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3.11 Molecular orbital theory  (Page 9/26)

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Molecular orbital diagrams, bond order, and number of unpaired electrons

Draw the molecular orbital diagram for the oxygen molecule, O 2 . From this diagram, calculate the bond order for O 2 . How does this diagram account for the paramagnetism of O 2 ?

Solution

We draw a molecular orbital energy diagram similar to that shown in [link] . Each oxygen atom contributes six electrons, so the diagram appears as shown in [link] .

A diagram is shown that has an upward-facing vertical arrow running along the left side labeled, “E.” At the bottom center of the diagram is a horizontal line labeled, “sigma subscript 2 s,” that has two vertical half arrows drawn on it, one facing up and one facing down. This line is connected to the right and left by upward-facing, dotted lines to two more horizontal lines, each labeled, “2 s,” and with two vertical half arrows drawn on them, one facing up and one facing down. These two lines are connected by upward-facing dotted lines to another line in the center of the diagram, but farther up from the first and labeled, “sigma subscript 2 s superscript asterisk.” This horizontal line has two vertical half-arrow drawn on it, one facing up and one facing down. Moving further up the center of the diagram is a horizontal line labeled, “sigma subscript 2 p subscript x,” which lies below two horizontal lines, lying side-by-side, and labeled “pi subscript 2 p subscript y,” and “pi subscript 2 p subscript z.” Both the bottom and top lines are connected to the right and left by upward-facing, dotted lines to three more horizontal lines, each labeled, “2 p,” on either side. These sets of lines each hold three upward-facing and one downward-facing half-arrow. They are connected by upward-facing dotted lines to another single line and then pair of double lines in the center of the diagram, but farther up from the lower lines. They are labeled, “sigma subscript 2 p subscript x superscript asterisk,” “pi subscript 2 p subscript y superscript asterisk,” and “pi subscript 2 p subscript z superscript asterisk,” respectively. The lower of these two central, horizontal lines each contain one upward-facing half-arrow. The left and right sides of the diagram have headers that read, ”Atomic orbitals,” while the center header reads, “Molecular orbitals.”
The molecular orbital energy diagram for O 2 predicts two unpaired electrons.

We calculate the bond order as

O 2 = ( 8 − 4 ) 2 = 2

Oxygen's paramagnetism is explained by the presence of two unpaired electrons in the (π 2 py , π 2 pz )* molecular orbitals.

Check your learning

The main component of air is N 2 . From the molecular orbital diagram of N 2 , predict its bond order and whether it is diamagnetic or paramagnetic.

Answer:

N 2 has a bond order of 3 and is diamagnetic.

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Ion predictions with mo diagrams

Give the molecular orbital configuration for the valence electrons in C 2 2− . Will this ion be stable?

Solution

Looking at the appropriate MO diagram, we see that the π orbitals are lower in energy than the σ p orbital. The valence electron configuration for C 2 is ( σ 2 s ) 2 ( σ 2 s * ) 2 ( π 2 p y , π 2 p z ) 4 . Adding two more electrons to generate the C 2 2− anion will give a valence electron configuration of ( σ 2 s ) 2 ( σ 2 s * ) 2 ( π 2 p y , π 2 p z ) 4 ( σ 2 p x ) 2 . Since this has six more bonding electrons than antibonding, the bond order will be 3, and the ion should be stable.

Check your learning

How many unpaired electrons would be present on a Be 2 2− ion? Would it be paramagnetic or diamagnetic?

Answer:

two, paramagnetic

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Creating molecular orbital diagrams for molecules with more than two atoms relies on the same basic ideas as the diatomic examples presented here. However, with more atoms, computers are required to calculate how the atomic orbitals combine. See three-dimensional drawings of the molecular orbitals for C 6 H 6 .

Key concepts and summary

Molecular orbital (MO) theory describes the behavior of electrons in a molecule in terms of combinations of the atomic wave functions. The resulting molecular orbitals may extend over all the atoms in the molecule. Bonding molecular orbitals are formed by in-phase combinations of atomic wave functions, and electrons in these orbitals stabilize a molecule. Antibonding molecular orbitals result from out-of-phase combinations of atomic wave functions and electrons in these orbitals make a molecule less stable. Molecular orbitals located along an internuclear axis are called σ MOs. They can be formed from s orbitals or from p orbitals oriented in an end-to-end fashion. Molecular orbitals formed from p orbitals oriented in a side-by-side fashion have electron density on opposite sides of the internuclear axis and are called π orbitals.

We can describe the electronic structure of diatomic molecules by applying molecular orbital theory to the valence electrons of the atoms. Electrons fill molecular orbitals following the same rules that apply to filling atomic orbitals; Hund’s rule and the Aufbau principle tell us that lower-energy orbitals will fill first, electrons will spread out before they pair up, and each orbital can hold a maximum of two electrons with opposite spins. Materials with unpaired electrons are paramagnetic and attracted to a magnetic field, while those with all-paired electrons are diamagnetic and repelled by a magnetic field. Correctly predicting the magnetic properties of molecules is in advantage of molecular orbital theory over Lewis structures and valence bond theory.
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Source:  OpenStax, Ut austin - principles of chemistry. OpenStax CNX. Mar 31, 2016 Download for free at http://legacy.cnx.org/content/col11830/1.13
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