Hamiltonian operator

Hamiltonian operator tutorial

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The Hamiltonian contains one- and two-electron terms. The two-electron terms (summed over i and j) are just the repulsion potential energies between all pairs of electrons. Thus:

 

  is the repulsion between a pair of electrons (distance   apart).

The one-electron terms (summed over i) are more varied. For each electron, there is a kinetic energy term and a sum of attractive potential energy terms for each nucleus, A, in the molecule.

 

  is the kinetic energy term with:

 

  is the coulombic attraction between electron i and nucleus A.

  is the nuclear charge (atomic number) of atom A and   is the distance between electron i and nucleus A.