Hylleraasins

Hylleraasins refers to a family of analytical solutions to the Schrödinger equation for the hydrogen molecular ion (H₂⁺) and the hydrogen molecule (H₂). These solutions were developed by the Norwegian physicist Egil A. Hylleraas in the early 20th century. They represent an important step in the development of quantum chemistry, providing a way to approximate the electronic structure and energies of simple molecules.

The Hylleraasins method is particularly notable for its use of a specific set of coordinates and basis functions that are well-suited to the diatomic molecular system. Unlike simpler methods that might use atomic orbitals centered on individual nuclei, Hylleraasins' approach incorporates interelectronic distances, which are crucial for accurately describing the behavior of electrons in molecules. This allows for a more refined calculation of the molecular binding energy and other properties.

While the original Hylleraasins solutions were for the simplest diatomic systems, the underlying principles have been extended and adapted in more sophisticated computational chemistry methods used today. These methods, often implemented in sophisticated software packages, build upon the foundational work of Hylleraas and others to tackle the electronic structure of much larger and more complex molecules. The development of Hylleraasins was a significant contribution to the early understanding of chemical bonding from a quantum mechanical perspective.