Home work Physical and Theoretical Chemistry IV

- Molecular Spectroscopy -

Discussion  Fr 1.5.2003 at 12:15,  HR30.1 (Hagenring 30)



 
 

Home work 2            The H2+-ion
 
 

Exercise 1:  Integrals, bond length and dissociation energy of the H2-ion

Draw the following:
  1. The overlap integral S, the Coulomb integral J, the exchange integral K, and the energies E+ (positive linear combination jA + jB) and E- (negative linear combination jA - jB) for the H2-ion in the range of 1 to 10 a.u.. Use those equations where the integral is already evaluated (see note given in lecture; R dependence).
  2. What is the meaning of the asymptotic value of E for large R?
  3. What is the bond length and the dissociation energy?
  4. Where is the minimum of K (dK/dR=0)?


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Exercise 2:  wave function of H2+

  1. Determine the coefficients cA und cB for die wave function Y = cA·jA + cB·jB of the H2-ions which describes the bonding state with energy E+.
  2. Draw Y and |Y|2 for R=2 as a function of r (one dimensional r dependence of the 1s wave function), where R represents the internuclear distance in atomic units.