Relativistic Pseudopotentials and Their Applications

Xiaoyan Cao and Anna Weigand Theoretical Chemistry, University of Cologne 

Computational Methods in Lanthanide and Actinide Chemistry, First Edition. Edited by Michael Dolg. 2015 John Wiley Sons, Ltd. Published 2015 by John Wiley Sons, Ltd. 

Besides the computational savings, ECPs have the advantage that they allow for the implicit inclusion of relativistic effects, even of the Breit interaction or quantum electrodynamic (QED) corrections, by simple parametrizations to relativistic AE data. Furthermore, ECPs permit the usage of smaller basis sets and thus the basis set superposition error is less significant compared to AE calculations. Even the difficulties due to open shells may be avoided by applying ECPs, if these open shells are included in the core system as it is the case for the 4f-in-core [7-9] and 5f-in-core [10-12] pseudopotentials (PP) for lanthanides and actinides, respectively. However, these PPs can only be applied, if the f orbitals do not participate significantly in chemical bonding (see Section 6.3.1). 

There are two main lines of ECPs, i.e., the model potential (MP) technique, which utilizes valence orbitals with a nodal stmcture corresponding exactly to those of the AE valence orbitals, and the PP scheme, which uses valence orbitals exhibiting a simplified nodal structure with respect to the AE valence orbitals, i.e., the so-called pseudovalence orbitals. This chapter will only focus on the PP approach, while the chapter from Barandi an and Seijo will deal with MPs. 

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. 

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Relativistic Pseudopotentials and Their Applications 169 Table6.9 Mean An "-O distances (in A) for [An " (hi20)c s ... 

Two methods are mainly responsible for the breakthrough in the application of quantum chemical methods to heavy atom molecules. One method consists of pseudopotentials, which are also called effective core potentials (ECPs). Although ECPs have been known for a long time, their application was not widespread in the theoretical community which focused more on all-electron methods. Two reviews which appeared in 1996 showed that well-defined ECPs with standard valence basis sets give results whose accuracy is hardly hampered by the replacement of the core electrons with parameterized mathematical functions" . ECPs not only significantly reduce the computer time of the calculations compared with all-electron methods, they also make it possible to treat relativistic effects in an approximate way which turned out to be sufficiently accurate for most chemical studies. Thus, ECPs are a very powerful and effective method to handle both theoretical problems which are posed by heavy atoms, i.e. the large number of electrons and relativistic effects. 

Before reviewing applications to large or extended systems (Section 4), we will illustrate the performance of various one- and two-component DKH-DF approaches using atoms and small molecules of heavy elements as benchmark systems. We will compare results of DKH calculations to those of four-component relativistic methods and other approaches based on transformed Hamiltonians. In many cases, results obtained with pseudopotentials are also available, but will be not considered here because of their computational efficiency, pseudopotential calculations are by far the most widely used strategy for heavy-element compounds. 

M. Dolg, X. Cao. Relativistic Pseudopotentials Their Development and Scope of Applications. Theor. Chem. Acc., 112 (2012) 403 80. 

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