The partition function of large biomolecules, and its relevance to terahertz and infrared spectroscopy

Molecules of biological interest such as proteins and enzymes are typically very large compared to those traditionally studied by infrared and terahertz spectroscopy. The ´average´ protein has some 5000 atoms and 15,000 vibrational modes. We show that this leads to extreme values of the partition function, essentially the probability of finding a molecule in the ground state, at room temperature. In fact for a practical sample at 300 K the probability of finding a molecule in the ground state (or any other specific state) is vanishingly small since the partition function exceeds the number of molecules present by many orders of magnitude. Some implications of this fact for spectroscopy of these molecules, such as the impact of ´anharmonic broadening´, sum and difference bands, are discussed.