Basis set (chemistry)

In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer.

The use of basis sets is equivalent to the use of an approximate resolution of the identity: the orbitals are expanded within the basis set as a linear combination of the basis functions , where the expansion coefficients are given by .

The basis set can either be composed of atomic orbitals (yielding the linear combination of atomic orbitals approach), which is the usual choice within the quantum chemistry community; plane waves which are typically used within the solid state community, or real-space approaches. Several types of atomic orbitals can be used: Gaussian-type orbitals, Slater-type orbitals, or numerical atomic orbitals.[1] Out of the three, Gaussian-type orbitals are by far the most often used, as they allow efficient implementations of post-Hartree–Fock methods.

  1. ^ Lehtola, Susi (2019). "A review on non-relativistic fully numerical electronic structure calculations on atoms and diatomic molecules". Int. J. Quantum Chem. 119 (19): e25968. arXiv:1902.01431. doi:10.1002/qua.25968.