Coulombic penalty

Pt(III)—>Pt(II) + Pt(IV). This involves the coulombic penalty of placing two electrons on one of the atoms, namely, Pt(II). However there is an energetic stabilization from the reduction in energy of the occupied orbital levels. So, once again, the distortion energetics are controlled by the ratio of one-electron to two-electron energy terms. 

However, two penalties, both associated with the energy density, arise from the disordered anode structure (1) a smaller Coulombic capacity than the theoretical value for LiCe and (2) a sloping potential profile during both charging and discharging. 

A comparison of Equations (2.78) and (2.79) yields that in both approaches, MO (= Hartree-Fock) and VB, the Pauli exchange has been correctly included. The difference between the two is solely given by their amount of electronic correlation. In the MO approach, the electrons are completely uncorrelated (independent), and they may even go into the same atomic orbital, albeit with different spins, thus producing ionic states (H H+). The MO approach therefore does not take care of the energy penalty due to the Coulomb repulsion between the two electrons (see Section 2.9). Because the electronic Coulomb correlation has been completely ignored, the correlation energy may be defined as the difference between the correct energy and that of the Hartree-Fock solution, that is... 

In contrast to this, the scaling theory of the PE star collapse developed in [27] suggested that, instead of the formation of a collapsed core, a decrease in the solvent strength may provoke the formation of bundles by the sticking of individual branches to each other. The bundle formation reduces the excess interfacial free energy of the collapsed domains, without a significant penalty in terms of the intramolecular Coulomb repulsion. More recently, the formation of bundles was theoretically predicted in colloidal PE brushes [42]. 

MM and MD use a force field to describe the molecule and estimate the potential energy of the given conformation. The standard force field contains a term for distortion of bond lengths, bond angles and dihedral angles plus non-bonded terms for Coulombic interactions and a Lennard-Jones description of the attraction/repulsion of atoms. The application of experimental restraints is achieved by simply introducing an additional term, a so-called penalty function. This penalty function serves to minimize the differences between the calculated values and experimental data. 

---