Phase competition underlies many remarkable and technologically important phenomena in transition metal oxides. Vanadium dioxide (VO2) exhibits a first-order metal-insulator transition (MIT) near room temperature, where conductivity is suppressed and the lattice changes from tetragonal to monoclinic on cooling. Ongoing attempts to explain this coupled structural and electronic transition begin with two alternative starting points: a Peierls MIT driven by instabilities in electron-lattice dynamics and a Mott MIT where strong electron-electron correlations drive charge localization. A key missing piece of the VO2 puzzle is the role of lattice vibrations. Moreover, a comprehensive thermodynamic treatment must integrate both entropic and energetic aspects of the transition. Here we report that the entropy driving the MIT in VO2 is dominated by strongly anharmonic phonons rather than electronic contributions, and provide a direct determination of phonon dispersions. Our ab initio calculations identify softer bonding in the tetragonal phase, relative to the monoclinic phase, as the origin of the large vibrational entropy stabilizing the metallic rutile phase. They further reveal how a balance between higher entropy in the metal and orbital-driven lower energy in the insulator fully describes the thermodynamic forces controlling the MIT. Our study illustrates the critical role of anharmonic lattice dynamics in metal oxide phase competition, and provides guidance for the predictive design of new materials.

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.

Nuclear resonance vibrational spectroscopy (NRVS) is an emerging site-specific probe of active site vibrational dynamics in metalloproteins. 1,2 NRVS is a synchrotron-based technique that uniquely targets the vibrations of a Mössbauer nucleus, such as 57 Fe, without interference from vibrations of other atoms, and reveals not only the frequency, but also the (mean squared) amplitude, 1b,2a of all vibrations of the probe nucleus along the direction of the incident X-ray beam. Quantitative characterization of vibrational modes involving a reactive probe atom can illuminate mechanisms of complex biomolecules.Reactions with heme proteins mediate the physiological effects of nitric oxide (NO). The proposed trigger for activation of soluble guanylate cyclase (sGC) is rupture of the covalent Fe-His bond 3a,b in the heme-containing domain 3c,d upon NO binding to the Fe. A thermodynamic consequence of NO-induced weakening of a trans Fe-imidazole bond, as observed in several heme systems, is that imidazole binding should weaken a trans Fe-NO bond. Model compound structures support such a reciprocal negative trans interaction, 4a although protein structural data 4b-d may not have sufficient precision to resolve the 3 pm increase in Fe-NO bond length due to imidazole binding.On the other hand, vibrational frequencies respond sensitively to bond length changes of this magnitude, and it is therefore puzzling that the frequency attributed to stretching of the Fe-NO bond in six-coordinate imidazole-ligated heme proteins 5 is higher, rather than lower, than the frequencies observed for five-coordinate iron nitrosyl hemes. For example, the assigned Fe-NO stretching frequencies of the 5-and 6-coordinate NO complexes with myoglobin (MbNO) are 521 cm −1 and 552 cm −1 , respectively. 5c NRVS measurements on 6-coordinate MbNO suggest reexamination of this issue (Fig. 1A). The Fe-weighted vibrational density of states (VDOS) D(ν) samples the vibrational kinetic energy distribution (KED), with each mode contributing an area e Fe 2 equal to the fraction of mode energy associated with Fe motion. 2a,d The e Fe 2 = 0.11 area of the feature at 547 cm −1 is well below the e Fe 2 = 0.23-0.33 range that we observed for the FeNO stretching mode in a series of 5-coordinate nitrosyl porphyrins, 2d but is clearly visible because of the distinctly improved signal quality compared to previously published NRVS measurements on myoglobin. 1a,b,d In contrast, a mode with an area e Fe 2 = 0.25 appears at 443 cm −1 , near a

We use nuclear resonance vibrational spectroscopy and computational predictions based on density functional theory (DFT) to explore the vibrational dynamics of (57)Fe in porphyrins that mimic the active sites of histidine-ligated heme proteins complexed with carbon monoxide. Nuclear resonance vibrational spectroscopy yields the complete vibrational spectrum of a Mössbauer isotope, and provides a valuable probe that is not only selective for protein active sites but quantifies the mean-squared amplitude and direction of the motion of the probe nucleus, in addition to vibrational frequencies. Quantitative comparison of the experimental results with DFT calculations provides a detailed, rigorous test of the vibrational predictions, which in turn provide a reliable description of the observed vibrational features. In addition to the well-studied stretching vibration of the Fe-CO bond, vibrations involving the Fe-imidazole bond, and the Fe-N(pyr) bonds to the pyrrole nitrogens of the porphyrin contribute prominently to the observed experimental signal. All of these frequencies show structural sensitivity to the corresponding bond lengths, but previous studies have failed to identify the latter vibrations, presumably because the coupling to the electronic excitation is too small in resonance Raman measurements. We also observe the FeCO bending vibrations, which are not Raman active for these unhindered model compounds. The observed Fe amplitude is strongly inconsistent with three-body oscillator descriptions of the FeCO fragment, but agrees quantitatively with DFT predictions. Over the past decade, quantum chemical calculations have suggested revised estimates of the importance of steric distortion of the bound CO in preventing poisoning of heme proteins by carbon monoxide. Quantitative agreement with the predicted frequency, amplitude, and direction of Fe motion for the FeCO bending vibrations provides direct experimental support for the quantum chemical description of the energetics of the FeCO unit.

