Lattice dynamics of macromolecules is complicated due to the large amount of existing vibrational modes. In contrast to the easily accessible structural information, there is still a poor knowledge on macromolecular dynamics because of the limited experimental access. For instance, coherent inelastic neutron scattering cannot handle dispersion relations of thousands of vibrational modes. On the other hand, incoherent inelastic neutron scattering gives a featureless distribution of density of phonon states (DOS), which does not allow any further analysis of vibrational modes. As a result, the information on lattice dynamics of macromolecules today is better accessible via theoretical simulations than through the experimental studies.

Addressing the problem, we have demonstrated a possibility of mode selective analysis of lattice dynamics in large macromolecules using nuclear inelastic absorption. The method is isotope selective, thus it is sensitive only to the vibrational modes involving the atoms of the resonant Mössbauer isotope. Other advantages of the technique are precise averaging over phonon momentum space, high count rate, and access to small samples.

At beamline ID18, we have measured the partial density of phonon states of iron atoms in [57Fe(bpp2)][BF4]2 macromolecular polycrystalline powder, where the ligand bpp is 2,6-bis (pyrazol-3-yl) pyridine (C11H9N5). Figure 58 shows a central part of the molecule. The unit cell of the molecular crystal has eight molecules and contains 488 atoms. Consequently there are 1464 vibrational modes, which makes problems in the application of conventional inelastic techniques.

The macromolecule belongs to a class of iron (II) complexes, which exhibit a thermally driven high-spin ¤ low-spin (5T2g 1A1g) transition. For this particular molecule it occurs at 179 K. We have measured the energy spectra of nuclear inelastic absorption in [57Fe(bpp2)][BF4]2 with an energy resolution of 0.65 meV at two temperatures, 9 K and 295 K, which correspond to the low-spin and high-spin states, respectively. The obtained iron-partial density of phonon states is shown in Figure 59. For both states the DOS has a continuous energy distribution at lower energy and several well-localised optical modes at higher energy. According to their energies, the latter may be assigned to the Fe-N bond stretching.

Initial parabolic growth of the density of states at low energy gives a mean sound velocity of about 2.6 km/s. This indicates that the acoustic part of the DOS is limited to 4...5 meV. The density of states in this energy region is identical for both spin states (Figure 59). Thus our results show that the spin crossover does not change the intermolecular dynamics of the system. In contrast to acoustic modes, the optical modes of intramolecular dynamics have completely different frequencies (Figure 59). In the low-spin state they spread up to 62 meV, whereas in the high-spin state, within statistical accuracy, there are no modes above 46 meV. Further processing of the experimental data allowed determination of the mean-square displacement, mean kinetic energy and mean force constant separately for each optical mode. Besides that, the partial contribution to entropy and specific heat from the iron atoms was calculated.

This example demonstrates a potential of nuclear inelastic absorption to provide accurate mode-selective information on lattice vibrations in complicated macromolecules. In the present experiment the measuring time was about 20 hours for each spectrum. The statistical accuracy of the results may be traced via the "scattering" of the experimental points. It is excellent for low temperature, though somewhat worse for room temperature data, where a significant contribution of the multiphonon absorption has been subtracted from the raw experimental spectrum. The characteristic energy of the Fe-N bond stretching in the low-spin state was determined with 0.4% accuracy. These experimental data show a possibility of new insight into the dynamics of large macromolecules and provide a solid basis to examine the corresponding theoretical simulations.

Authors
A. Chumakov (a), R. Rüffer (a), O. Leupold (a, b), H. Grünsteudel (a), A. Barla (a), T. Asthalter (a, c).

(a) ESRF
(b) Hamburg University (Germany)
(c) Munich Technical University (Germany)