12. Molecular Shapes & Valence Bond Theory

Molecular Orbital Theory

1.4 Molecular Orbital Theory

Indicate whether each statement is true or false. (c) Molecules containing electrons that occupy antibonding orbitals must be unstable.

Sketch the bonding molecular orbital that results from the linear 
combination of two 1s orbitals. Indicate the region where 
interference occurs and state the kind of interference (constructive 
or destructive).

For each of these contour representations of molecular orbitals, 
identify (c) whether the MO is bonding or antibonding 
(i) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/477ac91b35bb4879-1676664925364.jpg" alt="" />

(c) Is the p bond in NO2- localized or delocalized?

Electron orbital diagrams show electrons as residing within atomic orbitals.

The water molecule has similar bond vibrations to carbon 
dioxide. Decide whether the symmetric, asymmetric, and 
bending vibrations in water will result in the absorption of 
IR radiation.

Molecular Orbital Theory - Bonding & Antibonding MO - Bond Order

(b) When xenon absorbs 801 kJ/mol of energy, it is excited into a higher-energy state in which the outermost elec-tron has been promoted to the next available subshell. Write the electron configuration for this excited xenon.

In the MO diagram, there is only one bonding electron.

Correct, there is only one bonding electron in the MO diagram.

 Determine the total number electrons in the species, assign the electrons to molecular orbitals, then use the number of bonding and antibonding electrons to determine the bond order. 

Using molecular orbital theory, determine the bond order for Li2+.

The Molecular Orbital Theory.

(c) Would you expect N2O to exhibit delocalized p bonding?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/bf889613d49efd03-1661345367370.jpg" alt="" />

The molecular-orbital diagrams for two- and four-atom
linear chains of lithium atoms are shown in Figure 12.22.
Construct a molecular-orbital diagram for a chain containing
six lithium atoms and use it to answer the following
questions: (c) How many nodes are in the highest-energy
molecular orbital? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/d3d04636f7bfb3a7-1665579769598.jpg" alt="" />

Draw a picture that shows all three 2p orbitals on one atom
and all three 2p orbitals on another atom. (c) How many antibonding orbitals, and of what type can be made from the two sets of 2p orbitals?

The following diagrams illustrate p-p orbital overlap or s-p
orbital overlap. Which diagram represents a p bond in valence
bond theory? (LO 8.3)
(a) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/4d339a2bebfa754b-1670638229099.jpg" alt="" />
(b) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/473b1bfa31db2f42-1670638224736.jpg" alt="" />
(c) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/3bfe0d6672bc06a4-1670638169888.jpg" alt="" />
(d) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/defa0287100abf96-1670638173045.jpg" alt="" />

For each of these contour representations of molecular orbitals,
identify (b) the type of MO (s or p)
(iii) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/8f3be32548a3bbf1-1661349356789.jpg" alt="" />

The orbital diagram that follows presents the final step in the
formation of hybrid orbitals by a silicon atom. (a) Which of
the following best describes what took place before the step
pictured in the diagram: (i) Two 3p electrons became unpaired,
(ii) An electron was promoted from the 2p orbital to
the 3s orbital, or (iii) An electron was promoted from the 3s
orbital to the 3p orbital? 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/16e9e92b1bcde955-1664548335975.jpg" alt="" />

Sketch the bonding and antibonding molecular orbitals that result
from linear combinations of the 2pz atomic orbitals in a homonuclear
diatomic molecule. (The 2pz orbitals are those whose
lobes are oriented perpendicular to the bonding axis.) How do
these molecular orbitals differ from those obtained from linear
combinations of the 2py atomic orbitals? (The 2py orbitals are
also oriented perpendicular to the bonding axis, but also perpendicular to the 2pz orbitals.)

Correct, F2 has the largest bond order.

There is another species that has a higher bond order.

Bond strength is related to the bond order which can be determined from the given information.

 Using MO theory, determine the bond order of each fluorine species. 

Using molecular orbital theory, determine whether F2, F2&#8722;, or F22&#8722; would have the strongest bond.

The highest occupied molecular orbital of a molecule is
abbreviated as the HOMO. The lowest unoccupied molecular
orbital in a molecule is called the LUMO. Experimentally,
one can measure the difference in energy between
the HOMO and LUMO by taking the electronic absorption
(UV-visible) spectrum of the molecule. Peaks in the
electronic absorption spectrum can be labeled as p2p9p2p*,
s2s9s2s*, and so on, corresponding to electrons being promoted
from one orbital to another. The HOMO-LUMO transition
corresponds to molecules going from their ground
state to their first excited state. (c) The electronic absorption
spectrum of the N2 molecule has the lowest energy
peak at 170 nm. To what orbital transition does this correspond?

