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Having a half-filled or filled subshell is stabilising, as you say. But for Cl, the difference in energy between 3s and 3p is greater than the additional stabilisation from filling the 3p subshell. 3d and 4s are closer in energy, so for Cr it is favourable to promote a 4s electron and have a 4s1 configuration.

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In the case of 3$d$ and 4$s$ energies, there is an "anomaly" in the ordering, being the 3$d$ orbital energy higher than that of 4$s$. However, you are comparing the configuration of chromium (with 3$d$ and 4$s$ orbitals) with chlorine. The valence shell of the latter contains 3$s$ and 3$p$ orbitals, and the energy of 3$s$ orbitals are lower than that of 3$p$....

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In a very general aspect we could think of the following, if $X$ was the more electronegative element, say group 14 - group 17 and $M$ was the less electronegative element, then if the compound $M_mX_x$ forms, $M$ would give its electrons to $X$ so $X$ can form an octett which is the most stable electron configuration. To get this octett at $X$ you will ...

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First of all, one has to adopt an outdated concept of group number for the concept mentioned in the question to work. The group number of carbon, silicon, germanium ... is 14, not 4, per IUPAC. Reverting to the old definition (sometimes called main group), one notices that the old group number is equal to the valence electrons for the members of the group. ...

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