m2) The interatomic interaction energy for two atoms (with masses m2) of a diatomic molecule is given as: Eint. (r) = B r12 r A where is the distance between these two atoms (A and B are positive con- ndstants). Find the binding energy, equilibrium (bond) distance between two teratoms and vibrational frequency of the molecule in terms of given parameters.

p9C.1 Familiarity with the magnitudes of overlap integrals is useful when con- sidering bonding abilities of atoms, and hydrogenic orbitals give an indication of their values. (a) The overlap integral between two hydrogenic 2s orbitals is 1 ( ZR ZR +. 2а, " 12 а, 1 + ZR 240 a, -ZR/Z0 S(2s, 2s)={1+ Plot this expression. (b) For what internuclear distance is S(2s,2s) = 0.50? (c) The side-by-side overlap of two 2p orbitals of atoms of atomic number Z is ZR 1 ( ZR ZR S(2p,2p) ={1+ 10 a, 2a, 120 a. Plot this expression. (d) Evaluate S(2s,2p) at the internuclear distance you calculated in part (b).

The net potential energy E_N between two adjacent ions is sometimes represented by the expression: E_N = -C/r + D times exp (-r/rho) in which r is the interionic separation and C, d, and rho are constants whose values depend on the specific material. Derive an expression for the bonding energy E_0 in terms of the equilibrium interionic separation r_0 and the constants D and rho. Derive another expression for E_0 in terms of r_0, C and rho.

SAMPLE PROBLEMS & SOLUTIONS Example 1: The interacting potential energy between two ions is represented by the following expression: -1.252 5.625 x 10-6 U = ..Eqn(1) r8 Where (r) is the distance in nm (1nm = 10-m) (U) is in kJ Calculate: a) The equilibrium distance ro in nm. b) The minimum bond energy in kJ. c) The maximum interionic force for the bond in kN.