Repulsion internuclear

There are two electrons that can both be put into the lower-energy orbital with opposite spins so the electronic energy is 2e+. The internuclear repulsion term must also be included in the total energy expression, giving (through eq. 1.33) ... 

Since only the electronic Hamiltonian has been used, a term 1/R must be added to W, 2 to account for internuclear repulsion. Finally, the parameter k is varied at fixed values of R to minimize the energy. 

The total energy Et = Ee + Vnn, where Vnn describes internuclear repulsion. 

The electrostatic interaction energy between two spherical atoms or ions located at A and B is the sum of the internuclear repulsions, the nucleus-electron attractions, and the electron-electron repulsions (Su and Coppens 1995) ... 

Here we wish to show that the same real-space formulas apply to molecules as well, but V has to be redehned because it must now incorporate the internuclear repulsion energy Vnn and also accommodate more than one single core. Concerning and the terms appearing in Eq. (3.31), however, they need not be redehned. With for the energy of the Mi ionic core (say, H, O )... 

In this approximation, the net effect of the core interaction energy stands for the shielding of the nuclear charges in the internuclear repulsion. 

Neither interelectronic repulsions nor internuclear repulsions have been considered. To ignore interelectronic repulsions is not serious since the orbitals used in the two forms of the molecule are extremely similar. The internuclear repulsion in the 90° form would be larger than in the linear case, and contributes to the bond angle in the actual water molecule being greater than 90°. The actual state of the molecule, as it normally exists, is that with the lowest total energy and only detailed calculations can reveal the various contributions. At a qualitative level, as carried out so far in this section, the decision from MO theory is that the water molecule should be bent, in preference to being linear. 

Other calculations of the Cr—Cr interaction are based on a model in which there is weak antiferromagnetic interaction between high-spin Cr2+ atoms.191 This is not believed to be realistic, at least for the supershort bonds. 7 A computational method which supposes multiple bonds to be single bonds intensified by screening of the internuclear repulsion is said not to support the antiferromagnetic interaction mode.1 ... 

The Be and H nuclei will be farther apart in 2 than they will be in 3 or any other similar Arrangement, so there will be less internuclear repulsion with 2. We therefore expect the hydrogen to locate along a line going through the greatest extension of the 2p orbital. 

We have shown previously how we can predict bond angles on the assumption that interelectronic (and internuclear) repulsions tend to separate the electron pairs as much as possible. 

It should be made clear that there is no single, unique ab initio method. Rather, there is a multitude of approaches, all directed toward obtaining useful approximations to mathematical problems for which no solution in closed form is known or foreseeable. The calculations are formidable, because account must be taken of several factors the attractive forces between the electrons and the nuclei, the interelectronic repulsions between the individual electrons, the internuclear repulsions, and the electron spins. 

When the distance is reduced from re, the energy increases very rapidly because of internuclear repulsion. As the separation between the atoms increases, the energy of the system increases more slowly and finally approaches that of the entirely free atoms. 

Interatomic distances are determined by steric factors, of which the most important is the exclusion principle that depends directly on the geometry of space-time, observed as the golden ratio. Bond order depends on the ratio between the number of valence electrons and the number of first neighbours, or ligands, and affects interatomic distances by the screening of internuclear repulsion. 

An unexpected feature of Table 5.1 is the remarkable similarity between the energies calculated from the characteristic radius rc and those calculated from the ionization radius r0, for the same interactions, but with bond orders increased by unity. It means that the steric factor which is responsible for the increase in bond order i.e. screening of the internuclear repulsion) is also correctly described by an adjustment to r o to compensate for modified valence density. Calculating backwards from first-order D0 = 210 kjmol-1, an effective zero-order C-C bond length of 1.72 A is obtained. 

An alternative explanation is that the increased observed bond strength is due to an increase of cr-bond strength at the shorter internuclear distance in the double-bond2 situation. The primary attraction is assumed to arise from the interaction between atomic cores and the a pair in the diatomic stationary state that maximizes this attraction. Additional valence density is excluded from this state by the Pauli principle. The attraction curve of figure 1 therefore applies for any bond order. The repulsion may however, be modified by additional valence density if it screens the internuclear repulsion. Regardless of the identity of the atoms this screening must be the same for given bond order. 

It relates to the 50 percent s-character of the spz linear combination that allows the excess density to screen the internuclear repulsion. Acetylene [2 x H(s)C(pz)2 s2], like N2 has two excess pairs in s-states to screen the nuclei and generate the bond order 3. 

At very short distances the energy rises steeply because of the great importance of the internuclear repulsive forces at these distances. 

The Born-Oppenheimer approximation treats the nuclear motion and the electron motion as entirely independent, which is reasonable in view of the huge difference of mass for nuclei and electrons. This means that the electronic energy is calculated for a given geometric arrangement of the nuclei and the internuclear repulsion is then added as a separate term. 

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