Multielectron atoms ground state

The ground-state electron configuration of a multielectron atom is arrived at by following a series of rules called the aufbau principle. 

According to the selection rules, one-photon absorption occurs only if the change in angular momentum (change in L) is +1 or -1 (Al = 1, A/ = 0, 1 (0 o 0 not allowed), AL = 0, 1, AS = 0) (Al is according to the hydrogenic atom model, whereas AL is for multielectron atoms). The selection rules allow transition in one-photon absorption only to the p states from the s ground state as a result only even-to-odd parity is allowed. 

We begin with the assumption that the electrons in a multielectron atom can in fact be assigned to approximate hydrogen-like orbitals, and that the wavefunction of the complete atom is the product of the wavefunctions of each occupied orbital. These orbitals can be labeled with the quantum number labels Is, 2s, 2p, 3s, 3p, and so on. Each s,p,d,f,... subshell can also be labeled by an quantum number, where ranges from — to T (2T + 1 possible values). But it can also be labeled with a spin quantum number m either -f or —The spin part of the wavefunction is labeled with either a or p, depending on the value of for each electron. Therefore, there are several simple possibilities for the approximate wavefunction for, say, the lowest-energy state (the ground state) of the helium atom ... 

There are several commonly used approximation schemes that can be applied to the electronic states of multielectron atoms. The first approximation scheme was the variation method, in which a variation trial function is chosen to minimize the approximate ground-state energy calculated with it. A simple orbital variation trial function was found to correspond to a reduced nuclear charge in the helium atom. This result was interpreted to mean that each electron in a helium atom shields the other electron from the full charge of the nucleus. A better variation trial function includes electron correlation, a dependence of the wave function on the electron lectrcm distance. ... 

Results of various calculations were presented. In the orbital approximation, the energies of the orbitals in multielectron atoms depend on the angular momentum quantum number as well as on the principal quantum number, increasing as / increases. The ground state of a multielectron atom is identified by the Aufbau principle, choosing orbitals that give the lowest sum of the orbital energies consistent with the Pauli exclusion principle. 

The observed ground-state electron configuration is always the one that gives the lowest total energy for the atom. As discussed in the text, electron motions in a multielectron atom are highly correlated consequently, the total energy of an atom is, in some cases, a very delicate balance between electron-nuclear attractions and electron-electron repulsions. 

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