Cluster model calculations

Pacchioni G, Illas F. 2003. Electronic structure and chemisorption properties of supported metal clusters model calculations. In Wieckowski A, Savinova ER, Vayenas CG. editors. Catalysis and Electrocatalysis at Nanoparticle Surfaces. New York Marcel Dekker. 

The allyl-resonance stabilized E- and Z-pent-l,3-dienyl-2-cations (22 and 23) are the smallest member of vinyl cations observed as persistent species in superacid solution 49 These are difficult to generate experimentally50 but structures with only five heavy atoms are suitable candidates for coupled cluster model calculations. A challenging task of quantum chemistry was to assign the 13C NMR spectrum of the mixture of isomers (Fig. 3), which exhibits pairs of signals of 22 and 23 which differ only by a few ppm, to the chemical shifts for the specific carbon atoms of the E- and Z-isomers, respectively. 

Lu, X. and Lin, M. C. Bonding configurations of acetylene adsorbed on the Si(100)-2x 1 surface predicted by density functional cluster model calculations. Physical Chemistry Chemical Physics 2, 4213 1217 (2000). 

Alternatively, it is proposed that a comparison between theoretical frequencies obtained from cluster model calculations and experimental spectra is a worthwhile approach to study and assign the vibrational frequencies of oxy-anions adsorbed on single-crystal electrodes. 

Ab initio B3LYP cluster model calculations have been performed to describe the adsorptive behaviour of NO on MgO solid [108]. The most preferable configurations of the NO, NO22" and N2O32 surface complexes were determined. The calculated IR frequencies of these species accounted well for the temperature dependence of the experimental IR spectra. 

Konecny R. (2001) Reactivity of hydroxyl radicals on hydroxylated quartz surface. 1. Cluster model calculations. J Phys Chem B 105 6221-6226. 

Deformation density calculations [66] based on X-ray and neutron diffraction data indicated a substantial electron deficiency in the sulphur valence shell. Kappa refinement based on the point charge model relates a positive charge close to 1.8 to the sulphur, and about -1.0 on each of the sulphate oxygen atoms [66]. The comparison of these results to those obtained from MO cluster model calculations, provides an indication of the goodness of the applied atomic basis sets. Such a comparison is presented in Table 4. 

Fig. 20. Geometric structure of the (010) oriented single crystal surface of orthorhombic M0O3. Molybdenum (oxygen) centers are shown by large (small) balls and non-equivalent oxygen sites, 0(1, 2, 3), are labeled accordingly. The M015O56 surface section used in cluster model calculations is shown by shaded balls.

Figure 1. Ag2 adsorption on rutile (110) models for cluster model calculations. Structures a to c are optimized, d to f are initial atructures. - Ti, - O, - Ca, - Ag.

Electronic Structure and Chemisorption Properties of Supported Metal Clusters Model Calculations Gianfranco Pacchioni and Francesc Idas... 

For x-ray emission spectroscopy(XES), the accurate peak intensity can be evaluated by the calculation of dipole transition matrix, though the partial DOS usually give a good approximation. The theoretical analysis by the cluster model calculation is exhibited to be very useful for the investigations of the... 

X-ray absorption near edge structure(XANES) and electron energy loss near edge structure(ELNES) show similar spectra, thus almost the same theoretical analysis is valid both for these spectroscopies. The careful analysis including higher excited atomic orbitals in the basis set reproduce very well the spectral structure even in details. The core-hole effects are sometimes very important in the excited state electronic state. The theoretical analysis by the cluster model calculation provides very useful information on the local electronic property and the micro structure. 

VPI-5 is an aluminophosphate framework with very large one-dimensional pores defined by 18-member ring[22]. The crystal structure report[7j of synthesized VPI-5 revealed the possible role of water molecules as templates. The use of VPI-5 as a molecular sieve and as a catalyst primarily depend on the removal of the occluded water molecules without the destruction of the framework structure. Prasad et al.[23] reported from their TGA experiment that the seven distinct types of water molecules could be desorbed from VPI-5 in a step-wise fashion, in the temperature range of 35 to 60°C. The cluster model calculations[24] have revealed the actual electronic interaction of water molecules with VPI-5 framework. CG technique also indicated that the void volume in VPI-5 could be controlled by the partial removal of water molecules. 

The CG picture of the structure of the water network in VPI-5 molecular sieve as reported by the high resolution synchrotron powder diffraction study[7] is shown in Fig. 5. As mentioned earlier, quantum chemical cluster model calculations by MNDO method have also shown that the energetically favourable sites for the adsorption of water is in correspondence with the experimental reports. 

Due to the covalent nature of chemical bonding, properties of zeolitic protons depend on local electronic structure details. This is illustrated in Fig. 10 [105]. Using a basis set that predicts the NMR quadrupole coupling constants (QCC), accurately measured QCCs in zeolite ZMS-5 for Al tetrahedra in the proton form and deprotonated Al tetrahedra (e.g., by cation exchange) are compared with predicted QCCs from cluster model calculations. One... 

This area has received special attention from theoreticians. The most commonly used methodology for the calculation of the particle(ion)-metal interaction is to approximate the metal surface with a cluster of several atoms with the crystallographic organization typical of the metal studied. Although such an approach has many limitations and introduces certain difficulties, cluster-model calculations are becoming more popular in studies of interfacial interactions. Section 3.10.2 gives a brief review of quantum studies related to adsorption on metal surfaces in the cluster model approximation. In Section 3.10.3 a more detailed analysis of some aspects of this methodology is described, and is related to some recently published work on the problem of specific adsorption phenomenon. 

The density functional techniques that have been developed and significantly improved in the last decade have beeome a very tempting alternative to cluster-model calculations. They enable calculations to be performed at an electron-correlated level at a cost similar to that of the standard Hartree-Fock method. Some very recent studies performed in our laboratory by the application of DFT techniques to the calculation of the water-metal " and the ion-metal " " " interactions are summarized in Section 3.10.3. 

The B3LYP method applied to the cluster-model calculations... 

Because the new DFT techniques had not yet been applied to cluster-model calculations, many preliminary tests had to be performed to eliminate most uncertainty factors. First of all, from the variety of DFT functionals and the basis sets proposed in the literature one must select the combination which performs best for the system studied. This usually means that a large set of tests must be performed for a small sample representing the system of interest in the cluster caleulations. In the simplest approach, these tests can be performed by assuming that the metal cluster is re-... 

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