11 -- Part 4: Chemical Bonding II: Valence Bond and Molecular Orbital Theories
Three of the p molecular orbitals are bonding.
The next two p-bonding molecular orbitals have the same energy.
The fact that the two orbitals are higher in energy than the one with no nodes should not come as a surprise, as we have already seen.
The next pair of orbitals, which are antibonding p orbitals, have two nodes and the final one has three.
The three bonding orbitals fill with six electrons and the three antibonding orbitals are empty.
The bond order for the six electrons is 16 - 2 - 3.
Three of the six p molecular orbitals are filled with an electron pair.
There are no antibonding molecular orbitals at higher energy.
Each pair of C atoms have a half-bond between them.
The concept of resonance was introduced in Section 10-5.
In points 1 and 2, 2 hybrid orbitals are discussed.
The bond angle is calculated using the predicted trigonal-planar electron-group geometry and assignments of electrons.
The central O atom has a discussion of the hybridization scheme chosen for them.
The O atom uses the orbital set sp2 + p.
Four of these are bonding electrons and ten are lone-pair electrons.
There is no contribution to the wave function from the central atom.
The p molecular orbitals are shown on the right.
The second is antibonding.
A nonbonding molecular orbital has the same energy as the atomic orbitals from which it is formed, and it doesn't detract from bond formation.
The four remaining electrons are assigned to the p orbitals.
Two go into the bonding and two into the nonbonding.
The antibonding orbital is empty.
The bond order is 12 - 2.
This is the same as averaging the two Lewis structures.
Section 10-5 describes the O bond length suggested by this method.
The NO 3 ion has two bonds in the p system.
We first look at the electrons associated with the s bond framework.
Reasoning out the number of each type ofbonding, antibonding, nonbonding in the p system is the key to solving the problem.
The final step is to assign electrons in the p system.
The NO 3 ion has a total number of electrons.
The NO 13 * 6 + 5 + 12 = 24 3 ion and the corresponding s bond framework are shown below.
The N atom has three atoms and is hybridized.
The number of electrons in the p system is 24 and the number of electrons in the s bond framework is 18.
There are a lot of nonbonding molecular orbitals in the system.
The diagram shows how the six p electrons are assigned to the p orbitals.
The bond order of each nitrogen-to-oxygen bond is 11.
Represent chemical bonding in the molecule SO3 by using a combination of local and delocalized orbitals.
Represent chemical bonding in the ion NO 2 by using a combination of local and delocalized orbitals.
There are four 2p orbitals on the p-bonding molecule, one on the N atom and two on the three oxygen atoms.
The antibonding p orbital is at the highest energy.
We expect to get four molecular orbitals since we are combining four 2p orbitals.
Each of the remaining two molecular orbitals will have a single point of contact.
The NO 3 is for the nitrogen atom.
It must be nonbonding with respect to nitrogen.
The p-bonding molecular orbital has all the p orbitals in phase, while the p-antibonding orbital has all the p orbitals out of phase.
There is a nitrogen atom at each of the nonbonding orbitals.
We will see how it is used to explain the colors of plants.
The contiguous p system is a common feature of these molecules.
Antibonding bonds can be found in carotene.
It takes very little energy to get an electron from the HOMO to the LUMO.
The colors we see are caused by the absorption of the light's electrons across the energy gap between the HOMO and the LUMO.
The ideas introduced in this chapter can be used to describe bonding in metals.
You can find the Appendix to Chapter 11 Bonding in Metals on the website.
We presented a wide range of views of chemical bonding in Chapters 10 and 11.
Each of these models has deficiencies, and uncritical use can lead to incorrect conclusions.
The more fundamental view of molecular shapes is still an issue.
We might wonder how the theories are related.
The significance of electron density calculations will be stressed in this section.
Let's see if it is possible to describe the bonding in SF6 while keeping the octet rule.
The electronic structure is a combination of resonance structures and Valence Bond.
In the case of SF6, four electron pairs bond six F atoms to a central S atom.
When resonance structures are written in this way, the assumption is that the bond lines represent covalent bonds.
The molecule SF6 requires a total of 15 structures of the type shown.
The collective charge of -2 on the six F atoms is implied by this description.
The suggested charges on the S and F atoms can be compared with those obtained from a quantum-mechanical calculation.
There is a charge of +3.17 on sulfur and -0.53 on each fluorine.
To describe bonding through hyperconjugation that is in better agreement with the quantummechanical calculation, we would have to use additional resonance structures with higher charges and fewer covalent bonds.
