Exam 2 lecture 1

Now, let's move into the core of Valence Bond Theory. Quantum mechanics, introduced in the late 1920s, provided us with a powerful tool to calculate bond angles and bond lengths, building upon Lewis's model. The essence of Valence Bond Theory is that covalent bonds arise from the constructive interference of electron wave properties. Specifically, when unpaired electrons in the valence shell orbitals of neighboring atoms pair together, bonds are formed. The resulting shapes of these bonds are directly influenced by the overlap of atomic orbitals. Consider the simplest molecule, H₂. Each hydrogen atom has one electron in a 1s-orbital. When these two atoms approach each other, their 1s-electron pairs overlap, forming a sigma (σ) bond. This bond features a cylindrically symmetric distribution of electron density between the two nuclei. We also see this in the formation of H-F. Fluorine possesses an unpaired electron in its 2pz orbital, while hydrogen has an unpaired electron in its 1s orbital. When these orbitals overlap, they merge into an electron cloud that encompasses both atoms, forming another sigma bond. For a nitrogen molecule (N₂), a more complex scenario unfolds. Nitrogen has a single electron in each of its three 2p-orbitals. Due to specific bond angles, only one of these three orbitals undergoes an end-to-end overlap to form a sigma bond. The other two 2px and 2py orbitals are perpendicular to the internuclear axis. These p-orbitals overlap side-by-side, creating what we call pi (π) bonds. The two pi bonds effectively merge into a cloud that surrounds the central sigma bond cloud, contributing to the strong triple bond characteristic of While Valence Bond Theory is incredibly useful, it does have its drawbacks. For example, a carbon atom has an electron configuration [He]2s²2pₓ¹2py¹. This configuration might suggest a valence of two, forming only two perpendicular bonds. However, carbon is consistently tetravalent, meaning it always forms four bonds. To address this, we introduce the concept of promoting a 2s-electron into an empty 2pz-orbital, resulting in [He]2s¹2pₓ¹2py¹2pz¹. Yet, even this doesn't fully explain everything. The observed bond angles of 109.5° for a tetrahedral molecule do not align with the 90° angles of our original orbitals (px, py, pz). This highlights the need to merge the correct number of electrons with appropriate orbital shapes to achieve an accurate representation of molecular geometry. This leads us to the concept of Orbital Hybridization. Hybrid orbitals are formed by a linear combination of atomic orbitals (LCAO), which brings about a net stabilization to the atom. This new shape is a result of both constructive and destructive interference of the wave functions. For instance, the combination of an s orbital and a pz orbital results in an sp-orbital, which exhibits a distinct, elongated shape. We will further explore various types of hybridization and how they explain the diverse geometries of molecules.