Chapter 9. Chemical Bonds
- Gain an understanding of molecular orbital theory.
- Learn how to calculate bond orders.
- Learn how to draw electron configuration energy diagrams of molecular orbitals.
The valence bond theory is able to explain many aspects of bonding, but not all. To complement this theory, we use another one calledmolecular orbital (MO) theory. Molecular orbital theory is a more sophisticated model for understanding the nature of chemical bonds.
MO theory takes the idea of overlapping atomic orbitals to a new level, where new molecular orbitals are generated by a mathematical process calledlinear combination of atomic orbitals(LCAO).
Molecular orbitals share many similarities with atomic orbitals:
- They are filled from lowest energy to highest energy (Aufbau's principle).
- They can contain a maximum of two electrons of opposite spin per orbital (Pauli exclusion principle).
The main difference between atomic and molecular orbitals is that atomic orbitals represent the density of electrons in space associated with a given atom. Molecular orbitals are associated with the entire molecule, which means that the electron density is delocalized (spread out) over more than one atom.
combining the 1sorbitals of each hydrogen atom using LCAO, two σ molecular orbitals are generated1s(pronounced sigma ones) s*1s(pronounced sigma star ones).
the p1sThe orbital is generated by constructive combination (or interference), where the two wavefunctions of the atomic orbitals reinforce (add) each other. This is the lower energy of the two molecular orbitals and is known asbonding molecular orbital. Note in Figure 9.19 “Hydrogen Molecular Orbital Combination Diagram” that the electron density of this orbital is concentrated between the two nuclei. These electrons are stabilized by the attractions of both nuclei and hold the atoms together by a covalent bond.
O s*1sThe orbital is generated by a destructive combination (or interference), where the wave functions of the two atomic orbitals cancel each other out. This type of combination results in an area of zero electron density between the two nuclei, known asnodal plane (or node). This zero electron density node is destabilizing with respect to the bond, making it higher in energy, and later this type of orbital is known as aorbital molecular de antienlace(indicated by an asterisk in the orbital name).
Similar to atomic orbitals, we can write electron configuration energy diagrams for molecular orbitals (Figure 9.20 “Electronic configuration energy diagram of hydrogen molecular orbitals”). Note that the atomic orbitals of each atom are written on each side and the newly formed molecular orbitals are written in the center of the diagram. The bonding molecular orbital is filled and has a relatively lower energy than the contributing atomic orbitals, supporting the fact that hydrogen molecules (H2) are more stable than lone hydrogen atoms.
We have just seen that the bonding molecular orbital is of lower energy and promotes the formation of a covalent bond, while the antibonding molecular orbital is of higher energy with a node of zero electron density between the atoms that destabilizes the formation of a covalent bond. We can assess the strength of a covalent bond by determining itsmandatory order.
Link order values can be integers, fractions, or zero. These values correspond to the valence bonding model, so a bond order of 1 equals a single bond and 2 equals a double bond. A value of zero means that no bonds are present and that the atoms exist separately.
Determine the bond order of the hydrogen molecule.
So there is a single bond in the hydrogen molecule.
Generating molecular orbitals of molecules more complex than hydrogen using the LCAO method requires following some additional guidelines:
- The number of MO generated is equal to the number of atomic orbitals combined.
- The combined atomic orbitals must have similar energy levels.
- The effectiveness of combining atomic orbitals depends on the amount of orbital overlap. Greater overlap further reduces the energy of the bonding molecular orbital and increases the energy of the antibonding molecular orbital.
Let's follow these guidelines and generate a molecular orbital electron configuration diagram for Li2(Figure 9.21 "Energy diagram of molecular orbital electron configuration for dilithium"):
Note that we combine the 1satomic orbitals, as before in H2For example, to generate bonding and antibonding molecular orbitals that are fully occupied by both 1 atomsselectrons likewise 2sThe atomic orbitals combine, giving a bonding orbital and an antibonding orbital, which are filled with the remaining valence electrons starting from the bottom up. The combined atomic orbitals have similar energy levels; a 1s orbitalit is notcombine with one of the 2sorbitals
The binding order can be determined for this molecule as:
So, I2would have a simple link.
To determine the molecular orbitals of many other molecules, we need to look at howpagethe orbitals combine to give molecular orbitals. HepageOrbitals can overlap in two ways: face to face or sideways. Overlay face to facepageAtomic orbitals result in a bonding and antibonding molecular orbital, where the electron density is centered along the internuclear axis, making them σ orbitals (Figure 9.22 “Face-to-face coverage ofpageorbitals").
Lateral overlap of the remaining fourpageAtomic orbitals can occur along the other two axes, generating four molecular π orbitals that have electron densities on opposite sides of the internuclear axis (Figure 9.23 “Lateral overlap ofpageorbitals").
The head-to-head overlap you give the σ molecular orbitals results in more overlap, making your bonding molecular orbital the most stable and lowest in energy, while your antibonding σ* orbital is the least stable and has the highest energy. high (Figure 9.24 “ Energy diagram of molecular orbitals for homonuclear diatomic molecules formed by atoms of atomic number 8-10”). Lateral overlap gives four π molecular orbitals, two lower-energy degenerate bonding molecular orbitals, and two higher-energy antibonding orbitals.
The energy diagram we just generated fits experimentally to O2, F2, and not2, but does not fit in B2, C2, e n2. In the latter, homonuclear diatomic molecules (B2, C2, e n2), interactions occur between the 2sy 2pageatomic orbitals that are strong enough to switch the order of σ2pageAnd p2pagemolecular orbitals (Figure 9.25).
In heteronuclear diatomic molecules, where two different molecules are joined together, the energy levels of the atomic orbitals of the individual atoms can differ. However, the molecular orbital diagram shown in Figure 9.25 ("Molecular orbital energy diagram for homonuclear diatomic molecules made of atoms of atomic number 5-7") can be used to estimate electron configuration and bond order.
We can focus more on two very important types of molecular orbitals: thehighest occupied molecular orbital (HOMO)it's himLowest unoccupied molecular orbital (LUMO), also collectively referred to asfrontier molecular orbitals(Figure 9.26 “HOMO and LUMO boundary molecular orbitals”). As their names indicate, HOMO is the highest energy molecular orbital that contains electrons, while LUMO is the lowest energy molecular orbital that contains no electrons.
When molecules absorb energy, it is typical for a HOMO electron to use that energy to move from the Earth HOMO orbital to the excited state LUMO orbital. This type of transition can be observed in ultraviolet-visible radiation (UV-Vis) spectroscopy experiments. Furthermore, in many chemical reactions, a reactant molecule can donate HOMO electrons to the LUMO of another reactant (Figure 9.27 “Formation of a new bonding molecular orbital by the combination of HOMO and LUMO reactants”). Therefore, understanding the energy levels of molecular frontier orbitals can provide chemists with a wealth of insights in the areas of molecular spectroscopy and reactivity.
- Atomic orbitals can combine to form bonding and antibonding molecular orbitals.
- Bonding orbitals have less energy than antibonding orbitals.
- Molecular orbitals are filled using principles similar to atomic orbitals.
- Binding order can be used to assess binding strength.
- Frontier molecular orbitals are of particular importance in molecular spectroscopy and reactivity.