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Effective Core Potential Treatments

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. [Pg.205]

Model potentials using the Cowan-Griffin Hamiltonian have been reported for the lanthanide elements, first by Sakai et al. [26] and then by Seijo et al. [27]. The latter group also included the actinides in their study. Both model potentials for the lanthanides consist of a 46-electron core, while the actinide potentials utilized a 78-electron core. Primitive basis sets supplied with these potentials were larger in the Seijo et al. cases compared to Sakai [Pg.205]

Recently, new energy-consistent, small-core (60 electron) PPs for the f-block elements adjusted to extensive multiconfigurational Dirac-Hartree-Fock reference data (with contributions from the Breit interaction) have been reported for Ac-U [42,43]. In these cases the PPs were tested on both atomic and molecular calculations using large ANO basis sets. As in previous work the primitive sets were optimized primarily for the f s states with diffuse d and p functions added. The ANO contractions were based on either CASSCF or MRCI averaged density matrices. [Pg.206]


Basis sets for atoms beyond the third row of the periodic table are handled somewhat differently. For these very large nuclei, electrons near the nucleus are treated in an approximate way, via effective core potentials (ECPs). This treatment includes some relativistic effects, which are important in these atoms. The LANL2DZ basis set is the best known of these. [Pg.101]

The twin facts that heavy-atom compounds like BaF, T1F, and YbF contain many electrons and that the behavior of these electrons must be treated relati-vistically introduce severe impediments to theoretical treatments, that is, to the inclusion of sufficient electron correlation in this kind of molecule. Due to this computational complexity, calculations of P,T-odd interaction constants have been carried out with relativistic matching of nonrelativistic wavefunctions (approximate relativistic spinors) [42], relativistic effective core potentials (RECP) [43, 34], or at the all-electron Dirac-Fock (DF) level [35, 44]. For example, the first calculation of P,T-odd interactions in T1F was carried out in 1980 by Hinds and Sandars [42] using approximate relativistic wavefunctions generated from nonrelativistic single particle orbitals. [Pg.253]

The relativistic effects (Rl) and (R2) can be simulated by adjusting the sizes of basis functions used in a standard variational treatment. This adjustment is usually combined with an effective-core-potential [ECP] approximation in which inner-shell electrons are replaced by an effective [pseudo] potential of chosen radius. The calculations of this chapter were carried out with such ECP basis sets in order to achieve approximate incorporation of the leading relativistic effects.)... [Pg.546]

An important advantage of ECP basis sets is their ability to incorporate approximately the physical effects of relativistic core contraction and associated changes in screening on valence orbitals, by suitable adjustments of the radius of the effective core potential. Thus, the ECP valence atomic orbitals can approximately mimic those of a fully relativistic (spinor) atomic calculation, rather than the non-relativistic all-electron orbitals they are nominally serving to replace. The partial inclusion of relativistic effects is an important physical correction for heavier atoms, particularly of the second transition series and beyond. Thus, an ECP-like treatment of heavy atoms is necessary in the non-relativistic framework of standard electronic-structure packages, even if the reduction in number of... [Pg.713]

An even simpler approach to relativity, for heavy elements, is to use effective core potentials (ECPs) to represent the core electrons, taking the potentials from various compilations in the literature that explicitly include relativistic effects in the generation of the ECPs. References to such ECPs are given by Dyall et al. [103]. These relativistic ECPs (RECPs) allow the inclusion of some relativistic effects into a nonrelativistic calculation. Since ECPs will be treated in detail elsewhere, we will not pursue this approach further here. We may note, however, that recent comparisons with Dirac-Fock calculations suggest that the main weakness in the RECPs is not the treatment of relativity but the quality of the ECPs themselves [103]. Different RECPs gave spectroscopic constants with a noticeable scatter, compared to Dirac-Fock, but the relativistic corrections (difference between an RECP and the corresponding ECP value) were fairly consistent with one another. [Pg.394]

The one-center approximation allows for an extremely rapid evaluation of spin-orbit mean-field integrals if the atomic symmetry is fully exploited.64 Even more efficiency may be gained, if also the spin-independent core-valence interactions are replaced by atom-centered effective core potentials (ECPs). In this case, the inner shells do not even emerge in the molecular orbital optimization step, and the size of the atomic orbital basis set can be kept small. A prerequisite for the use of the all-electron atomic mean-field Hamiltonian in ECP calculations is to find a prescription for setting up a correspondence between the valence orbitals of the all-electron and ECP treatments.65-67... [Pg.136]

