bass - constructing the basis set
The bass program constructs the basis set starting from the HFD orbitals for the core and valence orbitals, formed by the hfd program. Then virtual orbitals are added to account for correlations and are constructed from either (1) previously constructed HFD orbitals or (2) B-splines. A reasonable basis set should consist of orbitals mainly localized at the same distances from the origin as the valence orbitals.
In the first case, virtual orbitals are formed using a recurrent procedure[1]. The lowest virtual orbitals can be constructed from the HFD orbitals. The large component of the radial Dirac bispinor, \(f_{n'l'j'}\), is obtained from a function \(f_{nlj}\) constructed previously by multiplying it by \(r^{l' - l}\, \sin(kr)\). Here \(l'\) and \(l\) are the orbital quantum numbers of the new and old orbitals (\(l' \geq l\)) and the coefficient \(k\) is determined by the properties of the radial grid. The small component \(g_{n'l'j'}\) is found from the kinetic balance condition:
where \(\boldsymbol{\sigma}\) are the Pauli matrices, \(\bf p\) and \(m\) are the electron momentum and mass, and \(c\) is the speed of light. The newly constructed functions are then orthonormalized to the functions of the same symmetry.
Another option is to construct large components of the orbitals from B-splines. Small components are still formed with the kinetic balance method. A more detailed description of this program is given in the 2015 CI-MBPT paper[2].
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