Numerical basis functions

Variational one-center restoration. In the variational technique of one-center restoration (VOCR) [79, 80], the proper behavior of the four-component molecular spinors in the core regions of heavy atoms can be restored as an expansion in spherical harmonics inside the sphere with a restoration radius, Rvoa, that should not be smaller than the matching radius, Rc, used at the RECP generation. The outer parts of spinors are treated as frozen after the RECP calculation of a considered molecule. This method enables one to combine the advantages of two well-developed approaches, molecular RECP calculation in a gaussian basis set and atomic-type one-center calculation in numerical basis functions, in the most optimal way. This technique is considered theoretically in [80] and some results concerning the efficiency of the one-center reexpansion of orbitals on another atom can be found in [75]. 

The numerical basis functions were used. As a result, H and S matrices were evaluated by the weighted sum of each value on the sample points distributed in the three-dimensional space. 

The standard procedure in LCAO calculations has been to use Gaussian Type Orbitals, GTO, or Slater Type Orbitals, STO, which are normally used in HF based codes but also in DFT codes. With such an approach the H and S could be given in closed forms. This was also partly the procedure used in the first molecular calculations using the DVM method by Baerends, Ellis and Ros [77]. The DVM method [22-24] is however quite general and very suitable for use of numerical basis functions, as first introduced by Averill and Ellis in 1973 [78]. They proposed that a first choice of basis functions for molecular calculations would be to solve the Schrodinger equation to self-consistency for the isolated atoms in a molecule, which will give... 

The second advantage of the DV-Xa method is that the basis functions of the DV-Xa method are atomic orbitals. Thus the number of nodes is exact as shown in Fig. 4, where Si 2s GTO in GAUSSIAN method is compared with the numerical basis function used in the DV-Xa method [17]. The use of the atomic orbital wavefunction makes it possible to perform the direct calculation of the electric dipole matrix elements, e.g. , using the DV-Xa MO, yielding better result than when using a GTO basis MO. 

As discussed in greater detail in the following section, the conceptual confusion over DODS-type splitting and orbital breathing effects often stems from mistaken attribution of physical significance to the numerical basis functions that are employed... 

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