Low-frequency Molecular Vibrations Research Articles

Tensor-Train Format Hierarchical Equations of Motion Formalism: Charge Transfer in Organic Semiconductors via Dissipative Holstein Models.

Hierarchical Equations of Motion (HEOM) in the Tensor-Train (TT) representation is applied to study the charge-transfer dynamics in organic semiconductors (OSCs). The theoretical formulation as well as the basic computational aspects of HEOM-TT are discussed in detail. Charge transfer in OSCs is modeled using dissipative polaronic models that incorporate the effects of both high- and low-frequency molecular vibrations, and it is simulated in a fully quantum and nonperturbative manner, which has not been studied intensively. The capability of treating complex electron-vibrational systems is examined by analyzing and comparing the numerical behavior of the time-dependent variational approach and the time-Alternating Minimal Energy methods and by calculating the current autocorrelation function and diffusivity across various models. Our results indicate that the HEOM-TT framework offers a robust tool for the detailed analysis of complex polaronic systems, suggesting its potential for broader applications.

Frequency-Selective Anharmonic Mode Analysis of Thermally Excited Vibrations in Proteins.

Low-frequency molecular vibrations at far-infrared frequencies are thermally excited at room temperature. As a consequence, thermal fluctuations are not limited to the immediate vicinity of local minima on the potential energy surface, and anharmonic properties cannot be ignored. The latter is particularly relevant in molecules with multiple conformations, such as proteins and other biomolecules. However, existing theoretical and computational frameworks for the analysis of molecular vibrations have so far been limited by harmonic or quasi-harmonic approximations, which are ill-suited to describe anharmonic low-frequency vibrations. Here, we introduce a fully anharmonic analysis of molecular vibrations based on a time correlation formalism that eliminates the need for harmonic or quasi-harmonic approximations. We use molecular dynamics simulations of a small protein to demonstrate that this new approach, in contrast to harmonic and quasi-harmonic normal modes, correctly identifies the collective degrees of freedom associated with molecular vibrations at any given frequency. This allows us to unambiguously characterize the anharmonic character of low-frequency vibrations in the far-infrared spectrum.

Structure and conformational dynamics of cyclobutanecarboxaldehyde in the ground electronic state

The study of the structure and conformational dynamics of cyclobutanecarboxaldehyde molecule in the ground electronic state was carried out by various quantum chemical methods. The geometrical structure of different conformers was investigated, and the topography of the potential energy surfaces in the low-energy region was studied. Four low-frequency molecular vibrations such as symmetric ring-CHO-bending, ring puckering, antisymmetric ring-CHO-bending and torsion are described in detail. The application of the anharmonic approach based on the variational principle makes it possible to predict the energies of vibrational transitions and to estimate qualitatively the complexity of the forms of studied vibrations.

Vibrational Dynamics in crystalline 4-(dimethylamino) benzaldehyde: Inelastic Neutron Scattering and Periodic DFT Study.

The structure and dynamics of crystalline 4-(dimethylamino) benzaldehyde, 4DMAB, are assessed through INS spectroscopy combined with periodic DFT calculations. The excellent agreement between experimental and calculated spectra is the basis for a reliable assignment of INS bands. The external phonon modes of crystalline 4DMAB are quite well described by the simulated spectrum, as well as the modes involving low-frequency molecular vibrations. Crystal field splitting is predicted and observed for the modes assigned to the dimethylamino group. Concerning the torsional motion of methyl groups, four individual bands are identified and assigned to specific methyl groups in the asymmetric unit. The torsional frequencies of the four methyl groups in the asymmetric unit fall in a region of ca. 190 ± 20 cm−1, close to the range of values observed for methyl groups bonding to unsaturated carbon atoms. The hybridization state of the X atom in X-CH3 seems to play a key role in determining the methyl torsional frequency.

