Quantum chemical calculation molecular cluster model

Nevertheless, ab initio or semiempirical quantum chemical calculations, with clusters to represent the catalytic solid material, can help build up a model of the catalytic system and study effects of modifications [52], Even simulation of the molecular dynamics of the interaction between reactants or intermediates, together with replication of the unit cell of the catalytic solid in a simple force field, may describe observed effects in a catalytic system and may be able to predict the effect of catalyst modifications [53]. 

In this brief section on solids we will only consider molecular quantum-chemical calculations on clusters that serve as models for segments of crystals. We will not review band-structure or related calculations. This means that we will deal primarily with local phenomena related to lanthanide ions embedded in crystals. The calculations are... 

The requirements for Raman resonance that must be fulfilled are the following (120,121) (a) total symmetry of the vibrations with respect to the absorbing center, and (b) same molecular deformation induced by the electronic and vibrational excitations. Quantum chemical calculations (41) of the vibrational frequencies and the electronic structure of shell-3 cluster models allowed the assignment of the main vibrational features, as shown in Fig. 7. The 1125 cm-1 band is unequivocally assigned to the symmetric stretching of the Ti04 tetrahedron. 

Quantum chemistry has so far had little impact on the field of photoelectrochemistry. This is largely due to the molecular complexity of the experimental systems, which has prevented reliable computational methods to be used on realistic model systems, although some theoretical approaches to various aspects of the performance of nanostructured metal oxide photoelectrochemical systems have appeared in the last 10 years, see e.g. [139, 140, 141]. Here we have focussed on quantum-chemical cluster and surface calculations of a number of relevant problems including adsorbates and intercalation. These calculations illustrate the emerging possibilities of using quantum chemical calculations to model complicated dye-sensitized photoelectrochemical systems. 

While quantum-chemical calculations related to gas-phase reactions or bulk properties have become now a matter of routine, calculations of local properties and, in particular, surface reactions are still a matter of art. There is no simple and consistent way of adequately constructing a model of a surface impurity or reaction site. We will briefly consider here three main approaches (1) molecular models, (2) cluster models, and (3) periodic slab models. 

In addition, several quantum chemical calculations of hydrated clay minerals with organic molecules using small cluster models of minerals, which consist of only several Al, Si, O, and H atoms, were published. Using small molecular models, aqueous aluminum acetate complexes [100, 101] and hydrolysis of a three-membered aluminosilicate ring were studied [102], Using... 

Whereas selective diffusion can be better investigated using classical dynamic or Monte Carlo simulations, or experimental techniques, quantum chemical calculations are required to analyze molecular reactivity. Quantum chemical dynamic simulations provide with information with a too limited time scale range (of the order of several himdreds of ps) to be of use in diffusion studies which require time scale of the order of ns to s. However, they constitute good tools to study the behavior of reactants and products adsorbed in the proximity of the active site, prior to the reaction. Concerning reaction pathways analysis, static quantum chemistry calculations with molecular cluster models, allowing estimates of transition states geometries and properties, have been used for years. The application to solids is more recent. 

TABLE 38 Results of Semiempirical (MINDO/3) Quantum Chemical Calculations of Energies of the Highest Occupied Molecular Orbitals (HOMO) and Lowest Unoccupied Molecular Orbitals (LUMO) for a Series of Aromatic Adsorbates and Model Carbon Clusters... 

Atomistic classical molecular dynamics modeling as well as quantum chemical calculation for small molecular species can give both insight and fundamental data on nucleation and cluster growth processes. 

A specialized MOPAC computer software package and, in particular, its PM3 quantum-chemical program has been successfully applied in calculations. The results of calculations have shown that both oxygen atoms form bonds with two more active carbon atoms of CP molecular cluster (so-called bridge model of adsorption). The total energy of system after a chemical adsorption at such active atoms is minimal. 

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