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We use brackets when the overall compound has a net charge, or when using ionic molecules, since in ionic molecules, the anions simply strip away the electron from the cation. Thus, leaving the cation with a new positive charge and the anion with the net negative charge.
When writing shorthand electron configurations, you would use brackets to indicate the element that comes before the compound you are writing the configuration for. For example, for Sc you will write [Ar] 3d^1 4s^2
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