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Molecular Orbital Theory - (Concept)

Molecular orbital theory (MO theory) provides an explanation of chemical bonding that accounts for the paramagnetism of the oxygen molecule. It also explains the bonding in a number of other molecules, such as violations of the octet rule and more molecules with more complicated bonding that are difficult to describe with Lewis structures. Additionally, it provides a model for describing the energies of electrons in a molecule and the probable location of these electrons. Unlike valence bond theory, which uses hybrid orbitals that are assigned to one specific atom, MO theory uses the combination of atomic orbitals to yield molecular orbitals that are delocalized over the entire molecule rather than being localized on its constituent atoms. MO theory also helps us understand why some substances are electrical conductors, others are semiconductors, and still others are insulators. The table given below explains the major differences between the valence bond theory and molecular orbital theory.

Comparison of Bonding Theories
Valence Bond Theory	Molecular Orbital Theory
considers bonds as localized between one pair of atoms	considers electrons delocalized throughout the entire molecule
creates bonds from overlap of atomic orbitals (s, p, d…) and hybrid orbitals (sp, sp², sp³…)	combines atomic orbitals to form molecular orbitals (σ, σ, π, π)
forms σ or π bonds	creates bonding and antibonding interactions based on which orbitals are filled
predicts molecular shape based on the number of regions of electron density	predicts the arrangement of electrons in molecules
needs multiple structures to describe resonance

Molecular orbital theory describes the distribution of electrons in molecules in much the same way that the distribution of electrons in atoms is described using atomic orbitals. Using quantum mechanics, the behavior of an electron in a molecule is still described by a wave function, Ψ, analogous to the behavior in an atom. Just like electrons around isolated atoms, electrons around atoms in molecules are limited to discrete (quantized) energies. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital (Ψ2). Like an atomic orbital, a molecular orbital is full when it contains two electrons with opposite spin.

We will consider the molecular orbitals in molecules composed of two identical atoms (H₂ or Cl₂, for example). Such molecules are called homonuclear diatomic molecules. In these diatomic molecules, several types of molecular orbitals occur.

The mathematical process of combining atomic orbitals to generate molecular orbitals is called the linear combination of atomic orbitals (LCAO). The wave function describes the wavelike properties of an electron. Molecular orbitals are combinations of atomic orbital wave functions. Combining waves can lead to constructive interference, in which peaks line up with peaks, or destructive interference, in which peaks line up with troughs as shown in the figure below. In orbitals, the waves are three dimensional, and they combine with in-phase waves producing regions with a higher probability of electron density and out-of-phase waves producing nodes, or regions of no electron density.

(a) When in-phase waves combine, constructive interference produces a wave with greater amplitude. (b) When out-of-phase waves combine, destructive interference produces a wave with less (or no) amplitude.

Concepts List

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Exam	Chapter
JEE MAIN	Chemical Bonding and Molecular Structure

A.	Minimum in the nodal place
B.	Maximum in the nodal place
C.	Zero in the nodal place
D.	Zero on the surface of the lobe

A.	Less than atomic orbitals
B.	More than atomic orbitals
C.	Can’t be predicted
D.	None of these.

A.	Equal to the number of combining atomic orbitals.
B.	Not equal to the number of combining atomic orbitals.
C.	Equal to twice the number of combining atomic orbitals.
D.	None of the these.

A.	Molecular orbital theory
B.	Crystal field theory
C.	Wemer's theory
D.	Valence bond theory

List -I (molecule)	List-II (Bond order)
a. $Ne_2$	i. 1
b. $N_2$	ii. 2
c. $F_2$	iii. 0
d. $O_2$	iv. 3

A.	a-i, b-ii, c-iii, d-iv
B.	a-ii, b-i, c-iv, d-iii
C.	a-iii, b-iv, c-i, d-ii
D.	a-iv, b-iii, c-ii, d-i

A.	$\mathrm{O}_{2}>\mathrm{O}_{3}>\mathrm{H}_{2} \mathrm{O}_{2}$
B.	$\mathrm{O}_{3}>\mathrm{H}_{2} \mathrm{O}_{2}>\mathrm{O}_{2}$
C.	$\mathrm{H}_{2} \mathrm{O}_{2}>\mathrm{O}_{3}>\mathrm{O}_{2}$
D.	$\mathrm{O}_{2}>\mathrm{H}_{2} \mathrm{O}_{2}>\mathrm{O}_{3}$

A.	Can have a negative quantity
B.	Has always an integral value,
C.	Can assume any positive or integral or fractional value including zero
D.	Is a non zero quantity

A.	The difference between the number of electrons in bonding and antibonding orbitals
B.	Total number of electrons in bonding and antibonding orbitals
C.	Twice the difference between the number of electrons in bonding and antibonding electrons
D.	Half the difference between the number of electrons in bonding and antibonding electrons

A.	Unpaired electrons in the bonding $\sigma$ molecular orbital
B.	Unpaired electrons in the antibonding $\sigma$ molecular orbital
C.	Unpaired electron in the bonding $\pi$ molecular orbital
D.	Unpaired electrons in the antibonding $\pi$ molecular orbital

A.	$\mathrm{C_{2}^{2-}<N_{2}^{2-}<O_{2}^{2-}}$
B.	$\mathrm{O_{2}^{2-}<N_{2}^{2-}<C_{2}^{2-}}$
C.	$\mathrm{C_{2}^{2-}<O_{2}^{2-}<N_{2}^{2-}}$
D.	$\mathrm{N_{2}^{2-}<C_{2}^{2-}<O_{2}^{2-}}$

