Pseudopotential Large-Core

Finally, some of the unexpected results revealed for iodophenols warn against the use of large core pseudopotentials in the ELF analysis. It is noteworthy that the analysis of the topology of the ELF enables us to predict favoured protonation sites with the help of a least topological change principle which will be discussed in a following section. 

Besides the reduction of frozen-core errors when going from large-core to medium-core or small-core potentials also the valence correlation energies obtained in pseudopotential calculations become more accurate since the radial nodal structure is partially restored [97,98]. Clearly the accuracy of small-core potentials is traded against the low computational cost of the large-core po-... 

Parameters of energy-consistent ab initio pseudopotentials and corresponding valence basis sets are available for almost all elements of the periodic table [93,94,117,190-192,194-201]. A compilation of parameters for the use within the MOLPRO program system also exists on the internet under the address http //www.theochem.uni-stuttgart.de. Special care has to be taken when spin-orbit coupling is included in calculations with small-core PPs some SO operators are constructed (similar to the large-core case) for a fully variational two-component treatment, whereas in some cases effective valence SO operators are defined. The latter have to be applied in SO-CI calculations for the valence electrons, in which the semi-core shells (outside the PP core) are frozen in their scalar-relativistic form. 

Figure 14. Static dipole polarizabilities (in a.u.) as used in the Stuttgart large-core main group pseudopotentials. The cores X"" " are n = 1 — 8 for the first to eighth main group.

As an example for the typical quality of molecular properties obtained with the newly developed basis sets of Martin and Sundermann [241] the results for the energy-consistent large-core Ge pseudopotential for the diatomics GeH, GeO and GeF is displayed in Table 8. In addition to their work on main group PP basis sets Martin and Sundermann [241] also proposed (2flg) correlation sets to be used with the (8s7p6d)/[5s4p3d] valence basis sets of the transition... 

Atomization energies E, (in a.u.), bond lengths (in A), and force constants k of the a, breathing mode (in a.u.) for tetr ydrides (for X = Si, Ge, Sn, Pb), from MR-ACPF calculations using scalar-relativistic energy-consistent large-core pseudopotentials (EC-PP) and (6s6p3d2flg) valence basis sets, in comparison to experimental data (Exp.). 

Recently, Stoll et al [94] used a very similar approach to EPCISO. One minor difference is the use of the DGCI Pitzer s code which works with CSFs basis functions instead of determinants. Apparently another difference here is the absence of a selection process of the spin-orbit matrix elements. In this study small-core and large-core energy-consistent pseudopotentials were combined for the calculation of spectroscopic constants of lead and bismuth compounds (BiH, BiO, PbX, BiX, (X=F, Cl, Br, I)). 

Let us first consider ground state spectroscopic properties. Schwerdtfeger et al tested relativistic and correlation effects using a large-core (seven valence electrons) energy-consistent pseudopotential, with or without U )... 

Once again the quality of the valence correlation treatment is crucial, making the large-core pseudopotential calculation (even without a CPP correction in this case) more accurate than a fiilly relativistic all-electron calculation. Another remark is relative to the comparison of the two pseudopotential SOCI calculations. A DGCI treatment, which in principle is better than a CI/SO one when large spin-orbit interaction is involved, does not guaranty by itself an accurate SOCI calculation, since in this example a CI /SO method gave much more re-... 

Large-core pseudopotentials are well known to lead to sizable errors [122-125] we thus recommend the use of small-core ECP s that include semicore orbitals in the valence space [120],... 

A priori it is not clear if effective core potentieds, which have for example been adjusted to reproduce atomic energy differences in wave function based calculations or to reproduce the shape of the valence orbitals outside the core, can successfully be used in density functional calculations. For so-called small core potentieds, where the atomic core has been chosen such that core and valence densities have little overlap, test calculations have shown that results from allelectron and pseudopotential calculations were virtually the same [74]. A related investigation on gold compounds comes to the same conclusion [75]. It is however not recommended to perform density functional investigations with large-core pseudopotentials that have been adjusted in wave function calculations. One example for a leirge-core situation is a transition metal where the vedence d orbiteds are (of course) treated explicitly, while the s emd p orbitals of the same principal quantum number are considered core orbitals. From an energetic view, such a separation seems well justified. However, problems arise since the densites of the s,p, and d orbitals of the same principal quantum number have considerable overlap. 

Pseudopotential. - Sierraalta and Herize proposed a new scheme for the development of ab initio eore potentials, whieh includes only valence electrons and one auxiliary s-type atomic function. They showed that the failine of large-core effective-core-potential (ECP) approaches in reproducing bond topological properties can be remedied. 

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). 

This Hamiltonian is written only for a valence subspace of electrons that are treated explicitly and denoted by indices and j (large-core approximation). As in the case of nonrelativistic pseudopotentials, this subspace is often extended by inclusion of some outermost core shells for better accuracy (smaU-core approximation) but below we consider them as the valence shells if these outermost core and valence shells are not treated using different approximations. In (8.55), h is the one-electron Schrodinger Hamiltonian... 

Table 9.26. The theoretical and experimental structural parameters for rutile (in A), numbers in parentheses indicate the percent deviation from low-temperature neutron-diffraction experiments. The references to the theoretical and experimental data, given in this table, can be found in [597]. SC,LC mean small-core and large-core pseudopotentials, AE -all electron calculations...

Fig. 17 (Color online) The Hg2o cluster for the calculation of the nearest-neighbour two-body increment in mercury. The central dark atoms are correlated, the light atoms in the surrounding are the embedding atoms deseribed with a large core pseudopotential and a valence-4 -basis only.

There are several sets of pseudopotentials for transition metals available in the literature. Pseudopotentials replace the chemically inert core electrons with a parametrized function. The appropriate core size of transition metals which should be replaced by a pseudopotential was unclear initially, but there is now general agreement that the outermost (n — l)s and (n — l)p core elections should not be replaced by a parametrized function, which means that the electron configuration of the transition metals becomes (n — l)s, (n — l)p, (n)s, (n — l)d. The corresponding functions are called small-core pseudopotentials. The use of large-core pseudopotentials for TMs, which leave only the ( )s and (n — l)d valence electrons, is discouraged. 

A table with a list of the most common pseudopotentials which are presently available is given by Frenking et al. The ECPs of Hay and Wadt and of Christiansen et al. " and the AIMPs of Huzinaga are available in a small-core and a large-core version. The ECPs of Stoll and Preuss and of Stevens et al. have a small core. 

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