You are analyzing the color of a transition metal complex in a solution. Describe how coordination compounds are formed from a central metal atom or ion surrounded by ligands. Discuss the role of d-orbitals in the bonding and geometry of coordination compounds. Explain how the arrangement of ligands around the metal center influences the color and magnetic properties of the complex. Describe the significance of coordination chemistry in biological systems, such as the role of hemoglobin in oxygen transport, and in industrial applications, such as catalysis and material science. What are the challenges in synthesizing and characterizing new coordination compounds for specific applications?