A.	(A), (B), (C) only
B.	(B), (C), (E) only
C.	(A), (C) only
D.	(D) only

A.	$\mathrm{O}_{2}^{2-}<\mathrm{O}_{2}^{-}<\mathrm{O}_{2}<\mathrm{O}_{2}^{+}$
B.	$\mathrm{O}_{2}^{-}<\mathrm{O}_{2}^{2-}<\mathrm{O}_{2}<\mathrm{O}_{2}^{+}$
C.	$\mathrm{O}_{2}^{-}<\mathrm{O}_{2}^{2-}<\mathrm{O}_{2}^{+}<\mathrm{O}_{2}$
D.	$\mathrm{O}_{2}^{-}<\mathrm{O}_{2}^{+}<\mathrm{O}_{2}^{2-}<\mathrm{O}_{2}$

List I	List II
$\mathrm{(A) \: \psi_{\mathrm{MO}}=\psi_{\mathrm{A}}-\psi_{\mathrm{B}}}$	(I) Dipole moment
$\mathrm{(B) \: \mu=\mathrm{Q} \times \mathrm{r}}$	(II) Bonding molecular orbital
$\mathrm{(C) \: \: \frac{\mathrm{N}_{\mathrm{b}}-\mathrm{N}_{\mathrm{a}}}{2}}$	(III) Anti-bonding molecular orbital
$\mathrm{(D) \: \psi_{\mathrm{MO}}=\psi_{\mathrm{A}}+\psi_{\mathrm{B}}}$	(IV) Bond order

A.	$NO^+$
B.	$NO$
C.	$NO^{2+}$
D.	$NO^{-}$

A.	$O_{2}$
B.	$O_{2}^{-1}$
C.	$O_{2}^{+1}$
D.	$O_{2}^{-2}$

A.	$N_{2}$
B.	$C_{2}$
C.	$N_{2}^{+}$
D.	$\mathrm{O}_{2}^{2-}$

A.	(A) - (II), (B) - (I), (C) - (IV), (D) - (III)
B.	(A) - (III), (B) - (IV) ,(C) - (I) ,(D) - (II)
C.	(A) - (III), (B) - (I), (C) - (IV), (D) - (II)
D.	(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

A.	$< CCl_4=\mathrm{CH}_4$ [dipole moment]
B.	$\mathrm{CF}_4<\mathrm{CH}_4<\mathrm{CCl}_4$ [Bond angle]
C.	$\mathrm{N}_2<\mathrm{O}_2^{2-}=\mathrm{O}_2^{2+}$ [Magnetic moment]
D.	$\mathrm{NH}_3 > \mathrm{PH}_3>\mathrm{AsH}_3$ [Bond angle]

A.	Both statement I and statement II are true
B.	Both statement I and statement II are false
C.	Statement I is true but statement II is false
D.	Statement I is false but statement II is true

A.	$H_{2}^{-},He_{2}^{2+}$
B.	$H_{2}^{+},He_{2}^{2-}$
C.	$H_{2}^{-},He_{2}^{2-}$
D.	$H_{2}^{2+},He_{2}$

A.	$Li_{2}^{-}< Li_{2}< Li_{2}^{+}$
B.	$Li_{2}< Li_{2}^{+}< Li_{2}^{-}$
C.	$Li_{2}^{-}< Li_{2}^{+} <Li_{2}$
D.	$Li_{2}<Li_{2}^{-}< Li_{2}^{+}$

A.	Atomic orbital
B.	molecular orbital
C.	hund's rule
D.	anti bonding orbital

A.	$\sigma(1 S) 2<\sigma^(1 S) 2<\sigma(2 s)^2<\sigma^(2 S)^2<\left(\pi 2 P_x^2=\pi 2 P_y^3\right)<\left(\sigma 2 P_z^2\right)$
B.	$\begin{aligned} & \sigma(1 S)<\sigma^(1 S)<\sigma(2 S)<\sigma^(2 S)<\pi\left(2 P_X\right)=\pi\left(2 P_Y\right)<\sigma\left(2 P_Z\right)< \\ & \pi^\left(2 P_X\right)=\pi^\left(2 P_Y\right)<\pi^*\left(2 P_Z\right)\end{aligned}$
C.	$\sigma(1 S)^2<\sigma^(1 S)^2<\sigma(2 s)^2<\sigma^(2 S)^2<\left(\pi 2 P_x^2=\pi 2 P_y^3\right)>\left(\sigma 2 P_z^2\right)$
D.	$\sigma(1 S) 2<\sigma^(1 S) 2<\sigma(2 s)^2<\sigma^(2 S)^2<\left(\sigma 2 P_z^2\right)<\left(\pi 2 P_x^2=\pi 2 P_y^3\right)$

A.	bonding molecules orbital
B.	antibonding molecule orbital
C.	follow aufbau rule
D.	none of these

A.	Assertion and reason are correct and reason is the correct explanation for the assertion.
B.	Assertion and reason are correct, but reason is not the correct explanation for the assertion.
C.	Assertion is correct, reason is incorrect.
D.	Assertion is incorrect, reason is correct.

A.	Be₂ is not a stable molecule.
B.	He₂ is not stable but $H e_2^{+}$ is expected to exist.
C.	Bond strength of N₂ is maximum amongst the homonuclear diatomic molecules belonging to the second period.
D.	The order of energies of molecular orbitals in N₂ molecule is $\sigma 2 s<\sigma^* 2 s<\sigma 2 p_z<(\pi 2 p x=\pi 2 p r)<\left(\pi^* 2 p x=\pi^* 2 p y\right)<\sigma^* 2 p z$

A.	Bonding molecular orbitals have higher energy than antibonding molecular orbitals.
B.	Electrons in antibonding orbitals strengthen the bond between atoms.
C.	The number of molecular orbitals formed is always less than the number of atomic orbitals combined.
D.	Electrons in bonding molecular orbitals are located between the nuclei of the bonding atoms.

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Molecular Orbital Theory - (Concept)

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