Density functional theory scalar relativistic

Assuming that substituted Sb at the surface may work as catalytic active site as well as W, First-principles density functional theory (DFT) calculations were performed with Becke-Perdew [7, 9] functional to evaluate the binding energy between p-xylene and catalyst. Scalar relativistic effects were treated with the energy-consistent pseudo-potentials for W and Sb. However, the binding strength with p-xylene is much weaker for Sb (0.6 eV) than for W (2.4 eV), as shown in Fig. 4. 

Suzumura, T., Nakajima, T. and Hirao, K. (1999) Ground-state properties of MH, MCI, and M2 (M—Cu, Ag, and Au) calculated by a scalar relativistic density functional theory International Journal of Quantum Chemistry, 75, lVJ-1. ... 

Schreckenbach, G., Ziegler, T., 1997a, Calculation of NMR Shielding Tensors Based on Density Functional Theory and a Scalar Relativistic Pauli-Type Hamiltonian. Application to Transition Metal Complexes , Int. J. 

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. 

In subsection 3.1, we will present GGA and LDA calculations for Au clusters with 6first principles method outlined in section 2, which employs the same scalar-relativistic pseudo-potential for LDA and GGA (see Fig 1). These calculations show the crucial relevance of the level of density functional theory (DFT), namely the quality of the exchange-correlation functional, to predict the correct structures of Au clusters. Another, even more critical, example is presented in subsection 3.2, where we show that both approaches, LDA and GGA, predict the cage-like tetrahedral structure of Au2o as having lower energy than amorphous-like isomers, whereas for other Au clusters, namely Auig, Au ... 

Autschbach and Ziegler presented relativistic spin-spin coupling constants based on the two-component ZORA formulation. They published four papers. In the first paper of their series, only the scalar relativistic part was included, and a full inclusion of the ZORA effects was implemented in the second paper. They used the density functional theory (DFT) approach. The first paper showed that scalar relativistic calculations are able to reproduce major parts of the relativistic effects on the one-bond metal-ligand couplings of systems containing Pt, Hg and Pb. It was found that the... 

Density functional theory (DFT) provides an accurate and inexpensive access to molecular electronic structure and properties and was already used for scalar relativistic EFG calculations for example on Fe in solids [145] or in molecules [146,147]. We will not report on nonrela-tivistic DFT EFG calculations here but focus on the ZORA [148-151] and especially ZORA-4 methods, the latter including the density from the small component. Since the ZORA method is a two-component method sizable picture change effects will occur when calculating a core property like the EFG. In order to briefly illustrate this method a few of the fundamental equations will be given. A concise treatment of the ZORA formalism and its applications can be found in [152]. 

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-... 

Magnetization can be calculated from first principles by band theory. Calculation methods are usually separated into (i) scalar-relativistic calculations and (ii) full-relativistic calculations. The scalar-relativistic calculations can predict the occurrence of ferromagnetism, the value of the spin moment, and several nonmagnetic properties. The fuU-relativistic calculations are additionally able to determine the magnetocrystalline anisotropy and the induced orbital moment. The most common approach uses the formalism of local density approximation (LDA) to the density functional theory (DFT) [10]. 

The field of relativistic electronic structure theory is generally not part of theoretical chemistry education, and is therefore not covered in most quantum chemistry textbooks. This is due to the fact that only in the last two decades have we learned about the importance of relativistic effects in the chemistry of heavy and super-heavy elements. Developments in computer hardware together with sophisticated computer algorithms make it now possible to perform four-component relativistic calculations for larger molecules. Two-component and scalar all-electron relativistic schemes are also becoming part of standard ab-initio and density functional program packages for molecules and the solid state. The second volume of this two-part book series is therefore devoted to applications in this area of quantum chemistry and physics of atoms, molecules and the solid state. Part 1 was devoted to fundamental aspects of relativistic electronic structure theory. Both books are in honour of Pekka Pyykko on his 60 birthday - one of the pioneers in the area of relativistic quantum chemistry. 

F. Aquino, N. Govind, J. Autschbach. Scalar Relativistic Computations of Nudear Magnetic Shielding and -Shifts with the Zeroth-Qrder Regular Approximation and Range-Separated Hybrid Density Functionals. /. Chem. Theory Comput., 7 (2011) 3278-3292. 

Aquino F, Govind N and Autschbach J 2011 Scalar relativistic computations of nuclear magnetic shielding and g-shifts with the zeroth-order regnlar approximation and range-separated hybrid density functionals. J. Chem. Theory Comput. 7, 3278-3292. 

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