Numerical atomic basis sets

The KS orbitals can be determined by a numerical procedure, analogous to numerical HF methods. In practice such procedures are limited to small systems, and essentially all calculations employ an expansion of the KS orbitals in an atomic basis set. 

Total energy (Etotai) and full Cl correlation energy (Ecorr) for the beryllium atom and the helium dimer (Rt = 5.6 bohr) obtained with the numerical molecular basis sets. All energies are in Hartree. 

Cmtempa-ary numerical methods allow routine calculation of polarizability. It is difficult with the hyperpolariz-abdities that are much more sraisitive to fhe quality of fhe atomic basis set used. The hyperpolarizabilities relate to nonlinear properties, which are in high demand in new materials for technological applications. 

The overall accuracy of calculated potential energy surfaces depends in today s state-of-the-art calculations almost entirely on the atomic-orbital (AO) basis set employed. There are numerous AO basis sets in the literature, but most of them have been tested only for ground-state calculations. Generally AO basis sets are optimized in order to give an optimal charge... 

In the LDA methods, the one-electron functions are usually expanded into atomic basis sets whereby numerical orbitals, GTO s, Slater-type orbitals (STO),... 

In our DF studies we used LDA, GGA and hybrid exchange and correlation functionals PWC, BLYP, PW91, B3LYP and B3PW91 [18,25-32], Throughout this work we have employed localised atomic basis sets in the form of numerical and... 

Linear dependencies of Gaussian-type orbital basis sets employed in the framework of the HF SCF method for periodic structures, which occur when diffuse basis functions are included in a basis set in an uncontrolled manner, were investigated [468]. The basis sets constructed avoid numerical linear dependences and were optimized for a number of periodic structures. The numerical AO basis sets for solids were generated in [469] by confining atoms within spheres and smoothing the orbitals so that the first and second derivatives go to zero at the boundary. This forms small atomic-like basis sets that can be applied to solid-state problems and are efficient for treating large systems. 

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