Pixel methods

Semi-classical Approaches the SCDS-Pixel Method... 

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]... 

The simplest crystal calculation consists of taking the atomic coordinates, cell data and space group for a crystal structure from an X-ray determination, building a static cluster of molecules to represent the crystal, and calculating all the interaction energies by some potential. This can be done by force field methods, Eq. (1.1.25) (time for one calculation a few milliseconds) or by Pixel, Eq. (1.1.34) (time for one calculation a few minutes). Figure 1.1.1 shows that the results are of comparable accuracy (remember that experimental values themselves are no more accurate than 5-10 kj mol-1). The UNI empirical force field [9] uses however about 100 parameters while the Pixel method uses only a few. 

Taken from ref. 25. Ujatt were calculated by the Pixel method from UNI atom-atom force field and E onf using MP2/6-31G calculations. Energy values are converted from kJ mol in the original paper to kcalmoU for comparison. 

Another approach that can be used to calculate intermolecular interaction energies is the PIXEL method, which has been apphed extensively to organic crystals. In principle, it can also be applied to molecular inorganic crystals. The interested reader is referred to the pixel section of the on-line supplement to Chapter 3 for further information. 

Full density models the SCDS-Pixel method 12.2.1 Theory... 

The philosophical transition from the atomic prejudice to a view of intermolecular interaction in terms of diffuse electron density has its proper computational counterpart in full quantum mechanical calculations, which, however, cannot at present provide complete intermolecular energies because of limitations in the treatment of electron correlation, a major ingredient of the intermolecular interaction recipe. In a different perspective, the classical atom-atom force-field approach is widely applicable but entirely parametric and of scarce adherence to physical principles. The need is felt for an extension to represent in a more realistic manner the effects of diffuse electron clouds. This is done in the so-called semi-classical density sums (SCDS) or briefly. Pixel approach [9], which will now be described. The Pixel method is based on numerical integrations over molecular electron densities, and allows a separation of the total intermolecular cohesion energy into coulombic, polarization, dispersion, and repulsion contributions. 

FULL DENSITY MODELS THE SCDS-PIXEL METHOD... 

---