Basissets

Basis sets are sets of functions used to expand molecular orbitals in quantum chemical calculations, typically Gaussian-type orbitals used to approximate Slater-type orbitals. They provide a mathematical representation of electron distribution around nuclei, enabling the solution of the electronic Schrödinger equation within approximate methods such as Hartree-Fock or density functional theory.

A basis set attaches to each atom and includes functions with angular momentum components (s, p, d, f). Each angular momentum channel has a number of contracted Gaussian functions, formed from a linear combination of primitive Gaussians. Minimal basis sets include a single function per occupied orbital; split-valence expand valence flexibility; polarization functions (d, f) allow deformation; diffuse functions (small exponents) help describe anions and weakly bound states.

Common families include Pople-style sets, such as 6-31G and 6-311G, often augmented with polarization and diffuse terms (for example, 6-31G(d) or 6-31+G(d,p)). Correlation-consistent basis sets (Dunning) cc-pVDZ, cc-pVTZ, and their augmented versions aug-cc-pVDZ, aug-cc-pVTZ, are designed for correlated methods. Basis sets vary by atom and element, with heavier elements sometimes using effective core potentials to replace core electrons.

Practical considerations include size and accuracy trade-offs. Larger basis sets improve accuracy but increase computational cost. Basis set incompleteness, basis set superposition error, and convergence behavior influence results; techniques such as extrapolation to the complete basis set limit or counterpoise corrections are common. The choice of basis set depends on the system, method, and the desired balance of precision and efficiency.