# How can atomic configurations represent excited states of atoms?

My lecture notes on condensed matter physics talk about pseudopotentials of atoms where the core electrons are replaced by an effective potential. This is in the context of DFT. In the lecture notes, my lecturer talks about transferability, i.e. the ability of the pseudopotential to work in various atomic configurations. My lecturer proposes a test of the transferability of a pseudopotential in the following way: Devise a series of atomic configurations representing (approximations to) excited states of the atom; then compute the energy difference between them for both the all-electron case and the pseudopotential approximation.

What is it meant by that atomic configurations represent excited states of the atoms? I thought only the electrons could be excited, and there should be different excited states for all configurations. Can you explain what is meant by this?

• I could not do the assignment, but for example neutral copper would have a ground state configuration like $3d^{10}4s^1$ with excited configurations like $3d^{10}4p^1,$ $3d^{10}4d^1$ and states with $3d^9$ and the extra electron in a $4s$- or $4p$-like band. – user137289 Jan 2 '20 at 23:53

Strictly speaking what they are speaking about is the electronic configuration ot the atom. For instance, the ground state of a neutral sodium atom is $$1s^22s^22p^63s^1$$ or, ore briefly $$[{\mathrm{Ne}}]3s^1$$. However the concept of transferability of pseudopotentials has to do with the possibility of an accurate description of the interaction between atom and valence-electrons even for electronic configurations different from the reference atomic ground state. This is a key requirement if one has to describe properly the electronic states in condensed phases where the atomic configuration, i.e. the local environment around an atom induces electronic configurations different from the isolated atom electronic ground state. For example, a $$[{\mathrm{Ne}}]3p^1$$ excited state, or, less physical, but often used in the context of pseudopotentials, a fractional occupation like $$[{\mathrm{Ne}}]3s^{0.8}3p^{0.2}$$.