Adoption of this large number of structures is not justified because it is cumbersome.
Lewis did not consider exceptions such as PCl5 and SF6 to be of great significance when he created his rule of eight.
The rule of two is more important than the rule of eight because the density of the electron pair is the most important factor in understanding bonding.
A special type of bonding is not the reason for bonding in the first place.
The bonds in these molecules are similar to the bonds in other molecules.
We seem to think about bonding in terms of atomic orbitals.
The concept of sp3 hybrid orbitals was introduced in order to describe bonding in the methane molecule.
The geometry of a molecule can be determined by using a theory.
The results of quantum-mechanical calculations have already been used to construct electrostatic potential maps.
Let's use the results of the calculations to improve our understanding of the bonding in SF6 and similar molecules.
In atomic units, the isodensity lines are shown in color in the order of 1 to 8.
The Densities are truncated at 2 o'clock.
The Bohr radius is adapted from Matta and Gillespie.
First, consider a simpler molecule.
The most striking feature of this diagram is that the electron density is very high at each nucleus; in order to show other features in the diagram, we truncated the very large maxima.
There is a ridge of electron density between the sulfur and chlorine atoms.
The ridge of electron density contributes to bond formation by transferring electron density from the atomic orbitals to the internuclear region.
A con tour map is an alternative representation of the electron density distribution.
The bond paths are connected by lines.
The bond critical points are depicted in red Xs.
Similar to a path along the valley floor between the "mountains" of electron density, this bifurcated line is a path tracing the minimum in the electron density.
The type of bond connecting a pair of atoms in a molecule can be described with the electron density at the bond critical point.
The higher the bond order is, the greater the electron density.
We will consider the sulfuric acid molecule and the sulfate anion to decide whether or not to use expanded valence shells.
We include less of the electron density distribution if we choose a surface with a higher electron density value.
The values for the outer isodensity envelope are set in the three figures for both species.
If there are bonds in the molecule that have more electron density at their bond critical points, then electron density will still appear in the three-dimensional representation.
The stick from the ball-and-stick model is apparent, but between the sulfur and the two oxygen atoms that do not, the electron density between the sulfur and the two oxygen atoms has disappeared.
The electron density between the sulfur atom and the nonprotonated oxygen does not disappear until the density of the calculated surface is increased to 0.33 Au.
There is more electron density in the bonds between the sulfur atom and the nonprotonated oxygen atoms than in the bonds between the sulfur and oxygen.
The double bond between the central S atom and the two terminal O atoms can be represented in a Lewis structure that reduces the formal charges seen in the octet Lewis structure of H2SO4.
The bond critical density is 0.28 Au for the four bonds between the sulfur atom and the oxygen atoms.
The bond between sulfur and the nonprotonated oxygen atoms is greater than the bond between sulfur and the protons.
Maybe the Lewis structure that reduces formal charges is the best because of the higher bond critical point in the sulfate anion.
The four sulfur-oxygen bonds have the same bond critical point, which can be used to write resonance structures.
We have reached a point where using expanded shells seems to be the best way to minimize formal charges.
A detailed analysis of the wavefunction of the sulfate anion suggests that the simple octet structure is the dominant form.
The answer to several questions posed in this section may be found in the work of R. J. Gillespie.
Lewis structures should be written as Lewis would have written them.
The C bond dissociation enthalpy is very low.
An analysis of the electron densities in SiF4 shows that they have a combination of very strong bonds.
You should not be too concerned by the controversy over how to write Lewis structures in the chemical literature.
Our approach to depicting the electronic structure of a molecule is based on the simplest Lewis structure and its use in determining the shape of a molecule through VSEPR theory.
To understand experimental results, such as bond enthalpy values, we must analyze a computed electron density map for that molecule rather than rely on the Lewis structure.
The structures of the molecule are studied.
The method involves passing a high-energy photon through a sample of molecule.
The focus on feature for Chapter 11 on the MasteringChemistry site is for a discussion of Photoelectron Spectroscopy.
The simpler ideas of the Lewis model are not related to the electronic structure of molecule numbers.
The transfer of atomic orbitals is used to generate them.
The electron-group electron density that extends over several atoms in a mole geometry is predicted by the VSEPR theory.
The concept of 11-4 Multiple Covalent Bonds--End-to-end overlap hyperconjugation was used in SF6.
In terms of bond paths and critical points, side-to-side overlap is lyzed.
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