Publication No: 3914 | Search all ORC publications |

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

**Harvey Rutt **

## Abstract

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 300K 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.

**IRMMW-THz 2007 [The Joint 32nd International Conference on Infrared & Millimetre Waves and 15th International Conference on Terahertz Electronics]** Cardiff Sep (2007)

**Southampton ePrint id:** 52056

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Copyright University of Southampton 2006