Vibrational Degrees Of Freedom Research Articles

Two-dimensional electronic-vibrational spectroscopic study of conical intersection dynamics: an experimental and electronic structure study.

The relaxation from the lowest singlet excited state of the triphenylmethane dyes, crystal violet and malachite green, is studied via two-dimensional electronic-vibrational (2DEV) spectroscopy. After excitation of the dyes at their respective absorption maxima, the ensuing excited state dynamics are tracked by monitoring the C[double bond, length as m-dash]C aromatic stretch. With the aid of electronic structure calculations, the observed transitions in the 2DEV spectra are assigned to specific geometries and a detailed story of the evolution of the nuclear wavepacket as it diffuses on the excited state potential energy surface (PES) and ultimately passes through the conical intersection is developed. Notably, it is revealed that the relaxation of the lowest singlet excited state involves intramolecular charge transfer while the nuclear wavepacket is on the excited state PES. Finally, through analyzing the center line slopes of the measured peaks, we show how both solvent motions and changes in the molecular dipole moment affect the correlation between electronic and vibrational degrees of freedom. This work clearly demonstrates the usefulness of 2DEV spectroscopy in following the motion of nuclear wavepackets after photoexcitation and in studying the interactions between the molecular dipole moment and surrounding solvent environment.

Accuracy of incidental dynamic analysis of mobile elevating work platforms

This paper presents the results of a study into the dynamic behaviour of a support structure of a mobile elevating work platform. The vibrations of the mechanical system of the observed structure are examined analytically, numerically, and experimentally. Within the analytical examination, a simple mathematical model is developed to describe free and forced vibrations. The dynamic analysis of the mechanical system is conducted using a discrete dynamic model with a reduced number of vibrational degrees of freedom. On the basis of the expression for the system energy, and by applying Lagrange\'s equations of the second kind, differential equations are derived for system vibrations, frequencies are determined, and the laws of forced platform vibration are established. At the same time, a nonlinear FEM model is developed and the laws of free and forced vibration are determined. The experimental and numerical part of the study deal with the examination of the real structure in extreme conditions, taking into account: the lowest eigenfrequency, forced actions that could endanger the general stability, the maximal amplitudes, and the acceleration of the work platform. The obtained analytical and numerical results are compared with the experiments. The experimental verification points to the adverse behaviour of the platform in excitation cases – swaying. In such a situation, even a relatively small physical force can lead to unacceptably high amplitudes of displacement and acceleration – exceeding the usual work values.

Another view on Gilbert damping in two-dimensional ferromagnets

A keen interest towards technological implications of spin-orbit driven magnetization dynamics requests a proper theoretical description, especially in the context of a microscopic framework, to be developed. Indeed, magnetization dynamics is so far approached within Landau-Lifshitz-Gilbert equation which characterizes torques on magnetization on purely phenomenological grounds. Particularly, spin-orbit coupling does not respect spin conservation, leading thus to angular momentum transfer to lattice and damping as a result. This mechanism is accounted by the Gilbert damping torque which describes relaxation of the magnetization to equilibrium. In this study we work out a microscopic Kubo-Středa formula for the components of the Gilbert damping tensor and apply the elaborated formalism to a two-dimensional Rashba ferromagnet in the weak disorder limit. We show that an exact analytical expression corresponding to the Gilbert damping parameter manifests linear dependence on the scattering rate and retains the constant value up to room temperature when no vibrational degrees of freedom are present in the system. We argue that the methodology developed in this paper can be safely applied to bilayers made of non- and ferromagnetic metals, e.g., CoPt.

Computation of Dynamic Polarizabilities and van der Waals Coefficients from Path-Integral Monte Carlo.

We demonstrate computation of total dynamic multipole polarizabilities using path-integral Monte Carlo method (PIMC). The PIMC approach enables accurate thermal and nonadiabatic mixing of electronic, rotational, and vibrational degrees of freedom. Therefore, we can study the thermal effects, or lack thereof, in the full multipole spectra of the chosen one- and two-electron systems: H, Ps, He, Ps2, H2, and HD+. We first compute multipole-multipole correlation functions up to octupole order in imaginary time. The real-domain spectral function is then obtained by analytical continuation with the maximum entropy method. In general, sharpness of the active spectra is limited, but the obtained off-resonant polarizabilities are in good agreement with the existing literature. Several weak and strong thermal effects are observed. Furthermore, the polarizabilities of Ps2 and some higher multipole and higher frequency data have not been published before. In addition, we compute isotropic dispersion coefficients C6, C8, and C10 between pairs of species using the simplified Casimir-Polder formulas.

