Effective Core Potentials Theoretical Grounds

It is well estabUshed from chemical experience that most chemical properties of molecules and soUds are determined by the valence electrons of the constituent atoms. The core states are weakly affected by changes in chemical bonding. The effect of core electrons is principally to shield the nuclear charges and to provide an effective potential for the valence electrons. The main reason for the limited role of the core electrons is the spatial separation of the core and valence shells that originates from the comparatively strong binding of the core electrons to the nucleus. This effect is illustrated in Fig. 8.2, [470], where the radial orbitals of the oxygen atom are plotted. The spatial separation of the Is core state from the valence 2s, 2p states and 

Radial pseudo- versus aU-electron orbitals of oxygen (a) 2s (b) 2p [470] 

The calculations of real systems (for example, color centers in ionic crystals, [475]) were made based on the model potential of Abarenkov and Heine [476]  

A giant step forward in psendopotentials was taken by Hamann et al. [472], who introduced norm conserving psendopotentials (NCPP). NCCP for angular momentum I is chosen so that 

Condition 1 automatically implies that the real and psendovalence eigenvalues agree for a chosen prototype configuration, as the eigenvalue determines the asymptotic decay of the orbitals. 

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Relativistic Effective Core Potential Theoretical Grounds. 

Titov, A.V., Mosyagin, N.S. Generalized relativistic effective core potentials Theoretical grounds. Int. J. Quant. Chem. 71, 359-401 (1999)... 

Finally, some spectroscopic applications for pseudopotentials within SOCI methods are presented in section 3. We focus our attention on applications related to relativistic averaged and spin-orbit pseudopotentials (other effective core potentials applications are presented in chapters 6 and 7 in this book). Due to the large number of theoretical studies carried out so far, we have chosen to illustrate the different SOCI methods and discuss a few results, rather than to present an extensive review of the whole set of pseudopotential spectroscopic applications which would be less informative. Concerning the works not reported here, we refer to the exhaustive and up-to-date bibliography on relativistic molecular studies by Pyykko [21-24]. The choice of an application is made on the basis of its ability to illustrate the performances on both the pseudopotential and the SOCI methods. One has to keep in mind that it is not easy to compare objectively different pseudopotentials in use since this would require the same conditions in calculations (core definition, atomic basis set, SOCI method). The applications are separated into gas phase (section 3.1) and embedded (section 3.2) molecular applications. Even if the main purpose of this chapter is to deal with applications to molecular spectroscopy, it is of great interest to underline the importance of the spin-orbit coupling on the ground state reactivity of open-shell systems. A case study is presented in section 3.1.4. 

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