Molecules that are brightly colored have a small energy gap 
between filled and empty electronic states (the HOMOLUMO 
gap; see Exercise 9.104). Suppose you have two samples, 
one is lycopene which is responsible for the red color 
in tomato, and the other is curcumin which is responsible 
for the yellow color in turmeric. Which one has the larger 
HOMO-LUMO gap?

The organic molecules shown here are derivatives of benzene
in which six-membered rings are “fused” at the edges
of the hexagons.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/022da238908ce695-1661271317273.jpg" alt="" />
(e) Benzene, naphthalene, and anthracene
are colorless, but tetracene is orange. What does this imply
about the relative HOMO–LUMO energy gaps in these molecules?
See the “Chemistry Put to Work” box on orbitals
and energy.

The energy-level diagram in Figure 9.36 shows that the
sideways overlap of a pair of p orbitals produces two molecular
orbitals, one bonding and one antibonding. In ethylene there
is a pair of electrons in the bonding π orbital between the two
carbons. Absorption of a photon of the appropriate wavelength
can result in promotion of one of the bonding electrons
from the p2p to the p*2p molecular orbital. (b) Assuming this
electronic transition corresponds to the HOMO-LUMO transition,
what is the LUMO in ethylene? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/7e3b7756e6689ea8-1661271108440.jpg" alt="" />

Repeat Exercise 12.51 for a linear chain of eight lithium 
atoms. 
(f) How does the HOMO–LUMO 
energy gap for this case compare to that of the four-atom 
case?

For each of these contour representations of molecular orbitals,
identify (a) the atomic orbitals (s or p) used to construct
the MO
(iii) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/446bd6ed566c54cf-1676670278922.jpg" alt="" />

Molecular Orbital Theory Example 3

The molecular-orbital diagrams for two- and four-atom
linear chains of lithium atoms are shown in Figure 12.22.
Construct a molecular-orbital diagram for a chain containing
six lithium atoms and use it to answer the following
questions: (e) How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/b6010c7bf54aab79-1665582755986.jpg" alt="" />

Molecular Orbital Theory Example 4

O2 is paramagnetic; O2&#8722; is diamagnetic.

In their MO diagrams, O2 has two unpaired electrons and O2&#8722; has one unpaired electron.

O2 is diamagnetic; O2&#8722; is paramagnetic.

Both O2 and O2&#8722; are diamagnetic.

Both O2 and O2&#8722; are paramagnetic.

Correct, both possess unpaired electrons.

 Paramagnetism is defined as having one or more unpaired electrons; diamagnetism is defined as having no unpaired electrons. 

Using molecular orbital theory, determine the magnetism of O2 and O2&#8722;.

For each of these contour representations of molecular orbitals,
identify (a) the atomic orbitals (s or p) used to construct
the MO
(i) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/0f5ddfedd927daeb-1661348568272.jpg" alt="" />

Molecular Orbital Theory Concept 2

The following is part of a molecular orbital energy-level diagram
for MOs constructed from 1s atomic orbitals.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/7089156319684209-1664548200114.jpg" alt="" />
(a) What labels do we use for the two MOs shown?

Consider the H2+ ion. (f) Which of the following
statements about part (e) is correct: (i) The light excites
an electron from a bonding orbital to an antibonding orbital,
(ii) The light excites an electron from an antibonding orbital
to a bonding orbital, or (iii) In the excited state there are more
bonding electrons than antibonding electrons?

Indicate whether each statement is true or false. (d) Electrons cannot occupy a nonbonding orbital.

Molecular Orbital Theory Concept 1

Bond vibrations for the symmetric and asymmetric stretch 
in methane are illustrated below. Decide whether each vibration 
will result in the absorption of IR radiation. Arrows 
indicate the movement of atoms during the vibration.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/92a2e18fed0477eb-1670865876517.jpg" alt="" />

The molecular-orbital diagrams for two- and four-atom 
linear chains of lithium atoms are shown in Figure 12.22. 
Construct a molecular-orbital diagram for a chain containing 
six lithium atoms and use it to answer the following 
questions: (a) How many molecular orbitals are there in 
the diagram?

Introduction to Molecular Orbital Theory

Cyclooctatetraene dianion, C8H8 
2-, is an organic ion with the 
structure shown. Considering only the p bonds and not the 
s bonds, cyclooctatetraene dianion can be described by 
the following energy diagrams of its p molecular orbitals: 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/6e95c003bd8f91e0-1670652367543.jpg" alt="" /> 
(b) Three of the p molecular orbitals are bonding, three are 
antibonding, and two are nonbonding, meaning that 
they have the same energy level as isolated p orbitals. 
Which is which?

