First Order Perturbation Theory: Helium Atom

Analytical Solution to Radial Part

The Mathematica Notebook He_Atom_PT1.nb (PDF He_Atom_PT1.pdf) illustrates how to obtain the first-order energy correction for the helium atom after analytically solving the Schrodinger equation for a zeroth-order Hamiltonian which neglects the electron-electron repulsion. It also demonstrates the capabilities of Mathematica to calculate fairly difficult integrals. Examine the file to solidify your understanding of ideas behind perturbation theory; notice that the first-order energy is rather far from the true energy. In the next part, you will use more elaborate calculations to obtain better energy for the helium atom ¹S ground state.

Gaussian Program

You will be using a computational chemistry program Gaussian03 (or Gaussian 09) to perform some calculations. Gaussian is a widely used commercial computational chemistry program, and it is important that you learn well how to use it. One valuable resource is their on-line technical documentation. Later in the course you can decide when to use Gaussian (e.g. geometry optimization with analytical derivatives) and when to use Firefly/PC GAMESS (e.g. single point calculations with s,p,d,f,g functions).

To continue reading click on the following link:

https://people.chem.ucsb.edu/kahn/kalju/chem126/public/gaussian_intro_11.html