Magnetic Behavior of Diatomic Species
 Page ID
 35868
Generally magnetic properties of diatomic molecules or ions whose total number electrons lie in the range (120) can be evaluated with the help of Molecular orbital theory (MO theory)^{1,}^{2}.^{ }The present study involves^{35} three (03) new formulae by just manipulating the number of unpaired electrons (n) for determination of magnetic properties without MO theory using mod function (based on Applied Mathematics) and by means of these n values one can easily stumble the magnetic moment values in BohrMagneton using spin only formula
\[\mu_s = \sqrt{n(n+2)} \mu_B\]
where
 \(\mu_B\) is the Bohr Magneton (unit of magnetic moment) and
 \(n\) is the number of unpaired electrons.
Classification
First of all we classify the molecules or ions depending on the total number of electrons present in them in the following three (03) sets.
 Set 1: Molecules or ions with (13), (35), (57), (710), or (1316) electrons
 Set 2: Molecules or ions with (1013) or (1619) electrons
 Set 3: Molecules or ions with 20 electrons
Then for different set we have to use three different formulae to calculate the number of unpaired electrons which have been presented in Table 1 and thus magnetic moment (\(\mu_s\)) can be evaluated in the following way:
SET 1: Species with (13), (35), (57), (710), or (1316) Electrons
For the prediction of number of unpaired electrons (n) of molecules or ions having total number of electrons (13),(35),(57),(710) and (1316)electrons:
In this case, the number of unpaired electrons n = [ I (ND  total electrons) I ]
Here, ND = next digit i.e. digit next to minimum digit and ‘I I’ indicates mod function.
Eg:Molecules or ions having (13)electrons, in this case ND = 2 because here minimum digit is 1.
+
He_{2}^{+} (3electrons), the total number of electrons will be 3, ND = 2, Hence, unpaired electron n = I (ND  total electrons) I = I (23) I = 1. Hence, Magnetic Moment μ_{s }= √n(n+2) \(\mu_B\) = √ 1(1+2) BM = √3 BM = 1.73BM.
For the molecules or ions containing (35)electrons, (57)electrons, (710)electrons, and (1316)electrons the ND value will be 4, 6, 8 and 14 respectively. Hence, the value of n = [ I (4total electrons) I ]; [ I (6 total electrons) I ] [ I (8 total electrons) I ] and [ I (14 total electrons) I ] respectively.
SET 2: Species with (1013) or (1619) Electrons
For the prediction of number of unpaired electrons (n) of molecules or ions having total number of electrons (1013) and (1619):
In this case, the number of unpaired electrons n = [ I (PD  total electrons) I ]
Here, PD = Penultimate electron digit (i.e. before last electron).

The \(C_2^\) diatomic ion has 13 electrons, so PD = 12. Hence, unpaired electron n = I (12  total electrons) I = I (1213) I = 1
Hence, Magnetic Moment μ_{s }= √n(n+2) \(\mu_B\) = √ 1(1+2) BM = √3 BM = 1.73BM
2
The \(F_2\) diatomic molecules has 18 electrons, the total number of electrons will be 18, PD = 18. Hence, unpaired electron n = I (18  total electrons) I = I (1818) I = 0
Hence, Magnetic Moment μ_{s }= √n(n+2) \(\mu_B\) = √ 0(0+2) BM = 0 BM = Diamagnetic in nature.
SET 3: Species with 20 Electrons
For the prediction of number of unpaired electrons (n) of molecules or ions having total number of electrons 20:
In this case, the number of unpaired electrons n = [ (20  total electrons) ]
2
The \(Ne_2\) diatomic molecules has 20 electrons, the total number of electrons will be 20. Hence, unpaired electron n = (20  total electrons) = (2020) = 0
Hence, Magnetic Moment μ_{s }= √n(n+2) \(\mu_B\) = √ 0(0+2) BM = 0 BM = Diamagnetic in nature.
Species (Molecules or ions) 
Total Number of electrons 
Number of unpaired electrons (n) 
Magnetic moment (μs) in Bohr Magneton (\(\mu_B\)) 
Magnetic Behavior 

H_{2}^{+} 
1 
1 
1.73 
Paramagnetic 
H_{2}, He_{2}^{2+} 
2 
0 
0 
Diamagnetic 
H_{2}^{},He_{2}^{+} 
3 
1 
1.73 
Paramagnetic 
He_{2}, 
4 
0 
0 
Diamagnetic 
Li_{2}^{+},He_{2}^{} 
5 
1 
1.73 
Paramagnetic 
Li_{2}, He_{2}^{2}, Be_{2}^{2+} 
6 
0 
0 
Diamagnetic 
Be_{2}^{+},Li_{2}^{} 
7 
1 
1.73 
Paramagnetic 
Be_{2},Li_{2}^{2} 
8 
0 
0 
Diamagnetic 
Be_{2}^{},B_{2}^{+} 
9 
1 
1.73 
Paramagnetic 
B_{2}, Be_{2}^{2}, HF 
10 
2 
2.82 
Paramagnetic 
B_{2}^{},C_{2}^{+} 
11 
1 
1.73 
Paramagnetic 
C_{2},B_{2}^{2},N_{2}^{2+}, CN^{+} 
12 
0 
0 
Diamagnetic 
C_{2}^{},N_{2}^{+} 
13 
1 
1.73 
Paramagnetic 
N_{2},CO,NO^{+},C_{2}^{2},CN^{},O_{2}^{2+} 
14 
0 
0 
Diamagnetic 
N_{2}^{},NO,O_{2}^{+} 
15 
1 
1.73 
Paramagnetic 
NO^{},O_{2} 
16 
2 
2.82 
Paramagnetic 
O_{2}^{} 
17 
1 
1.73 
Paramagnetic 
F_{2},O_{2}^{2},HCl 
18 
0 
0 
Diamagnetic 
F_{2}^{} 
19 
1 
1.73 
Paramagnetic 
Ne_{2} 
20 
0 
0 
Diamagnetic 
References
 “Spectroscopy. Molecular Orbitals and Chemical Bonding”, Nobel Lectures, Chemistry 19631970,Elsevier Publishing Company, 19721966
 Hall, George G. LennardJones Paper of “Foundations of Molecular Orbital Theory”,Advances in Quantum Chemistry,1929,22. Bibcode:1991AdQC…22…1H. doi:10.1016/S00653276(08)603615, ISBN9780120348220, ISSN 00653276
 Arijit Das,‘Simple Thinking Makes Chemistry Metabolic And Interesting A Review Article’, IOSRJAC,2013,6(4), 815, eISSN: 22785736, doi:10.9790/57360640815
 Arijit Das, ‘A rapid and innovative method for the easy prediction of Magnetic behavior of homo and heteronuclear mono and diatomic molecules or ions without MOT’,IJAR,2013, 3(10), 1, ISSN2249555X
 Arijit Das, R.Sanjeev and V.Jagannadham, “Innovative And Time Economic Pedagogical Views In Chemical Education – A Review Article”, World Journal of Chemical Education, 2014, 2(3), 2938, Science and Education Publishing , USA, DOI:10.12691/wjce231
External Links
 https://communities.acs.org/docs/DOC46667
 https://communities.acs.org/docs/DOC45853
 www.drarijitdaschem.in/Innova...Views%20in.pdf
Contributor
 Dr. Arijit Das, Ph.D. (Inorganic Chemistry), MACS ( Invited,USA ), SFICS, MISC, MIAFS (India), Assistant Professor, Department of Chemistry, Ramthakur College, Agartala, Tripura(W), Tripura, India, Pin799003.