Relativistic pseudopotential approximation

A comparison of different methods was undertaken for the hydride of element 111 (Seth et al. 1996). The conclusion of this study was that Dirac-Fock calculations, all-electron DKH calculations and relativistic pseudopotential calculations give very similar results, showing that relativistic effects are also well described in the more approximate methods. A large relativistic bond length contraction of about 50 pm was found, which makes the bond length of (111)H even slightly shorter than that of AuH, which is 152.4 pm, with a relativistic effect of the order of 20 pm (see Kaldor and Hess 1994). 

Relativistic effective core potential (RECP) methods, also called relativistic pseudopotential (PP) methods, are probably the most successful approximate methods for the various properties of molecules containing heavy atoms. 

Another pertinent question is related to the accuracy of the common approximation to describe relativistic effects at the pseudopotential level. Our AE scalar relativistic DKH scheme allows to evaluate the precision of the latter scheme. A relativistic pseudopotential [196] was utilized to treat the heavy element Pd in the Pd-0 complexes employing extended EPE-embedded cluster models of the quality comparable to that for the AE cluster model. This resulted in the adsorption energy value 123 kJ/mol and the Pd-0 bond length 213 pm. For the Pd-0 complexes under scrutiny the deviations from the corresponding scalar relativistic values, by 3 kJ/mol and 2 pm respectively, are rather small. Clearly, relativistic pseudopotentials for heavier atoms have to be constructed with due care [8]. The AE scalar relativistic DKH approach certainly provides an attractive alternative. 

W i) is an integral operator with kernel W p, p ) and V p, p ) is the Fourier-transformed external potential. Hess s code has been implemented in several program codes like TURBOMOLE or MOLCAS3. Most of the applications are carried out scalar (one-component) without spin-orbit coupling and usually the two-electron operator is chosen as the simple Coulomb operator. This scheme (extended to spin-orbit coupling it necessary) leads to very accurate molecular properties for even the heaviest elements. A large number of applications in the chemistry of heavy elements are carried out by using either the scalar relativistic pseudopotential or density functional approximations. The pseudopotentials most widely used are linear... 

We briefly discuss the performance of the relativisitic pseudopotential approximation with respect to all-electron methods, as this is the most widely used relativistic... 

An efficient way to solve a many-electron problem is to apply relativistic effective core potentials (RECP). According to this approximation, frozen inner shells are omitted and replaced in the Hamiltonian hnt by an additional term, a pseudopotential (UREP)... 

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. 

Relativistic effects may be also considered by other methods than pseudopotentials. It is possible to carry out relativistic all-electron quantum chemical calculations of molecules. This is achieved by various approximations to the Dirac equation, which is the relativistic analogue to the nonrelativistic Schrodinger equation. We do not want to discuss the mathematical details of this rather complicated topic, which is an area where much progress has been made in recent years and where the development of new methods is a field of active research. Interested readers may consult published reviews . A method which has gained some popularity in recent years is the so-called Zero-Order Regular Approximation (ZORA) which gives rather accurate results ". It is probably fair to say that... 

A further reduction of the computational effort in investigations of electronic structure can be achieved by the restriction of the actual quantum chemical calculations to the valence electron system and the implicit inclusion of the influence of the chemically inert atomic cores by means of suitable parametrized effective (core) potentials (ECPs) and, if necessary, effective core polarization potentials (CPPs). Initiated by the pioneering work of Hellmann and Gombas around 1935, the ECP approach developed into two successful branches, i.e. the model potential (MP) and the pseudopotential (PP) techniques. Whereas the former method attempts to maintain the correct radial nodal structure of the atomic valence orbitals, the latter is formally based on the so-called pseudo-orbital transformation and uses valence orbitals with a simplified radial nodal structure, i.e. pseudovalence orbitals. Besides the computational savings due to the elimination of the core electrons, the main interest in standard ECP techniques results from the fact that they offer an efficient and accurate, albeit approximate, way of including implicitly, i.e. via parametrization of the ECPs, the major relativistic effects in formally nonrelativistic valence-only calculations. A number of reviews on ECPs has been published and the reader is referred to them for details (Bala-subramanian 1998 Bardsley 1974 Chelikowsky and Cohen 1992 Christiansen et... 

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