
	http://www.catalysis.nl/~chembond/

How quantum chemistry is done.

The normal quantum chemical method to determine the structure of a molecule and the corresponding energy consists of the following steps.

1.

Start with a guess for the structure of the molecule. This can be done by using conventional knowledge of bond lengths and bond angles.

2.

Solve the electronic Schrödinger equation.

[T_e+V_ne+V_ee] Y_el(r;R) = E_el(R)Y_el(r;R).

This gives us the electronic energy E_el(R) and the electronic wave function Y_el(r;R) depending on the positions of all nuclei R.

3.

Add the repulsion V_nn(R) between the nuclei. This gives us the total energy E(R) = E_el(R)+V_nn(R) again depending on the positions of all nuclei R.

4.

Minimize the total energy by varying the structure and repeating steps 2 and 3.

5.

After the structure of minimal energy has been determined the total energy can, if desired, be corrected for the nuclear motion by solving the Schrödinger equation for the nuclei. (This is not part of the course.)

[T_n+V_nn(R)+E_el(R)] Y_n(R) = EY_n(R).

The description above does not specify how the Schrödinger equation for the electrons is to be solved. Using MO theory is one possibility, but they are also more and less sophisticated methods. The description above also does not specify how the total energy E(R) is to be minimized. Here too there are many methods developed for function minimization.