Anharmonic Motion Research Articles

Anharmonic thermal motion in glutathion investigated by the maximum entropy method (MEM)

Anharmonic thermal motion in glutathion investigated by the maximum entropy method (MEM)

Enhanced x-ray emission from nano-particle doped bacteria.

Recently, it has been greatly appreciated that intense light matter interaction is modified due to the nano- and microstructures in the target by--surface plasmons, laser energy localization scattering etc. Extreme laser intensities produce dense plasmas and collective mechanisms generate energetic electrons, ions and hard x-rays. Recently, it is postulated that the anharmonic electron motion, driven by ultrashort, high-intensity laser pulses, provides a universal mechanism for the laser absorption. Here, we provide the first demonstration of anharmonic-resonance-aided high laser-absorption in a biological system. At intensities of ∼ 10¹⁶⁻¹⁸ W/cm², 40 fs pulses excite a plasma formed with E. coli bacteria. The density-inhomogeneities due to the micro- and nanostructures in the bacterial target increase anharmonic resonance (AHR) heating and result in a 10⁴-fold enhancement in the hard x-ray yield compared to plain solid targets. These observations lead to novel high-energy x-ray sources that have implications to lithography, imaging and medical applications.

Anharmonic Nuclear Motion and the Relative Stability of Hexagonal and Cubic ice

We use extensive first-principles quantum mechanical calculations to show that, although the static lattice and harmonic vibrational energies are almost identical, the anharmonic vibrational energy of hexagonal ice is significantly lower than that of cubic ice. This difference in anharmonicity is crucial, stabilising hexagonal ice compared with cubic ice by at least 1.4 meV/H2O, in agreement with experimental estimates. The difference in anharmonicity arises predominantly from molecular O-H bond stretching vibrational modes and is related to the different stacking of atomic layers.

Dynamic cooperative behavior of constituting species at the glass transition vicinity

Liquid and its freeze-in form of constrained glasses are assumed to consist from both the mechanically divided structure formed by blocks and the individual semi-evaporated units subjected to nonlinear anharmonic motions of high amplitudes. The sequence of characteristic temperatures is classified from the boiling point temperature T b through crossover temperature T cr, transition temperature of glassy state T g and down to the Vogel’s temperature T v, recognizing that T b ≥ T cr ≥ T g ≥ T v and taking into account distinct characteristics of vibration modes at different temperatures. Above T cr, the termination of bridge-over effect of blocks is assumed and the level of shear modulus contributed by bridging falls down to zero. The Angell’s famous equation on fragility dealing with the shear viscosity derivative relatively to inverse absolute temperature is replaced by the thermal sensitivity seeing it as an alternative expression when the quantity G is employed to represent the Young’s module of elasticity in shear. An outlook of Czech and Slovak sourced papers on glass structure and its formability is available.

Moving solitons in a one-dimensional fermionic superfluid

A fully analytical theory of a traveling soliton in a one-dimensional fermionic superfluid is developed within the framework of time-dependent self-consistent Bogoliubov-de Gennes equations, which are solved exactly in the Andreev approximation. The soliton manifests itself in a kink-like profile of the superconducting order parameter and hosts a pair of Andreev bound states in its core. They adjust to soliton's motion and play an important role in its stabilization. A phase jump across the soliton and its energy decrease with soliton's velocity and vanish at the critical velocity, corresponding to the Landau criterion, where the soliton starts emitting quasiparticles and becomes unstable. The "inertial" and "gravitational" masses of the soliton are calculated and the former is shown to be orders of magnitude larger than the latter. This results in a slow motion of the soliton in a harmonic trap, reminiscent to the observed behavior of a soliton-like texture in related experiments in cold fermion gases [T. Yefsah et al., Nature 499, 426, (2013)]. Furthermore, we calculate the full non-linear dispersion relation of the soliton and solve the classical equations of motion in a trap. The strong non-linearity at high velocities gives rise to anharmonic oscillatory motion of the soliton. A careful analysis of this anharmonicity may provide a means to experimentally measure the non-linear soliton spectrum in superfluids.

Nuclear-weighted X-ray maximum entropy method - NXMEM.

