Slaterfüggvények

Slaterfüggvények, also known as Slater-type orbitals (STOs), are a set of analytical mathematical functions used in quantum chemistry to approximate the wave functions of electrons in atoms and molecules. They were introduced by John C. Slater in 1930 as an alternative to the more complex solutions derived from the Schrödinger equation.

The general form of a Slater-type function for an electron in an atom is given by $ \psi_{nlm}(r, \theta, \phi) = N r^{n-1} e^{-\zeta r} Y_{lm}(\theta, \phi) $, where $N$ is a normalization constant, $n$ is the principal quantum number, $\zeta$ is an exponent that determines the orbital's size and effective nuclear charge, $r$ is the distance from the nucleus, and $Y_{lm}(\theta, \phi)$ are the spherical harmonics representing the angular part of the wave function. The exponent $\zeta$ is crucial as it reflects the shielding effect of inner electrons on the outer ones.

STO's are computationally simpler than the exact solutions from the Schrödinger equation, making them practical for calculations. However, they have limitations. For instance, they do not satisfy the cusp condition at the nucleus (where the derivative of the wave function should be discontinuous), and they are not orthogonal to each other for different atoms. Despite these drawbacks, STOs served as a foundational concept in early quantum chemical calculations and paved the way for more sophisticated orbital basis sets. In modern computational chemistry, STOs are often used as building blocks in more complex basis sets, such as Gaussian-type orbitals (GTOs), which are computationally more efficient for molecular calculations.