Magnetic Behavior of Diatomic Species

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Generally magnetic properties of diatomic molecules or ions whose total number electrons lie in the range (1-20) can be evaluated with the help of Molecular orbital theory (MO theory)^1,².The present study involves³^-5 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 Bohr-Magneton 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 (1-3), (3-5), (5-7), (7-10), or (13-16) electrons
Set 2: Molecules or ions with (10-13) or (16-19) 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 (1-3), (3-5), (5-7), (7-10), or (13-16) Electrons

For the prediction of number of unpaired electrons (n) of molecules or ions having total number of electrons (1-3),(3-5),(5-7),(7-10) and (13-16)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 (1-3)electrons, in this case ND = 2 because here minimum digit is 1.

+

He₂⁺ (3electrons), the total number of electrons will be 3, ND = 2, Hence, unpaired electron n = I (ND - total electrons) I = I (2-3) 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 (3-5)electrons, (5-7)electrons, (7-10)electrons, and (13-16)electrons the ND value will be 4, 6, 8 and 14 respectively. Hence, the value of n = [ I (4-total electrons) I ]; [ I (6- total electrons) I ] [ I (8- total electrons) I ] and [ I (14- total electrons) I ] respectively.

SET 2: Species with (10-13) or (16-19) Electrons

For the prediction of number of unpaired electrons (n) of molecules or ions having total number of electrons (10-13) and (16-19):

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 (12-13) 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 (18-18) 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) = (20-20) = 0

Hence, Magnetic Moment μ_s= √n(n+2) \(\mu_B\) = √ 0(0+2) BM = 0 BM = Diamagnetic in nature.

Table 1: Magnetic moments of homonulcear and heteronuclear diatomic species
Species (Molecules or ions)	Total Number of electrons	Number of unpaired electrons (n)	Magnetic moment (μs) in Bohr Magneton (\(\mu_B\))	Magnetic Behavior
H₂⁺	1	1	1.73	Paramagnetic
H₂, He₂²⁺	2	0	0	Diamagnetic
H₂^-,He₂⁺	3	1	1.73	Paramagnetic
He₂,	4	0	0	Diamagnetic
Li₂⁺,He₂^-	5	1	1.73	Paramagnetic
Li₂, He₂^2-, Be₂²⁺	6	0	0	Diamagnetic
Be₂⁺,Li₂^-	7	1	1.73	Paramagnetic
Be₂,Li₂^2-	8	0	0	Diamagnetic
Be₂^-,B₂⁺	9	1	1.73	Paramagnetic
B₂, Be₂^2-, HF	10	2	2.82	Paramagnetic
B₂^-,C₂⁺	11	1	1.73	Paramagnetic
C₂,B₂^2-,N₂²⁺, CN⁺	12	0	0	Diamagnetic
C₂^-,N₂⁺	13	1	1.73	Paramagnetic
N₂,CO,NO⁺,C₂^2-,CN^-,O₂²⁺	14	0	0	Diamagnetic
N₂^-,NO,O₂⁺	15	1	1.73	Paramagnetic
NO^-,O₂	16	2	2.82	Paramagnetic
O₂^-	17	1	1.73	Paramagnetic
F₂,O₂^2-,HCl	18	0	0	Diamagnetic
F₂^-	19	1	1.73	Paramagnetic
Ne₂	20	0	0	Diamagnetic

References

“Spectroscopy. Molecular Orbitals and Chemical Bonding”, Nobel Lectures, Chemistry 1963-1970,Elsevier Publishing Company, 1972-1966
Hall, George G. Lennard-Jones Paper of “Foundations of Molecular Orbital Theory”,Advances in Quantum Chemistry,1929,22. Bibcode:1991AdQC…22…1H. doi:10.1016/S0065-3276(08)60361-5, ISBN-978-0-12-034822-0, ISSN 0065-3276
Arijit Das,‘Simple Thinking Makes Chemistry Metabolic And Interesting- A Review Article’, IOSR-JAC,2013,6(4), 8-15, e-ISSN: 2278-5736, doi:10.9790/5736-0640815
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, ISSN-2249-555X
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), 29-38, Science and Education Publishing , USA, DOI:10.12691/wjce-2-3-1

External Links

communities.acs.org/docs/DOC-46667
communities.acs.org/docs/DOC-45853
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, Pin-799003.