Quasi-relativistic pseudopotentials

At MP2/VTZ + D + P. Quasi-relativistic pseudopotentials were used for Si, Ge, Sn, Pb, from Ref. 93. At MP2/CEP. Compact effective core potentials (CEPs) were used for C and Si. Their relativistic counterparts (RCEP) were used for Ge, Sn and Pb. Correction for basis set superposition errors is included, from Ref. 95. 

At MP4SDQ with a quasi-relativistic pseudopotential for Pb from Reference 44. 

Calculated at B3LYP/DZ+P. The core electrons of all group 14 elements were replaced by quasi-relativistic pseudopotentials. KRS = Kapp, Remko and Schleyer from... 

At MP2/VDZ+P, quasi-relativistic pseudopotentials were used for Si to Pb from Reference 473. cAt MP2/6-31G(d) from Reference 4. 

The first calculation of the complete hydroformylation cycle with Rh-phosphine catalysts (substrate = ethylene, model ligand = PH3) was published in 1997 [3]. The QM methods used are HF and MP2, respectively (cf. Section 3.1.2.1). Hybrid DFT methods such as B3LYP [4], however, are more appropriate in terms of both accuracy and efficiency [5, 6] (cf. Section 3.1.2.1). Therefore, the same model system was recalculated [7] on the level B3LYP functional/DZVP basis set [8]/quasi-relativistic pseudopotentials on rhodium [9]. Since homologous Ir catalysts are interesting alternatives from an economic point of view [10], calculations with the central metal Ir were also made. This comparative treatment is supported by the experimental assumption of a common mechanism [11], which equals the Heck-Breslow mechanism of the cobalt-catalyzed reaction [12],... 

Spin-orbit (SO) coupling corrections were calculated for the Pt atom since the relativistic effects are essential for species containing heavy elements. Other scalar relativistic corrections like the Darwin and mass-velocity terms are supposed to be implicitly included in (quasi)relativistic pseudopotentials because they mostly affect the core region of the considered heavy element. Their secondary influence can be seen in the contraction of the outer s-orbitals and the expansion of the d-orbitals. This is considered in the construction of the pseudoorbitals. The effective SO operator can be written within pseudopotential (PS) treatment in the form71 75... 

While many organometallic dusters with interstitial atoms are known, the detailed nature of the bonding of these interstitial atoms, usually H, B, C, N, P, Si, Ge, etc., with the metal atoms of the duster has been ad essed in very few theoretical studies. [239, 248, 250, 283] In a comparative relativistic DV-Xa investigation [239, 2M] on a series of octahedral duster ions [(R3P)Au] X ", where Xj = B, X2 = C, and X3 = N, it was shown that the central atom formally takes up electrons that would otherwise reside in energetically unfavorable molecular orUtals. In this way, the central atom contributes to the stabilization of the duster by forming radial bonds to the Au atoms. This has also been found in quasi-relativistic pseudopotential calculations on ligand fiee, element centered gold dusters. [285]... 

Figure 7 Dissociation energies of the lanthanide monoxides from quasi-relativistic pseudopotential calculations for the 4f"(T (SC I) and 4f (SC II) superconfigurations in comparison to experimental data (exp) ...

Similarly as in Section 1.2, one starts from atomic AE reference calculations at the independent-particle level (some kind of quasi-relativistic HF or fully relativistic DHF). The first step now in setting up pseudopotentials consists in a smoothing procedure for valence orbitals/spinors ( pseudo-orbital transformation ). In the DHF case, to be specific, the radial part ( )/ of the large component of the energetically lowest valence spinors for each //-combination is transformed according to... 

Pseudopotentials (PP) were originally proposed to reduce the computational cost for the heavy atoms with the replacement of the core orbitals by an effective potential. Modern pseudopotentials implicitly include relativistic effects by means of adjustment to quasi-relativistic Har-tree-Fock or Dirac-Hartree-Fock orbital energies and densities [35]. In the present research, we adopted Peterson s correlation-consistent cc-pVnZ-PP (n — D, T, Q, 5) basis sets [23] with the corresponding relativistic pseudopotential for the Br atom. The corresponding cc-pVnZ (n = D, T, Q, 5) basis sets were used for the O and H atoms. The optimized geometries and relative energies for the stationary points are reported in Table 1 and Fig. 3, and the harmonic vibrational frequencies and zero-point vibrational energies are reported in Table 4. 

Pseudopotential parameters are usually derived from quasi-relativistic atom calculations, which consider the most important relativistic terms. One important exception is the set of ECPs published by Hay and Wadt which are found in the program package Gaussian, where the first TM row is parametrized nonrelatiMstically. Calculations have shown that relativistic effects are usually negligible for the elements Sc-Zn, except for Cu. ... 

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