First-principles study of vibrational entropy effects on the PbTe-SrTe phase diagram

We present first-principles calculations of the solid-state phase diagram of PbTe-SrTe that include both configurational and vibrational contributions to the free energy. These configurational and vibrational free energies were calculated using the cluster expansion (CE) approach and quasiharmonic phonon calculations, respectively. The coupled configurational and vibrational degrees of freedom were taken into account by including temperature-dependent CE interactions with the $T=0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ values and temperature dependence of the interactions determined from total energies and phonon free energies, both calculated using density functional theory. This Hamiltonian was then employed in Monte Carlo simulations to obtain a quantitative prediction of the PbTe-SrTe phase diagram. The phase diagram consists of a miscibility gap with a maximum temperature of \ensuremath{\sim}500 K, with the inclusion of the vibrational entropy resulting in a more than fourfold increase in the calculated solubility limits of SrTe in PbTe. Our results suggest that the equilibrium solubility of this system is likely much larger than previously thought and deserves further experimental investigation.

Time-Dependent Density Matrix Renormalization Group Algorithms for Nearly Exact Absorption and Fluorescence Spectra of Molecular Aggregates at Both Zero and Finite Temperature.

We implement and apply time-dependent density matrix renormalization group (TD-DMRG) algorithms at zero and finite temperature to compute the linear absorption and fluorescence spectra of molecular aggregates. Our implementation is within a matrix product state/operator framework with an explicit treatment of the excitonic and vibrational degrees of freedom, and it uses the locality of the Hamiltonian in the zero-exciton space to improve the efficiency and accuracy of the calculations. We demonstrate the power of the method by calculations on several molecular aggregate models, comparing our results against those from multilayer multiconfiguration time-dependent Hartree and n-particle approximations. We find that TD-DMRG provides an accurate and efficient route to calculate the spectrum of molecular aggregates.

Theoretical study of the phonon states and thermodynamic properties on surfaces of energetic material

We develop a method to calculate the local phonon states on crystal surfaces, and use it to investigate a high energy explosive, β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX). The required force constants are obtained by first principles calculations under the GGA+vdW functional. By using them, the phonon density of states (PDOSs) for thirteen kinds of surfaces are calculated, including the (100), (010), (001), (110), (1−10), (101), (10−1), (011), (01−1), (111), (11−1), (1−11) and (−111) faces. We find that there are five representative phonon states on β-HMX surfaces, and obtain the corresponding vibrational modes and atomic displacement fields. Based on the PDOSs, a set of surface properties are evaluated, such as the vibrational degree of freedom, surface free energy and surface heat capacity. The particle morphology of β-HMX in vacuum is predicted by using the surface free energies. We prove that at fixed temperature, the particle morphology is independent of the particle size. The evolution of particle morphology with respect to temperature is obtained.

Dynamics at Conical Intersections.

The nonadiabatic coupling of electronic and vibrational degrees of freedom is the defining feature of electronically excited states of polyatomic molecules. Once considered a theoretical curiosity, conical intersections (CIs) are now generally accepted as being the dominant source of coupled charge and vibrational energy flow in molecular excited states. Passage through CIs leads to the conversion of electronic to vibrational energy, which drives the ensuing photochemistry, isomerization being a canonical example. It has often been remarked that the CI may be thought of as a transition state in the excited state. As such, we expect that both the direction and the velocity of approach to the CI will matter. We explore this suggestion by looking for dynamical aspects of passage through CIs and for analogies with well-known concepts from ground-state reaction dynamics. Great progress has been made in the development of both experimental techniques and ab initio dynamics simulations, to a degree that direct comparisons may now be made. Here we compare time-resolved photoelectron spectroscopy results with on-the-fly ab initio multiple spawning calculations of the experimental observables, thereby validating each. We adopt a phenomenological approach and specifically concentrate on the excited-state dynamics of the C=C bond in unsaturated hydrocarbons. In particular, we make use of selective chemical substitution (such as replacing an H atom by a methyl group) so as to alter the inertia of certain vibrations relative to others, thus systematically varying (mass-weighted) directions and velocities of approach to a CI. Chemical substituents, however, may affect both the nuclear and electronic components of the total wave function. The former, which we call an inertial effect, influences the direction and velocity of approach. The latter, which we call a potential effect, modifies the electronic structure and therefore the energetic location and topography of the potential energy surfaces involved. Using a series of examples, we discuss both types of effects. We argue that there is a need for dynamical pictures and simple models of nonadiabatic dynamics at CIs and hope that the phenomenology presented here will help inspire such developments.

