Full density models the SCDS-Pixel method

2 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. 

In the Pixel formulation, the basic concept is the electron density unit, or e-pixel. Consider a molecule (molecule A) with nuclei of charge Zj at points (/) = [xj yj zj]. Let Pk be the electron density in an elementary volume Vk centered at point (k) = [J kykZkl- Pk is readily obtained through an MO wavefunction (see Chapter 3, Box 3.1) the whole Pixel theory has been developed and calibrated using valence 

Consider now a second molecule, B (see Fig. 12.6) with nuclei of charge Zm at points (m) = [Xm Jm Zm], and whose e-pixels of charge qi = piVi are at positions (i) = [Xi yi Zil. For the calculation of the intermolecular Coulombic energy, let / in be the distance between any two centers of pixels or nuclear positions Z and n the electrostatic potential generated by molecule A at point (Z) of the charge density of molecule B is  

When two molecules approach one another their electron densities overlap to some extent. In principle, this overlap should be treated as a partially bonding effect, but Pixel preserves the identity of two separate electron clouds, so that when pixels overlap, singularities in the R dependence may result for very short pixel-pixel distances. As a practical countermeasure, all pixel-pixel distances below half the stepsize of the pixel mesh are reset at half the stepsize (the collision avoidance procedure). 

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FULL DENSITY MODELS THE SCDS-PIXEL METHOD... 

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