Weak electronic repulsion

Nonbonded interactions are the forces be tween atoms that aren t bonded to one another they may be either attractive or repulsive It often happens that the shape of a molecule may cause two atoms to be close in space even though they are sep arated from each other by many bonds Induced dipole/induced dipole interactions make van der Waals forces in alkanes weakly attractive at most distances but when two atoms are closer to each other than the sum of their van der Waals radii nuclear-nuclear and electron-electron repulsive forces between them dominate the fvan derwaais term The resulting destabilization is called van der Waals strain... 

The fluoride ion is the least polarizable anion. It is small, having a diameter of 0.136 nm, 0.045 nm smaller than the chloride ion. The isoelectronic E and ions are the only anions of comparable size to many cations. These anions are about the same size as K" and Ba " and smaller than Rb" and Cs". The small size of E allows for high coordination numbers and leads to different crystal forms and solubiUties, and higher bond energies than are evidenced by the other haUdes. Bonds between fluorine and other elements are strong whereas the fluorine—fluorine bond is much weaker, 158.8 kj/mol (37.95 kcal/mol), than the chlorine—chlorine bond which is 242.58 kJ/mol (57.98 kcal/mol). This bond weakness relative to the second-row elements is also seen ia 0-0 and N—N single bonds and results from electronic repulsion. 

The existence of the first HK theorem is quite surprising since electron-electron repulsion is a two-electron phenomenon and the electron density depends only on one set of electronic coordinates. Unfortunately, the universal functional is unknown and a plethora of different forms have been suggested that have been inspired by model systems such as the uniform or weakly inhomogeneous electron gas, the helium atom, or simply in an ad hoc way. A recent review describes the major classes of presently used density functionals [10]. 

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... 

In vinylphosphinidine, the open- and closed-shell singlets lie 17 and 23 kcal/mol above the ground triplet state. The energies of the two singlet states of vinylphosphinidine are comparable because electron-electron repulsion in the 3p orbitals is reduced and because the overlap of 2p and 3p orbitals of carbon and phosphorus is poor and the resulting carbon-phosphoms double bond is relatively weak. ... 

Even in atoms in molecules which have no permanent dipole, instantaneous dipoles will arise as a result of momentary imbalances in electron distribution. Consider the helium atom, for example. It is extremely improbable that the two electrons in the Is orbital of helium will be diametrically opposite each other at all times. Hence there will be instantaneous dipoles capable of inducing dipoles in adjacent atoms or molecules. AnothCT way of looking at this phenomenon is to consider the electrons in two or more "nonpolar" molecules as synchronizing their movements (at least partially) to minimize electron-electron repulsion and maximize electron-nucleus attraction. Such attractions are extremely short ranged and weak, as are dipole-induced dipole forces. The energy of such interactions may be expressed as... 

The weaknesses of the standard EHM probably arise at least in part from the fact that it does not (contrast the ab initio method, Chapter 5) take into account electron spin or electron-electron repulsion, ignores the fact that molecular geometry is partly determined by intemuclear repulsion, and makes no attempt to overcome these defects by parameterization (unlike the variation which, with the aid of careful parameterization, has been claimed to give good geometries [67]). 

The weaknesses of the EHM are due largely to its neglect of electron spin and electron-electron repulsion and the fact that it bases the energy of a molecule simply on the sum of the one-electron energies of the occupied orbitals, which ignores electron-electron repulsion and intemuclear repulsion this is at least partly the reason it usually gives poor geometries. 

For the weak field case, we have the situation where the crystal field interaction is much weaker than the electronic repulsion. In this approximation, the Russell-Saunders terms 3F, 3P, 1G, lD, and 5 for the d2 configuration are good basis functions. When the crystal field is turned on, these terms split according to the results given in Table 8.4.2 ... 

The relatively large change in size in going from the first to the second member of a group also has important consequences for the Group 7A elements. For example, fluorine has a smaller electron affinity than chlorine. This violation of the expected trend can be attributed to the fact that the small size of the fluorine 2p orbitals causes unusually large electron-electron repulsions. The relative weakness of the bond in the F2 molecule can be explained in terms of the repulsions among the lone pairs, shown in the Lewis structure ... 

As we saw in Chapter 2, electron-electron repulsions cause a given electron configuration to be split into terms. However, for the simplest case, d. there will be no such splitting of the free ion levels because there is only one electron. Thus we have only one term, the ground stale D. because the five dorbitals are degenerate and the electron has an equal probability of being in any one of them. As we have also seen previously, these five d orblals will, under the influence of an octahedral field (either weak or strong), be split into and orbitals. The D term likewise will be s rfit into and terms in an octahedral complex. 

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