Shape consistent relativistic effective core potentials

Shape consistent relativistic effective core potentials 

Other SC RECPs start from different reference data, mostly omitting spin-orbit interactions, but all approaches use, as reference data, the shape of the valence orbitals in the spatial valence region and their corresponding one-particle energies. We omit details concerning energy-adjusted and other types of relativistic pseudopotentials or effective core potentials. At this point, we summarize some characteristics of valence-only methods such as RECPs. 

1) Valence-only methods are computationally far more efficient than allelectron methods, especially up to the integral transformation step necessary for most post-HF calculations. 

2) Most of the relativistic effects relevant to quantum chemistry can be treated efficiently by modifying only the one-electron matrices. 

3) In general, good results are obtained for structures and structure related properties. 

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In 1992 Dmitriev, Khait, Kozlov, Labzowsky, Mitrushenkov, Shtoff and Titov [151] used shape consistent relativistic effective core potentials (RECP) to compute the spin-dependent parity violating contribution to the effective spin-rotation Hamiltonian of the diatomic molecules PbF and HgF. Their procedure involved five steps (see also [32]) i) an atomic Dirac-Hartree-Fock calculation for the metal cation in order to obtain the valence orbitals of Pb and Hg, ii) a construction of the shape consistent RECP, which is divided in a electron spin-independent part (ARECP) and an effective spin-orbit potential (ESOP), iii) a molecular SCF calculation with the ARECP in the minimal basis set consisting of the valence pseudoorbitals of the metal atom as well as the core and valence orbitals of the fluorine atom in order to obtain the lowest and the lowest H molecular state, iv) a diagonalisation of the total molecular Hamiltonian, which... 

Shape consistent relativistic effective core potentials... 

Ah initio relativistic effective core potentials can be derived from the relativi.stic all-electron Dirac-Fock solution of the atom the.se potentials are called the relativistic effective core potentials (RECP). and have been extensively used by several investigators to study the electronic structure of polyatomics containing very heavy atoms. The shape-consistent RECP method formulated by Christiansen, Lee, and Pitzer differs from the Phillips-Kleinman method in the representation of the nodeless pseudo-orbital in the inner region. The one-electron valence equation in an effective potential Vq of the core electrons can be expressed as... 

There have been a number of basis sets for lanthanide and actinide elements previously reported in the literature that are based on relativistic effective core (ECP) potentials, or pseudopotentials (PP). These can be most easily categorized by the type of underlying ECP used (a) shape consistent pseudopotentials, (b) energy consistent pseudopotentials, and (c) model potentials. 

Conventional shape-consistent effective potentials (67-70), whether relativistic or not, are typically formulated as expansions of local potentials, U (r), multiplied by angular projection cperators. The expansions are tnmcated after the lowest angular function not contained in the core. The last (residual) term in the expansion typically represents little more than the simple ooulombic interaction between a valence electron and the core (electrons and corresponding fraction of the nuclear charge) and is predominantly attractive. The lower A terms, on the other hand., include strongly... 

DFT-Based Pseudopotentials. - The model potentials and shape-consistent pseudopotentials as introduced in the previous two sections can be characterized by a Hartree-Fock/Dirac-Hartree-Fock modelling of core-valence interactions and relativistic effects. Now, Hartree-Fock has never been popular in solid-state theory - the method of choice always was density-functional theory (DFT). With the advent of gradient-corrected exchange-correlation functionals, DFT has found a wide application also in molecular physics and quantum chemistry. The question seems natural, therefore Why not base pseudopotentials on DFT rather than HF theory ... 

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