Energy-adjusted ECPs

Each ECP is unique in the way it is developed, and generally the method used to construct effective core potentials is either the shape-consistent method or the energy-adjusted extraction method. The former method defines the ECPs by solving an eigenvalue problem from the all-electron reference calculation, while the latter involves constructing ECPs so that they reproduce observables. The LANL2, SBKJC, and CRENBL ECPs are all deemed shape-consistent, while the SDB ECP is energy-adjusted. ... 

Another group of methods successfully used for calculations of the electronic structures of the heaviest element molecules are effective core potentials (ECP) (see the Chapters of M. Dolg and Y.-S. Lee in these issues). The relativistic ECPs (RECP) were applied to calculations of the electronic structures of halides and oxyhalides of Rf and Sg and of some simple compounds (mostly hydrides and fluorides) of elements 113 through 118 [126-131]. Using energy-adjusted pseudo-potentials (PP) [132] electronic structures and properties, and the influence of relativistic effects were studied for a number of compounds of elements at the end of the 6d series (elements 111 and 112), as well as at the beginning of the 7p series (elements 113 and 114) (see Refs. 26 and 133 for reviews and references therein). Some other methods, like the Douglas-Kroll-Hess (DKH) [134], were also used for calculations of small heaviest-element species (e.g. IIIH [95]). 

Some scalar relativistic effects are included implicitly in calculations if pseudopotentials for heavy atoms are used to mimic the presence of core electrons there are several families of pseudopotentials available the effective core potentials (ECP) (Cundari and Stevens 1993 Hay and Wadt 1985 Kahn et al. 1976 Stevens et al. 1984), energy-adjusted pseudopotentials (Cao and Dolg 2006 Dolg 2000 Peterson 2003 Peterson et al. 2003), averaged relativistic effective potentials (AREP) (Hurley et al. 1986 Lajohn et al. 1987 Ross et al. 1990), model core potentials (MCP) (Klobukowski et al. 1999), and ab initio model potentials (AIMP) (Huzinaga et al. 1987). 

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. 

One further distinguishes ECPs by the kind of their adjustment, i.e., energy-consistent PPs (see Section 6.3.1) and shape-consistent PPs/MPs (see Section 6.3.2). Furthermore, ECPs are categorized by the size of their core, e.g., one differs between f-in-valence small-core [21,22] and f-in-core large-core PPs (LPP) [7-12] for the f elements. Finally, the accuracy of the underlying AE reference data determines the ECP type, e.g., for early actinides scalar-relativistic Wood-Boring (WB) [22] or relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) [23,24] small-core PPs (SPP) are available. 

---