The ground state electron configuration of Gadolinium (Gd) is [Xe]6s² 4f⁷ 5d¹. The most common valence of Gd is Gd(111). The first two electrons lost by Gd are the 6s electrons. What is the expected ground state electron configuration of Gd(111)? Explain your reasoning and provide mathematical support for complete credit using slaters rules.