Pseudoorbitals

Pseudoorbitals are a concept used in quantum chemistry, particularly in the context of density functional theory (DFT) calculations. They are not the true, physical orbitals of an atom or molecule, which are described by the exact solution to the Schrödinger equation. Instead, pseudoorbitals arise from approximations made in DFT, most commonly the use of pseudo-potentials.

Pseudo-potentials are designed to simplify electronic structure calculations by replacing the strong Coulombic potential of the atomic nucleus and the core electrons with a weaker, effective potential. This approximation is particularly useful for heavy elements where treating all electrons explicitly becomes computationally prohibitive. The core electrons are effectively "frozen" and their contribution to the valence electron behavior is modeled by the pseudo-potential.

The pseudoorbitals are then the solutions obtained for the valence electrons in the presence of this pseudo-potential. They often exhibit smoother radial behavior than true atomic orbitals, especially near the nucleus, because the strong nuclear attraction has been removed. This smoothness can lead to more efficient calculations.

While pseudoorbitals are computational constructs and not directly observable, they are useful for analyzing bonding, molecular properties, and visualizing electron density in DFT. They share many of the same qualitative features as true orbitals and are often interpreted in a similar manner. However, it is important to remember their approximate nature and that their properties can differ quantitatively from those of true atomic or molecular orbitals.