Ballhausen-Gray approximation

The quantity (Hn + H22) may not be the best way to combine Coulomb integrals for cases where the atoms have gready different ionization potentials. In such cases, it is preferable to use the Ballhausen-Gray approximation,... 

Although the energy of a chemical bond as a function of internuclear distance can be represented by the potential energy curve shown in Figure 3.2, neither the Wolfsberg-Helmholtz nor the Ballhausen-Gray approximation is a function that possesses a minimum. However, the approximation of Cusachs is a mathematical expression that does pass through a minimum. 

The constant K has been assigned various values from 1 to 3. A value of 1.75 is common. A slightly different version is employed by Ballhausen and Gray, who use the geometric mean instead of the arithmetic mean in approximating... 

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