Lattice energy calculation molecular mechanics

Values for the partial charges of atoms can be derived from quantum mechanical calculations, from the molecular dipole moments and from rotation-vibration spectra. However, often they are not well known. If the contribution of the Coulomb energy cannot be calculated precisely, no reliable lattice energy calculations are possible. 

The starting point for the application of molecular mechanics to ionic solids is similar to the starting point for lattice energy calculations. Indeed the method can be used to calculate lattice energies, but it is also used to study the effect of defects, the nature of crystal surfaces and properties of crystals. 

The quantum mechanical approach cannot be used for the calculation of complete lattice energies of organic crystals, because of intrinsic limitations in the treatment of correlation energies. The classical approach is widely applicable, but is entirely parametric and does not adequately represent the implied physics. An intermediate approach, which allows a breakdown of the total intermolecular cohesion energy into recognizable coulombic, polarization, dispersion and repulsion contributions, and is based on numerical integrations over molecular electron densities, is called semi-dassical density sums (SCDS) or more briefly Pixel method. [12-14]... 

Many properties are calculated by introducing a theoretical probe molecule or group of atoms at each point in the lattice, and determining the energy of the interaction between the probe and the molecules under study. For example, an ion might be used to determine the electrostatic interaction, or a neutral atom used to determine the intermolecular forces. Such calculations rely on molecular mechanics methods and can be performed extremely rapidly, so that the interaction of every molecule with a probe at each grid point can be ascertained. Suppose a cubic grid ofnx XB points were used and the interaction with two probes at every point calculated. There would now be 2n3 variables to fit to the Molecule in a typical 3D-QSAR... 

Nanocluster models were formed on the basis of Pt lattice with the principle of closed atom packing. Binary nanoclusters were built by substitution of Pt atoms by Co, Cr, Fe, Ni, Ru. Valence states in our DFT method were accepted as depicted in Table 1. In common case during the formation of 5 5-atomic cubo-octahedral Pt nanocluster from a metal specimen a sufficient curvature take place for cluster geometry. Thus, equilibrium relaxed geometry was obtained molecular mechanics approximation as implemented in HyperChem 8.0 [30] software. After such calculations stable in energy 55 atomic clusters were fixed with distances, shown in Table 2. Calculated interatomic distances are less than app. 10%, if compared with volume and satisfy other authors data [31]. 

This polymer has been the archetypal one for applications of molecular mechanics to lattice packing. It is found for well-calibrated energy function parameter sets, i.e., force fields , that the crystal structure is rqjroduced well. Table 1 shows a comparison for lattice parameters between a calculation [6] and experiment... 

Gavezzotti developed a method for calculating lattice energy by integrating over the molecular electron density in the crystal. The molecular electron density is typically taken from a molecular quantum mechanical calculation, although it is not restricted in this way as the density could come from solid state calculations too. The Coulomb interaction between the molecules is calculated by a numerical integration over the tabulated electron densities. The repulsion between molecules is calculated from the overlap between... 

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