Reconstructive clustering methods

Vaughan et al. (1987) propose that the rapid surface oxidation of bor-nite, and the products of this reaction, may result from the surface reconstruction that leads to Cu+ and Fe " being in approximately trigonal planar coordination. Calculations using the multiple-scattering Xa cluster method (MS-SCF-Aa) on Cu+ in tetrahedral and triangular planar coordination with sulfur (on CuS/ and CuSj - clusters see Tossell, 1978b ... 

In 1985 Car and Parrinello invented a method [111-113] in which molecular dynamics (MD) methods are combined with first-principles computations such that the interatomic forces due to the electronic degrees of freedom are computed by density functional theory [114-116] and the statistical properties by the MD method. This method and related ab initio simulations have been successfully applied to carbon [117], silicon [118-120], copper [121], surface reconstruction [122-128], atomic clusters [129-133], molecular crystals [134], the epitaxial growth of metals [135-140], and many other systems for a review see Ref. 113. 

Ground-State Energies from the ACSE with V, NY, and M 3-RDM Reconstructions Compared with the Energies from Several Wavefunction Methods, Including Hartree-Fock (HF), Second-Order Many-Body Perturbation Theory (MP2), Coupled-Cluster Singles-Doubles (CCSD), and Full Configuration Interaction (FCI), for Molecules in Valence Double-Zeta Basis Sets."... 

The ACSE has important connections to other approaches to electronic structure including (i) variational methods that calculate the 2-RDM directly [36-39] and (ii) wavefunction methods that employ a two-body unitary transformation including canonical diagonalization [22, 29, 30], the effective valence Hamiltonian method [31, 32], and unitary coupled cluster [33-35]. A 2-RDM that is representable by an ensemble of V-particle states is said to be ensemble V-representable, while a 2-RDM that is representable by a single V-particle state is said to be pure V-representable. The variational method, within the accuracy of the V-representabihty conditions, constrains the 2-RDM to be ensemble N-representable while the ACSE, within the accuracy of 3-RDM reconstruction, constrains the 2-RDM to be pure V-representable. The ACSE and variational methods, therefore, may be viewed as complementary methods that provide approximate solutions to, respectively, the pure and ensemble V-representabihty problems. 

One approach for identifying the type of iron center in a protein has been to remove the center, intact, by ligand exchange between the protein and an exogenous acceptor ligand (reviewed by Berg and Holm, 1982). The removed, or extruded, center is identified by comparison of its spectral properties (usually absorption spectrum) to known model compounds. Alternatively, the extruded center can be inserted into a second apoprotein which has been previously determined to accept only one type of iron center. The reconstructed standard protein is then analyzed by EPR. The latter method, interprotein cluster transfer, requires that acceptor apoproteins for all known classes of centers are included in the reaction mixture and that the reconstituted reporter ... 

In the case of adsorption of a vapor by a porous material, a three phase system in terms of SAS is produced pore/adsorbed film or capillary condensed vapor/solid. Since the s.l.d. of H2O and D2O are known while the pore space s.l.d. equals to zero, contrast matching conditions are achieved if an appropriate mixture of H2O/D2O that has the same s.l.d. as the solid is used as the adsorbate. In this case the adsorbed film as well as the condensed cluster of pores will cease to act as scatterers, and only the remaining empty pores will produce measurable scattering. In terms of SANS, contrast matching reduces the solid/film/pore system to a binary one [1]. By determining a number of scattering curves corresponding to the same sample equilibrated at various relative pressures, for both the adsorption and desorption branches of the adsorption isotherm, a correlation of the two methods could be possible. If the predictions of the Kelvin equation are in accordance with the SAS analysis, a reconstruction of the adsorption isotherm can be obtained from the SAS data [2]. 

An ideal tool for the investigation of the electronic structure of metal clusters is offered by scanning probe methods which have been used in three pioneering studies of nanometer-size clusters of Au on GaAs(llO) [229], Fe clusters on the same surface [230], and of size-selected Siio clusters on a reconstructed Au(OOl) surface [231], which all have been published already in 1989. In the first investigation [229], a characteristic spectrum of band-gap states was observed for the Au particles grown on GaAs. Both donor and acceptor states... 

The reconstruction of the Si(lll)7 X 7 surface is the largest known [25]. The unit cell contains 49 atoms per layer. When 5 to 8 layers are considered, this means that there are hundreds of atoms per unit cell. We have chosen the periodic extended Hiickel approach, EHT-TB [26,27]. Most of the calculations with more sophisticated methods use cluster models [28] or simplified unit cells [29]. The actual 7x7 reconstruction has been calculated by density functional method with the use of symmetry [30,31] for adsorption, the symmetry is reduced and does not lead to a similar benefit. Recently, the adsorption of 19 hydrogen atoms has been performed by LDA [28] this coverage retains most of the symmetry. 

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