In ozone, O3, the two oxygen atoms on the ends of the molecule
are equivalent to one another. (d) How many
electrons are delocalized in the p system of ozone?

For each of these contour representations of molecular orbitals,
identify (b) the type of MO (s or p)
(i)

For a given type of MO, use a s2s as an example, is the 
bonding or antibonding orbital higher in energy? Explain.

Molecular Orbital Diagrams represent chemical bonding as combination of valence electrons from atomic orbitals of elements into molecular orbitals.

Molecular Orbital Diagrams

Write orbital diagrams (boxes with arrows in them) to represent
the electron configurations—without hybridization—for all
the atoms in SF2. Circle the electrons involved in bonding. Draw
a three-dimensional sketch of the molecule and show orbital
overlap. What bond angle do you expect from the unhybridized
orbitals? How well does valence bond theory agree with the experimentally 
measured bond angle of 98.2° ?

The energy-level diagram in Figure 9.36 shows that the
sideways overlap of a pair of p orbitals produces two molecular
orbitals, one bonding and one antibonding. In ethylene there
is a pair of electrons in the bonding π orbital between the two
carbons. Absorption of a photon of the appropriate wavelength
can result in promotion of one of the bonding electrons
from the p2p to the p*2p molecular orbital. (a) Assuming
this electronic transition corresponds to the HOMO-LUMO
transition, what is the HOMO in ethylene? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/b6b03521b92bdffc-1661271090798.jpg" alt="" />

Make a sketch showing the location and geometry of the
p orbitals in the nitrite ion, NO2-. Describe the bonding in
this ion using a localized valence bond model for s bonding
and a delocalized MO model for p bonding.

Examples of s-p Mixing in Molecular Orbital Theory

Bonding Molecular Orbital&nbsp;is region of high electron density between elements, promotes bond formation.Anti-bonding Molecular Orbital is region with low electron density and prevents bond formation.

Molecular Orbital Theory Example 1

Sketch the bonding and antibonding molecular orbitals that result
from linear combinations of the 2px atomic orbitals in a homonuclear
diatomic molecule. (The 2px orbitals are those whose
lobes are oriented along the bonding axis.)

What is the difference in spatial distribution between electrons 
in a bonding MO and electrons in an antibonding MO?

Molecular Orbital Theory Example 2

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Chad's Prep

1. Intro to General Chemistry

2. Atoms & Elements

3. Chemical Reactions

4. BONUS: Lab Techniques and Procedures

5. BONUS: Mathematical Operations and Functions

6. Chemical Quantities & Aqueous Reactions

7. Gases

8. Thermochemistry

9. Quantum Mechanics

10. Periodic Properties of the Elements

11. Bonding & Molecular Structure

13. Liquids, Solids & Intermolecular Forces

14. Solutions

15. Chemical Kinetics

16. Chemical Equilibrium

17. Acid and Base Equilibrium

18. Aqueous Equilibrium

19. Chemical Thermodynamics

20. Electrochemistry

21. Nuclear Chemistry

22. Organic Chemistry

23. Chemistry of the Nonmetals

24. Transition Metals and Coordination Compounds

[BOOK CHEM] Clutch Version

MO Theory: Homonuclear Diatomic Molecules

Homonuclear Diatomic Molecules are composed of 2 identical elements bonded together.

Equatorial and Axial Positions

Covalent compounds with 5 or 6&nbsp;electron groups have equatorial and axial positions for surrounding elements

MO Theory: Heteronuclear Diatomic Molecules

Heteronuclear Diatomic Molecules are composed of 2 different elements bonded together.

Bond Angles

Bond Angles&nbsp;result from surrounding elements and lone pairs around the central element positioning themselves at an optimal distance.&nbsp;

Molecular Orbital Theory&nbsp;allows us to predict the distribution of electrons within a molecule.&nbsp;

MO Theory: Bond Order

Molecular Orbital Diagrams can be used to determine the bond order of a molecule.

Electron Geometry

The simplest system for geometrical shapes that focuses on the number of electron groups around the central atom.

Hybridization

How would an&nbsp;s orbital combine with a p orbital to form a covalent bond? The answer is through hybridization where a hybrid&nbsp;oribital is formed.&nbsp;

Molecular Geometry

True Shape of Molecules that takes into account differences&nbsp;in repulsion between lone pairs and surrounding elements.