Collective dynamics of lysozyme in water: terahertz absorption spectroscopy and comparison with theory

To directly measure the low-frequency vibrational modes of proteins in biologically relevant water environment rather than previously explored dry or slightly hydrated phase, we have developed a broadband terahertz spectrometer suitable for strongly attenuating protein solutions. Radiation is provided by harmonic multipliers (up to 0.21 THz), a Gunn oscillator (at 0.139 THz), and the UCSB free-electron lasers (up to 4.8 THz). Our spectrometer combines these intense sources with a sensitive cryogenic detector and a variable path length sample cell to detect radiation after it is attenuated by more than 7 orders of magnitudes by the aqueous sample. Using this spectrometer, we have measured the molar extinction of solvated lysozyme between 0.075 and 3.72 THz (2.5-124 cm(-1)), and we made direct comparison to several published theoretical models based on molecular dynamics simulations and normal-mode analysis. We confirm the existence of dense, overlapping normal modes in the terahertz frequency range. Our observed spectrum, while in rough qualitative agreement with these models, differs in detail. Further, we observe a low-frequency cutoff in terahertz dynamics between 0.2 and 0.3 THz, and we see no evidence of a predicted normal mode at approximately 0.09 THz for the protein.     

丙氨酸晶体太赫兹振动光谱的实验和理论研究

利用太赫兹时域光谱和低频拉曼光谱仪研究了丙氨酸晶体在0.2-2.6 THz 范围内的太赫兹吸收和拉曼散射光谱. 研究表明: 在该低频范围有四个振动模式, 其中两个只具有拉曼活性, 其余两个同时具有红外和拉曼活性. 基于B3LYP杂化密度泛函的自洽场晶体轨道法对丙氨酸周期性结构进行了理论研究和光谱计算. 通过比较实验和理论结果, 指认了实验光谱特征峰所属的不可约表示. 通过理论计算得到的图形, 得出在此低频范围的振动模式主要包含分子间氢键的扭转和摇摆运动.     

The phonon spectrum of phase-I ammonia: reassignment of lattice mode symmetries from combined molecular and lattice dynamics calculations

The zone-center phonon spectra of phase-I ammonia and deuterated ammonia have been obtained from plane-wave DFT molecular dynamics and localized basis set harmonic lattice dynamics simulations. These data have proved to be excellent for benchmarking the two approaches. Significant changes to the assignments of the experimental low-frequency lattice modes are proposed on the basis of the calculated data. The magnitude of the splitting of the longitudinal and transverse optical modes has been determined and is shown to be significant in some cases. The high-frequency internal mode region of the spectrum has also been obtained and is shown to be in excellent agreement with the results of previous studies. The symmetry coordinates and Davydov splittings of the internal modes are fully analyzed.     

Terahertz time-domain and Raman spectroscopy of the sulfur-containing peptide dimers: Low-frequency markers of disulfide bridges

The terahertz time-domain and Raman spectra of sulfur-containing cystein-based peptides in the region of the low-frequency infrared vibrations have been measured at room temperature. The low-frequency bands that can be assigned to the S–S bridges are observed. The vibrational modes found in molecular crystalline materials should be described as phonon modes with strong coupling to the intra molecular vibrations.     

Terahertz spectrum and normal-mode relaxation in pentaerythritol tetranitrate: effect of changes in bond-stretching force-field terms

Terahertz (THz) active normal-mode relaxation in crystalline pentaerythritol tetranitrate (PETN) was studied using classical molecular dynamics simulations for energy and density conditions corresponding to room temperature and atmospheric pressure. Two modifications to the fully flexible non-reactive force field due to Borodin et al. [J. Phys. Chem. B 112, 734 (2008)] used in a previous study of THz-active normal-mode relaxation in PETN [J. Chem. Phys. 134, 014513 (2011)] were considered to assess the sensitivity of the earlier predictions to details of the covalent bond-stretching terms in the force field. In the first modification the harmonic bond-stretching potential was replaced with the Morse potential to study the effect of bond anharmonicity on the THz-region mode relaxation. In the second modification the C-H and nitro-group N-O bond lengths were constrained to constant values to mimic lower quantum occupation numbers for those high-frequency modes. The results for relaxation times of the initially excited modes were found to be insensitive to either force-field modification. Overall time scales for energy transfer to other modes in the system were essentially unaffected by the force-field modifications, whereas the detailed pathways by which the energy transfer occurs are more complicated for the Morse potential than for the harmonic-bond and fixed-bond cases. Terahertz infrared absorption spectra constructed using calculated normal-mode frequencies, transition dipoles, and relaxation times for THz-active modes were compared to the spectra obtained from the Fourier transform of the dipole-dipole time autocorrelation function (DDACF). Results from the two approaches are in near agreement with each other and with experimental results in terms of main peak positions. Both theoretical methods yield narrower peaks than observed experimentally and in addition predict a weaker peak at ω ～ 50 cm(-1) that is weak or absent experimentally. Peaks obtained using the DDACF approach are broader than those obtained from the normal-mode relaxation method.     

