3.4: Molecular Orbital Theory

Molecular Orbital Theory

Molecular Orbital (MO) Theory is a sophisticated bonding model. It is generally considered to be more powerful than Lewis and Valence Bond Theories for predicting molecular properties; however, this power comes at the price of complexity. In its full development, MO Theory requires complex mathematics, though the ideas behind it are simple. Atomic orbitals (AOs) that are localized on individual atoms combine to make molecular orbitals (MOs) that are distributed over the molecule. The simplest example is the molecule dihydrogen (H₂), in which two independent hydrogen 1s orbitals combine to form the \(\sigma\) bonding MO and the \(\sigma\) antibonding MO of the dihydrogen molecule (see figure). The MO’s are also called Linear Combinations of Atomic Orbitals (LCAO).

Types of Bonds

Inorganic compounds use s, p, and d orbitals (and more rarely f orbitals) to make bonding and antibonding combinations. These combinations result in σ, π, and δ bonds (and antibonds).

In inorganic chemistry, π bonds can be made from p- and/or d-orbitals. δ bonds are more rare and occur by face-to-face overlap of d-orbitals, as in the ion Re₂Cl₈^2-. The fact that the Cl atoms are eclipsed in this anion is evidence of δ bonding.

Figure \(\PageIndex{1}\): The octachlorodirhenate(III) anion, [Re₂Cl₈]²⁻, which has a quadruple Re-Re bond.^[3]

Some possible σ (top row), π (bottom row), and δ bonding combinations (right) of s, p, and d orbitals are sketched below. In each case, we can make bonding or antibonding combinations, depending on the signs of the AO wavefunctions. Because pπ-pπ bonding involves sideways overlap of p-orbitals, it is most commonly observed with second-row elements (C, N, O). π-bonded compounds of heavier elements are rare because the larger cores of the atoms prevent good π-overlap. For this reason, compounds containing C=C double bonds are very common, but those with Si=Si bonds are rare. δ bonds are generally quite weak compared to σ and π bonds. Compounds with metal-metal δ bonds occur in the middle of the transition series.

Transition metal d-orbitals can also form σ bonds, typically with s-p hybrid orbitals of appropriate symmetry on ligands. For example, phosphines (R₃P:) are good σ donors in complexes with transition metals, as shown below.

pπ-dπ bonding is also important in transition metal complexes. In metal carbonyl complexes such as Ni(CO)₄ and Mo(CO)₆, there is sideways overlap between filled metal d-orbitals and the empty π-antibonding orbitals (the LUMO) of the CO molecule, as shown in the figure below. This interaction strengthens the metal-carbon bond but weakens the carbon-oxygen bond. The C-O infrared stretching frequency is diagnostic of the strength of the bond and can be used to estimate the degree to which electrons are transferred from the metal d-orbital to the CO π-antibonding orbital.

The same kind of backbonding occurs with phosphine complexes, which have empty π orbitals, as shown at the right. Transition metal complexes containing halide ligands can also have significant pπ-dπ bonding, in which a filled pπ orbital on the ligand donates electron density to an unfilled metal dπ orbital. We will encounter these bonding situations in Chapter 5.

Attributions

• 2.4: σ, π, and δ orbitals, Chemistry 310, Penn State University, CC-BY-SA 4.0
• 5: Molecular Orbitals, Kathryn Haas, Duke University, CC-BY-SA 4.0

• 3.4.1: Formation of Molecular Orbitals from Atomic Orbitals

  Molecular orbital theory extends from quantum theory and the atomic orbital wavefunctions ( ψ ) described by the Schrödinger equation. While the Schrödinger equation defines a Ψ for electrons in individual atoms, we can approximate a the molecular wavefunction ( Ψ would look like if we combined the ψ of individual atoms. The addition or subtraction of wavefunctions is termed linear combination of atomic orbitals (LCAO). Molecular orbital theory applied LCAO to describe bonding.

• 3.4.2: Molecular Orbitals from s Orbitals

• 3.4.3: Molecular Orbitals from p Orbitals

• 3.4.4: Molecular orbitals from d orbitals

• 3.4.5: Nonbonding Orbitals and Other Factors

• 3.4.6: Features of Molecular Orbital Diagrams

  There are several cases where our more elementary models of bonding (like Lewis Theory and Valence Bond Theory) fail to predict the actual molecular properties and reactivity. A classic example is the case of O₂ and its magnetic properties. At very cold temperatures, O₂ is attracted to a magnetic field, and thus it must be paramagnetic (unpaired electrons give rise to magnetism, see video). However, both its Lewis structure and Valance Bond Theory predict that O₂ is diamagnetic.

• 3.4.7: Diatomic Molecules of the First and Second Periods

• 3.4.8: Molecular Orbitals of Heteronuclear Diatomic Molecules

  The molecular orbital diagram of a heteronuclear diatomic molecule is approached in a similar way to that of homonuclear diatomic molecule. The orbital diagrams may also look similar. A major difference is that the more electronegative atom will have orbitals at a lower energy level. Two examples of heteronuclear diatomic molecules will be explored below as illustrative examples.

• 3.4.9: Ionic Compounds and Molecular Orbitals