Molecular vibrations reduce the maximum achievable photovoltage in organic solar cells

The low-energy edge of optical absorption spectra is critical for the performance of solar cells, but is not well understood in the case of organic solar cells (OSCs). We study the microscopic origin of exciton bands in molecular blends and investigate their role in OSCs. We simulate the temperature dependence of the excitonic density of states and low-energy absorption features, including low-frequency molecular vibrations and multi-exciton hybridisation. For model donor-acceptor blends featuring charge-transfer excitons, our simulations agree very well with temperature-dependent experimental absorption spectra. We unveil that the quantum effect of zero-point vibrations, mediated by electron-phonon interaction, causes a substantial exciton bandwidth and reduces the open-circuit voltage, which is predicted from electronic and vibronic molecular parameters. This effect is surprisingly strong at room temperature and can substantially limit the OSC’s efficiency. Strategies to reduce these vibration-induced voltage losses are discussed for a larger set of systems and different heterojunction geometries.

First-principles study of the phonon spectrum and heat capacity of TATB crystal

The widely used energetic material 1, 3, 5-triamino-2, 4, 6-trinitrobenzene (TATB) is an extremely powerful explosive and known for its extraordinary insensitivity to external stimuli (i.e., shock, friction, impact). TATB crystal exhibits graphitic-like sheets with significant inter- and intra-molecular hydrogen bondings within each layer and weak van der Waals (vdW) interactions between layers. Although TATB has been extensively studied both theoretically and experimentally, a fully understanding of its unique detonation phenomenon at a microscopic level is still lacking. Before establishing the exact pathway through which the initial energy is transferred, a fundamental knowledge of both the lattice vibrations (phonons) and molecule internal vibrations must be gained at the first step. Recently, it has been demonstrated that density functional theory (DFT) is inadequate in treating conventional energetic materials, within which dispersion interactions appear to be major contributors to the binding forces. In the present work, phonon spectrum and specific heat of TATB crystal are calculated in the framework of DFT with vdW-DF2 correction, which has been validated in our previous studies of the equation of state, structure and vibration property of TATB crystal under pressures in a range of 0-8.5 GPa. Structure optimization is preformed at zero-pressure, followed by calculating the equation of state, crystal density and lattice energy. The computed results are found to fit well with the experimental and other theoretical values. Frozen phonon method is used to calculate the phonon spectrum and phonon density of states. We find that the phonon density of states reaches its maximum at a vibration frequency of 2.3 THz, which is in good agreement with the strong absorption peak at 2.22 THz observed by THz spectroscopy. The assignment of several Raman active vibrations of TATB above 7.5 THz is given, and a comparison with other published results is also made in this study. Furthermore, the contributions of different phonon vibration modes to the specific heat are derived from the phonon density of states. The number of doorway modes (i.e., the low frequency molecular vibrations that is critical to detonation initiation) of TATB in a range of 6.0-21.0 THz is estimated based on the phonon density of states. It is shown that the phonon modes in a range of 0-27.5 THz would contribute 93.7% of the total specific heat at room temperature. By combining a Mulliken population analysis of TATB with the relative contribution of phonon vibration modes to the specific heat at 300-600 K, we conclude that C-NO2 bond might be the trigger bond of TATB during thermolysis.

Terahertz radiation induces non-thermal structural changes associated with Fröhlich condensation in a protein crystal.

