orbitalformen

Orbitalformen (orbital shapes) describe the spatial distribution of electron density associated with atomic or molecular orbitals in quantum mechanics. They arise from solving the Schrödinger equation for electrons in atoms or molecules and are visualized as surfaces or isodensity contours. In hydrogen-like atoms, orbital shapes are determined by quantum numbers n, l, and m. The angular part is given by spherical harmonics Y_lm, generating characteristic shapes: s orbitals (l = 0) are spherical; p orbitals (l = 1) are dumbbell-shaped with three degenerate orientations; d orbitals (l = 2) have four-lobed shapes with different orientations; f orbitals are more complex. Nodal surfaces and the radial part R_nl(r) control the number of nodes and the radial extent. In multi-electron atoms, electron–electron repulsion splits degeneracies, yet the underlying l-dependent shapes persist and are often described by effective quantum numbers or orbitals from approximate methods such as Hartree–Fock or density functional theory.

In chemistry, orbitalformen influence bonding and hybridization: sp, sp2, and sp3 hybrids create directional lobes, while molecular orbitals formed from linear combinations of atomic orbitals yield sigma and pi character with corresponding spatial patterns. Limitations: orbital shapes are approximations; actual electron density is a probability distribution, and correlation and relativistic effects can modify shapes. Visualization and interpretation of orbitalformen aid in understanding bonding, reactivity, and spectra, while remaining idealized representations of the true many-electron problem.