Atomic properties model

Molecules are usually represented as 2D formulas or 3D molecular models. WhOe the 3D coordinates of atoms in a molecule are sufficient to describe the spatial arrangement of atoms, they exhibit two major disadvantages as molecular descriptors they depend on the size of a molecule and they do not describe additional properties (e.g., atomic properties). The first feature is most important for computational analysis of data. Even a simple statistical function, e.g., a correlation, requires the information to be represented in equally sized vectors of a fixed dimension. The solution to this problem is a mathematical transformation of the Cartesian coordinates of a molecule into a vector of fixed length. The second point can... 

Until about 20 years ago, the valence bond model discussed in Chapter 7 was widely used to explain electronic structure and bonding in complex ions. It assumed that lone pairs of electrons were contributed by ligands to form covalent bonds with metal atoms. This model had two major deficiencies. It could not easily explain the magnetic properties of complex ions. 

Molecular modeling helps students understand physical and chemical properties by providing a way to visualize the three-dimensional arrangement of atoms. This model set uses polyhedra to represent atoms, and plastic connectors to represent bonds (scaled to correct bond length). Plastic plates representing orbital lobes are included for indicating lone pairs of electrons, radicals, and multiple bonds—a feature unique to this set. 

Chapter S examines various models used to describe solution and compmmd phases, including those based on random substitution, the sub-lattice model, stoichiometric and non-stoichiometric compounds and models applicable to ionic liquids and aqueous solutions. Tbermodynamic models are a central issue to CALPHAD, but it should be emphasised that their success depends on the input of suitable coefficients which are usually derived empirically. An important question is, therefore, how far it is possible to eliminate the empirical element of phase diagram calculations by substituting a treatment based on first principles, using only wave-mecbanics and atomic properties. This becomes especially important when there is an absence of experimental data, which is frequently the case for the metastable phases that have also to be considered within the framework of CALPHAD methods. 

Throughout the editorial stages of the emerging review it was continually necessary to spell out the differences between (a) the use of an ideal solution model, (b) the use of a regular solution model with parameters derived solely from atomic properties and finally (c) the use of interaction parameters derived by feedback from experiment. A proper luiderstanding of the differences between these three approaches lay at the heart of any realistic assessment of the value of calculations in relation to experimentally determined diagrams. 

The simplest representation of a molecule, with respect to computing physicochemical properties, is to assume the property to be the sum of the property values of the individual constituent atoms, or groups of atoms. Extensive data bases (1,2) of atomic and group (fragment) property values have been compiled to facilitate implementation of this model. The most notable physicochemical properties employed in QSARs using an additive property model are ... 

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

The dual wave/particle description of light and matter is really just a mathematical model. Since we can t see atoms and observe their behavior directly, the best we can do is to construct a set of mathematical equations that correctly account for atomic properties and behavior. The wave/particle description does this extremely well, even though it is not easily understood using day-to-day experience. 

E-state indices, counts of atoms determined for E-state atom types, and fragment (SMF) descriptors. Individual structure-complexation property models obtained with nonlinear methods demonstrated a significantly better performance than the models built using MLR. However, the consensus models calculated by averaging several MLR models display a prediction performance as good as the most efficient nonlinear techniques. The use of SMF descriptors and E-state counts provided similar results, whereas E-state indices led to less significant models. For the best models, the RMSE of the log A- predictions is 1.3-1.6 for Ag+and 1.5-1.8 for Eu3+. 

Well determined masses of nuclei which lie far from beta stability can provide very sensitive tests of atomic mass models While a single new mass measurement from one previously uncharacterized isotope carries with it only limited information about the quality of mass predictions from the models, important trends frequently become evident across isotopic sequences or when global comparisons of many new masses are made against the various mass models It is in this context that a comprehensive and critical assessment of the predictive properties of atomic mass models is presented with the aim of identifying both the successes and failures in the models A summary of a portion of this effort has been published earlier [HAU84] ... 

The analysis methods described here have highlighted some of the systematic features in the predictive properties of several of the commonly used atomic mass models. Additional understanding of these features and the availability of many new atomic masses for isotopes far from the stability line will serve as a basis for improving the models. The need clearly exists for a comprehensive revision and update of the mass predictions. A project, coordinated by the author, has been started to accomplish this. It is expected that new sets of mass predictions from a number of groups may be available late in 1986. 

The idea of calculating atomic and molecular properties from electron density appears to have arisen from calculations made independently by Enrico Fermi and P.A.M. Dirac in the 1920s on an ideal electron gas, work now well-known as the Fermi-Dirac statistics [19]. In independent work by Fermi [20] and Thomas [21], atoms were modelled as systems with a positive potential (the nucleus) located in a uniform (homogeneous) electron gas. This obviously unrealistic idealization, the Thomas-Fermi model [22], or with embellishments by Dirac the Thomas-Fermi-Dirac model [22], gave surprisingly good results for atoms, but failed completely for molecules it predicted all molecules to be unstable toward dissociation into their atoms (indeed, this is a theorem in Thomas-Fermi theory). 

The electronic properties of Ag cluster adsorbed on a C model have been examined by Baetzold (60). In this CNDO calculation, properties of interest included bond energies, ionization potential, and charge transfer with the substrate. A 10-atom C model consisting of fused hexagons was employed as the substrate. The 2 s and 2p orbitals of C are included in this calculation as well as the 4d, 5s, and 5p orbitals of Ag. 

The 13-atom crystal model has been used to calculate properties qualitatively similar to those of bulk nickel. The calculated rf-band width is 1.81 eV versus 2.44 eV found experimentally. The calculated value of rf-band holes per atom is 0.68 compared to an experimental value of 0.6, and the cohesive energy is about... 

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