Embedded cluster calculations

L. Seijo and Z. Barandiaran. The ab initio model potential method A common strategy for effective core potential and embedded cluster calculations. In J. Leszczynski, (ed), Computational chemistry Reviews of Current Trends, 4, pp. 55-152, World Scientific, Singapore, 1999. 

Extensive DFT and PP calculations have permitted the establishment of important trends in chemical bonding, stabilities of oxidation states, crystal-field and SO effects, complexing ability and other properties of the heaviest elements, as well as the role and magnitude of relativistic effects. It was shown that relativistic effects play a dominant role in the electronic structures of the elements of the 7 row and heavier, so that relativistic calculations in the region of the heaviest elements are indispensable. Straight-forward extrapolations of properties from lighter congeners may result in erroneous predictions. The molecular DFT calculations in combination with some physico-chemical models were successful in the application to systems and processes studied experimentally such as adsorption and extraction. For theoretical studies of adsorption processes on the quantum-mechanical level, embedded cluster calculations are under way. RECP were mostly applied to open-shell compounds at the end of the 6d series and the 7p series. Very accurate fully relativistic DFB ab initio methods were used for calculations of the electronic structures of model systems to study relativistic and correlation effects. These methods still need further development, as well as powerful supercomputers to be applied to heavy element systems in a routine manner. Presently, the RECP and DFT methods and their combination are the best way to study the theoretical chemistry of the heaviest elements. 

Binding energies, De, and frequency shifts, Aco, for CO adsorbed on various sites of the MgO (100) surface from embedded cluster calculations... 

The inclusion of impurity atoms in MgO is much more interesting from a chemical point of view when alkali metals are used to replace Mg ions. In fact, this results in trapped-hole centers. The MVO pairs have been extensively studied in the bulk of alkaline-earth oxides by optical studies, EPR and ENDOR measurements [185,186] as well as by embedded cluster calculations [187]. The LiVO ions create an effective dipole which polarizes the surrounding lattice, with the two ions moving toward each other. The presence of an O radical, however, is most interesting when one is dealing with surface properties. This center in fact is very reactive and is the subject of the next paragraph. 

FeibelmanPJ (1998) Interlayer self-diffusion on stepped Pt(111). Phys Rev Lett 81 168-171 Fisher AJ, Harding JH, Harker AH, Stoneham AM (1991) Embedded cluster calculations of defect processes. Rev Solid State Sci 2 133-147... 

The Ab Initio Model Potential Method A Common Strategy for Effective Core Potential and Embedded Cluster Calculations (L. Seijo Z. Barandiaran)... 

Fig. 2.2. Space partitioning in EPE embedded cluster calculations. I - internal region treated at a QM level II - shell model enviromnent of the QM cluster subdivided into regions of explicit optimization (Ila), of the effective (Mott-Littleton) polarization (lib) and of the external area (lie). The sphere indicates an auxiliary surface charge distribution which represents the Madelung field acting on the QM cluster (dashed line).

Relativistic Ab Initio Model Potential embedded cluster calculations on the structure and spectroscopy of local defects created by actinide impurity ions in solid hosts are the focus of attention here. They are molecular like calculations which include host embedding effects and electron correlation effects, but also scalar and spin-orbit coupling relativistic effects, all of them compulsory for a detailed understanding of the large manifolds of states of the 5f" the 5f" 6d configurations. The results are aimed at showing the potentiality of Relativistic Quantum Chemistry as a tool for prediction and interpretation in the field of solids doped with heavy element impurities. 

The AIMP method as a common strategy for effective core potential calculations in molecules and for embedded cluster calculations, has been detailed and reviewed [17]. In this paper, we will pay special attention to its applications in the field of structure and spectroscopy of crystal defects created by actinide element impurities, where relativistic effects are a determinant factor, electron correlation and host embedding effects are also key elements, and not only the ground state but also large manifolds of hundreds of excited states are involved in the chemical and physical processes of interest. 

This is the Hamiltonian used in the calculations presented in Section 3. Simple changes in it, which are explicit in 2.1.2, would lead to a DKH-AIMP embedded cluster Hamiltonian. Embedding AIMPs have been obtained for a number of halide and oxide crystals [37]. AIMP embedded cluster calculations can readily be performed with the MOLCAS code [15]. 

Very briefly, the characteristics of the AIMP/SM method for embedded cluster calculations with relaxation and electric dipole polarisation of the environment are the following (i) The Group Function Theory expression for the total energy of a system that has been partitioned in a cluster and an environment is adopted. 

In this Section, we will show the results of sfss CGWB-AIMP embedded cluster calculations on the structure and spectroscopy of several actinide ions in chloride hosts. Altogether, they are aimed at showing the potentialities of present days wavefunction-based ab initio methods of Quantum Chemistry in materials made of heavy element ions in solids, with several open-shell electrons and a very large number of excited states of interest. 

Ning et al. calculated the electronic properties and 4/ 5d transitions of Ce " substituted at the La and Ca " sites of La2CaBioOi9 crystal using the hybrid function theory and wave function-based embedded cluster calculation [94]. The PBE, PBEO, and HSE06 functional calculation band gaps are 4.1, 8.1 and... 

J. A. Mejias and J. F. Sanz Unrestricted compact model potentials for ab initio embedded cluster calculations Magnetic interactions in KNiFa, J. Chem. Phys. 102, 850-858 (1995). 

The first two-periodic all-electron HP LCAO calculations of the rutile relaxed surfaces, made in [779], gave atomic displacements of surface atoms that did not differ significantly from the later results of DPT-PW investigations. Purther periodic LCAO studies of Ti02 bare surfaces have been made in [777,799,800]. Por studies of H2O adsorption on Ti02 the single-slab periodic HP-LCAO and DPT-LCAO methods were first applied in [790] and compared with PW-DPT results to test various methods with cyclic- and embedded-cluster calculations and resolve discrepancies between the methods. 

Embedded-cluster calculations were carried out on stoichiometric clusters of different size Ti70i4, Tii3026 and Tii70s4 (the largest cluster is shown in Figures 11.14 and 11.15). 

The results for embedded-cluster calculations are different from that for the periodic models. Adsorption energies of a water molecule in the cluster case were much more favorable for the associative mechanism (Table 11.13), which is in better agreement with experimental observations. The predicted adsorption energies for the asso-... 

Herschend B, Baudin M, Hermansson K CO adsorption on Ce02(l 10) using hybrid-DFT embedded-cluster calculations, Chem Phys 328(1—3) 345—353, 2006. 

Figure 9.4(a) shows the energy curves obtained in the embedded cluster calculations including host effects, 68 valence electron correlation, and relativistic effects up to spin-orbit coupling [29], Above the dense 5/ and 5f6d(t2g) manifolds, and below the 5f6d eg) states, a set of levels appear from 62000 to 76000 cm that can be identified with what... 

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