Pauli “repulsion

This term is essential to obtain the correct geometry, because there is no Pauli repulsion between quantum and classical atoms. The molecular mechanics energy tenn, E , is calculated with the standard potential energy term from CHARMM [48], AMBER [49], or GROMOS [50], for example. 

Multiple M=P bonding in (OC)5M=PR becomes evident with ADF s bond energy analysis in terms of electrostatic interactions, Pauli repulsion, and orbital interactions from which the a,Ti-separation is obtained using a symmetry decomposition scheme [21]. For singlet (OC)5Cr=PR, which has a BDEst of 40.5 kcal/mol, the a- and n-components are 62.4 and 40.9 kcal/mol, respectively. 

Figure 6.2. Potential energy diagram showing the attractive Van der Waals interaction and the repulsive interaction due to Pauli repulsion,...

The mutual electrostatic repulsion of the electrons and the Pauli repulsion between electrons having the same spin. The Pauli repulsion contributes the principal part of the repulsion. It is based on the fact that two electrons having the same spin cannot share the same space. Pauli repulsion can only be explained by quantum mechanics, and it eludes simple model conceptions. 

For over a decade, the topological analysis of the ELF has been extensively used for the analysis of chemical bonding and chemical reactivity. Indeed, the Lewis pair concept can be interpreted using the Pauli Exclusion Principle which introduces an effective repulsion between same spin electrons in the wavefunction. Consequently, bonds and lone pairs correspond to area of space where the electron density generated by valence electrons is associated to a weak Pauli repulsion. Such a property was noticed by Becke and Edgecombe [28] who proposed an expression of ELF based on the laplacian of conditional probability of finding one electron of spin a at t2, knowing that another reference same spin electron is present at ri. Such a function... 

The nonequivalence in the size and shape of bonding and nonbonding electron pair domains can alternatively be expressed in terms of the relative magnitude of their mutual Pauli repulsions, which decrease in the following order ... 

The VSEPR model was originally expressed in these terms, but because Pauli repulsions are not real forces and should not be confused with electrostatic forces, it is preferable to express the nonequivalence of electron pairs of different kinds in terms of the size and shape of their domains, as we have done in this chapter. 

In a pericyclic reaction, the electron density is spread among the bonds involved in the rearrangement (the reason for aromatic TSs). On the other hand, pseudopericyclic reactions are characterized by electron accumulations and depletions on different atoms. Hence, the electron distributions in the TSs are not uniform for the bonds involved in the rearrangement. Recently some of us [121,122] showed that since the electron localization function (ELF), which measures the excess of kinetic energy density due to the Pauli repulsion, accounts for the electron distribution, we could expect connected (delocalized) pictures of bonds in pericyclic reactions, while pseudopericyclic reactions would give rise to disconnected (localized) pictures. Thus, ELF proves to be a valuable tool to differentiate between both reaction mechanisms. 

Due to the integral approximations used in the MNDO model, closed-shell Pauli exchange repulsions are not represented in the Hamiltonian, but are only included indirectly, e.g., through the effective atom-pair correction terms to the core-core repulsions [12], To account for Pauli repulsions more properly, the NDDO-based OM1 and OM2 methods [23-25] incorporate orthogonalization terms into the one-center or the one- and two-center one-electron matrix elements, respectively. Similar correction terms have also been used at the INDO level [27-31] and probably contribute to the success of methods such as MSINDO [29-31],... 

The nature of bonding of the adsorbed species to the model cluster of metal surfaces can be analyzed in terms of the so-called constrained space orbital variation (CSOV) method. For halogen anions adsorbed on various silver surfaces, it has been found that Pauli repulsion, metal polarization, and charge transfer to the metal surface mainly contribute to the binding energy of the ions [104, 301]. 

The d band model, including Pauli repulsion, can therefore be used to understand variations in oxygen binding energies in the periodic table. It turns out that a similar description can be used for a number of other adsorbates [4,18]. 

The bonding of ions to metals is dominated by Coulomb attraction since there is a significant difference in electron affinity between the metals and ions. The bonding also involves a redistribution of charge through intermolecular charge transfer (between adsorbed ions and the surface) and intramolecular polarization (in ions and on the surface), which reduces the Pauli repulsion. 

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