Effective Core Potentials and Valence Basis Sets

Derivation of Effective Core Potentials and Valence Basis Sets 153... 

DERIVATION OF EFFECTIVE CORE POTENTIALS AND VALENCE BASIS SETS... 

Barandiaran Z, Seijo L. The ab initio model potential method. Cowan-Griffin relativistic core potentials and valence basis sets from Li (Z = 3) to La (Z = 57). Can J Chem. 1992 70 409. Seijo L. Relativistic ab initio model potential calculations including spin-orbit effects trhough the Wood-Boring Hamiltonian. J Chem Phys. 1995 102 8078. 

At B3LYP/6-311G(2d,p), pseudo-relativistic effective core potential and a (31/31/1) valence basis set were used for Si, Ge, Sn, Pb, from Ref 40. 

Ermler WC, TUson JL (2012) GeneraUy contracted valence-core/ valence basis sets for use with relativistic effective core potentials and spin-orbit coupUng operators. Comp Theor Chem 1002 24-30. doi 10.1016/j.comptc.2012.09.020... 

Lastly, we mention the basis sets. All ab initio ECP computations after 1984 described in this chapter were done using valence Gaussian basis sets in conjugation with effective core potentials. Typically, valence Gaussian basis sets for the heavy metal are of (3s 3p 3d) quality where the numbers in front of s, p and d specify the numbers of contracted Gaussian functions. For lanthanides and actinides, obviously 4f-type Gaussian functions are included in the basis set. We will describe in individual sections the basis sets used prior-to describing the calculational results. We will also describe the valence space of electrons when ECPs are included. 

In this section we discuss those effective core potentials and the corresponding valence basis sets that are used for Gaussian-fxmction-based LCAO periodic computations implemented in the computer codes CRYSTAL [23] and GAUSSIAN [107]. 

Unlike semiempirical methods that are formulated to completely neglect the core electrons, ah initio methods must represent all the electrons in some manner. However, for heavy atoms it is desirable to reduce the amount of computation necessary. This is done by replacing the core electrons and their basis functions in the wave function by a potential term in the Hamiltonian. These are called core potentials, elfective core potentials (ECP), or relativistic effective core potentials (RECP). Core potentials must be used along with a valence basis set that was created to accompany them. As well as reducing the computation time, core potentials can include the effects of the relativistic mass defect and spin coupling terms that are significant near the nuclei of heavy atoms. This is often the method of choice for heavy atoms, Rb and up. 

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