Large-core ECPs

A key issue in the construction of ECPs is just how many electrons to include in the core. So-called large-core ECPs include everything but the outermost (valence) shell, while small-core ECPs scale back to the next lower shell. Because polarization of the sub-valence shell can be chemically important in heavier metals, it is usually worth the extra cost to explicitly include that shell in the calculations. Thus, the most robust ECPs for the elements Sc-Zn, Y-Cd, and La-Hg, employ [Ne], [Ar], and [Kr] cores, respectively. There is less consensus on the small-core vs. large-core question for the non-metals. 

The frozen-core approximation is one basic assumption underlying all ECP schemes described so far. Especially for main group elements, where a large-core ECP approximation works fairly well if not too high accuracy is desired, the polarizability of the cores (Fig. 14) has nonnegligible effects for elements from the lower part of the periodic table. Within the ECP approach it is indeed possible to account for both static (polarization of the core at the HF level) and dynamic (core-valence correlation) polarization of the cores in an efficient way. Meyer and coworkers [202] proposed in the framework of AE calculations the... 

The classical case for the application of large-core ECPs in connection with CPPs are the alkaline elements, which possess a single valence electron outside a closed shell core. Such a one-valence electron approach appears to be very attractive from a computational point of view and numerous studies of alkaline atoms and their molecules exist. In those cases where ns and np valence orbitals are present together with (n-l)d and (n-2)f valence orbitals, e.g., for Cs, it proved to be more accurate to augment the CPP by a short-range local potential [137]... 

In case of large overlapping or mutually penetrating cores a core-core repulsion correction (CCRC) to the point charge repulsion model in Eq. 27 is needed. A similar core-nucleus repulsion correction (CNRC) has to be applied for the interaction between nuclei of atoms treated without ECP and centers with large-core ECPs. A Bom-Mayer type ansatz proved to be quite successful to model the pairwise repulsive correction [206,207]... 

Bond distance (in pm) and vibrational frequencies (in cm ) of UFe obtained by various density functional methods quasi-relativistic frozen core Becke-Lee-Yang-Parr (QR-FC BYLP), Hay-Martin large core ECP hybrid DFT (HM ECP B3LYP and VWN), Stoll-Preuss small core ECP LDA (SP ECP VWN) and an all-electron scalar relativistic LDA (AE SR VWN). 

Other, scalar relativistic effects are usually minor. Among them, the most important is the contraction of s-orbitals caused by the increase in electron mass due to high velocity near the nucleus. Except in the most careful work, such effects are modeled using relativistic effective core potentials (ECPs), also called core pseudopotentials [76]. When an ECP is used, the corresponding valence basis set should be used for the remaining electrons. A small-core ECP, in which fewer electrons are replaced by the effective potential, is a weaker approximation and therefore more reliable than the corresponding large-core ECP. The selection of basis sets to accompany ECPs is more restricted than the selection of all-electron basis sets, but appropriate correlation-consistent basis sets are available for heavy p-block elements [77-80]. 

It is obvious from Table 1 that the quality of the valence basis sets of the available pseudopotentials varies considerably. The large-core ECPs by Hay and Wadt have a low number of electrons in the valence space. Also, the valence orbitals are described by a rather small basis set. We recommend use of the small-core ECPs, which give clearly better results.The same comment applies to the two sets of ECPs that have been published by Christiansen et al 85-88 xhe (n - l)s and (n - l)p electrons should be treated as part of the valence electrons (see also below). 

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