Subtle structural features such as disorder and anharmonic motion may be accurately characterized from nuclear density distributions (NDDs). As a viable alternative to neutron diffraction, this paper introduces a new approach named the nuclear-weighted X-ray maximum entropy method (NXMEM) for reconstructing pseudo NDDs. It calculates an electron-weighted nuclear density distribution (eNDD), exploiting that X-ray diffraction delivers data of superior quality, requires smaller sample volumes and has higher availability. NXMEM is tested on two widely different systems: PbTe and Ba(8)Ga(16)Sn(30). The first compound, PbTe, possesses a deceptively simple crystal structure on the macroscopic level that is unable to account for its excellent thermoelectric properties. The key mechanism involves local distortions, and the capability of NXMEM to probe this intriguing feature is established with simulated powder diffraction data. In the second compound, Ba(8)Ga(16)Sn(30), disorder among the Ba guest atoms is analysed with both experimental and simulated single-crystal diffraction data. In all cases, NXMEM outperforms the maximum entropy method by substantially enhancing the nuclear resolution. The induced improvements correlate with the amount of available data, rendering NXMEM especially powerful for powder and low-resolution single-crystal diffraction. The NXMEM procedure can be implemented in existing software and facilitates widespread characterization of disorder in functional materials.

On the nonlinear dynamics of a quantum oscillator

A quantum version of the asymptotic approach in the theory of anharmonic oscillator motion is proposed. It is shown that quantum transitions from the most likely stationary state to the nearest quantum level correspond to the classical Eigen frequency. This frequency depends on the oscillator amplitude. Quantum corrections to the motion of a classical nonlinear oscillator are determined.

First experimental charge density study using a Bruker CMOS-type PHOTON 100 detector: the case of ammonium tetraoxalate dihydrate.

The aim of this study was to test the applicability of a Bruker AXS CMOS-type PHOTON 100 detector for the purpose of a fine charge density quality data collection. A complex crystal containing oxalic acid, ammonium oxalate and two water molecules was chosen as a test case. The data was collected up to a resolution of 1.31 Å(-1) with high completeness (89.1%; Rmrg = 0.0274). The multipolar refinement and subsequent quantum theory of atoms in molecules (QTAIM) analysis resulted in a comprehensive description of the charge density distribution in the crystal studied. The residual density maps are flat and almost featureless. It was possible to derive reliable information on intermolecular interactions to model the anharmonic motion of a water molecule, and also to observe the fine details of the charge density distribution, such as polarization on O and H atoms involved in the strongest hydrogen bonds. When compared with our previous statistical study on oxalic acid data collected with the aid of CCD cameras, the complementary metal-oxide semiconductor (CMOS) detector can certainly be classified as a promising alternative in advanced X-ray diffraction studies.

Universality of Anharmonic Motion of Heavy Rare-Earth Atoms in Hexaborides

Phonons of TbB6 are studied by inelastic X-ray scattering and compared with those of GdB6 and DyB6. Measured low-lying phonon modes located near 6 meV soften distinctly with decreasing temperature, particularly the longitudinal phonon that is dominated by the motion of Tb ions at \(\boldsymbol{{q}}_{1} = (1/2,0,0)\). The magnitude and temperature dependence of phonon energy are between those of GdB6 and DyB6. We derive a Landau-type free-energy expansion with respect to the atomic displacement in TbB6, and discuss a general feature among these three compounds. The systematic variation in the phonon characteristics of these hexaborides and the first-order-like instability indicate the universality of the anharmonic motion of heavy rare-earth atoms in RB6 (R = Gd, Tb, and Dy).

Efficient anharmonic vibrational spectroscopy for large molecules using local-mode coordinates.

This article presents a general computational approach for efficient simulations of anharmonic vibrational spectra in chemical systems. An automated local-mode vibrational approach is presented, which borrows techniques from localized molecular orbitals in electronic structure theory. This approach generates spatially localized vibrational modes, in contrast to the delocalization exhibited by canonical normal modes. The method is rigorously tested across a series of chemical systems, ranging from small molecules to large water clusters and a protonated dipeptide. It is interfaced with exact, grid-based approaches, as well as vibrational self-consistent field methods. Most significantly, this new set of reference coordinates exhibits a well-behaved spatial decay of mode couplings, which allows for a systematic, a priori truncation of mode couplings and increased computational efficiency. Convergence can typically be reached by including modes within only about 4 Å. The local nature of this truncation suggests particular promise for the ab initio simulation of anharmonic vibrational motion in large systems, where connection to experimental spectra is currently most challenging.

