- #1
thinktank1985
- 17
- 0
[tex]E\Psi(\vec{r_1},\vec{r_2})=(-h^2/2m*\nabla^2+U(\vec{r_1})+U(\vec{r_2})+U_{ee} (\vec{r_1},\vec{r_2}))\Psi(\vec{r_1},\vec{r_2})[/tex]
Now this is the equation for a 2 electron system, and [tex]U(\vec{r_1})[\tex] and [tex]U(\vec{r_2})[\tex] are the nuclear potentials for the 2 electrons and U_ee are the electron electron interaction potential.
From what I understand, this equation can be solved using numerical methods but becomes very cumbersome for atoms with large number of electrons or for molecules. So some simplifications are made. However the book I am reading from doesn't explain these approximations just states the Self Consistent field theory. If I understand correctly the Born Openheimer and Hartree-fock approximations are necessary to arrive at a formulation where you can use the self consistent field theory, however these approximations are not stated in the book..
Could someone please clarify how these approximations connect together, or give a not too mathematical reference from which I can atleast get an overview of where these concepts stand?
Now this is the equation for a 2 electron system, and [tex]U(\vec{r_1})[\tex] and [tex]U(\vec{r_2})[\tex] are the nuclear potentials for the 2 electrons and U_ee are the electron electron interaction potential.
From what I understand, this equation can be solved using numerical methods but becomes very cumbersome for atoms with large number of electrons or for molecules. So some simplifications are made. However the book I am reading from doesn't explain these approximations just states the Self Consistent field theory. If I understand correctly the Born Openheimer and Hartree-fock approximations are necessary to arrive at a formulation where you can use the self consistent field theory, however these approximations are not stated in the book..
Could someone please clarify how these approximations connect together, or give a not too mathematical reference from which I can atleast get an overview of where these concepts stand?