Relativistic methods scalar effects

Quantum mechanical methods have been used to calculate Sn NMR properties such as chemical shifts and coupling constants, for stannane, tetramethylstannane, methyltin halides, tin halides, and some stannyl cations. Relativistic effects were included by using the ZORA method. Each method allows the possibility of including only scalar effects or spin orbit coupling as well. " Sn chemical shifts and spin-spin couplings were calculated and compared to experimental values. A favorable correlation was shown for the chemical shifts, except for organotin species where heavy atoms are bound to tin, in which case a good correlation was obtained only at the spin-orbital level. Therefore, it is clear that relativistic effects must be considered for these heavy-element tin systems. 

The different approximations for all-electron relativistic calculations using one-component methods have recently been compared with each other and with relativistic ECP calculations of TM carbonyls by several workers (47,55). Table 6 shows the calculated bond lengths and FBDEs for the group 6 hexacarbonyls predicted when different relativistic methods are used. The results, which were obtained at the nonrelativistic DFT level, show the increase in the relativistic effects from 3d to 4d and 5d elements. It becomes obvious that the all-electron DFT calculations using the different relativistic approximations—scalar-relativistic (SR) zero-order regular approximation (ZORA), quasi-relativistic (QR) Pauli... 

Scalar relativistic (mass-velocity and Darwin) effects for the valence electrons were incorporated by using the quasi-relativistic method (55), where the first-order scalar relativistic Pauli Hamiltonian was diagonalized in the space of the nonrelativistic basis sets. The Pauli Hamiltonian used was of the form... 

Diatomic molecules containing heavy elements are often used as benchmark of relativistic methods because they are small enough to be treated by demanding approaches like four-component methods nevertheless, diatomics with a variety of chemical bonds afford a thorough testing. To illustrate the accuracy of the DKH approach to relativistic DF calculations, we chose Auz and Bi2. Au2 shows predominantly scalar relativistic effects, spin-orbit interaction is not important because bonding is predominantly mediated by the interaction of the... 

The Douglas-Kroll approach to relativistic electronic structure theory in the framework of density functional theory was reviewed focussing on recent method developments and illustrative applications which demonstrate the capabilities of this approach. Compared to other relativistic methods, which often are only applied to small molecules for demonstration purposes, the DK approach has been used in a variety of fields. Besides the very popular pseudopotential approach, which accounts for relativistic effects by means of a potential replacing the core electrons, until now the scalar relativistic variant of the second-... 

Shamov GA and Schreckenbach G 2005 Density functional studies of actinyl aquo complexes studied using small-core effective core potentials and a scalar four-component relativistic method. The Journal of Physical Chemistry A 109(48), 10961-10974. 

We extend the method over all three rows of TMs. No systematic study is available for the heavier atoms, where relativistic effects are more prominent. Here, we use the Douglas-Kroll-Hess (DKH) Hamiltonian [14,15] to account for scalar relativistic effects. No systematic study of spin-orbit coupling has been performed but we show in a few examples how it will affect the results. A new basis set is used in these studies, which has been devised to be used with the DKH Hamiltonian. 

All calculations were carried out with the software MOLCAS-6.0 [16]. Scalar relativistic effects were included using a DKH Hamiltonian [14,15]. Specially designed basis sets of the atomic natural orbital type were used. These basis sets have been optimized with the scalar DKH Hamiltonian. They were generated using the CASSCF/CASPT2 method. The semi-core electrons (ns, np, n — 3,4, 5) were included in the correlation treatment. More details can be found in Refs. [17-19]. The size of the basis sets is presented in Table 1. All atoms have been computed with basis sets including up to g-type function. For the first row TMs we also studied the effect of adding two h-type functions. 

In this paper we present the first application of the ZORA (Zeroth Order Regular Approximation of the Dirac Fock equation) formalism in Ab Initio electronic structure calculations. The ZORA method, which has been tested previously in the context of Density Functional Theory, has been implemented in the GAMESS-UK package. As was shown earlier we can split off a scalar part from the two component ZORA Hamiltonian. In the present work only the one component part is considered. We introduce a separate internal basis to represent the extra matrix elements, needed for the ZORA corrections. This leads to different options for the computation of the Coulomb matrix in this internal basis. The performance of this Hamiltonian and the effect of the different Coulomb matrix alternatives is tested in calculations on the radon en xenon atoms and the AuH molecule. In the atomic cases we compare with numerical Dirac Fock and numerical ZORA methods and with non relativistic and full Dirac basis set calculations. It is shown that ZORA recovers the bulk of the relativistic effect and that ZORA and Dirac Fock perform equally well in medium size basis set calculations. For AuH we have calculated the equilibrium bond length with the non relativistic Hartree Fock and ZORA methods and compare with the Dirac Fock result and the experimental value. Again the ZORA and Dirac Fock errors are of the same order of magnitude. 

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