Whether long-range quantum coherent states could exist in biological systems, and beyond low-temperature regimes where quantum physics is known to be applicable, has been the subject to debate for decades. It was proposed by Fröhlich that vibrational modes within protein molecules can order and condense into a lowest-frequency vibrational mode in a process similar to Bose-Einstein condensation, and thus that macroscopic coherence could potentially be observed in biological systems. Despite the prediction of these so-called Fröhlich condensates almost five decades ago, experimental evidence thereof has been lacking. Here, we present the first experimental observation of Fröhlich condensation in a protein structure. To that end, and to overcome the challenges associated with probing low-frequency molecular vibrations in proteins (which has hampered understanding of their role in proteins' function), we combined terahertz techniques with a highly sensitive X-ray crystallographic method to visualize low-frequency vibrational modes in the protein structure of hen-egg white lysozyme. We found that 0.4 THz electromagnetic radiation induces non-thermal changes in electron density. In particular, we observed a local increase of electron density in a long α-helix motif consistent with a subtle longitudinal compression of the helix. These observed electron density changes occur at a low absorption rate indicating that thermalization of terahertz photons happens on a micro- to milli-second time scale, which is much slower than the expected nanosecond time scale due to damping of delocalized low frequency vibrations. Our analyses show that the micro- to milli-second lifetime of the vibration can only be explained by Fröhlich condensation, a phenomenon predicted almost half a century ago, yet never experimentally confirmed.

From light-scattering measurements to polarizability derivatives in vibrational Raman spectroscopy: The 2ν5 overtone of SF6

The room-temperature isotropic spectrum of SF6 was recorded at the frequency of the 2ν5 overtone by running high-sensitivity incoherent Raman experiments for two independent polarizations of the incident beam and for gas densities varying from 2 to 27 amagat. Weak yet observable pressure effects were found. A transparent analysis of the Raman cross-section problem along with the first-ever prediction of the value of the mean polarizability second derivative ∂(2)α/∂q5(2) are made and the hitherto underestimated role of the hot bands of SF6 is brought to the wider public. The emergence of an analytic hotband factor is shown whose magnitude is dramatically increased with the order of the overtone and the gas temperature and all the more so upon considering low-frequency molecular vibrations. Our formulas, which in the harmonic approximation are exact, are still applicable to real situations provided certain conditions are fulfilled. For nondegenerated modes, generalization to higher order overtones is made, an issue addressing the much challenging problem of the IR-allowed second overtone bands. The content of this paper is also an invitation towards ab initio derivative-calculations for sulfur hexafluoride, especially given the today's needs in interpreting spectra of significance for greenhouse atmospheric issues.

Phonon dynamics and electron–phonon coupling in pristine picene

The paper reports a complete analysis of the phonon structure of crystalline picene, a recently announced organic semiconductor. Both lattice and intramolecular vibrations are investigated. An exhaustive assignment of lattice phonons is obtained through polarized Raman spectra assisted by lattice dynamics calculations based on a well tested atom-atom potential model. Raman, infrared spectra and density functional (DFT) calculations are used for the characterization of intramolecular modes. Coupling between low-frequency molecular vibrations and lattice phonons is accounted for. Molecule-to-molecule transfer integrals, as well as the Peierls and Holstein (non-local and local) coupling constants, are evaluated through the semiempirical method INDO/S (Intermediate Neglect of Differential Overlap with Spectroscopic parametrization).

Use of Solution-Phase Vibrational Frequencies in Continuum Models for the Free Energy of Solvation

We find that vibrational contributions to a solute's free energy are in general insensitive to whether the solute vibrational frequencies are computed in the gas phase or in solution. In most cases, the difference is smaller than the intrinsic error in solvation free energies associated with the continuum approximation to solvation modeling, although care must be taken to avoid spurious results associated with limitations in the quantum-mechanical harmonic-oscillator approximation for very low-frequency molecular vibrations. We compute solute vibrational partition functions in aqueous and carbon tetrachloride solution and compare them to gas-phase molecular partition functions computed with the same level of theory and the same quasiharmonic approximation for the diverse and extensive set of molecules and ions included in the training set of the SMD continuum solvation model, and we find mean unsigned differences in vibrational contributions to the solute free energy of only about 0.2 kcal/mol. On the basis of these results and a review of the theory, we conclude, in contrast to previous work (Ho, J.; Klamt, H.; Coote, M. L. J. Phys. Chem. A 2010, 114, 13442), that using partition functions computed for molecules optimized in solution is a correct and useful approach for averaging over solute degrees of freedom when computing free energies of solutes in solution, and it is moreover recommended for cases where liquid and gas-phase solute structures differ appreciably or when stationary points present in liquid solution do not exist in the gas phase, for which we provide some examples. When gas-phase and solution-phase geometries and frequencies are similar, the use of gas-phase geometries and frequencies is a useful approximation.

