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In each term of an electron configuration, n is the positive integer that precedes each orbital letter (helium's electron configuration is 1s 2, therefore n = 1, and the orbital contains two electrons). An atom's nth electron shell can accommodate 2n 2 electrons. For example, the first shell can accommodate two electrons, the second shell eight ...
This book contains predicted electron configurations for the elements up to 172, as well as 184, based on relativistic Dirac–Fock calculations by B. Fricke in Fricke, B. (1975). Dunitz, J. D. (ed.). "Superheavy elements a prediction of their chemical and physical properties". Structure and Bonding. 21.
Note that these electron configurations are given for neutral atoms in the gas phase, which are not the same as the electron configurations for the same atoms in chemical environments. In many cases, multiple configurations are within a small range of energies and the small irregularities that arise in the d- and f-blocks are quite irrelevant ...
The process to calculate all possible term symbols for a given electron configuration is somewhat longer. First, the total number of possible states N is calculated for a given electron configuration. As before, the filled (sub)shells are discarded, and only the partially filled ones are kept.
The one-electron functions are then expanded as a linear combination of a finite set of basis functions. This approach has the advantage that it can be made to converge to the exact solution, when the basis set tends toward the limit of a complete set and where all possible configurations are included (called "Full CI"). However this ...
The lightest atom that requires the second rule to determine the ground state term is titanium (Ti, Z = 22) with electron configuration 1s 2 2s 2 2p 6 3s 2 3p 6 3d 2 4s 2. In this case the open shell is 3d 2 and the allowed terms include three singlets ( 1 S, 1 D, and 1 G) and two triplets ( 3 P and 3 F).
It can however determine the relative energy of different geometrical configurations. It involves calculations of the electronic interactions in a rather simple way for which the electron-electron repulsions are not explicitly included and the total energy is just a sum of terms for each electron in the molecule.
The rule then predicts the electron configuration 1s 2 2s 2 2p 6 3s 2 3p 6 3d 9 4s 2, abbreviated [Ar] 3d 9 4s 2 where [Ar] denotes the configuration of argon, the preceding noble gas. However, the measured electron configuration of the copper atom is [Ar] 3d 10 4s 1. By filling the 3d subshell, copper can be in a lower energy state.