Hemoglobin does not bind with:

Hemoglobin Combines Reversibly With Oxygen. Carbon monoxide (CO) combines with hemoglobin at the same point on the hemoglobin molecule as does O2 ; it can therefore  displace  O2   from  the  hemoglobin. CO2   reacts  directly  with  amine  radicals  of  the hemoglobin  molecule  to  form  the  compound  carbaminohemoglobin  (CO2 Hgb).   This  combination  of  CO2   and hemoglobin  is  a  reversible  reaction  that  occurs  with  a  loose  bond,  so  the  CO2   is  easily  released  into  the alveoli, where the PCO2  is lower than in the pulmonary capillaries. Reference: : Guyton physiology pg no 532,535