Chapter 9, Problem 46GQ

Which of the following molecules or ions are para-magnetic? What is the highest occupied molecular orbital (HOMO) in each one? Assume the molecular orbital diagram in Figure 9.16 applies to all of them.

(a) NO

(b) OF^–

(c) O₂^2–

(d) Ne₂⁺

Interpretation Introduction

Interpretation:

The molecule or ions which shows Para magnetism should be identified from the given molecules and ions. The HOMO in each of the given molecules and ions has to be determined.

Concept Introduction:

Valance bond (VBT) theory: This theory explain a chemical bonding theory that explains the bonding between two atoms is caused by the overlap of half-filled atomic orbitals. The two atoms share each other's unpaired electron to form a filled orbital to form a hybrid orbital and bond together.

Bond order: The bond order has defined as the net number of bonding electrons pairs linking a pair of atoms. This same concept can be applied directly to molecular orbital theory, but not bond order is defined as.

$\text{Bond}\text{order}\text{=}\frac{\text{1}}{\text{2}}\left(\begin{array}{l}\text{Number}\text{of}\text{electrons}\text{in}\text{bondoing}\text{MOs-}\\ \text{Number}\text{of}\text{electrons}\text{in}\text{antibonding}\text{MOs}\end{array}\right)$

Paramagnetic: The Paramagnetic properties are due to the presence of some unpaired electrons, and from the realignment of the electron paths caused by the external magnetic field.

HOMO and LUMO: This statement stand for highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), respectively. So this energy difference between the HOMO and LUMO is termed the HOMO–LUMO gap.

Diamagnetic: The molecule or atoms have paired electrons in respective shell, this type of alignments diamagnetic.

Answer to Problem 46GQ

The nitric oxide molecule ($\text{NO}$) has paramagnetic character and one $\left( \pi {*}_{\text{2px}}\right)$ electrons occupied in HOMO shell.

The ${\text{OF}}^{\text{-}}$ ion has a paramagnetic and two unpaired electron in HOMO $\left( \pi {*}_{\text{2py}}\right)$ and $\left({\text{σ*}}_{\text{2pz}}\right)$ shells.

O₂^2- ions has a diamagnetic character there is no unpaired electron in HOMO only paired electron in HOMO $\left( \pi {*}_{\text{2px}}\right)$ $\left( \pi {*}_{\text{2py}}\right)$

Ne₂⁺ ions has obeyed for paramagnetic character, the four unpaired electron in $\left( \pi {*}_{\text{2px}}\right)$ $\left( \pi {*}_{\text{2py}}\right)$ shell and one unpaired electron in $\left({\text{σ*}}_{\text{2pz}}\right)$

Explanation of Solution

Molecular orbital correlation diagram of (NO) molecule

$\begin{array}{l}{\text{σ*}}_{\text{2p}}{}_{{}_{\text{z}}}\\ --\boxed{}--\to (\text{Anti}\text{bonding}\text{electrons})\\ \\ --\boxed{\uparrow }-\boxed{}--\\ {\text{π*}}_{\text{2p}}{\text{π*}}_{\text{2p}}\\ \\ --\boxed{}-\boxed{}-\boxed{}----\boxed{}-\boxed{}-\boxed{}--\\ {\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}{\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}\\ \\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow \downarrow }--\\ {\text{π}}_{\text{2px}}{\text{π}}_{\text{2py}}\\ {\text{σ}}_{\text{2pz}}\\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ \end{array}$

      $\begin{array}{l}\\ --\boxed{\uparrow \downarrow }--\to (\text{Anti}\text{bonding}\text{electrons})\\ \left(\sigma *2s\right)\\ \\ --\boxed{\uparrow \downarrow }----\boxed{\uparrow \downarrow }--\\ 2s2s\\ \\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ {\left(\sigma 2s\right)}^2\end{array}$

Analyzing magnetic properties: The (NO) molecule has one unpaired electron from $\left( \pi {*}_{\text{2px}}\right)$  corresponding shells. So this molecule obeyed for paramagnetic nature.