Dithiadiazolyl Radicals—Structures and Charge Densities of Their Crystals and Co-Crystal

The results of experimental charge density studies on single crystals of two pure 1,2,3,5-dithiadiazolyl radical compounds (PhCN2S2, H-radical and C6F5CN2S2, F-radical) and their co-crystal (HF-radical) are presented. For all three cases, the use of anharmonic motions of the sulfur atoms (in the form of the Gram–Charlier expansion up to the third order) significantly improved the final refinement results. All of the above moieties form dimers in the crystal lattices of the studied compounds and have very similar geometrical parameters. The strength of the interactions in the dimers increases in the order: H-, F-, and HF-radicals, respectively. Calculated spin densities are almost entirely located on the nitrogen and sulfur atoms of the dithiadiazolyl rings, which results in a strong attraction between these molecular fragments in the dimers. Experimental electron density parameters obtained for all crystals are very consistent. The S–S bonds in all of the moieties have a partially shared character as conf...

Applications of X-ray Wavefunction Refinement

X-ray wavefunction refinement (XWR) is a way of modeling the total aspherical electron density from an X-ray diffraction experiment on a single crystal of a molecular compound. It is a combination of existing quantum-crystallographical techniques: In the first step, geometry is determined using Hirshfeld atom refinement,[1] which is based on a stockholder partitioning of quantum-mechanical aspherical electron densities. In the second step, the same wavefunction is fitted to the experimental data to reproduce the diffraction pattern and simultaneously minimize the molecular energy.[2] The XWR protocol involves embedding the molecule into a field of point charges and dipoles as well as termination strategies to avoid overfitting.[3] Results from an X-ray wavefunction refinement are not restricted to the analysis of electron density: the full reconstructed density matrix is available. Therefore, chemical problems can be tackled with suitable tools for any given question including, e.g., experimentally derived bond orders, electron-pair localisation information, or energetics. We will present first applications of this protocol for a selection of organic (hydrogen maleate salts, sulfur-containing protease inhibitors) and inorganic (siloxanes, sulfur dioxide) compounds, for which we measured high-resolution low-temperature X-ray diffraction data at various synchrotron facilities. We will show geometry improvements, anisotropic displacement parameters for hydrogens, anharmonic motion parameters for sulfur and chlorine atoms, and improved total electron-density distributions in comparison to results from multipole modeling. Moreover, we will discuss the contribution of the experimental data to the final constrained wavefunction (defect density) and demonstrate how the experimentally derived orbital-based descriptors assist in solving fundamental chemical problems.

Hydrogen bond coupling in sodium dihydrogen triacetate.

The coupling of hydrogen bonds is central to structures and functions of biological systems. Hydrogen bond coupling in sodium dihydrogen triacetate (SDHTA) is investigated as a model for the hydrogen bonded systems of the type O-H…O. The two-dimensional potential energy surface is derived from the full-dimensional one by selecting the relevant vibrational modes of the hydrogen bonds. The potential energy surfaces in terms of normal modes describing the anharmonic motion in the vicinity of the equilibrium geometry of SDHTA are calculated for the different species, namely, HH, HD, DH, and DD isotopomers. The ground state wave functions and their relation to the hydrogen bond structural parameters are discussed. It has been found that the hydrogen bonds in SDHTA are uncoupled, that is elongation of the deuterated hydrogen bond does not affect the non-deuterated one.

How does glycerol enhance the bioprotective properties of trehalose? Insight from protein-solvent dynamics.

