Bond order is one of the vital important terms used in the field of chemistry. Determination of bond order provides us information about the chemical bonds present in between two atmos. And also using bond order, one can have an idea about stability of molecules, bond energy, bond length, thermal stability of molecules. But evaluation of bond order using MOT or by drawing molecular orbitals, is time consuming. So, in this manuscript, I have tried to represent a different approach to calculate the bond order with the help of applied mathematics and some basic concepts of chemistry, which can be used especially for any competitive exam, that will be beneficial for all students to save their valuable time. To use this new method, the student need not compulsorily know the MOT. This method is applicable for those diatomic molecules and ions, which have their total electron number (01-20).

1. _____________________________________________________________________________________________________
*Corresponding author: Email: pritam.oam@gmail.com;
Short Research Article
Journal of Applied Chemical Science International
8(3): 106-110, 2017
ISSN: 2395-3705 (P), ISSN: 2395-3713 (O)
A DIFFERENT APPROACH FOR DETERMINATION OF
BOND ORDER OF HOMO AND HETERO NUCLEAR
DIATOMIC MOLECULES AND IONS WITHOUT USING
MOLECULAR ORBITAL THEORY (M.O.T)
PRITAM DEBNATH1*
1
Department of Civil Engineering, National Institute of Technology Agartala, Tripura, Jirania 799046, India.
AUTHOR’S CONTRIBUTION
The sole author designed, analyzed and interpreted and prepared the manuscript.
Received: 4th
November 2017
Accepted: 21st
December 2017
Published: 28th
December 2017
__________________________________________________________________________________
ABSTRACT
Bond order is one of the vital important terms used in the field of chemistry. Determination of bond order
provides us information about the chemical bonds present in between two atmos. And also using bond order,
one can have an idea about stability of molecules, bond energy, bond length, thermal stability of molecules. But
evaluation of bond order using MOT or by drawing molecular orbitals, is time consuming. So, in this
manuscript, I have tried to represent a different approach to calculate the bond order with the help of applied
mathematics and some basic concepts of chemistry, which can be used especially for any competitive exam, that
will be beneficial for all students to save their valuable time. To use this new method, the student need not
compulsorily know the MOT. This method is applicable for those diatomic molecules and ions, which have their
total electron number (01-20).
Keywords: Atomic number; bond order; electronic charge molecules; MOT; total electron number; value of d;
value of l; value of Ad; value of e.
1. INTRODUCTION
Using MOT or by drawing molecular orbitals, one can
find the bond order of any diatomic molecules. The
calculation of bond order is very important in the field
of inorganic chemistry. The conventional method for
evaluation of bond order using MOT [1-9] is time
consuming. In case of the conventional method to
evaluate the bond order, at first, one should draw the
molecular orbitals for the corresponding molecule.
After that, distribution of electrons in those molecular
orbitals is done and then using formulae, bond order
can be found out. Concept of MOT is great, but to use
MOT, one should know about the molecular orbitals
and the distribution of electron in those orbitals and
also need to draw the molecular orbitals for
distribution of electrons and then need to use
formulae, which need time. So with a very simple
concept, the author represents here a rapid way to
calculate bond order by using the value of l (described
below in section 2.1 & 2.2), value of d (described in
section 2.3), value of Ad (described in section 2.4) and
value of e (described in section 2.5). By using the
same concept of value of l, earlier three rapid method
has been introduced by the author for easy prediction
of ‘Magnetic Moment’ [10] and ‘Spin Multiplicity
Value’ [11] and ‘Unpaired Electron Number’ [12]
for the benefit of students.

