WALSH DIAGRAMS AND dπ-pπ BOND DIAGRAMS AND dπ-pπBOND
Prof. A.D. Walsh was a researcher who introduced Walsh diagrams to rationalize the shapes adopted by polyatomic molecules in their ground and excited states. These diagrams graphically represent the calculated orbital binding energies of a molecule plotted against bond angles. Walsh diagrams are used to predict the geometries of small molecules and explain why a given molecule is more stable in one geometry over another. Additionally, Walsh diagrams and dπ-pπbond provide insights into how molecular stability and geometry are influenced by the interactions between p and d orbitals.
Walsh’s rule assumes that the most favorable geometry maximizes the stability of the highest occupied molecular orbital (HOMO). Walsh diagrams help explain the structural trends of related molecules with similar valence electron counts. For example, methane (CH₄) and silane (SiH₄) exhibit comparable structures. Additionally, the diagrams explain how changes in molecular geometry occur due to alterations in electron number or spin state. The detail in https://en.wikipedia.org/wiki/Walshdiagram.
WALSH DIAGRAM FOR TRI-ATOMIC MOLECULES WALSH DIAGRAMS AND dπ-pπBOND
The Walsh diagram, which illustrates triatomic molecules, shows a graph of energy versus bond angle in the figure below. Note that the presented energy levels are qualitative and require calculation using appropriate simulations for real systems. The MO levels on the left represent the bent configuration with a bond angle of 90°, while those on the right correspond to the linear configuration with a bond angle of 180°.
The correlation lines connecting the energy levels at the left and right ends represent the energy levels for bond angles (θ) within the range 90° ≤ θ < 180°. These plots provide a quick comparison of the energies for bent and linear geometries at a given bond angle (θ). It is evident that the molecule favors the geometry with the lower HOMO energy.
WALSH DIAGRAM FOR PENTA-ATOMIC MOLECULES WALSH DIAGRAMS AND dπ-pπBOND
For penta-atomic molecules, chemists consider an imaginary AH₄ model, which can adopt either a tetrahedral or square planar geometry. Methane (CH₄) and sulfur tetrafluoride (SF₄) serve as real examples of this category. For instance, when forming a methane molecule, the carbon atom uses one 2s orbital and three 2p orbitals, while each hydrogen atom contributes one 1s orbital for bonding. These eight orbitals create four bonding orbitals and four antibonding orbitals, with the bonding orbitals accommodating all eight electrons involved in the molecule’s formation. In tetrahedral geometry, the carbon and hydrogen orbitals significantly overlap, which lowers the energy of the bonding orbitals. In contrast, in a square planar configuration, the overlap weakens, leading to higher energy orbitals. Thus, the CH₄ molecule prefers a tetrahedral geometry over square planar or any intermediate distorted geometries.
dπ-pπ BOND
Inorganic molecules form differently from organic ones, notably with dπ-pπ bonds being present in inorganic compounds. Organic molecules generally form π bonds through the lateral overlap of p orbitals on atoms like carbon or nitrogen.
Inorganic molecules also commonly form δ bonds through interactions between two d orbitals. Additionally, inorganic molecules can use both p and d orbitals simultaneously. When p (or p*) and d orbitals from two different atoms overlap laterally, they form a dπ-pπ bond. Chemists often find such bonds in metal complexes like carbonyls and nitrosyls, and sulfur trioxide (SO₃) serves as a simple example. Main group compounds, such as phosphine oxides and disiloxanes, can also exhibit dπ-pπ bonds.
The presence of dπ-pπ bonding interactions typically leads to shorter bond lengths and a planar configuration of the involved atoms. However, these molecular features cannot always be solely attributed to dπ-pπ bonding, as other factors may also contribute. Therefore, a thorough evaluation of the electronic and orbital symmetries is necessary.
Phosphine oxide provides an example of dπ-pπ bonding in a molecule composed of nonmetallic elements. In this case, all the p orbitals on phosphorus are engaged in hybridization, leaving them unavailable for lateral overlap. The empty d orbitals on phosphorus accept electron density from the occupied p orbitals of the oxygen atom. This dπ-pπ bonding results in a stronger interaction between the two atoms, reflected in the short bond distance (150 pm) and the bond’s stability (bond energy 544 kJ/mol).
A classic example of dπ-pπ bonding is in metal carbonyls, where the metal’s d orbitals donate electron density to the empty π* orbital of the carbonyl oxygen, enhancing the metal-carbon bond order.
