Preexponential-limited solid state chemistry: Ultrafast rebinding of a heme-ligand complex in a glass or protein matrix

Ultrafast spectroscopy is used to investigate the temperature dependence of a bimolecular chemical reaction occurring at reaction centers embedded in a glycerol:water glass. The reaction centers consist of carbon monoxide bound to protoheme (PH-CO), or to myoglobin at pH = 3 (Mb3-CO), a protein containing PH-CO with a broken proximal histidine-Fe bond. These systems have in common a small energetic barrier for rebinding of the photodissociated ligand. In the glass, the ligand is caged, so that only geminate rebinding is possible. Rebinding is not exponential in time. For t>20 ps, the survival fraction of deligated heme N(t) ∝ t^-n(n≥0). Below 100 K, rebinding is dominated by an inhomogeneous distribution of activation enthalpy P(△H ^‡) and n is temperature dependent. Inhomogeneous means that every site has a unique barrier. Above 150 K, n becomes independent of temperature. In this high temperature limit, the distribution of preexponential factors, attributed to a distribution of activation entropy P(△S ^‡), dominates rebinding. A picosecond two-pulse experiment demonstrates that the entropy distribution is also inhomogeneous. This work is the first study of heme-ligand rebinding in both low and high temperature limits, which allows a direct investigation of the nature of the activation entropy distribution in a glass. Because ligand rebinding in Mb3-CO and PH-CO is similar, despite the existence of a protein in Mb3-CO which provides a larger free volume for the ligand than does PH-CO, it is concluded that the low energetic barrier encourages immediate ligand rebinding and that the ligand does not diffuse far from the rebinding site at low temperature.