含硫氨基酸的太赫兹光谱

利用太赫兹时域光谱(THz-TDS)技术研究室温条件下多晶含硫氨基酸L-蛋氨酸(Met)和L-半胱氨酸(Cys)的光谱特性, 得到相应的吸收谱和折射率谱, 表明含硫氨基酸在THz波段具有区别于其它氨基酸的显著特征. 在实验测量的有效光谱范围0.2～2.8 THz内, L-蛋氨酸的THz吸收峰分别位于1.06, 1.88和2.70 THz; L-半胱氨酸的吸收峰分别位于1.40, 1.70, 2.33和2.61 THz, 两种氨基酸的平均折射率均为1.44. 利用GAUSSIAN 03软件包中的Hartree-Fock理论计算了蛋氨酸双分子的低频振动谱, 表明了与蛋氨酸各吸收峰对应的分子微观振动模式, 并对实验光谱进行了解析讨论.     

THz spectroscopic investigation of 2,4-dinitrotoluene

We have investigated the terahertz (THz) spectrum of 2,4-DNT by using Fourier transform infrared spectroscopy in the 0.2–19.5 THz region. We also examined low-frequency intermolecular or phonon modes between 0.2 and 1.8 THz via THz time-domain spectroscopy. The extracted absorption coefficient and refractive index of an intermolecular band at 1.08 THz are 110 cm⁻¹ and 1.67, respectively. Density functional theory (DFT) was applied to obtain structure and vibrational frequencies of 2,4-DNT. The calculated results are in agreement with the experimental data. Observed vibrational frequencies have been interpreted using DFT. Two intermolecular or phonon modes were identified at 1.08 and 2.52 THz.     

Semi-Empirical Model to Retrieve Finite Temperature Terahertz Absorption Spectra using Morse Potential

Terahertz (THz) absorption is a fingerprint property of materials, due to the underlying low-frequency vibration/phonon modes being strongly dependent on the chemical constitutions and microscopic structures. The low excitation energies (0.414-41.4 meV) are related to two intrinsic properties of THz vibrations: the potential energy surfaces (PESs) are shallow, and the vibrationally excited states are usually populated via thermal fluctuations. The shallow PESs make the vibrations usually anharmonic, leading to redshifted vibrational excited state absorption; combined with considerable vibrational excited states population, characteristic THz signals are usually redshifted and congested with varying degrees at different temperatures. Combining existing experimental THz spectra at low temperatures, first principles vibration analysis, and the Morse potential, we developed a semi-empirical model to evaluate the anharmonicity of the low-frequency modes. The model was benchmarked with purine molecular crystal to generate THz spectra at different temperatures, the results were consistent with experiments. The good agreement suggests this model would facilitate the application of THz spectroscopy in molecular crystal characterization.     

Theoretical analysis of the terahertz spectrum of the high explosive PETN.

The experimental solid-state terahertz (THz) spectrum (3 to 120 cm(-1)) of the high explosive pentaerythritol tetranitrate (PETN, C(5)H(6)N(4)O(12)) has been modeled using solid-state density functional theory (DFT) calculations. Solid-state DFT, employing the BP density functional, is in best qualitative agreement with the features in the previously reported THz spectrum. The crystal environment of PETN includes numerous intermolecular hydrogen-bonding interactions that contribute to large (up to 80 cm(-1)) calculated shifts in molecular normal-mode positions in the solid state. Comparison of the isolated-molecule and solid-state normal-mode calculations for a series of density functionals reveals the extent to which the inclusion of crystal-packing interactions and the relative motions between molecules are required for correctly reproducing the vibrational structure of solid-state THz spectra. The THz structure below 120 cm(-1) is a combination of both intermolecular (relative rotations and translations) and intramolecular (torsions, large amplitude motions) vibrational motions. Vibrational-mode analyses indicate that the first major feature (67.2 cm(-1)) in the PETN THz spectrum contains all of the optical rotational and translational cell modes and no internal (molecular) vibrational modes.     