HOMO-LUMO Analysis: There is one unpaired electron in HOMO orbital.

1. 1. Molecular orbital correlation diagram of (OF^‑) ions.

   $\begin{array}{l}{\text{σ*}}_{\text{2p}}{}_{{}_{\text{z}}}\\ --\boxed{\uparrow }--\to (\text{Anti}\text{bonding}\text{electrons})\\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow }--\\ {\text{π*}}_{\text{2py}}{\text{π*}}_{\text{2py}}\\ \\ --\boxed{}-\boxed{}-\boxed{}----\boxed{}-\boxed{}-\boxed{}--\\ {\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}{\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}\\ \\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow \downarrow }--\\ {\text{π}}_{\text{2px}}{\text{π}}_{\text{2py}}\\ {\text{σ}}_{\text{2pz}}\\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ \end{array}$

          $\begin{array}{l}\\ --\boxed{\uparrow \downarrow }--\to (\text{Anti}\text{bonding}\text{electrons})\\ \left(\sigma *2s\right)\\ \\ --\boxed{\uparrow \downarrow }----\boxed{\uparrow \downarrow }--\\ 2s2s\\ \\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ {\left(\sigma 2s\right)}^2\end{array}$

Analyzing for magnetic character: OF^- ions has a paramagnetic and two unpaired electron in HOMO $\left( \pi {*}_{\text{2py}}\right)$ and $\left({\text{σ*}}_{\text{2pz}}\right)$ shells.

1. 2. Molecular orbital correlation method of oxygen (O₂^2-) ions

  $\begin{array}{l}\text{σ*2p}\\ --\boxed{}--\to (\text{Anti}\text{bonding}\text{electrons})\\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow \downarrow }--\\ {\text{π*}}_{\text{2p}}{\text{π*}}_{\text{2p}}\\ \\ --\boxed{}-\boxed{}-\boxed{}----\boxed{}-\boxed{}-\boxed{}--\\ {\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}{\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}\\ \\ {\text{σ}}_{\text{2p}}\\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow \downarrow }--\\ {\text{π}}_{\text{2p}}{\text{π}}_{\text{2p}}\end{array}$

  $\begin{array}{l}\\ --\boxed{\uparrow \downarrow }--\to (\text{Anti}\text{bonding}\text{electrons})\\ \left(\sigma *2s\right)\\ \\ --\boxed{\uparrow \downarrow }----\boxed{\uparrow \downarrow }--\\ 2s2s\\ \\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ {\left(\sigma 2s\right)}^2\end{array}$

Magnetic properties of oxygen (O₂^2-) ions

The molecular orbital correlation clearly explains for oxygen (O₂^2-) ion has diamagnetic   nature because (phi-orbitals) completely occupied for respective for (2p) orbital shell.

1. 3. Molecular orbital correlation method of oxygen (O₂^2-) ions

   $\begin{array}{l}{\text{σ*}}_{\text{2p}}{}_{{}_{\text{z}}}\\ --\boxed{\uparrow }--\to (\text{Anti}\text{bonding}\text{electrons})\\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow \downarrow }--\\ {\text{π*}}_{\text{2py}}{\text{π*}}_{\text{2py}}\\ \\ --\boxed{}-\boxed{}-\boxed{}----\boxed{}-\boxed{}-\boxed{}--\\ {\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}{\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}\\ \\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow \downarrow }--\\ {\text{π}}_{\text{2px}}{\text{π}}_{\text{2py}}\\ {\text{σ}}_{\text{2pz}}\\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ \end{array}$

          $\begin{array}{l}\\ --\boxed{\uparrow \downarrow }--\to (\text{Anti}\text{bonding}\text{electrons})\\ \left(\sigma *2s\right)\\ \\ --\boxed{\uparrow \downarrow }----\boxed{\uparrow \downarrow }--\\ 2s2s\\ \\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ {\left(\sigma 2s\right)}^2\end{array}$

Analyzing for magnetic character:

Due to the presence of unpaired electrons Ne₂⁺ ions shows paramagnetic character.