Point molecular-cluster model

The idea to use relatively small cyclic clusters for comparative perfect-crystal and point-defect calculations appeared as an alternative to the molecular-cluster model in an attempt to handle explicitly the immediate environment of the chemisorbed atom on a crystalline surface [285] and the point defects in layered solids [286,287] or in a bulk crystal [288,289,292,293]. The cluster is formed by a manageable group of atoms around the defect and the difference between the molecular-cluster model (MCM) and the cychc cluster model (COM) is due to the choice of boundary conditions for the one-electron wavefunctions (MOs). Different notations of COM appeared in the literature molecular vmit ceU approach [288], small periodic cluster [286], large rmit cell [289,290]. We use here the cychc cluster notation. 

LCAO calculations of the charged point defects in metal oxides are made mainly in the molecular-cluster model, considered in the next section. As we already noted PW molecular-cluster calculations are impossible as use of the PW basis requires the periodicity of the structure under consideration. 

Another way of performing calculations using the cluster model is the use of a hybrid method. It is a theoretical method, which uses different approaches for different parts of the molecular system. The ONIOM method is one of the hybrid methods developed quite recently to facilitate accurate ab initio calculations of large chemical species. The ONIOM method (n-layered integrated molecular orbital and molecular mechanics approach) [29] is a multi-level extrapolation method, in which the studied molecular system is divided into two or more parts or layers. The most important part of the system from the chemical point of view (the inner part, IP) is treated at a high" level of theory (the HL method - a high level of ab initio molecular orbital method) and the rest of the system is described by a computationally less demanding method (the LL method - the lowest ab initio approximation or even semiempirical or molecular mechanic approximations) [30]. 

The structural strengths of the hybridization model were combined with the electronic strengths of the crystal-field model in a molecular-orbital model albeit with the loss of the simplicity of the earlier models. The essential aspects of this MO model will be discussed in Chapter 1. The key point here is that, if one wishes to understand the electronic structure of metal-coordination compounds, one need go beyond the Lewis model of two-center-two-electron bonds. It should be obvious, then, that this is also a requirement for organometallic complexes, metal clusters and extended solid-state systems containing metal atoms. 

The focus then shifts to the delocalized side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field method (MS-SCF-ATa) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is... 

As has been discussed above, molecular clusters produced in a supersonic expansion are preferred model systems to study solvation-mediated photoreactions from a molecular point of view. Under such conditions, intramolecular electron transfer reactions in D-A molecules, traditionally observed in solutions, are amenable to a detailed spectroscopic study. One should note, however, the difference between the possible energy dissipation processes in jet-cooled clusters and in solution. Since molecular clusters are produced in the gas phase under collision-free conditions, they are free of perturbations from many-body interactions or macro-molecular structures inherent for molecules in the condensed phase. In addition, they are frozen out in their minimum energy conformations which may differ from those relevant at room temperature. Another important aspect of the condensed phase is its role as a heat bath. Thus, excess energy in a molecule may be dissipated to the bulk on a picosecond time-scale. On the other hand, in a cluster excess energy may only be dissipated to a restricted number of oscillators and the cluster may fragment by losing solvent molecules. 

It is not possible to give here a complete review of DMol applications, so only a non-systematic selection of applications is mentioned here. Applications to chemical reactions have been studied by Seminario, Grodzicki and Politzer [10]. Buckminster-fullerenes have been studied by various groups [11] including also nonlinear optical properties [8] and the geometrical structure of Cs4 [13]. Cluster model studies of surfaces with adsorbates are reported in [14-17]. Cluster models for point defects in solids, in particular spin density studies of interstitial muon can be found in [18,19]. Spin density studies of molecular magnetic materials are in ref [20]. Polymers have been studied by Ye et al [21]. 

The cluster model approach is based on the premise that it is only necessary to use a limited nuinber of atoms to calculate, with a certain degree of confidence, the local properties that reproduce the experimental data. From the molecular modelling point of view, the cluster model is one of the most widely used toots to study phenomena like chemisorption, physorption and reactions on large atomic aggregates. such as electronic transitions on metal... 

The cluster model of HAp/methyl acetate interface was shown in Fig.2 overlap population analysis was applied to this model. Using Monte Carlo method, 300 sampling points were put around each atom in the cluster. Molecular orbitals in the cluster were constructed by a linear combination of atomic orbitals (LCAO). Atomic orbitals used in this model were ls-2p for C, ls-2p for O, Is for H, ls-3d for P and ls-4p for Ca, which were numerically calculated for atomic Hartree-Fock method. Overlap population was evaluated by Mulliken s population analysis. 

Whereas Eq.(5.58) serves for the determination of local interactions between cluster models of a zeolite and interacting molecules, analytical expressions are needed for the interaction potential if one wishes to compute vibrational frequencies for purpose of comparison with experiment or if the potentials are to be used in Monte Carlo or molecular-dynamics simulation calculations. Sauer and co-workers developed such analytical potentials for the water-silica interaction system. The method makes use of the molecular electrostatic potential (MEP) maps and the functional form of EPEN/2 (Empirical Potential based on interactions of Electrons and Nuclei). EPEN/2 potential functions consist of a point-charge interaction term and... 

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