Local Vibrational Modes Research Articles

PyVibMS: a PyMOL plugin for visualizing vibrations in molecules and solids.

Visualizing vibrational motions calculated with different ab initio packages requires dedicated post-processing tools. Here, we present a PyMOL plugin called PyVibMS for visualizing the vibrational motions for both molecular and solid systems calculated by mainstream quantum chemical computer programs including Gaussian, Q-Chem, VASP, and CRYSTAL. Benefiting from the continuing development of the PyMOL platform, PyVibMS provides powerful functionalities and user-friendly interface. PyVibMS was written in Python and its open-source nature makes it flexible and sustainable. As an example, the motions of the Konkoli-Cremer local vibrational modes are shown in this work for the first time. PyVibMS is freely available at https://github.com/smutao/PyVibMS . Graphical abstract In this work, a PyMOL plugin named PyVibMS is developed to visualize molecular and lattice vibrations.

Critical assessment of the FeC and CO bond strength in carboxymyoglobin: a QM/MM local vibrational mode study.

The interplay between FeC and CO bonding in carboxymyoglobin (MbCO) and the role of potential hydrogen bonding between the CO moiety and the side chains of the surrounding protein amino acids have been the subject of numerous experimental and theoretical studies. In this work, we present a quantitative measure for the intrinsic FeC and CO bond strength in MbCO, as well as for CO⋯H bonding, based on the local vibrational mode analysis, originally developed by Konkoli and Cremer. We investigated a gas phase model, two models of the wild-type protein, and 17 protein mutations that change the distal polarity of the heme pocket, as well as two protein mutations of the heme porphyrin ring. Based on local mode force constants, we could quantify for the first time the suggested inverse relationship between the CO and FeC bond strength, the strength of CO⋯H bonding, and how it weakens the CO bond. Combined with the natural orbital analysis, we could also confirm the key role of π back donation between Fe and the CO moiety in determining the FeC bond strength. We further clarified that CO and FeC normal modes couple with other protein motions in the protein environment. Therefore, normal mode frequencies/force constants are not suited as bond strength descriptors and instead their local mode counterparts should be used. Our comprehensive results provide new guidelines for the fine-tuning of existing and the design of MbCO models with specific FeC, CO, and CO⋯H bond strengths.Graphical abstract.

Equilibrium Geometries, Adiabatic Excitation Energies and Intrinsic C=C/C–H Bond Strengths of Ethylene in Lowest Singlet Excited States Described by TDDFT

Seventeen singlet excited states of ethylene have been calculated via time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the geometries of 11 excited states were optimized successfully. The local vibrational mode theory was employed to examine the intrinsic C=C/C–H bond strengths and their change upon excitation. The natural transition orbital (NTO) analysis was used to further analyze the C=C/C–H bond strength change in excited states versus the ground state. For the first time, three excited states including πy′ → 3s, πy′ → 3py and πy′ → 3pz were identified with stronger C=C ethylene double bonds than in the ground state.

Modeling, dynamics, and parametric studies of a multi-cable-stayed beam model

To study the dynamic behavior of cable-stayed bridges, a linear multi-cable-stayed beam model is developed to investigate its in-plane and out-of-plane transverse vibrations. From the full-bridge perspective, an in-plane nonlinear single-mode discrete model is established. First, the in-plane and out-of-plane motion equations of the system and their boundary conditions are derived. Second, by employing the separation of variables method, the linear eigenvalue problems are solved. The influences of the mass ratio, stiffness ratio, and cable sag on the occurrence of global, local, and coupled vibration modes are studied. Third, frequency response, amplitude response, phase diagram, time history, and power spectrum are extracted to investigate the system’s nonlinear dynamic behaviors. The obtained results demonstrate that for the in-plane motion, the occurrence of global and local modes of the system depends on the mass and stiffness ratios between cable and beam significantly; for the out-of-plane motion, without the elastic support of the cable, the global modes occur, which can be suppressed by adjusting the mass and stiffness ratios between cable and beam but may in turn induce the cable’s local vibration modes; for the nonlinear analysis, the single-degree-of-freedom system behaves like a hardening spring. Its lower branch behaves more complicated than the higher one and has a double-periodic steady-state solution. The system with large damping ratio behaves shows weak hardening spring property.

