- #1

Dario56

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Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ [(\sum_{i=1}^N - \frac {h^2} {2m} \nabla _i ^2) + \sum_{i=1}^N V(r_i) + \sum_{i < j}^N U(r_i,r_j)] \Psi = E \Psi $$

Terms in Hamiltonian are as follows:

1) Kinetic energy of electrons

2) Potential energy of electron - nuclei interaction

3) Potential energy of electron - electron interaction

It is said that for N electron system, kinetic and potential energy of electron - electron interaction are system independent which means that their value depends only on number of electrons ##N##and nothing else. Potential energy of electron - nuclei interaction depends on specific system and isn't determined only by ##N##.

Why is this?

Terms in Hamiltonian are as follows:

1) Kinetic energy of electrons

2) Potential energy of electron - nuclei interaction

3) Potential energy of electron - electron interaction

It is said that for N electron system, kinetic and potential energy of electron - electron interaction are system independent which means that their value depends only on number of electrons ##N##and nothing else. Potential energy of electron - nuclei interaction depends on specific system and isn't determined only by ##N##.

Why is this?

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