Home work Physical and Theoretical Chemistry IV
- Molecular Spectroscopy -
Discussion Fr 3.5.2002 at 10:30, 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:
-
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).
-
What is the meaning of the asymptotic value of E for large R?
-
What is the bond length and the dissociation energy?
-
Where is the minimum of K (dK/dR=0)?
.
Exercise 2: wave function of H2+
-
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+.
-
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.