Summary of functions and orbitals

In Create mode the (conceptual) approach is:

BAS ⇒ (core-orthogonalization) ⇒ CBAS ⇒ (symmetry) ⇒ CSBAS ⇒ (orthonormality) ⇒ LOW ⇒ (Fock diagonalization) ⇒ MO

In Fragment mode:

FO (=MO from fragment file) ⇒ (symmetry) ⇒ SFO ⇒ (core-orth.) ⇒ CSFO ⇒ (orthonormality) ⇒ LOW ⇒ (Fock diagonalization) ⇒ MO

Acronyms:

BAS

Elementary cartesian basis functions, consisting of a radial part (exponential factor and power of r) and an angular part (cartesian spherical harmonic). The complete BAS set contains spurious lower-l combinations; these combinations are projected out and not used in the calculation. The BAS set contains also Core Functions.

SBAS

Symmetry-adapted combination of BAS functions.

CF

Core Function, part of the bas set. The CFs do not represent degrees of freedom in the basis set but serve only to ensure orthogonalization of the valence space to all frozen Core Orbitals.

CBAS

Core-orthogonalized elementary basis functions: the true valence (not-CF) BAS functions transformed by adding a suitable combination of the CFs. The total number of CBAS + the total number of of CFs equals the total number of BAS.

CSBAS

Symmetry-adapted combination of cbas functions.

CO

Frozen Core Orbitals, expressed as linear combinations of an auxiliary corbas basis set. The corbas set plays no role in the further discussion. The corbas functions are not the CFs.

The number of COs equals the number of CFs.

LOW

Lowdin orthonormalized symmetry-adapted core-orthogonalized basis. In Create mode they are derived directly from the BAS functions, in Fragment mode from the Fragment Orbitals, which are themselves of course expressible in the BAS set.

FO

Fragment Orbital: the MO of a fragment calculation, now used as a basis function in the molecule of which the fragment is part.

SFO

Symmetry adapted combination of FOs.

CSFO

Core-orthogonalized SFO.