Collective Vibrational Motion Research Articles

The Marcus dimension: identifying the nuclear coordinate for electron transfer from ab initio calculations.

The Marcus model forms the foundation for all modern discussion of electron transfer (ET). In this model, ET results in a change in diabatic potential energy surfaces, separated along an ET nuclear coordinate. This coordinate accounts for all nuclear motion that promotes electron transfer. It is usually assumed to be dominated by a collective asymmetric vibrational motion of the redox sites involved in the ET. However, this coordinate is rarely quantitatively specified. Instead, it remains a nebulous concept, rather than a tool for gaining true insight into the ET pathway. Herein, we describe an ab initio approach for quantifying the ET coordinate and demonstrate it for a series of dinitroradical anions. Using sampling methods at finite temperature combined with density functional theory calculations, we find that the electron transfer can be followed using the energy separation between potential energy surfaces and the extent of electron localization. The precise nuclear motion that leads to electron transfer is then obtained as a linear combination of normal modes. Once the coordinate is identified, we find that evolution along it results in a change in diabatic state and optical excitation energy, as predicted by the Marcus model. Thus, we conclude that a single dimension of the electron transfer described in Marcus-Hush theory can be described as a well-defined nuclear motion. Importantly, our approach allows the separation of the intrinsic electron transfer coordinate from other structural relaxations and environmental influences. Furthermore, the barrier separating the adiabatic minima was found to be sufficiently thin to enable heavy-atom tunneling in the ET process.

Influence of Vibrational Strong Coupling on an Ordered Liquid Crystal

Vibrational strong coupling and the formation of vibrational polaritons are a result of strong light-matter interaction between a cavity photon and a molecular vibrational mode. The Rabi splitting parameter, which reflects the microscopic light-matter interaction strength, reveals information about the molecular alignment and concerted vibrational motion inside the cavity. We have investigated vibrational strong coupling of 4-cyano-4'-octylbiphenyl liquid crystal molecules in isotropic and smectic A phases. We observed a ∼30% change in the Rabi splitting with the phase transition from isotropic to smectic A by controlling the temperature, together with the onset of polarization-dependent anisotropy of the Rabi splitting in the smectic A phase. Based on the estimated orientational distribution function, we show that the observed Rabi splitting difference in the isotropic and smectic A phases can only be explained by taking into account the influence of collective vibrational motion in the cavity, which affects the molecular properties under the vibrational strong coupling regime.

Front Cover: Length‐Dependent Collective Vibrational Dynamics in Alpha‐Helices (ChemPhysChem 12/2022)

The Front Cover shows collective vibrational motions of alpha-helices inside a protein. Studying the vibrations allows connecting protein structure and function, and therefore benefits de novo protein design. More information can be found in the Research Article by Yunfei Chen and co-workers.

Length‐Dependent Collective Vibrational Dynamics in Alpha‐Helices

The front cover artwork is provided by Prof. Yunfei Chen's group at the Southeast University. The image shows collective vibrational motions of alpha-helices inside a protein. Studying the vibrations allows connecting protein structure and function, and therefore benefits de novo protein design. Read the full text of the Research Article at 10.1002/cphc.202200082.

Long-range DNA-water interactions

DNA functions only in aqueous environments and adopts different conformations depending on the hydration level. The dynamics of hydration water and hydrated DNA leads to rotating and oscillating dipoles that, in turn, give rise to a strong megahertz to terahertz absorption. Investigating the impact of hydration on DNA dynamics and the spectral features of water molecules influenced by DNA, however, is extremely challenging because of the strong absorption of water in the megahertz to terahertz frequency range. In response, we have employed a high-precision megahertz to terahertz dielectric spectrometer, assisted by molecular dynamics simulations, to investigate the dynamics of water molecules within the hydration shells of DNA as well as the collective vibrational motions of hydrated DNA, which are vital to DNA conformation and functionality. Our results reveal that the dynamics of water molecules in a DNA solution is heterogeneous, exhibiting a hierarchy of four distinct relaxation times ranging from ∼8 ps to 1 ns, and the hydration structure of a DNA chain can extend to as far as ∼18 Å from its surface. The low-frequency collective vibrational modes of hydrated DNA have been identified and found to be sensitive to environmental conditions including temperature and hydration level. The results reveal critical information on hydrated DNA dynamics and DNA-water interfaces, which impact the biochemical functions and reactivity of DNA.

