Cu(ii)–porphyrin molecular dynamics as seen in a novel EPR/Stochastic Liouville equation study

Copper porphyrin dissolved in CH2Cl2:toluene as fluid and frozen solution was studied as a function of temperature using X-band electron paramagnetic resonance (EPR). Quantitative interpretation was obtained using a recently developed Stochastic Liouville simulation method. For the first time we address the large spin system that translates into a 400 000 dimensional Liouville equation solved under slow-motion conditions. Using a simple three parameter microscopic model, the temperature dependence of porphyrin rotational correlation time is determined to be in the range 1–10 ns and a fast local motion is in the subpico-second regime with an amplitude increasing with temperature. The methodology provides an important tool for arriving at an accurate set of spin Hamiltonian parameters since determining a unique set of parameters from a frozen solution EPR experiment is often difficult. Thus, the proposed method discriminates between parameters proposed from frozen solution EPR experiments or quantum chemistry calculations. The methodology presented is expected to be valuable in obtaining a molecular dynamics picture of metal proteins using EPR as well as in the study of artificial photosynthetic systems.