Embedded Cluster Methods

Kruger S and Rdsch N 1994 The moderately-large-embedded-cluster method for metal surfaces a density-functional study of atomic adsorption J. Phys. Condens Matters 8149... 

Introduction of partial order at finite temperatures adds another level of complexity and difficulty. This situation is handled by the cluster variation method (CVM) free energy functional, which is expressed as a function of multisite correlation functions, whose coefficients are obtained by the generalized perturbation method (GPM) or the embedded cluster method (ECM). All of these methods are highly computationally intensive at present, this area is probably the principal frontier of alloy phase theory. 

It is also possible to include in addition to the ionic part an additional external potential Vg t in the Hamiltonian in Eq. (11) in the self-consistent procedure. This could be the long-range static potential from a surrounding crystalline environment, as used in the embedded cluster method. Fig. 7. Clusters are here used to model a small section of an infinite solid or surface. 

Application of the Embedded Cluster Method to the Electronic State of Silicate Glasses... 

Thus we find the embedded cluster method, with a modest number of atoms in the variational space, is very useful to discuss experimental UPS spectra quantitatively and we can get reliable electronic state information on silicate clusters with reasonable computational time. 

We have used the DV-Xa embedded cluster method which is explained in detail elsewhere (3,4). Here we give a summary of main feature. The DV-Xa method is based on density functional theory in which the Coulomb and exchange potential energy is a functional of the electronic density. 

Since many experimental studies of 7-Fe were performed for 7-Fe particles in a Cu matrix (or Cu alloy, including Cu-Al) [113], [114], it is important to probe the electronic structure of the particle-matrix systems. Embedded-cluster methods are ideally taylored to treat small particles of a metal in a host matrix, a system that would require a very large supercell in band-structure calculations. DV calculations were performed for the 14-atom Fe particle in copper shown in Fig. 21 [118]. Spin-density contour maps were obtained to assess the polarization of the Cu matrix by the coherent magnetic 7-Fe particle. Examples are given in Figs. 22 and 23 for a Fe particle in Cu and 7-Fe in Cu with two substitutional Al. If the matrix is a Cu-Al alloy, this element is known to penetrate the Fe particle [114]. 

In a recent series of articles [179-181], Seijo and Barandiaran have investigated the spectroscopy of several actinide impurities (Pa" - -, and in crystal environments. In particular, they discuss the relative position of the 5 and 5/ " 6i/ manifolds (see also chapter 7 of this book). All calculations use relativistic large-core AIMPs on the actinide centres and on the chlorine ligands. The transferability of these frozen core potentials from the neutral / elements to their cation has been discussed in Ref [182]. The crystal environment is described by the AIMP embedding cluster method. Electron and spin-orbit interactions are treated simultaneously by the three-step spin-fi e-state-shifted method detailed in section 2.2.5, using either MRCI or CASSCF/MS-CASPT2 methods in the spin-fi ee step. The active space includes the 5/ and 6d orbitals of the actinide centre, as well as the Is orbitals in order to avoid the prob-... 

In the case of localized states related to the dopants—including transition-metal (TM) and rare-earth (RE) ions—the effect of hydrostatic pressure on the local energetic stmcture and electronic transitions is simulated by the reduction of the size of the cluster, which includes the dopant ion and the ligands. The influence of pressure on the energetic stmcture of the TM and RE ions can be simulated using crystal-field phenomenological model calculations [10-12]. However, a more advanced approach, i.e., ah initio model potential embedded-cluster method, also has been used [13]. 

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