Structure and dynamical properties of hydrated F-actin investigated by X-ray scattering

Structure and dynamical properties of hydrated actin filament (F-actin) are revealed by X-ray diffraction and inelastic X-ray scattering (IXS) in a temperature range of 180–298 K, respectively. We assigned the peaks in the radial distribution functions of the hydrated F-actin by molecular dynamics (MD) simulation for F-actin in water. Although the hydration water of F-actin does not freeze in the temperature range measured, the hydrogen-bonded network where hydration water molecules mediate the hydrophilic groups of F-action becomes enhanced with decreasing temperature, as previously seen for many hydrated proteins. By applying a damped harmonic oscillator model to the dynamical structure factor obtained from the IXS spectra of hydrated F-actin, we investigated the intensity and energy of the phonon excitation as a function of temperature. The phonon excitation energy decreased and the phonon population which is proportional to the intensity of the phonon excitation increased with increasing temperature as previously reported for hydrated lysozyme and could be related to the conformational flexibility of the protein regarding the intraprotein short-time collective vibrational motions. In contrast to hydrated lysozyme, these phenomena for hydrated F-actin were observed at ~11 nm−1 of momentum transfer, Q, indicating that they arise from water dimer mediating the hydrophilic parts of F-actin.

Considering vibrations in the thermodynamic functions of a solid adsorbate in slit-like pores

Problems that arise in refining calculations of the equilibrium thermodynamic functions of an adsorbate located near an adsorbent’s surface or inside slit-like pores when its collective vibrational motions are considered are discussed. A technique is proposed for calculating collective vibrations for a small number of vacancies in a defective heterogeneous adsorbate from changes in the number of degrees of freedom and the local frequencies in the frequency distribution function in an ideal bulk crystal.

Inelastic X-ray Scattering Studies of the Short-Time Collective Vibrational Motions in Hydrated Lysozyme Powders and Their Possible Relation to Enzymatic Function

High-resolution inelastic X-ray scattering was used to investigate the collective vibrational excitations in hydrated lysozyme powders as a function of hydration level and temperature. It is found that the samples with strong enzymatic function are "soft", in the sense that they exhibit low frequency and large amplitude intraprotein collective vibrational motions on certain length scales. This is not the case for samples with weak or no enzymatic activity. Thus, we identify a possible correlation between the short-time intraprotein collective vibrational motions and the establishment of enzymatic function in hydrated lysozyme powders, and bring new insight to notions of protein "conformational flexibility" and "softness" in terms of these motions.

Vibration-enhanced quantum transport

In this paper, we study the role of collective vibrational motion in the phenomenon of electronic energy transfer (EET) along a chain of coupled electronic dipoles with varying excitation frequencies. Previous experimental work on EET in conjugated polymer samples suggested that the common structural framework of the macromolecule introduces correlations in the energy gap fluctuations that cause coherent EET. Inspired by these results, we present a simple model in which a driven nanomechanical resonator mode modulates the excitation energy of coupled quantum dots and we find that this can indeed lead to an enhancement in the transport of excitations across the quantum network. Disorder in the on-site energies is a key requirement for this to occur. We also show that, in this solid state system, phase information is partially retained in the transfer process, as experimentally demonstrated in conjugated polymer samples. Consequently, this mechanism of vibration-enhanced quantum transport might find applications in quantum information transfer of qubit states or entanglement.

Observation of quantum-measurement backaction with an ultracold atomic gas

Current research on micromechanical resonators strives for quantum-limited detection of the motion of macroscopic objects. Prerequisite to this goal is the observation of measurement backaction consistent with quantum metrology limits. However, thermal noise currently dominates measurements and precludes ground-state preparation of the resonator. Here, we establish the collective motion of an ultracold atomic gas confined tightly within a Fabry–Perot optical cavity as a system for investigating the quantum mechanics of macroscopic bodies. The cavity-mode structure selects a particular collective vibrational motion that is measured by the cavity’s optical properties, actuated by the cavity optical field and subject to backaction by the quantum force fluctuations of this field. Experimentally, we quantify such fluctuations by measuring the cavity-light-induced heating of the intracavity atomic ensemble. These measurements represent the first observation of backaction on a macroscopic mechanical resonator at the standard quantum limit. Nanoscale beams are one platform for exploring quantum-mechanical phenomena in ever-larger systems. The collective motion of a macroscopic ensemble of ultracold atoms confined in an optical cavity is established as an alternative approach.

Vibrational Raman optical activity as a mean for revealing the helicity of oligosilanes: A quantum chemical investigation

Using theoretical simulations based on Hartree-Fock and density-functional theory calculations, the simulated vibrational Raman optical activity spectra of helical conformers of heptasilane are shown to present signatures sensitive to the helicity. These signatures are associated with collective wagging, twisting, and rocking motions. These simulated spectra have been obtained by combining analytical and numerical differentiation procedures to evaluate the geometry derivatives of the optical tensors entering into the expressions of the vibrational Raman optical activity intensities. From an investigation of basis set and electron correlation effects, it is shown that, like for local vibrations, diffuse functions are compulsory for evaluating the vibrational Raman optical activity intensities of collective vibrational motions.

