Selective Spin-State Switch and Metal-Insulator Transition in \boldmath $\mathrm{G}\mathrm{d}\mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{o}}_2{\mathrm{O}}_{5.5}$

Ultra-high resolution synchrotron diffraction data for $\mathrm{G}\mathrm{d}\mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{o}}_2{\mathrm{O}}_{5.5}$ throw new light on the metal-insulator transition of Co${}^{3+}$ Ba-cobaltites. An anomalous expansion of CoO${}_6$ octahedra is observed at the phase transition on heating, while CoO${}_5$ pyramids show the normal shrinking at the closing of the gap. The insulator-to-metal transition is attributed to a sudden excitation of some electrons in the octahedra ($t_{2g}^6$ state) into the Co $e_g$ band (final $t_{2g}^4{e}_g^2$ state). The $t_{2g}^5{e}_g^1$ state in the pyramids does not change and the structural study also rules out a $d_{3x^2-r^2}\mathrm{/}{d}_{3y^2-r^2}$ orbital ordering at $T_{MI}$.