Equilibrium internuclear distances

The minimum for the equilibrium internuclear distance in Hj is 2.49 bohrs in this first... 

Consider a stable diatomic molecule with nuclei denoted as A and B. The Born-Oppenheimer potential V for such a molecule will depend on the internuclear distance rAB and will typically have the form shown in Fig. 3.1. The potential energy has a minimum at r0, which is often referred to as the equilibrium internuclear distance. As the distance rAB increases, the potential V increases and finally reaches a limiting value where the molecule is now better described as two separated atoms (or depending on the electronic state of the system, two separated atomic species one or both of which may be ions). The difference in energy between the two separated atoms and the minimum of the potential is the dissociation energy De of the molecule. As the internuclear distance of the diatomic molecule is decreased... 

Despite the difference in the asymptotic limits, some features characteristic for molecules in magnetic fields can also be seen in the present work. Table 5 shows that the binding energy of the ground state H2 increases with the strength of the potential and the equilibrium internuclear distance decreases. Meanwhile, the monotonically increasing suggests that the potential well becomes more steeper. 

Very accurate values of the dipole and quadrupole polarizability for the equilibrium internuclear distance of HF can be found in a review article by Maroulis [71], calculated with finite-field Mpller-Plesset perturbation theory at various orders and coupled cluster theory using a carefully selected basis set. 

Table 2.3. Comparison ofMCVB coefficients for orthogonalized AOs and raw AOs at the equilibrium internuclear distance. The ordering is determined by the orthogonalized AOs.

Table 13.2. Principal standard tableaux functions for CH at the equilibrium internuclear distance. This is the x-component of a TV-pair.

The reduced mass and moment of inertia of H The equilibrium internuclear distance = 127.5... 

Much larger differences occur for the X parameter. There are also large differences between the two DF calculations for X, which cannot be explained by the small change in internuclear separation. The value of X may be expected to be less stable than M [127]. The conclusion in [19] is that the RCC-S value for X, which is higher than that of [89, 127], is more correct. The electron correlation effects are calculated by the RCC-SD method at the molecular equilibrium internuclear distance Rg. A major correlation contribution is observed, decreasing M by 17% and X by 22%. 

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. 

In hydrogen fluoride the situation is different. For this molecule the ionic curve and the covalent curve are nearly coincident in the neighborhood of the equilibrium internuclear distance. In conse-... 

We may attempt to make a rough quantitative statement about the bond type in these molecules by the use of the values of their electric dipole moments. For the hydrogen halogenides only very small electric dipole moments would be expected in case that the bonds were purely covalent. For the ionic structure H+X-, on the other hand, moments approximating the product of the electronic charge and the internuclear separations would be expected. (Some reduction would result from polarization of the anion by the cation this we neglect.) In Table 3-1 are given values of the equilibrium internuclear distances r0, the electric moments er0 calculated for the ionic structure H+X , the observed values of the electric moments /, and the ratios of these to the values of er0.ls These ratios may be interpreted in a simple... 

Here k is the force constant, De the equilibrium internuclear distance, and an and values determined by the nature of the bonded atoms, as given in Table 7-7. 

The Helium Molecule-Ion.—The simplest molecule in which the three-electron bond can occur is the helium molecule-ion, HeJ, consisting of two nuclei, each with one stable Is orbital, and three electrons. The theoretical treatment7 of this system has shown that the bond is strong, with bond energy about 55 kcal/mole and with equilibrium internuclear distance about 1.09 A. The experimental values for these qualities, determined from spectroscopic data for excited states of the helium molecule, are a bout 58 kcal/mole and 1.080 A, respectively, which agree well with the theoretical values. It is seen that the bond energy in He He4 is about the same as that in H H+, and a little more than half as great as that of the electron-pair bpnd in H H. 

First tlie hydrogen bond is a bond by hydrogen between two atoms the coordination number of hydrogen does not exceed two.7 The positive hydrogcu ion is a bare proton, with no electron shell about it. This vanishingly small cation would attract one anion (which we idealize here as a rigid sphere of finite radius—see Chap. 13) to the equilibrium internuclear distance equal to the anion radius, and could then similarly attract a second anion, as shown in Figure 12-1, to form... 

By differentiating V with respect to r and equating the derivative to zero, the equilibrium internuclear distance rfl is found to be... 

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