A study into the effect of subtle structural details and disorder on the terahertz spectrum of crystalline benzoic acid

The phonon modes of crystalline benzoic acid have been investigated using terahertz time-domain spectroscopy, rigid molecule atom-atom model potential and plane-wave density functional theory lattice dynamics calculations. The simulation results show good agreement with the measured terahertz spectra and an assignment of the terahertz absorption features of benzoic acid is made with the help of both computational methods. Focussing on the strongest interactions in the crystal, we describe each vibration in terms of distortions of the benzoic acid hydrogen bonded dimers that are present in the crystal structure. The terahertz spectrum is also shown to be highly sensitive to the location of the carboxylic acid hydrogen atoms in the cyclic hydrogen-bonded dimers and we have systematically explored the influence of the observed disorder in the hydrogen atom positions on the lattice dynamics.     

Vibrational spectra of anhydrous and monohydrated caffeine and theophylline molecules and crystals

Density functional theory and classical molecular dynamics simulations are used to investigate the vibrational spectra of caffeine and theophylline anhydrous and monohydrate molecules and those of their crystalline anhydrous and monohydrated states, with emphasis in the terahertz region of the spectra. To better understand the influence of water in the monohydrate crystal spectra, we analyze the vibrational spectra of water monomer, dimer, tetramer, and pentamer, and also those of liquid water at two different temperatures. In small water clusters, we observe the progressive addition of translational and librational modes to the terahertz region of the spectra. The water spectra predicted by rigid and flexible water models is examined with classical molecular dynamics, and the respective peaks, especially in the terahertz region, are compared with those found in the small clusters. Similar analysis done for caffeine and theophylline monohydrate molecules using density functional theory clearly shows the presence of water modes in the librational states and in the water stretching region. Molecular dynamics of caffeine and theophylline anhydrous and monohydrate crystals reveal the influence of vibrations from the molecule-molecule (caffeine or theophylline) crystal stacks and those from the water-molecule interactions found in the monohydrate molecules and new modes from molecule-molecule, water-molecule, and water-water hydrogen bonding interactions arising from collective effects in the crystal structure. Findings illustrate challenges of terahertz technology for the detection of specific substances in condensed phases.     

Measuring molecular force fields: Terahertz,inelastic neutron scattering,Raman, FTIR,DFT, and BOMD molecular dynamics of solid l-serine

A vibrational analysis of polycrystalline l-serine is provided using experimental terahertz, FTIR, Raman and inelastic neutron scattering (INS) spectra, calculated INS spectra – and Born–Oppenheimer molecular dynamics (BOMD) simulations from which the power spectra for the electronegative elements are compared to the THz spectra. Corrections are made to density functional theory (DFT) calculations for van der Waals interactions. Assignments and potential energy distributions are included for all 3N = 336 normal modes of an eight molecule supercell, including those for 48 non-bonded whole molecule translating and rotating vibrations, of which three are acoustic modes, usually not considered. Calculated and observed frequencies differ by an average 3 cm⁻¹ (s = 4). The INS spectrum of these modes below 100 cm⁻¹, calculated from energy second derivatives, show a remarkable similarity to the experimental 10 K spectra. The calculated low frequency modes are insensitive to small changes in cell parameters and geometry. THz intensities are represented by power spectra and not calculated explicitly. Nevertheless, power spectra of 13 ps BOMD trajectories at classical temperatures of 20 K, 400 K, and 500 K are markedly similar to the experimental terahertz spectra at 77 K and 298 K. Calculations on a serine crystal supercell 2 × 2 × 2 molecules deep appear to include, in a crude but fortuitously accurate way, enough of the principle out of phase dispersion to yield a match with experimental frequencies and intensities.     

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).     

Explicit representation of anisotropic force constants for simulating intermolecular vibrations of multiply hydrogen-bonded systems

We investigated the mechanical nature of multiply hydrogen-bonded systems by means of ab initio quantum chemical calculations, and we derived a set of force constants to reproduce the anisotropic vibration modes of such systems. Twenty multiply hydrogen-bonded molecular dimers were selected for evaluation of the stiffness of their hydrogen bonds. By means of a multivariate analysis, the principal values of the stiffness tensor were divided into the contributions from each hydrogen bond. Force constants in the stretching directions were estimated to be 20.2 and 11.5 N m(-1) for NH...O and NH...N pairs, respectively. The obtained parameter set was used to reconstruct the various intermolecular vibration motions, and reasonable values in the low-frequency (ca. terahertz) region were obtained. Comparison of the multivariate analysis with the normal-mode analysis suggested that the off-diagonal terms for the transverse and rotational motions may appreciably contribute to the coupling of those basic motions.     