2. Debnath; JACSI, 8(3): 106-110, 2017
107
This method contains 2(two) new formulae with two
sets of electron number. By placing only the value of
l, d, Ad and e in the respective formula, one can easily
calculate the bond order of different diatomic
molecules and ions.
This rapid method will be very much helpful for all
students of chemistry, particularly for those situations,
where calculation of bond order is to be done within a
very short interval of time.
So, on the basis of all these things, the author can
strongly recommend that this method will be most
rapid method for calculation of bond order of homo
and hetero nuclear diatomic molecules or ions having
total electron number (01-20), without using M.O.T.
2. MATERIALS AND METHODS
First of all, we take certain range of total electron
number of different diatomic molecules and ions,
which are shown in two sets as follows.
Set-1:-Molecules or ions having 1-14 electrons
Set-2:- Molecules or ions having 15-20 electrons
The above two sets, with their corresponding
formulae for finding bond order is shown in Table 1.
Table 1. Formulae for finding bond order
Total electron range Formula
1-14 | − 4( + )|
2
15-20 | ( )|
+Ad±e
2.1 Introduction to l
l is a variable, which can take only two value 0 or 1,
depending on the total electron number of a molecule
or ion.
If, the total electron number for a molecule or ion lies
between ‘1-8’, then value of l = 0.
If, the total electron number for a molecule or ion lies
between ‘9-20’, then value of l =1.
2.2 Source of Conception behind the Value of l
Actually this concept is taken from azimuthal
quantum number [13,14] of quantum chemistry;
where it is observed, for s orbital, quantum number l
is taken as 0 (considering l represents azimuthal
quantum number) and for p orbital l is taken as 1. The
same concept has been used here. If an atom contains
only s orbital, the value of l is taken as 0, and if an
atom contains both s and p orbital, then the value of l
is taken as 1. The value of l depends on the two atoms
of which a diatomic molecule is composed. But in
case of such diatomic molecules, where one atom has
only s orbital and another atom has both s and p
orbital, then it is observed that, if the atom consisting
both s and p orbital is taken under consideration, then
the calculation (using applied mathematics) goes in an
appropriate way and gives the desired result. But, if
the atom, which has only s orbital is taken under
consideration, then the process does not give any
suitable result. That is why; that atom is taken into
consideration, which contains both s and p orbital in
case of the ionic molecule or hetero nuclear diatomic
molecules (e.g. - HF) to find the value of l.
Hence, from the above observations it can be said
that, the value of l is 0 for those molecules, which
contain (1-8) total electrons and the value of l is 1 for
those molecules, which contain (9-20) total electrons.
E.g.:
i. N + N = N2
Electronic configuration of N: 1S2
2S2
2P3
We can observe that N2 contain two N (nitrogen
atom), and both N atom contain both s and p orbital.
So, the value of l for N2 molecule is taken as 1.
ii. H + F = HF
Electronic configuration of H: 1S1
Electronic configuration of F: 1S2
2S2
2P5
We can observe that HF contains one H (hydrogen)
atom and one F (fluorine) atom. And, H atom has only
s orbital, whereas F atom has both s and p orbital. So,
according to the considering rule, value of l is taken
as 1.
2.3 Introduction to d
d is the difference between the electron number
present in s orbital and p orbital of the last shell of an
atom of a molecule.
Step to find the value of d:
1. At first, find the electronic configuration of the
last shell of the two atoms of the molecule (i.e,
ns and np)
2. If molecule is composed of similar type of
atoms, then find the difference d.

