Molecular Orbital (MO) Theory

Molecular orbital theory is a flexible model for describing electron behavior in main group and transition metal complexes.

Chemical bonds and electronic behavior can be represented with several types of models. While simple models, such as Lewis dot structures and VSEPR theory, provide a good starting point for understanding molecular reactivity, they involve broad assumptions about electronic behavior that are not always applicable.

MO theory models the geometry and relative energies of orbitals around a given atom. Thus, this theory is compatible with both simple diatomic molecules and large transition metal complexes.

This video will discuss the underlying principles of MO theory, illustrate the procedure for synthesizing and determining the geometry of two transition metal complexes, and introduce a few applications of MO theory in chemistry.

In MO theory, two atomic orbitals with matching symmetry and similar energies can become a lower-energy bonding molecular orbital and a higher-energy antibonding molecular orbital. The number of molecular orbitals in a diagram must equal the number of atomic orbitals.

The difference in energy between atomic orbitals and the resulting bonding and antibonding orbitals is approximated from simple diagrams of orbital overlap. Head-on interactions are generally stronger than side-on overlap.

MO diagrams use group theory to model transition metal complexes. Ligand atomic orbitals are represented by symmetry-adapted linear combinations, or short SALC, that can interact with the metal atomic orbitals.

SALCs are generated by determining the point group of the molecule, creating a reducible representation of the ligand atomic orbitals, and finding the irreducible representations corresponding to the orbital symmetries.

MOs are formed between SALCs and atomic orbitals with matching symmetry. Atomic orbitals that do not match the SALC symmetries become nonbonding orbitals at the same energy as the starting atomic orbitals.

When the MO diagram is populated with electrons, the frontier orbitals are generally those with d orbital character. These orbitals can be considered separately as d orbital splitting diagrams, and they will always be populated with the number of d electrons on the metal center.

Now that you understand the principles of MO theory, let's go through a procedure for synthesizing two metal complexes and predicting their geometries using MO theory.

To begin the procedure, close the Schlenk line vent and open the system to N2 gas and vacuum. Once the dynamic vacuum is reached, cool the vacuum trap with a mixture of dry ice and acetone.

Next, place 550 mg of dppf and 40 mL of isopropanol in a 250 mL three-neck round-bottom flask with a stir bar. Securely clamp the flask in the fume hood with the Schlenk line over a hotplate. Fit the center neck of the flask with a reflux condenser and a vacuum adaptor. Fit the remaining necks with a glass stopper and a rubber septum.

Under stirring, degas the solution by bubbling N2 gas through the solution for 15 minutes. Leave the vacuum adapter open as a vent.

Once the solution has been degassed, open a new nitrogen line and connect it to the vacuum adapter. Lower the flask into the water bath. Connect a water hose to the condenser, turn on the stir motor, and start heating the bath to 90 °C while stirring the solution.

While the dppf solution heats, place 237 mg of NiCl2•6H2O and 4 mL of a 2:1 mixture of reagent-grade isopropanol and methanol in a 25 mL round-bottom flask.

Sonicate the mixture until the Ni salt has completely dissolved. Then, stopper the flask with a rubber septum and securely clamp the flask in the fume hood.

Degas the Ni solution by bubbling N2 gas through the solution for 5 minutes. Then, use cannula transfer to add the Ni precursor to the dppf solution.

Reflux the mixture for 2 hours at 90 °C under N2 gas. Then, cool the reaction mixture in an ice bath.

Collect the resulting green precipitate on a medium type frit by vacuum filtration. Wash the precipitate with 10 mL of cold isopropanol, followed by 10 mL of cold hexanes.

Allow the product to air-dry in a vial and acquire a 1H NMR spectrum in CDCl3.

To begin the procedure, prepare the Schlenk line and vacuum trap as previously described. Using a 125 mL round bottom flask, degas 20 mL of toluene by bubbling N2 gas through the solvent. Then, place 550 mg of dppf and 383 mg of Pd(PhCN)2Cl2 in a 200 mL Schlenk flask.

Equip the flask with a stir bar and a glass stopper. Evacuate and purge the system three times using N2. Keeping the N2 on, replace the glass stopper with a rubber septum.

Use cannula transfer to add the degassed toluene to the reactants. Stir the reaction mixture at room temperature for 12 hours.

Collect the resulting orange precipitate on a frit by vacuum filtration. Wash the precipitate with 10 mL of cold toluene, followed by 10 mL of cold hexanes.

Allow the product to air-dry in ambient conditions. Acquire a 1H NMR spectrum of the product in CDCl3.

The 1H NMR spectrum of the Ni complex shows a peak at 21 ppm, followed by two peaks below 0 ppm, suggesting that it is a paramagnetic species. The Pd complex does not show any such peaks. Given that the complexes are both d8, the different electronic states likely result from different geometries at the metal center.

Four-coordinate complexes are approximated with either tetrahedral or square planar d orbital splitting patterns. When eight electrons are placed in the four-coordinate diagrams, the tetrahedral configuration has two unpaired electrons, while the square planar configuration has no unpaired electrons. This indicates that the Pd complex is square planar.

To determine the number of unpaired electrons in the Ni complex, prepare an Evans' method sample with 10 to 15 mg of the product in a 50:1 by volume mixture of deuterated chloroform and trifluorotoluene.

Place a capillary of 50:1 deuterated chloroform and trifluorotoluene in the NMR tube. Acquire an 19F NMR spectrum and calculate the magnetic moment from the change in the chemical shift of trifluorotoluene.

The observed magnetic moment is close to the reported value of 3.39 μB. As some orbital contribution is predicted in d8 tetrahedral complexes, the observed magnetic moment is expected to be higher than the spin-only value. The observed value is thus consistent with two unpaired electrons in a tetrahedral complex.

MO theory is widely used in inorganic chemistry. Let's look at a few examples.

Computational chemistry applies statistical modeling to predict the properties and reactivity of molecules. Semi-empirical and ab initio computational methods both incorporate MO theory into their calculations to varying extents. The output is often in the form of orbital energies and 3D models of each molecular orbital.

Ligand field theory is a more detailed molecular model that combines crystal field theory and MO theory to refine the d orbital splitting diagram, along with other aspects of the models.

In crystal field theory, degeneracy at a metal center is affected to varying degrees by the ligands and the metal center properties. The stability of the complex is estimated with the crystal field stabilization energy, which compares the stabilizing and destabilizing effects of electrons populating lower- and higher-energy orbitals.

Ligand field theory can provide more insight into orbital splitting by examining the nature of the orbital overlap between metal centers and ligands. The orbital overlap symmetry is considered together with the stabilizing and destabilizing effects of the orbital populations. This is used to predict spin states, the strength of metal-ligand interactions, and other important molecular properties.

You've just watched JoVE's introduction to MO theory. You should now understand the underlying principles of MO theory, the procedure for determining the geometry of a complex from d-orbital splitting diagrams, and a few examples of how MO theory is applied in chemistry. Thanks for watching!