20Joint Inelastic Neutron and X Ray Scattering measurements have been performed on heavy water across the melting point. The spectra bear clear evidence of a low and a high frequency inelastic shoulders related to a transverse and a longitudinal mode, respectively. Upon increasing the momentum transfer, the spectral shape evolves from a viscoelastic regime, where the low frequency mode is clearly over-damped, towards an elastic one where its propagation becomes instead allowed.The crossover between the two regimes occurs whenever both the characteristic frequency and the line-width of the low frequency mode match the inverse of the structural relaxation time. Furthermore, we observe that the frequency of the transverse mode undergoes a discontinuity across the melting, whose extent reduces upon increasing the exchanged momentum. PACS numbers: 62.60.+v,25.40.Fq 1 I. INTRODUCTION 2The presence of a second, low-frequency and weakly dispersing mode in the THz spectrum of water is a common 3 finding of several Inelastic Neutron 1-4 and X Ray 5-9 Scattering (INS and IXS respectively) experiments. Its onset 4 was at first predicted in the mid-1970s by a molecular dynamics (MD) simulation 10 and more recently interpreted, by 5 similar computational methods, as the manifestation of a THz viscoelastic behavior 11 . This low-frequency excitation 6 appears in the spectrum of density fluctuations , S(Q, ω), when the exchanged momentum, Q, exceeds some 7 threshold value, Q T ≈ 4 nm −1 , and, according to a broadly accepted interpretation 7-9,11 , it arises from the coupling 8 of density fluctuations with shear waves 12 . This explanation stems from the analogy with ice, whose spectrum is 9 characterized by an optic transverse phonon at comparable frequencies 13 . Furthermore, it is supported by MD 10 results 8,11 demonstrating the presence of an analogous peak in the correlation function of transverse velocities. 11 12 In summary, the body of literature results on the S(Q, ω) of water outlines a rather coherent scenario: owing to the 13 lack of translational invariance typical of liquids, longitudinal and transverse modes become mutually intertwined and 14 their symmetry somehow ill-defined at distances shorter than some threshold ≈ Q −1 T . Such longitudinal-transverse 15 (L-T) coupling causes the onset of an inelastic transverse mode in the S(Q, ω), even if the latter, in principle, only 16 couples with longitudinal modes. 17 18It seems natural to ascribe the strength of the L-T coupling in water to the presence of a hydrogen bond network, 19 which enhances the correlations between the movements of molecules belonging to adjacent layers of the liquid, 20 thus fostering the propagation of shear waves. An L-T coupling has been demonstrated in other simulated network 21 systems such as glassy glycerol 14 and also experimentally observed in SiO 2 15 , GeO 2 16 and GeSe 2 17 , samples sharing 22 with water the property of a tetrahedral arrangement of local intermolecular structure. The circumstance that L-T 23 coupling was evi...

Inelastic x-ray scattering is used to investigate charge-density wave (CDW) formation and the low-energy lattice dynamics of the underdoped high-temperature superconductor ortho-II YBa 2 Cu 3 O 6.54 . We find that, for a temperature ∼1/3 of the CDW onset temperature (≈155 K), the CDW order is static within the resolution of the experiment, that is the inverse lifetime is less than 0.3 meV. In the same temperature region, low-energy phonons near the ordering wave vector of the CDW show large increases in their linewidths. This contrasts with the usual behavior in CDW systems where the phonon anomalies are strongest near the CDW onset temperature.

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We present an investigation of the lattice dynamics of the charge-density-wave compound 2H-NbSe 2 . We analyze the precise nature of the wave vector dependent electron-phonon coupling (EPC) and derive the bare dispersion of the charge-density-wave (CDW) soft phonon mode using inelastic x-ray scattering combined with ab-initio calculations. Experimentally, phonon modes along the Γ -M line, i.e. q = (h, 0, 0) with 0 ≤ h ≤ 0.5, with the same longitudinal symmetry (Σ 1 ) as the CDW soft mode were investigated up to 32 meV. In agreement with our calculations we observe significant EPC in the optic modes at h ≤ 0.2. We analyze the EPC in the optic as well as acoustic modes and show that the q dependences stem from scattering processes between two bands at the Fermi surface both having Nb 4d character. Finally, we demonstrate that the soft mode dispersion at T = 33 K (= T CDW ) can be well described on the basis of a strongly q dependent EPC matrix element and an acoustic-like bare phonon dispersion in agreement with observations near room temperature.