Topology optimization of dynamic acoustic–mechanical structures using the ersatz material model

Topology optimization of dynamic acoustic–mechanical structures is challenging due to the interaction between the acoustic and structural domains and artificial localized vibration modes of structures. This paper presents a floating projection topology optimization (FPTO) method based on the mixed displacement/pressure (u/p) finite element formulation and the ersatz material model. The former is able to release the need for tracking the interface boundaries explicitly between the structural and acoustic domains during the optimization process. The ersatz material model enables us to entirely avoid artificial localized vibration modes caused by the extremely high ratio between mass and stiffness. The floating projection simulates the original 0/1 constraints, and it gradually pushes the design variables toward 0 or 1 at the desired level so that the optimized element-based design can be accurately represented by a smooth design. Some 2D and 3D numerical examples, including minimizing sound pressure at the designated domain, restraining structural vibration, and maximizing sound transmission loss, are presented to demonstrate the effectiveness of the proposed topology optimization algorithm. The optimized solutions achieve the consistency of the objective function between the element-based design using the mixed formulation and the smooth design using the segregated formulation. The study suggests that the FPTO method using the ersatz material model is a promising approach for optimizing dynamic acoustic-mechanical structures.

Theoretical Study of the Local Vibrational Modes at Shock Wave Front for Energetic Material

AbstractWe evaluate the shock wave profile of β‐octahydro‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocine (β‐HMX) by steady flow theory and calculate the force constants by density functional theory. Based on these results, a method to calculate the local phonon states at shock front is developed. We find that the phonon density of states (PDOS) of shock front is non‐intersect with the PDOS of crystal, and obtain four important vibrational modes for shock wave: N−NO2 stretch, NO wagging, CH2 wagging, and N‐NC2 stretch. According to the vibrational modes, the initial decomposition reactions of β‐HMX at shocked state are denitrification, hydrogen transfer, and ring‐opening reactions.

Probing Local Vibration Modes at Single Planar Defects by Vibrational Spectroscopy

Probing Local Vibration Modes at Single Planar Defects by Vibrational Spectroscopy

Substitutional Sulfur in CdSe: Localized Vibrational Modes

The substitutional sulfur at the selen site in wurtzite CdSe is identified by a combination of infrared absorption spectroscopy and first principles calculations. The dominant isotope gives rise to two local vibrational modes at 270.6 and 271.4 cm−1 (10 K) assigned to the nondegenerate and the twofold degenerate E representations of the point group. The corresponding signals of the isotope occur at 263.6 and 264.4 cm−1. The results of measurements performed on a set of samples supplied by different manufacturers highlight that sulfur is an ubiquitous impurity in CdSe unintentionally incorporated into the crystals during the process of growth.

Local Vibrational Mode Analysis of π–Hole Interactions between Aryl Donors and Small Molecule Acceptors

11 aryl–lone pair and three aryl–anion π –hole interactions are investigated, along with the argon–benzene dimer and water dimer as reference compounds, utilizing the local vibrational mode theory, originally introduced by Konkoli and Cremer, to quantify the strength of the π –hole interaction in terms of a new local vibrational mode stretching force constant between the two engaged monomers, which can be conveniently used to compare different π –hole systems. Several factors have emerged which influence strength of the π –hole interactions, including aryl substituent effects, the chemical nature of atoms composing the aryl rings/ π –hole acceptors, and secondary bonding interactions between donors/acceptors. Substituent effects indirectly affect the π –hole interaction strength, where electronegative aryl-substituents moderately increase π –hole interaction strength. N-aryl members significantly increase π –hole interaction strength, and anion acceptors bind more strongly with the π –hole compared to charge neutral acceptors (lone–pair donors). Secondary bonding interactions between the acceptor and the atoms in the aryl ring can increase π –hole interaction strength, while hydrogen bonding between the π –hole acceptor/donor can significantly increase or decrease strength of the π –hole interaction depending on the directionality of hydrogen bond donation. Work is in progress expanding this research on aryl π –hole interactions to a large number of systems, including halides, CO, and OCH3− as acceptors, in order to derive a general design protocol for new members of this interesting class of compounds.

Charge Accumulation of Amplified Spontaneous Emission in a Conjugated Polymer Chain and Its Dynamical Phonon Spectra.

In this article, the detailed photoexcitation dynamics which combines nonadiabatic molecular dynamics with electronic transitions shows the occurrence of amplified spontaneous emission (ASE) in conjugated polymers, accompanied by spontaneous electric polarization. The elaborate molecular dynamic process of ultrafast photoexcitation can be described as follows: Continuous external optical pumping (laser of 70 µJ/cm2) not only triggers the appearance of an instantaneous four-level electronic structure but causes population inversion for ASE as well. At the same time, the phonon spectrum of the conjugated polymer changes, and five local infrared lattice vibrational modes form at the two ends, which break the original symmetry in the system and leads to charge accumulation at the ends of the polymer chain without an external electric field. This novel phenomenon gives a brand-new avenue to explain how the lattice vibrations play a role in the evolution of the stimulated emission, which leads to an ultrafast effect in solid conjugated polymers.

