Internuclear repulsion energy

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 )... 

This approximation is similar to the point-charge-potential simplifications introduced [10] for core-other-core and core-other-nucleus interactions, showing that the net effect of the core interaction energy is to shield the nuclear charges in the internuclear repulsion energy.) Hence the E of Eq. (9) becomes... 

To obtain the total (electronic plus nuclear) energy, we add the internuclear repulsion energy for the N nuclei ... 

Figure A10.9 The various terms in the electron-nuclear potential energy plotted as a function of Internuclear separation for (a) H2 in the ground state, with theelectron in 1

Fig.1.2. Electronic energy Ee(R), internuclear repulsive energy ii(R) and total energy (R) as a function of internuclear distance R for the ground state of the hydrogen molecule-ion, Ht, shown in the inset... 

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) ... 

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

To obtain an accurate assessment of the interelectronic repulsion energy of the H2 molecule it is essential to carry out calculations in which the hydrogen nuclei are a constant distance apart. The following calculations are for an internuclear distance of 74 pm for both molecules, which is the equilibrium internuclear distance in the dihydrogen molecule. 

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. 

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. 

At internuclear distances outside the repulsive structure, the triplet repulsive energy lies lower than the singlet, for argon, krypton, and deuterium partners,103 as well as for helium (see Section III.C). 

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. 

---