We present Raman investigations on lysozyme/trehalose/glycerol solutions at low water content, from room temperature up to the occurrence of the protein thermal denaturation. We studied the Amide I band and the low-frequency spectrum as a function of the glycerol content. The former allows us to monitor the protein unfolding; the latter probes the protein and solvent dynamics in anharmonic and quasi-harmonic regimes. It was shown that adding a small amount of glycerol to trehalose stiffens the dry matrix in which proteins are embedded, thus improving their stability. The analysis of the Amide I band reveals that glycerol enhances the stabilization effect of trehalose on proteins for low water content, but still liquid, systems. Data show that the protein unfolding temperature has a maximum value around 5% Glyc/TRE g/g. The overlapping low-frequency contributions, corresponding to fast anharmonic and quasi-harmonic motions, respectively, related to the mean square displacement ⟨u(2)⟩ and the vibrational density of states (VDOS) usually determined by neutron scattering experiments, have been carefully analyzed to understand the effect of glycerol. The intensity of the quasi-elastic scattering (QES) peak reveals a dynamical-like transition at high temperatures, close to the denaturation temperature. This one, as well as the low-frequency vibrational modes, reflects the same enhanced trend of the Amide I band with respect to the glycerol concentration, but at lower temperatures. A linear correlation is found among the transition temperatures of both the dynamical-like transition and the low-frequency modes, as well as the temperature dependent change of the Amide I frequency. This confirms the solvent dynamics as a necessary precursor to promote protein unfolding. Glycerol anti-plasticizes the matrix with respect to the trehalose by enhancing the stability of the protein in a more rigid trehalose/water/glycerol matrix. As expected from the analysis of the Amide I band, the maximum effect of glycerol on trehalose is determined for 5% Glyc/TRE content.

Anharmonicity and isomorphic phase transition: a multi-temperature X-ray single-crystal and powder diffraction study of 1-(2'-aminophenyl)-2-methyl-4-nitroimidazole.

The harmonic model of atomic nuclear motions is usually enough for multipole modelling of high-resolution X-ray diffraction data; however, in some molecular crystals, such as 1-(2'-aminophenyl)-2-methyl-4-nitro-1H-imidazole [Paul, Kubicki, Jelsch et al. (2011 ▶). Acta Cryst. B67, 365-378], it may not be sufficient for a correct description of the charge-density distribution. Multipole refinement using harmonic atom vibrations does not lead to the best electron density model in this case and the so-called 'shashlik-like' pattern of positive and negative residual electron density peaks is observed in the vicinity of some atoms. This slight disorder, which cannot be modelled by split atoms, was solved using third-order anharmonic nuclear motion (ANM) parameters. Multipole refinement of the experimental high-resolution X-ray diffraction data of 1-(2'-aminophenyl)-2-methyl-4-nitro-1H-imidazole at three different temperatures (10, 35 and 70 K) and a series of powder diffraction experiments (20 ≤ T ≤ 300 K) were performed to relate this anharmonicity observed for several light atoms (N atoms of amino and nitro groups, and O atoms of nitro groups) to an isomorphic phase transition reflected by a change in the b cell parameter around 65 K. The observed disorder may result from the coexistence of domains of two phases over a large temperature range, as shown by low-temperature powder diffraction.

The Role of Water in Dynamics of Biomacromolecules: A Mutual Interplay!

We studied the dynamics of hydrated model RNA and protein using neutron and dielectric spectroscopy techniques combined with MD simulations. A comparison of our results with earlier data reveals that the dynamics of hydrated RNA is slower and varies more strongly with temperature than the dynamics of hydrated proteins. We demonstrate that a similar difference appears in the dynamics of hydration water for these biomolecules. In addition, we investigated the role of water and monovalent ion on the appearance of anharmonic motions in RNA by MD simulations of hydrated hammerhead RNA at various temperatures. While the dynamics of monovalent ions interacting with RNA infers a stronger coupling than that of water, it is found that the relaxation of water from the surface of RNA is sufficient for the increase in anharmonic motions above the dynamical transition temperature. The nature and temperature dependence of fast and slow hydrogen bond dynamics between proteins and RNA were found to be similar thus indicating that the dynamical transition of RNA and proteins are governed by relaxation of surface hydration water. Our results demonstrate that the dynamics of biological macromolecules and their hydration is a result of the mutual influence of biomolecules and their hydration water.