Quantitative assessment of intramolecular hydrogen bonds in neutral histidine

Experimentalists recently characterized the difficulty in isolating gaseous histidine in its neutral form. To understand the factors which stabilize neutral histidine, the intrinsic nature of the intramolecular hydrogen bonding networks in the four most stable histidine conformers was investigated via density functional theory combined with the local vibrational mode analysis originally introduced by Konkoli and Cremer, quantum theory of atoms in molecules, non-covalent interaction analysis, and natural bond orbital population analysis. Our results show a positive correlation between intramolecular hydrogen bond strength and structural stability, where the presence of the $$\hbox {O}{-}\hbox {H}\cdots \hbox {N}_{\alpha }$$ bond type is a major factor.

Local vibrational modes of natural isotopes of substitutional oxygen in CdTe

We investigated the localized vibrational modes (LVM) of natural oxygen containing $^{16}$O, $^{17}$O, and $^{18}$O isotopes at a substitutional tellurium site in cadmium telluride using infrared absorption spectroscopy at cryogenic temperatures. The main absorption peak observed at 350 cm$^{-1\, }$was formerly attributed to a fundamental LVM mode ($\nu _{0})$ of oxygen at a tellurium site. The relatively weak absorption peaks observed at 331 cm$^{-1\, }$and 340 cm$^{-1\, }$are assigned as the same $\nu_{0}$ mode of the $^{17}$O and $^{18}$O isotopes, respectively, based on their relative intensities and spectral positions. The spectral positions were confirmed with theoretical calculations using a linear chain model where the peak position at 350 cm$^{-1}$ was taken as the reference for the $^{16}$O isotope. From a least square analysis of the observed peak positions we were able to calculate the force constants from perturbation theory. A Lorentzian line shape analysis of each $\nu_{0}$ absorption peak, considering the effects of isotopic mass and natural abundance variations of the host Cd atoms, was also carried out to further confirm their assignments. Reasonably good line shape fittings were obtained for $\nu _{0}$ modes of all isotopes of oxygen.

Anomalous low energy phonon dispersion in bulk silicon-germanium observed by inelastic x-ray scattering

We report on an anomalous mode distinct from both optical and acoustic modes in phonon dispersion curves of bulk Si1−xGex alloy with x taking the values of 0.16, 0.32, 0.45, and 0.72. The anomalous mode at approximately 13 meV was observed directly using inelastic x-ray scattering along the Γ–X ([00q]) direction. The phonon dispersion relations of the anomalous mode indicate that there was no momentum dependence, similar to those of the longitudinal and transverse optical modes (Ge–Ge, Si–Ge, and Si–Si modes). In contrast to the acoustic and optical phonon modes, the energy of the anomalous mode shows no Ge fraction dependence. The molecular dynamics simulation corroborates that the Ge–Ge pairs or Ge atom clusters, which are surrounded by Si atoms, provide the anomalous mode, which is unique to the alloy structure. It has been suggested that such a localized vibration mode with no propagation significantly affects the acoustic modes, leading to low thermal conductivity in the SiGe alloy.

Quantification of Ge fraction using local vibrational modes in Raman spectra of silicon germanium by oil-immersion Raman spectroscopy

We demonstrate that Raman spectra of the local vibrational mode (LVM) for Ge-rich SiGe are useful for the precise determination of Ge fraction. The relationship between Ge fraction and the Raman peak relative intensities of the Si–Si mode and LVM relating to the Si–Si mode was evaluated in detail. Clear negative correlation was found between the intensity ratio and the Ge fraction especially for Ge-rich SiGe thin films obtained by oil-immersion Raman spectroscopy. The present technique provides Ge composition independently from the strain states, therefore we can derive more reliable results than other techniques using peak position, especially for fine structures.

Phase segregation induced third order nonlinear saturable absorption behavior in Erbium doped ZnO nanoparticles synthesized by facile hydrothermal method

Abstract Here in this work, we present the dominance of rare earth dopant (Er) in association with the surfactant (Oleylamine) on the structural, surface morphology, optical, and nonlinear optical properties of hydrothermally grown ZnO nanoparticles. The polycrystalline nature of the prepared nanostructures is confirmed by the XRD diffractograms. The formation of erbium related compound (erbium oxide) in the highest Er doped ZnO nanoparticles is visible from the XRD diffractogram. The incorporation of Er at different doping concentrations (1 at. wt.%, 3 at. wt.%, and 5 at. wt.%) brings noticeable morphological changes in the FESEM images. The Raman spectra reveal the retention of wurtzite structure in undoped and Er doped nanoparticles. The disappearance of A1 (TO) mode in ZnEr3 and ZnEr5 nanoparticles shows the deteriorated polar lattice bond strength. The phase segregation observed from XRD spectrum of ZnEr5 nanoparticles is further confirmed by the detection of local vibrational mode (LVM). A severe decrement in the bandgap of the Er doped nanoparticles is noticed from UV–Vis spectroscopy. A continuous fall in the intensity in the NBE emission with increasing Er doping concentration is attributed to the formation of surface defects below the conduction band edge. The nonlinear optical parameters of the nanoparticles are quantified with the assistance of open aperture and closed aperture Z-scan curves. A remarkable switching from reverse saturable absorption (RSA) to saturable absorption (SA) and self-defocusing to self-focusing mechanisms in ZnEr5 shed light on the impact of phase segregation on the nonlinear response of the Er doped nanoparticles. The quantified values of nonlinear parameters look promising in the fabrication of photonic devices.