Our above-mentioned conclusions are contrary to the results reported from previous less rigorous calculations e.g.. Hay et al. (11) concluded from an effective core potential (ECP) calculation using an approximate treatment of relativity that the 5d core does not appear to play a dominant role in the chemical bond in AuH this conclusion is incorrect in view of our result that 5d electrons cannot be left in the core in AuH. Our extended basis set (EBS), DF SCF calculation predicts a value of 1.682 eV for the D of AuH and our relativistic configuration interaction calculation with the... [Pg.295]

With the exception of Ligand Field Theory, where the inclusion of atomic spin-orbit coupling is easy, a complete molecular treatment of relativity is difficult although not impossible. The work of Ellis within the Density Functional Theory DVXa framework is notable in this regard [132]. At a less rigorous level, it is relatively straightforward to develop a partial relativistic treatment. The most popular approach is to modify the potential of the core electrons to mimic the potential appropriate to the relativistically treated atom. This represents a specific use of so-called Effective Core Potentials (ECPs). Using ECPs reduces the numbers of electrons to be included explicitly in the calculation and hence reduces the execution time. Relativistic ECPs within the Hartree-Fock approximation [133] are available for all three transition series. A comparable frozen core approximation [134] scheme has been adopted for... [Pg.37]

A remark should be made here with respect to the generation and adjustment of the widely used effective core potentials (ECP, or pseudopotentials) [85] in standard non-relativistic quantum chemical calculations for atoms and molecules. The ECP, which is an effective one-electron operator, allows one to avoid the explicit treatment of the atomic cores (valence-only calculations) and, more important in the present context, to include easily the major scalar relativistic effects in a formally non-relativistic approach. In general, the parameters entering the expression for the ECP are adjusted to data obtained from numerical atomic reference calculations. For heavy and superheavy elements, these reference calculations should be performed not with the PNC, but with a finite nucleus model instead [86]. The reader is referred to e.g. [87-89], where the two-parameter Fermi-type model was used in the adjustment of energy-conserving pseudopotentials. [Pg.243]

The extended computations [150] started from the four optimized stmctures [148] derived using ab initio HF treatment with a combined basis set 3-21G basis for C atoms and a dz basis set [365] with the effective core potential (ECP) on Ca (for the sake of simplicity, the treatment is coded by HF/3-21G dz). The stmctures [148] were reoptimized at the B3LYP/3-21G dz level. The B3LYP/6-31G dz//B3LYP/3-21G dz relative energies for the (b), (c), (d) and (a) stmctures are 0.0, 0.8, 18.9 and... [Pg.901]

Effective core potentials became more accurate in the last decade also, and the description of molecular properties with an accurate treatment of electron correlation (mainly CCSD(T) procedures) allowed the study of a large number of gas-phase molecules of the heaviest elements up to Z=118. Density... [Pg.70]

We review the Douglas-Kroll-Hess (DKH) approach to relativistic density functional calculations for molecular systems, also in comparison with other two-component approaches and four-component relativistic quantum chemistry methods. The scalar relativistic variant of the DKH method of solving the Dirac-Kohn-Sham problem is an efficient procedure for treating compounds of heavy elements including such complex systems as transition metal clusters, adsorption complexes, and solvated actinide compounds. This method allows routine ad-electron density functional calculations on heavy-element compounds and provides a reliable alternative to the popular approximate strategy based on relativistic effective core potentials. We discuss recent method development aimed at an efficient treatment of spin-orbit interaction in the DKH approach as well as calculations of g tensors. Comparison with results of four-component methods for small molecules reveals that, for many application problems, a two-component treatment of spin-orbit interaction can be competitive with these more precise procedures. [Pg.656]

Despite this ubiquitous presence of relativity, the vast majority of quantum chemical calculations involving heavy elements account for these effects only indirectly via effective core potentials (ECP) [8]. Replacing the cores of heavy atoms by a suitable potential, optionally augmented by a core polarization potential [8], allows straight-forward application of standard nonrelativistic quantum chemical methods to heavy element compounds. Restriction of a calculation to electrons of valence and sub-valence shells leads to an efficient procedure which also permits the application of more demanding electron correlation methods. On the other hand, rigorous relativistic methods based on the four-component Dirac equation require a substantial computational effort, limiting their application in conjunction with a reliable treatment of electron correlation to small molecules [9]. [Pg.657]

For clusters containing more than a very few heavy metal atoms, it is impossible to carry out an all-electron ab initio molecular orbital treatment. Instead the atomic cores must be replaced by effective core potentials or pseudopotentials which do not take part in the bonding. Clearly the choice of which electrons to keep... [Pg.49]


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