Structure of A0, A1 and A3 conformational substates of carbonmonoxy myoglobin

Infrared absorption spectra of carbon monoxide molecule coordinated by the heme iron of carbonmonoxy heme proteins are widely used to study their structure and dynamics. In this paper we use results of X-ray study of carbonmonoxy myoglobin to elucidate the structures of spectroscopically observed conformational substates of this protein. It is shown that A3 substate corresponds to the structure with water molecule hydrogen bonded to the distal histidine, whereas in the A1 conformation this molecule is absent. We also show that redistribution of electronic density of the distal histidine and the water molecule as a result of their interaction must be taken into account when predicting their positions in the heme pocket. 1. Background Relationship between the dynamics of biological molecules their structure and function is an important problem of modern chemistry and physics. Heme proteins play a special role in these studies because their active center, heme, can be studied by virtually all spectroscopic techniques. In particular, kinetic measurements of CO recombination after photolysis of carbonmonoxy myoglobin (Mb(CO)) lead to the view of conformational substates (CSS) and energy barriers (2,3,5). Population of different CSSs is very important for the protein function and causes strongly anharmonic motion of proteins and their very specific function (1,4). It was shown that in Mb(CO) there are at least three structurally different CSSs, which correspond to three peaks in the infrared absorption spectrum of the carbon monoxide coordinated by the heme iron at: νCO ≈ 1966 cm −1 , 1945 cm −1 and 1933 cm −1 (11). These three peaks were ascribed to three conformational substates: A0 ,A 1 and A3, respectively. The variation in the CO peak position was shown to be caused by electrostatic interaction of the heme with the protein electric filed (7-9,13). The A0 CSS was ascribed to a conformation with the distal histidine located out of the heme pocket (7,8,12,13,16). The structures of the A1 and A3 CSSs were discussed intensively, but all attempts to elucidate these structures using different theoretical approaches, including molecular dynamics (10,14), failed. At the same time recently the crystal structure of Mb(CO) (15) was revised (PDB entrance 1a6g), the latest data clearly showed presence of three CSSs.

Computation of Nonlinear Optical Properties of Molecules with Large Amplitude Anharmonic Motions. III. Arbitrary Double-Well Potentials.

We thank David Lauvergnat for helpful advice concerning the programs TNUM and ELVIBROT. H.R, J.M.L., and. MG.-B. gratefully acknowledge support from the European Union (MTKD-CT-2006-042488). J.M.L. and M.G.-B. thank the Spanish Ministerio de Ciencia e Innovacion (MICINN, CTQ2011-23156/BQU) and the DIUE of the Generalitat de Catalunya (2009SGR637) for financial support. M.G.-B. thanks the Spanish MEC for a doctoral fellowship (No. AP2010-2517)

Physical, optical and nonlinear properties of InS single crystal

Indium Sulphide (InS) single crystals are successfully grown by In flux. Single crystal X-ray diffraction shows orthorhombic structure of Pnnm space group. Ellipsometry measurements performed on the (010) oriented crystal exhibit low anisotropy in the 300–1000nm wavelength range and consequently negligible THz transmission is observed. Optical band gap of 2.09eV is deduced from linear optical measurements. Nonlinear optical properties are studied by single beam Z-scan measurements at 800nm, where two-photon absorption is present. Nonlinear refractive index and absorption coefficient are estimated to be n2=2.3×10−11cm2/W and β=62.4cm/GW, respectively for excitation intensity of 0.32GW/cm2. The origin of nonlinearity in InS crystal is accounted to be due to the third-order anharmonic motion of the bound electrons.

Role of Water and Ions on the Dynamical Transition of RNA

We have performed molecular dynamics simulations of hydrated polycrystalline powder hammerhead ribozyme at various temperatures from 50 to 300 K to determine the role of water and ions on the dynamical transition of RNA. Calculated mean-square displacement as a function of temperature is in agreement with existing neutron scattering experiments. Using this model, we were able to investigate the role of water and monovalent ion structure and dynamics on the appearance of anharmonic motions in RNA as a function of temperature. Compared to experimental and simulation results of proteins under similar environmental conditions, the amplitude of motions in RNA are smaller. While the structure and dynamics of monovalent ions interacting with RNA infer a stronger coupling than that of water, it is found that the relaxation of water from the surface of RNA is sufficient for the increase in anharmonic motions above the dynamical transition temperature. The nature and temperature dependence of fast and slow hydrogen bond dynamics between proteins and RNA were found to be similar, thus indicating that the dynamical transition of RNA and proteins are governed by relaxation of surface hydration water.