Core projection effects in atomic frozen‐core calculations: A numerical analysis

Abstract

Frozen-core calculations on the (He) 2s22p6 -'S state of the F-ion and the (Ar) 3d44sZ -5D state of the Cr atom, obtained with differently reduced basis sets and different core-projection schemes, are presented and compared with the corresponding all-electron results in order to analyze the behavior of the core projection under these circumstances. Severe truncation of the valence basis set can give frozen-core results noticeably deviated from the all electron values if the regular projection (projection factors xg = 2.0) is adopted. Much better results are obtained in these cases if a softer projection (xg = 1 .O) is used for those core orbitals having high electronic density in regions where the valence basis set has low flexibility. In these circumstances the expectation value of the core projector becomes a nonvanishing correction to the valence energy because the core-valence orthogonality is incomplete after core projection.

The self-consistent nonorthogonal group function approach in reduced basis frozen-core calculations

“…No fully satisfactory choice of these parameters is available. Theoretical arguments suggest that they have to be chosen as 2 [7, 191, but their values should depend on the basis set truncation, and reduced values, e.g., 1, may be more appropriate to obtain a good quality wave function [8][9][10]. Then, the nonorthogonal formulation which is exempt from these parameters and predicts equilibrium geometrical parameters at least as reliably as the orthogonal formulation is an attractive alternative for reduced basis frozen-core calculations.…”

“…Therefore, in numerical applications, both the orbital equation and the energy formula deviate from those derived for the strictly orthogonal case. Projection factors [5,[7][8][9][10] are introduced in the orbital equation and their magnitude is chosen to achieve a compromise between the two factors: One is the flexibility of the wave function, which requires a low value for the projection factors. The other is to avoid variational distortion which requires a high value for them.…”