = 6+8=14), Therefore B.O.= I 8-14 I / 2 = 3

SET 4: Molecules and ions having total no of electrons within the range (14-20):

In such case Bond order = (20-n) / 2 ; [Where n = Total no of electrons]

Eg. NO (Total electrons = 15), Therefore B.O. = 20-15/2 = 2.5

Table 1: Bond order values for homonuclear and heteronuclear diatomic species having (1-20)electrons

Species (Molecules or ions)

Total Number of electrons (n)

Bond-Order (B.O.)

Bond-Order Values for the species having (1-2) electrons ; Bond order = n/2

H2+

H2, He22+

1

2

0.5

1

Bond-Order Values for the species having (2-6) electrons ; Bond order = I 4- n I / 2

H2-,He2+

He2,

Li2+,He2-

Li2, He22-, Be22+

3

4

5

6

0.5

0

0.5

1

Bond-Order Values for the species having (6-14) electrons ; Bond order = I 8- n I / 2

Be2+, Li2-

Be2, Li22-

Be2-, B2+

B2, Be22-, HF

B2-, C2+

C2, B22-, N22+, CN+

C2-, N2+

N2, CO, NO+, C22-, CN-,O22+

7

8

9

10

11

12

13

14

0.5

0

0.5

1

1.5

2

2.5

3

Bond-Order Values for the species having (14-20) electrons; Bond order = (20-n) / 2

N2-, NO, O2+

NO-, O2

O2-

F2, O22-, HCl

F2-

Ne2

15

16

17

18

19

20

2.5

2

1.5

1

0.5

0

## Graphical Presentation of Bond-Order

The graphical representation presented in Fig. 1 shows that bond-order gradually increases to 1 in the range (0-2) electrons then falls to zero in the range (2-4) electrons then it further rises to 1 for (4-6) electrons and once again falls to zero for (6-8) electrons then again rises to 3 in the range (8-14) electrons and then finally falls to zero for (14-20) electrons. For total no of electrons 2, 6 and 14, we may use multiple formulae, because they fall in the overlapping region in which they intersect with each other.