What actually determines which amino acids are linked in a functional hemoglobin molecule?
Your question is vague. I think you’re asking about either primary structure, which is the straight up sequence of amino acids in a protein (where amino acids are linked one by one according to how they were coded for by their mRNA); or tertiary structure, which is the three-dimensional superstructure of a protein (where amino acids can interact with others that they are not directly covalently bonded to, such as through hydrogen bonds, or disulfide links between cysteines).