Non-Clausius heat transfer: the example of harmonic chain with an impurity

Motivated by recent discussion about the possibility of non-Clausius (from cold to hot) heat flow, we revisit the familiar model of an impurity atom of mass M embedded in an otherwise uniform one-dimensional harmonic lattice of host atoms of mass m. Assuming that the initial distributions for the impurity and the rest of the lattice are uncorrelated and have canonical forms with given temperatures, we show that the average kinetic energy of the impurity may increase with time even if its initial temperature is higher than or equal to that of the lattice. Such an increase is only temporary in uniform lattices and in lattices with a heavy impurity (M ⩾ m), but may be permanent in lattices with a localized vibrational mode generated by a light impurity (M < m). Thus the model shows a non-Clausius spontaneous heat transfer directed from a colder lattice to a hotter impurity.

Experimental investigation for wheel polygonisation of high-speed trains

The wheel polygonisation is the harmonic wave along the wheel circumference, which has been widely reported in high-speed railway vehicles in China in recent years. The polygonization mechanism has not been fully understood yet, and this work discusses one possible mechanism through several experiments. Firstly, a field test for the CRH3 high-speed train with polygonal wheels is carried out. It is found that the vibration in vertical takes major responsibility, and there are several resonance bands for the train-track system. Another field test shows that the rail is sensitive to the polygonisation characteristic frequency, but the wheel axle is not. Then the rail local vibration modes are analyzed by the operational deflection shape (ODS) test in the laboratory. A loaded bogie is fixed on the tested track to simulate the real working conditions. The result shows that the frequency of one local mode is 591 Hz, which is a typical wheel polygonisation frequency. Besides, the wheel-rail contact point is not on the vibration node of this local mode. Thus, the resonance of this local rail mode can be one possible mechanism for the high-order wheel polygonisation.

Intermittent turbulence in a many-body system

In natural settings, intermittent dynamics are ubiquitous and often arise from a coupling between external driving and spatial heterogeneities. A well-known example is the generation of transient, turbulent puffs of fluid through a pipe with rough walls. Here we show how similar dynamics can emerge in a discrete, crystalline system of particles driven by noise. Polydispersity in particle masses leads to localized vibrational modes that effectuate a transition to a gas-like phase. A minimal model for the evolution of the system's mechanical energies exhibits quasi-cyclic oscillations, and a single, dimensionless number captures the essential features of the intermittent dynamics, analogous to the Reynolds number for pipe flow.

Carbon doping of GaN: Proof of the formation of electrically active tri-carbon defects

Carbon doping is used to obtain semi-insulating GaN crystals. If the carbon doping concentration exceeds 5 × 1017 cm−3, the carbon atoms increasingly form triatomic clusters. The tri-carbon defect structure is unambiguously proven by the isotope effect on the defects' local vibrational modes (LVMs) originally found in samples containing carbon of natural isotopic composition (∼99% 12C, ∼1% 13C) at 1679 cm−1 and 1718 cm−1. Number, spectral positions, and intensities of the LVMs for samples enriched with the 13C isotope (∼99% and ∼50%) are consistently interpreted on the basis of the harmonic oscillator model taking into account the probability of possible isotope combinations. Including the polarization dependence of the LVM absorption, we show that the tri-carbon defects form a triatomic molecule-like structure in two crystallographically different configurations: a basal configuration with the carbon bonds near the basal plane and an axial configuration with one of the carbon bonds along the c axis. Finally, the disappearance of the LVMs under additional below-bandgap illumination is interpreted as defect recharging, i.e., the tri-carbon defects possess at least one charge state transition level within the bandgap and contribute to optical absorption as well as to the electrical charge balance.

Metal–ring interactions in actinide sandwich compounds: A combined normalized elimination of the small component and local vibrational mode study

The relativistic Hamiltonian Normalised Elimination of the Small Component with atomic unitary transformation (NESCau) was used for the first time to calculate geometries and harmonic vibrational frequencies of actinide sandwich compounds (An: Th, Pa, U, Np, Pu; ). In addition, the Local Vibrational Mode analysis, the Natural Bond Orbital analysis, and the Atoms in Molecules analysis were applied to quantitatively assess the intrinsic strength and the nature of the An-ring interactions. Our results show that actinide sandwich compounds prefer strong covalent interactions between actinide and carbon atoms, similar to those found for homologous ferrocene-type complexes . The metal centre rather than the ring size plays a key role in the strength of those interactions.