Extended Kohn-Sham

STRUTINSKY S SHELL-CORRECTION METHOD IN THE EXTENDED KOHN-SHAM SCHEME APPLICATION TO THE IONIZATION POTENTIAL, ELECTRON AFFINITY, ELECTRONEGATIVITY AND CHEMICAL HARDNESS OF ATOMS... 

Abstract. Calculations of the first-order shell corrections of the ionization potential, 6il, electron affinity, 5 A, electronegativity, ix, and chemical hardness. Sir] are performed for elements from B to Ca, using the previously described Strutinsky averaging procedure in the frame of the extended Kohn-Sham scheme. A good agreement with the experimental results is obtained, and the discrepancies appearing are discussed in terms of the approximations made. 

In the next section we shall recall the definitions of the chemical concepts relevant to this paper in the framework of DFT. In Section 3 we briefly review Strutinsky s averaging procedure and its formulation in the extended Kohn-Sham (EKS) scheme. The following section is devoted to the presentation and discussion of our results for the residual, shell-structure part of the ionization potential, electron affinity, electronegativity, and chemical hardness for the series of atoms from B to Ca. The last section will present some conclusions. 

In fact, there is another approach to DFT that allows fractional electron numbers, namely the extended Kohn-Sham (EKS) scheme [23,26,27]. ft allows the use of fractional occupation numbers fi 0 < fi < 1, hence... 

Note that the extended Kohn-Sham energy functional is dependent on the orbitals and implicitly on through the electron-nucleus attraction terms... 

Delchev, Y.I., A.I. Kuleff, J. Maruani, T. Mineva, and F. Zahariev. 2006. Strutinsky s shell-correction method in the extended Kohn-Sham scheme Application to the ionization potential, electron affinity, electroneg ativity and chemical hardness of atoms. In Recent Advances in the Theory of Chemical and Physical Systems, edited by Jean-Pierre Julien, Jean Maruani, and Didier Mayou, 159-177. New York Springer-Verlag. 

Lately, the CP-MD approach has been combined with a mixed QM/MM scheme [10-12] which enables the treatment of chemical reactions in biological systems comprising tens of thousands of atoms [11, 26]. Furthermore, CP-MD and mixed QM/MM CP-MD simulations have also been extended to the treatment of excited states within a restricted open-shell Kohn-Sham approach [16, 17, 27] or within a linear response formulation of TDDFT [16, 18], enabling the study of biological photoreceptors [28] and the in situ design of optimal fluorescence probes with tailored optical properties [32]. Among the latest extensions of this method are also the calculation of NMR chemical shifts [14]. 

It is also possible to extend the Kohn-Sham formalism by defining an energy term Ts that includes the kinetic energy of the noninteracting system, and the total... 

On matrix form the non-unitary transformations (27) and (30) of the previous section are easily extended to the complete Hamiltonian and have therefore allowed relativistic and non-relativistic spin-free calculations of spectroscopic constants and first-order properties at the four-component level (see, for instance. Refs. [45 7]). In this section, we consider the elimination of spin-orbit interaction in four-component calculations of second-order electric and magnetic properties. Formulas are restricted to the Hartree-Fock [48] or Kohn-Sham [49] level of theory, but are straightforwardly generalized. 

In Refs [10, If] we have shown that Eqn (30) is an expression for the first-order shell correction term in the EKS-DFT frame. As we pointed it out, the extended version [26,27] of the Kohn-Sham scheme [46] is appropriate because it allows fractional occupation numbers, thus permitting the... 

All electron calculations were carried out with the DFT program suite Turbomole (152,153). The clusters were treated as open-shell systems in the unrestricted Kohn-Sham framework. For the calculations we used the Becke-Perdew exchange-correlation functional dubbed BP86 (154,155) and the hybrid B3LYP functional (156,157). For BP86 we invoked the resolution-of-the-iden-tity (RI) approximation as implemented in Turbomole. For all atoms included in our models we employed Ahlrichs valence triple-C TZVP basis set with polarization functions on all atoms (158). If not noted otherwise, initial guess orbitals were obtained by extended Hiickel theory. Local spin analyses were performed with our local Turbomole version, where either Lowdin (131) or Mulliken (132) pseudo-projection operators were employed. Broken-symmetry determinants were obtained with our restrained optimization tool (136). Pictures of molecular structures were created with Pymol (159). 

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