Anisotropic 2s2p Orbitals as Simple Descriptors of the Chirality of Carbon Centres

Abstract

The traditional description of carbon chemistry in terms of hydrogenic 2s and isotropic 2p orbitals leads to simple descriptions of chemical bonding as well as to accurate quantitative methodologies but fails to provide a simple and intuitive description of chirality. An alternative simple qualitative description of carbon chemistry is presented using instead anisotropic 2s2p orbitals. These orbitals arise naturally from the mathematical description of geometries in four-dimensional space through the solution of the quaternity equation, and as solutions to the Schrödinger equation must take on the same fundamental form in spherical quantities, the orbitals provide simple molecular-bonding descriptors. For carbon, the appropriate orbitals are usually named 2s, 2p_x, 2p_y, and 2p_z but here, only the 2s orbital is analogous to the similarly named spherical orbital; instead, 2p_α refers to a linear radius, 2p_β to a semicircular arc, and 2p_γ to a hemisphere. Each orbital represents space in a fundamentally different way. They may be combined to provide simple descriptions of the chemical bonding in methane, ethane, ethyne, and other organic compounds as well as providing a direct description of chiral centres. Their usefulness is demonstrated through successful prediction of the chirality of carbon centres where the density gradients of the anisotropic orbitals are preserved by four different substituents, considering how basic chemical effects such as substitution by electron-withdrawing and electron-donating groups modulate the molecular handedness.