The effective spin dependent Debye temperature of Gd(0001)

The collective vibrational motions along the surface normal direction of the expansively strained Gd(0001) surface has been investigated. The effective Debye temperature, indicative of the dynamic motion of lattice normal to the surface, is 137±35 K from X-ray photoemission. With angle-resolved spin polarized photoemission spectroscopy, the Debye temperature is determined to be 79±35 K in spin majority, and 125±35 K for spin minority. Residual spin-mixing contributions to bands with Stoner like behavior as well as contributions from the spin dependent plasmon modes for Gd(0001) are implicated.

Cold trapped ions as quantum information processors

In this tutorial we review the physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multiple-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on off-resonance transitions associated with a qualitative estimation of the weak-coupling regime is included in Appendix A and of the Lamb-Dicke regime in Appendix B.

Raman cooling and heating of two trappedBa+ions

We study cooling of the collective vibrational motion of two 138Ba+ ions confined in an electrodynamic trap and irradiated with laser light close to the resonances S_1/2-P_1/2 (493 nm) and P_1/2-D_3/2 (650 nm). The motional state of the ions is monitored by a spatially resolving photo multiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions' temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split S_1/2-D_3/2 Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.

Low frequency vibrational anomalies in hydrated copper azurin: A neutron scattering and MD simulation study

Abstract Azurin, a β-sheet copper containing protein, has been studied by inelastic neutron scattering at different temperatures in a dry and a deuterium hydrated state. At low temperature, an excess of vibrational modes, centered at about 3 meV, has been registered in both the dynamical structure factor and density of states of the hydrated sample; a similar bump, but slightly shifted to a lower frequency, having been observed in the dry sample. The inelastic peak is found to be very similar to the so-called “boson peak”, a common feature of amorphous, glassy, systems. The most relevant features of the spectra have been well-reproduced by molecular dynamics simulations; in particular, the inelastic bump, although peaking at a lower frequency, has been detected in both the simulated dynamical structure factor and density of states. A detailed analysis, exploiting the atomic resolution of molecular dynamics simulation, has been performed to single out the contribution, to both the quasielastic and the inelastic spectral components, arising from the different mobility classes of protein protons. Such an approach has revealed that the main contribution to the inelastic peak arises from protein protons with low mobility; suggesting a possible connection between the inelastic bump and the collective vibrational motions involving elements of the secondary structure of the macromolecule.

Multiparticle Entanglement of Hot Trapped Ions

We propose an efficient method to produce multi-particle entangled states of ions in an ion trap for which a wide range of interesting effects and applications have been suggested. Our preparation scheme exploits the collective vibrational motion of the ions, but it works in such a way that this motion need not be fully controlled in the experiment. The ions may, e.g., be in thermal motion and exchange mechanical energy with a surrounding heat bath without detrimental effects on the internal state preparation. Our scheme does not require access to the individual ions in the trap.

Measurements on Trapped Laser-Cooled Ions Using Quantum Computations

There are some interesting connections between the theory of quantum computation and quantum measurement. As an illustration, we present a scheme in which an ion trap quantum computer can be used to make arbitrarily accurate measurements of the quadrature phase variables for the collective vibrational motion of the ion. We also discuss some more general aspects of quantum computation and measurement in terms of the Feynman-Deutsch principle.

Dynamical deformations in nucleon momentum distributions of colliding ions

We analyze the effects of nucleon momentum distributions of colliding ions arising from excitation of collective vibrational motions. Phonon states are described in RPA and are excited through the action of the mean field of the partner nucleus. The 40Ca + 40Ca system is considered at E A =10 and 44 MeV, around a grazing trajectory. With increasing energy we have clear transition in the dominant collective states, from low-lying modes to the giant quadrupole resonance. Correspondingly we have a noticeable enhancement of dynamical distortions in momentum space, particularly around the Fermi momentum. The importance of nonlinear terms, describing the coupling of different phonon states, is stressed. Some clear effect on energetic particle production is expected.

Raman investigations of collective vibrational motions in van der Waals liquids

Recent investigations of collective vibrational motions in pure van der Waals liquids and in their isotopic mixtures are reviewed. Experimental data are enumerated first. The theory is presented later, separately, for non-composite and composite bands of both isotropic and anisotropic Raman spectra. It is shown that isotropic Raman processes are partially coherent and contain information about collective vibrational motions in liquids. In turn, anisotropic Raman processes are incoherent in the zero-order description and their study is less important in the present context.

Note on the description of the giant angle dipole mode in heavy deformed nuclei

An angular analogue to the Giant Dipole (the Giant Angle Dipole) is described. Such collective vibrational motion is specifically investigated for the case of a spin saturated large particle number system contained in a deformed harmonic oscillator well. The model predicts the ratio of the Angle Dipole to Giant Dipole excitation as equal to the deformation.