Dynamic processes and disorder in crystal structures as seen by temperature-dependent diffraction experiments

Single crystal diffraction experiments with X-rays or neutrons routinely provide average atomic positions and atomic mean square displacement parameters (ADPs). Atomic positions are easily converted to interatomic distances, angles, conformational descriptors and other quantities of interest in structural science. ADPs which encode information on atomic motion and disorder are more difficult to decipher. This is because the interatomic or correlation ADPs, which describe the coupling of atomic displacements, are lost in Bragg diffraction. The missing information can be retrieved, however, from the temperature dependence of ADPs. Measurements in the (low temperature) quantum and the (high temperature) classical regimes provide the relative and absolute atomic displacements associated with low frequency molecular vibrations on the one hand, and the contributions from high frequency vibrations and positional disorder on the other. Diffraction as a function of temperature is often a simpler alternative to vibrational spectroscopy and diffuse scattering studies. It is a potentially rich source of information on dynamic processes and disorder phenomena in crystals. The information is relatively easy to obtain and extends the scope of crystal structure analysis.

Raman scattering study of low-frequency molecular vibrations in orthoterphenyl and perdeuterated orthoterphenyl

The low-frequency Raman spectra of orthoterphenyl and perdeuterated orthoterphenyl crystals and melts were studied in a temperature range from 10 to 335K. Attention was devoted particularly to the low-frequency part of the spectrum (10–200cm−1). Several low-frequency intramolecular modes with frequencies below 150cm−1 were clearly observed in the orthoterphenyl melt. The implication of the present results on the existing empirical models of the liquid–glass transition in orthoterphenyl is discussed.

Photoisomerization in dendrimers by harvesting of low-energy photons

Infrared radiation can induce low-frequency molecular vibrations, but, with the exception of hydrogen-bond reorganization1,2,3, the excitation energy tends to be dissipated rapidly through molecular collisions rather than inducing photochemical changes. Here we show that in a macromolecular system that is designed to be insulated against collisional energy scattering, infrared absorption can excite photoisomerization by multiphoton intramolecular energy transfer. We have prepared highly branched dendrimers4,5,6 from aryl ethers with a photoisomerizable azobenzene core, in which infrared excitation of the aromatic units is apparently followed by a channelling of the absorbed energy to the core while the dendrimer matrix protects against collisional de-excitation. These findings suggest a strategy for harvesting low-energy photons to effect chemical transformations.

Low-energy molecular vibrations investigated by inelastic scattering of He atoms

Low-frequency molecular vibrations in the energy regime relevant for thermodynamical properties (< 24 meV or 200 cm −1) are important for a variety of fields, including molecular dynamics simulations of large molecules and physical properties of polymers. Here we present a novel approach for determining the energy of these modes by scattering thermal energy He atoms off molecular monolayers physisorbed on solid substrates. The merits of the new approach will be demonstrated for the case of different n-alkanes.

Shocked Energetic Molecular Materials: Chemical Reaction Initiation and Hot Spot Formation

AbstractA theoretical model is developed to describe multiphonon up-pumping of internal vibrations. The dominant mechanism for up-pumping is anharmonic coupling of excited phonon modes with low frequency molecular vibrations, termed doorway modes. Quantitative calculations were performed which show the extent and rate of multiphonon up-pumping caused by shock excitation. The time dependence of chemical reactivity behind the front is calculated using reaction rate laws for the decomposition of nitramine explosives. A mechanism for hot spot formation, based on defect induced local increases in anharmonic coupling, is discussed.

