For many years, Mössbauer spectroscopy has been applied to measure recoilless absorption of x-ray photons by nuclei. Recently, synchrotron radiation sources have enabled the observation of weaker features separated from the recoilless resonance by the energy of vibrational quanta. This enables a form of vibrational spectroscopy with a unique sensitivity to the probe nucleus. Biological applications are particularly promising, because it is possible to selectively probe vibrations of a single atom at the active site of a complex biomolecule, while avoiding interference from the vibrations of thousands of other atoms. In contrast with traditional site-selective vibrational spectroscopies, nuclear resonance vibrational spectroscopy (NRVS) is not hampered by solvent interference and faces selection rule limitations only if the probe nucleus lies on a symmetry element. Here, we formulate a mathematical language appropriate for understanding NRVS measurements on molecular systems and apply it to analyse NRVS data recorded on ferrous nitrosyl tetraphenylporphyrin, Fe(TPP)(NO). This compound mimics the haem group found at the active site of many proteins involved in the biological usage of oxygen and nitric oxide. Measurements on such model compounds provide a baseline for evaluating the extent to which vibrations are localized at the active site of a protein, with the goal of elucidating the mechanisms of biological processes, such as intersite communication in allosteric proteins.

We use quantitative experimental and theoretical approaches to characterize the vibrational dynamics of the Fe atom in porphyrins designed to model heme protein active sites. Nuclear resonance vibrational spectroscopy (NRVS) yields frequencies, amplitudes, and directions for 57Fe vibrations in a series of ferrous nitrosyl porphyrins, which provide a benchmark for evaluation of quantum chemical vibrational calculations. Detailed normal mode predictions result from DFT calculations on ferrous nitrosyl tetraphenylporphyrin Fe(TPP)(NO), its cation [Fe(TPP)(NO)]+, and ferrous nitrosyl porphine Fe(P)(NO). Differing functionals lead to significant variability in the predicted Fe-NO bond length and frequency for Fe(TPP)(NO). Otherwise, quantitative comparison of calculated and measured Fe dynamics on an absolute scale reveals good overall agreement, suggesting that DFT calculations provide a reliable guide to the character of observed Fe vibrational modes. These include a series of modes involving Fe motion in the plane of the porphyrin, which are rarely identified using infrared and Raman spectroscopies. The NO binding geometry breaks the four-fold symmetry of the Fe environment, and the resulting frequency splittings of the in-plane modes predicted for Fe(TPP)(NO) agree with observations. In contrast to expectations of a simple three-body model, mode energy remains localized on the FeNO fragment for only two modes, an N-O stretch and a mode with mixed Fe-NO stretch and FeNO bend character. Bending of the FeNO unit also contributes to several of the in-plane modes, but no primary FeNO bending mode is identified for Fe(TPP)(NO). Vibrations associated with hindered rotation of the NO and heme doming are predicted at low frequencies, where Fe motion perpendicular to the heme is identified experimentally at 73 and 128 cm-1. Identification of the latter two modes is a crucial first step toward quantifying the reactive energetics of Fe porphyrins and heme proteins.