Embedded cluster schemes

We have utilized the embedded cluster DV scheme to study the electronic structure of the Y(Ni] IMI)B2C superconductors (M=Fe, Co, and Ru), with 71 atom variational clusters centered on the substitutional site [109] as shown in Fig. 13. Bonding within the RC plane is found to be highly ionic, while B-C and Ni-B bonding structures are analyzed as typically covalent. In addition, the strong overlap between atoms in the transition metal plane has typical metallic character. Thus the entire spectrum of chemical bonding including ionic, covalent, and metallic structures is found within this peculiar crystal structure. The Ni-B slab is found to be electron-rich, as the result of charge transfer from the RC planes. 

Another pertinent question is related to the accuracy of the common approximation to describe relativistic effects at the pseudopotential level. Our AE scalar relativistic DKH scheme allows to evaluate the precision of the latter scheme. A relativistic pseudopotential [196] was utilized to treat the heavy element Pd in the Pd-0 complexes employing extended EPE-embedded cluster models of the quality comparable to that for the AE cluster model. This resulted in the adsorption energy value 123 kJ/mol and the Pd-0 bond length 213 pm. For the Pd-0 complexes under scrutiny the deviations from the corresponding scalar relativistic values, by 3 kJ/mol and 2 pm respectively, are rather small. Clearly, relativistic pseudopotentials for heavier atoms have to be constructed with due care [8]. The AE scalar relativistic DKH approach certainly provides an attractive alternative. 

Currently, the vast majority of cluster calculations for local properties of bulk oxides or oxide surfaces is performed by means of embedded clusters. Several embedding schemes have been proposed in the literature [6, 7]. A typical scenario used for modeling a local adsorption site at an oxide surface is depicted in Fig. 3. The whole cluster consists of three regions ... 

The embedded cluster approach is based on schemes that smoothly link the quantum-mechanical solution of the cluster to the perfect crystal. Different methods have been developed based on either Green function " or group-function (localized crystalHne orbitals) " techniques. 

We have employed an embedded cluster approach in which a QM cluster was embedded into a finite nano-cluster representation of the polarisable host lattice via the shell model. Relaxation of both electronic and ionic subsystems of the host lattice is performed self-consistently with the charge density of the QM cluster calculated using the B3LYP density functional. The self-consistent scheme of calculations has been described in more details elsewhere [82,83], The QM cluster used in these studies is shown in Fig, 4,5a, All anions and all fully coordinated cations have been treated as all electron atoms using the standard 6-3IG basis set. Cations at the border of the QM cluster have been treated using Hay and Wadt effective core pseudopotentials [84] and one contracted s-function. 

In order to describe the short-range correlations properly we developed an embedding scheme, where we can calculate the short-range correlations within finite embedded clusters, whereas the long-range part, which is neglected in the previous applications, has to be described within a random-phase approximation. " Regarding the further improvement of... 

One of the first cluster embedding schemes was put forth by Ellis and co-workers [172]. They were interested in studying transition metal impurities in NiAl alloys, so they considered a TMAl cluster embedded in a periodic self-consistent crystal field appropriate for bulk p -NiAl. The field was calculated via calculations, as was the cluster itself The idea was to provide a relatively inexpensive alternative to supercell DET calculations. 

Gutdeutsch U, Birkenheuer U, Kruger S and Rdsch N 1997 On cluster embedding schemes based on orbital space partitioning J. Chem. Phys. 106 6020... 

Further treatment with NH3 at 553 K promoted neither the catalytic performance nor further growth of the Re clusters. Thus the 120 min NH3 treatment gave the best performance of the Re-CVD/HZSM-5 catalyst for phenol synthesis. DFT calculations of Rejo cluster structures embedded in the pore of HZSM-5 revealed the most stabilized structure in the pore of HZSM-5 to be as shown in Scheme 10.4b. The edge-shared Rejo structure may be due to the structure and size of the pore ofthe HZSM-5 zeolite. A broader peak at 5 3.6 ppm than that of fresh HZSM-5 in the Al solid-state NMR spectrum implies a positive interaction between the A1 sites and the Reio clusters inside the pore of HZSM-5. 

Four kinds of supported Pd complexes are prepared (Scheme 3.13) catalyst I is the PEG-modified silica-supported Pd cluster catalyst II is the PEG-modified silica-supported (Cp)Pd(allyl) complex catalyst III is the silica-supported Pd cluster catalyst IV is the silica embedded in a thin PEG film-supported Pd cluster. 

Another way to treat the influence of the surrounding lattice on a cluster is to use the embedded or immersed cluster technique. A number of realizations of this scheme have been proposed. We shall merely mention the directions of the evolution of these schemes rather than considering the question in detail. One way is to match the cluster and band solutions. This method, generally based on the early works of Grimley, was realized in Pisani (22) within the scope of CNDO/2. The whole system being considered (support and adsorbate) was subdivided into the cluster (adsorbate and a part of adsorbent) and the environment. Then the self-consistent calculation was carried out at a fixed environment. This approach was used to compute the adsorption of H (22) and CO (23) on graphite. 

A particular scheme of introducing the pseudo-atom A depends both on the type of a quantum-chemical method and on a specified set of experimental properties whose reproduction is assumed to be the most important in the forthcoming investigations. This set of properties can also include, instead of experimental values, the values obtained by a more rigorous theoretical method (extended cluster, embedded or periodic cluster, band approach). In the scope of ZDO-type methods, the following parameters of pseudo-atom A can in principle be adjusted (77). 

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