Born-Oppenheimer failure in the separation of low-frequency molecular vibrations

Changes in the effective potential function of a low-frequency large-amplitude molecular vibration, resulting from excitation of a high-frequency vibration, are discussed. It is shown that in some situations a significant contribution to such changes may arise from failure of the Born-Oppenheimer separation of the low-frequency mode. In the particular example of the HF dimer, recent evidence that the tunneling barrier increases on exciting either of the H-stretching vibrations is probably due to this effect.

Quaternary structures and low frequency molecular vibrations of haems of deoxy and oxyhaemoglobin studied by resonance Raman scattering

The influence of quaternary structure on the low frequency molecular vibrations of the haem within deoxyhaemoglobin (deoxy Hb) and Oxyhaemoglobin (oxy Hb) was studied by resonance Raman scattering. The FeO 2 stretching frequency was essentially identical between the high affinity (R) state (Hb A) and low affinity (T) state (Hb Kansas and Hb M Milwaukee with inositol hexaphosphate). However in deoxy Hb, only one of the polarized lines showed an appreciable frequency shift upon switch of quaternary structure, i.e. 215 to 218 cm −1 for the T state (Hb A, des-His(146β) Hb, and des-Arg(141α) Hb (pH 6.5)) and 220 to 221 cm −1 for the R state (des-Arg(141α) Hb (pH 9.0), des-His(146β)-Arg(141α) Hb and NES des-Arg(141α) Hb). Based on the observed 54Fe isotopic frequency shift of the corresponding Raman lines of deoxy Hb A (214 → 217 cm −1), of deoxy NES des-Arg Hb (220 → 223 cm −1), of the protoporphyrinato-Fe(II)-(2-methylimidazole) complex in the ferrous high spin state (207 → 211 cm −1) and of deoxymyoglobin (220 → 222 cm −1) (Kitagawa et al., 1979), and on substitution of perdeuterated for protonated 2-methylimidazole in the deoxygenated picket fence complex (T pivPP)Fe 2+ (2-MeIm) (209 → 206 cm −1), and on the results of normal co-ordinates calculation carried out previously, we proposed that the 216 cm −1 line of deoxy Hb is associated primarily with the FeN ε(HisF8) stretching mode and accordingly that the FeN ε(HisF8) bond is stretched in the T state due to a strain exerted by globin.

Far‐Infrared Fourier Spectroscopy as a Method for Structure Determination in Chemistry

AbstractCouched in the often confusing term “Fourier Spectroscopy” is the combined exploitation of a fundamental physical concept, a simple mathematical principle, and use of modern data technology. Introduction of this relatively young method into instrument technology has given great impetus to nuclear magnetic resonance and infrared spectroscopy. The infrared spectroscopic investigation of low frequency molecular vibrations has especially profited; in this connection one speaks of far infrared (FIR) Fourier Spectroscopy, which has opened up numerous interesting applications in organic, inorganic, and physical chemistry.

Low-frequency molecular vibrations in solid n -paraffins by neutron inelastic scattering: n -Pentane, n -hexane, n -heptane, and n -octane

The torsional and skeletal bending fundamentals in solid n -pentane, n -hexane, n -heptane, and n -octane are measured by the method of cold neutron inelastic scattering. For this series of n -paraffins, the maximum frequencies of the skeletal torsion and skeletal bending modes approach 190 and 500 cm−1, respectively, in agreement with previous measurements on polyethylene. The average frequency of the two end-methyl torsions is found to be 240 cm−1. A normal coordinate analysis, performed using only intramolecular valence force fields for each molecule, is used as a guide in spectral assignments. These results are compared to theoretical dispersion curves of polyethylene, with and without intermolecular forces. Chain-end effects appear to be of little significance for these low-frequency modes, even in chain lengths as short as seven or eight carbons.

Musk odour and far infrared vibration frequencies.

THE hypothesis that there is a relationship between low frequency molecular vibrations (in the 100 to 500 cm−1 range) and osmic quality has been proposed and discussed in earlier papers1–5.