Far-infrared characteristics of ZnS nanoparticles measured by terahertz time-domain spectroscopy

The optical and dielectric properties of ZnS nanoparticles are studied by use of terahertz time-domain spectroscopy (THz-TDS) over the frequency range from 0.3 to 3.0 THz. The effective medium approach combined with the pseudo-harmonic model of the dielectric response, where nanoparticles are embedded in the host medium, provides a good fit on the experimental results. The extrapolation of the measured data indicates that the absorption is dominated by the transverse optical mode localized at 11.6+/-0.2 THz. Meanwhile, the low-frequency phonon resonance of ZnS nanoparticles is compared with the single-crystal ZnS. The THz-TDS clearly reveals the remarkable distinction in the low-frequency phonon resonances between ZnS nanoparticles and single-crystal ZnS. The results demonstrate that the acoustic phonons become confined in small-size nanoparticles.     

Understanding the influence of polymorphism on phonon spectra: lattice dynamics calculations and terahertz spectroscopy of carbamazepine

Rigid molecule atomistic lattice dynamics calculations have been performed to predict the phonon spectra of the four polymorphs of carbamazepine, and these calculations predict that there should be differences in the spectra of all four forms. Terahertz spectra have been measured for forms I and III, and there are clearly different features between polymorphs' spectra, that are accentuated at low temperature. While carbamazepine adopts the same hydrogen bonded dimers in all of its known polymorphs, the calculations show that differences in packing arrangements of the dimers lead to changes in the frequency ranges for each type of hydrogen bond vibration, giving a physical explanation to the observed differences between the spectra. Although the agreement between calculated and observed spectra does not allow a definitive characterization of the spectra, it is possible to make tentative assignments of many of the observed features in the terahertz region for the simpler form III; we can only make some tentative assignments of specific modes in the more complex spectrum of form I. While harmonic rigid molecule lattice dynamics shows promise for understanding the differences in spectra between polymorphs of organic molecules, discrepancies between observed and calculated spectra suggest areas of improvement in the computational methods for more accurate modeling of the dynamics in molecular organic crystals.     

Analysis of low-frequency phonons in guanosine dihydrate based on molecular dynamics simulations

Fourier analysis, using the atomic trajectory calculated by molecular dynamics simulation at 300 K, is applied to the study of low-frequency phonons of guanine dihydrate. The vibrational modes of guanine bases are analyzed, and the optically active modes associated with the guanine moieties are extracted. There are a few significant peaks in the low-frequency region. A possible assignment of the Raman active mode near 27 cm(-1), whose origin would be common to the S-mode of DNA double helices, is discussed.     

Exciton dissociation at donor-acceptor polymer heterojunctions: quantum nonadiabatic dynamics and effective-mode analysis

The quantum-dynamical mechanism of photoinduced subpicosecond exciton dissociation and the concomitant formation of a charge-separated state at a semiconducting polymer heterojunction is elucidated. The analysis is based upon a two-state vibronic coupling Hamiltonian including an explicit 24-mode representation of a phonon bath comprising high-frequency (C==C stretch) and low-frequency (torsional) modes. The initial relaxation behavior is characterized by coherent oscillations, along with the decay through an extended nonadiabatic coupling region. This region is located in the vicinity of a conical intersection hypersurface. A central ingredient of the analysis is a novel effective mode representation, which highlights the role of the low-frequency modes in the nonadiabatic dynamics. Quantum dynamical simulations were carried out using the multiconfiguration time-dependent Hartree method.     

Importance of accurate spectral simulations for the analysis of terahertz spectra: citric acid anhydrate and monohydrate

The terahertz (THz) spectra of crystalline solids are typically uniquely sensitive to the molecular packing configurations, allowing for the detection of polymorphs and hydrates by THz spectroscopic techniques. It is possible, however, that coincident absorptions may be observed between related crystal forms, in which case careful assessment of the lattice vibrations of each system must be performed. Presented here is a THz spectroscopic investigation of citric acid in its anhydrous and monohydrate phases. Remarkably similar features were observed in the THz spectra of both systems, requiring the accurate calculation of the low-frequency vibrational modes by solid-state density functional theory to determine the origins of these spectral features. The results of the simulations demonstrate the necessity of reliable and rigorous methods for THz vibrational modes to ensure the proper evaluation of the THz spectra of molecular solids.