The frozen core approximation

An important aspect of ADF is the (optional) use of a frozen core to trim down the computational time by reducing the size of the variational basis set. Because deep-core atomic orbitals change very little upon bond formation, the frozen core approximation saves time without sacrificing much in quality. Use of frozen cores is preferred over pseudopotentials, which ADF does not support, because it is, in essence, an all-electron calculation. With a frozen core calculation you obtain the total charge density and potential in the valence and in the core region, ignoring only the slight change in the deep-core orbitals upon formation of the chemical bond.

To ensure orthogonality between the frozen core orbitals and the valence basis functions, the valence basis set used in the SCF equations is explicitly orthogonalized to the frozen core. This is achieved by adding to the valence set a series of auxiliary 'core functions' χ_μ^core, precisely one for each frozen core orbital. Each valence function is replaced by a linear combination

χ_ν^valence → χ_ν^valence + ∑_μ c_μν χ_μ^core

The condition that each such modified valence function be orthogonal to each frozen core orbital determines exactly all the coefficients c_μν. The frozen core orbitals are taken from very accurate single-atom calculations with large STO basis sets. Note that the core functions do not add variational freedomto the (valence) basis set, and hence, do not increase the size of the secular (Fock) matrix to be diagonalized. The ADF database offers for most atoms in the periodic table several basis sets with different 'levels' of frozen core approximation, including allelectron basis sets to avoid the frozen core approximation altogether. The exact definition of the frozen core orbitals (expansion functions and coefficients) used with a basis set is stored in the corresponding database file.

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Related: Slater-type basis sets