3. Debnath; JACSI, 8(3): 106-110, 2017
108
e.g.: O+O=O2
3. If molecule is composed of two different type
of atoms, then find the electronic configuration
of both atoms and take difference.
4. If value of d is different for two atoms of a
molecule, then take lowest value of d.
Special for d:
1. If only 1s orbital is present in an atom, then
always take d=1.
2. The value of d always will be greater than 0.If
d becomes 0 after taking difference, always
take d=1 in place of 0.
Two exception:
1. As per above described condition, d≠0. But for
total electron no 1, we have to consider, d=0.
2. As per above described condition, if the value
of d becomes different for two atom, we will
take always lowest value of d.
But for total electron no 7, we have to take highest
value of d.
Eg: (1) O2, which has value of n= 16 and Electronic
configuration of O2 is 1s2
2s2
2p4
In the last shell, electron number in 2s is 2 and 2p is 4.
Hence, d = (4-2) = 2
(2) Be2, which has value of n= 8, and Electronic
configuration of Be2 is 1s2
2s2
In the last shell, electron number in 2s is 2 and 2p is 0
Hence, d = (2-0) = 2
2.4 Introduction to Ad
Ad will come, when a molecule is composed of two
different type of atom.
Ad is the difference between the atomic number of the
two atom, of which a molecule is composed of.
e.g.:
1. C + O = CO
Atomic no. of C is 6.
Atomic no. of O is 8.
Therefore;
Ad = (Atomic no. of O ~ Atomic no. of C)
= (8 – 6) = 2.
2. C + O- = CO-
Atomic no. of C is 6.
Atomic no.(total electron no.) of O is 8.
**[Do not take the total electron number of O-
, always
take atomic number of neutral atom]**
*If a molecule is composed of similar type of atom ,
then Ad is always 0, irrespective of ionic or neural
molecule.
*Ad depends only on the type of atoms, of which a
molecule is composed.
2.5 Introduction to e
‘e’ is electronic charge present in a molecule .If a
molecule contain positive(+ve) charge ,then take
positive value of e. And if a molecule contain
negative(-ve) charge ,then take negative value of e.
2.6 Introduction to n
n is total electron number of a molecule.
e.g.: O+O=O2
Total electron no of O2 is (8+8 =16) 16.
3. RESULTS AND DISCUSSION
3.1 Discussion for Set 1
Total electron range: 1- 14
In this case, Formula for finding unpaired electron
number =
| ( )|
E.g.: (1) N2, which has value of n= 14, value of l= 1
and d=1
Hence, bond order for N2 =
| ( )|
=3
(2) C2
-
, which has value of n= 13, value of l= 1 and
d=1
Hence, bond order for C2
-
=
| ( )|
=2.5
3.2 Discussion for Set 2
Total electron range: 15-20
In this case, Formula for finding unpaired electron
number =
| ( )|
+Ad±e
E.g.: (1) O2, which has value of n= 16, value of l= 1,
d=2, Ad =0, e=0.

4. Debnath; JACSI, 8(3): 106-110, 2017
109
Hence, bond order for O2 =
| ( )|
+0+0 = 2
(2) CO-
, which has value of n= 15, value of l= 1, d=2,
Ad =2, e= 1.
Hence, bond order for CO-
=
| ( )|
-1+2=2.5
The bond order of different molecules and ions are
shown in Table 2.
Table 2. Bond Order of different molecules by using new method
Different
molecules
Total electron
no. (n)
Value of ‘d’ Value of ‘l’ Value of ‘Ad’ New formula
H2 2 1 0 | ( )|
=1
He2 4 1 0 | ( )|
=0
Li2 6 1 0 | ( )|
=1
Be2 8 2 0 | ( )|
=0
B2 10 1 1 | ( )|
=1
C2 12 1 1 | ( )|
=2
N2 14 1 1 | ( )|
=3
O2 16 2 1 0 | ( )|
=2
F2 18 3 1 0 | ( )|
=1
Ne2 20 4 1 0 | ( )|
=0
H2
+
1 0 0 | ( )|
=0.5
H2
-
3 1 0 | ( )|
=0.5
He2
+
3 1 0 | ( )|
=0.5
Li2
+
5 1 0 | ( )|
=0.5
Be2
+
7 2 0 | ( )|
=0.5
HF 10 1 1 | ( )|
=1
C2
+
11 1 1 | ( )|
=1.5
C2
-
13 1 1 | ( )|
=2.5
N2
+
13 1 1 | ( )|
=2.5
N2
-
15 1 1 0 | ( )|
− 1=2.5
O2
+2
14 1 1 | ( )|
=3
O2
-2
18 2 1 0 | ( )|
− 2=1
O2
-
17 2 1 0 | ( )|
− 1=1.5
O2
+
15 2 1 0 | ( )|
+ 1=2.5
NO+
14 1 1 | ( )|
=3
NO-
16 2 1 1 | ( )|
− 1 + 1=2
CN 13 1 1 | ( )|
=2.5
CN+
12 1 1 | ( )|
=2
CO-
15 2 1 2 | ( )|
− 1 + 2=2.5

5. Debnath; JACSI, 8(3): 106-110, 2017
110
4. CONCLUSION
In the conclusion, it can be stated that, the new
method offers the student an innovative as well as a
rapid process for prediction of bond order of homo
and hetero nuclear diatomic molecules and ions
without using MOT. This method proposes an
enhanced, simpler process which will curtail the
calculation time.
COMPETING INTERESTS
Author has declared that no competing interests exist.
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