Chemical Understanding of the Limited Site-Specificity in Molecular Inner-Shell Photofragmentation.

In many cases fragmentation of molecules upon inner-shell ionization is very unspecific with respect to the initially localized ionization site. Often this finding is interpreted in terms of an equilibration of internal energy into vibrational degrees of freedom after Auger decay. We investigate the X-ray photofragmentation of ethyl trifluoroacetate upon core electron ionization at environmentally distinct carbon sites using photoelectron-photoion-photoion coincidence measurements and ab initio electronic structure calculations. For all four carbon ionization sites, the Auger decay weakens the same bonds and transfers the two charges to opposite ends of the molecule, which leads to a rapid dissociation into three fragments, followed by further fragmentation steps. The lack of site specificity is attributed to the character of the dicationic electronic states after Auger decay instead of a fast equilibration of internal energy.

Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method.

The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.

Supersonic plasma outflow in a plasmochemical method of amorphous silicon thin films formation

As a result of the numerical modeling of gasdynamic functions of a nozzle of Laval there obtained its parameters which form supersonic plasma jet outflow in a process of amorphous silicon thin films deposition. According to the nozzle design parameters, there obtained amorphous silicon thin films and studied uniformity of the thickness of the synthesized coatings. It was also performed that due to a low translational temperature at the nozzle exit the relaxation losses reduce significantly, “freezing” the vibrational degrees of freedom and the degrees of freedom of the transverse motion of the particles, and increasing the energy efficiency of the film formation process. All this is caused by the fact that on the surface of a growing film only the products of primary interaction of electrons with molecules of a silicon-containing gas in the plasmatron do interact.

Contribution of low-temperature single-molecule techniques to structural issues of pigment-protein complexes from photosynthetic purple bacteria.

As the electronic energies of the chromophores in a pigment-protein complex are imposed by the geometrical structure of the protein, this allows the spectral information obtained to be compared with predictions derived from structural models. Thereby, the single-molecule approach is particularly suited for the elucidation of specific, distinctive spectral features that are key for a particular model structure, and that would not be observable in ensemble-averaged spectra due to the heterogeneity of the biological objects. In this concise review, we illustrate with the example of the light-harvesting complexes from photosynthetic purple bacteria how results from low-temperature single-molecule spectroscopy can be used to discriminate between different structural models. Thereby the low-temperature approach provides two advantages: (i) owing to the negligible photobleaching, very long observation times become possible, and more importantly, (ii) at cryogenic temperatures, vibrational degrees of freedom are frozen out, leading to sharper spectral features and in turn to better resolved spectra.

Electron Transfer Assisted by Vibronic Coupling from Multiple Modes

Understanding the effect of vibronic coupling on electron transfer (ET) rates is a challenge common to a wide range of applications, from electrochemical synthesis and catalysis to biochemical reactions and solar energy conversion. The Marcus-Jortner-Levich (MJL) theory offers a model of ET rates based on a simple analytic expression with a few adjustable parameters. However, the MJL equation in conjunction with density functional theory (DFT) has yet to be established as a predictive first-principles methodology. A framework is presented for calculating transfer rates modulated by molecular vibrations, that circumvents the steep computational cost which has previously necessitated approximations such as condensing the vibrational manifold into a single empirical frequency. Our DFT-MJL approach provides robust and accurate predictions of ET rates spanning over 4 orders of magnitude in the 106-1010 s-1 range. We evaluate the full MJL equation with a Monte Carlo sampling of the entire active space of thermally accessible vibrational modes, while using no empirical parameters. The contribution to the rate of individual modes is illustrated, providing insight into the interplay between vibrational degrees of freedom and changes in electronic state. The reported findings are valuable for understanding ET rates modulated by multiple vibrational modes, relevant to a broad range of systems within the chemical sciences.

Exact States and Spectra of Vibrationally Dressed Polaritons

Strong coupling between light and matter is possible with a variety of organic materials. In contrast to the simpler inorganic case, organic materials often have a complicated spectrum, with vibrationally dressed electronic transitions. Strong coupling to light competes with this vibrational dressing, and if strong enough, can suppress the entanglement between electronic and vibrational degrees of freedom. By exploiting symmetries, we can perform exact numerical diagonalization to find the polaritonic states for intermediate numbers of molecules, and use these to define and validate accurate expressions for the lower polariton states and strong-coupling spectrum in the thermodynamic limit. Using this approach, we find that vibrational decoupling occurs as a sharp transition above a critical matter-light coupling strength. We also demonstrate how the polariton spectrum evolves with the number of molecules, recovering classical linear optics results only at large $N$.

Fusion dynamics of stable and weakly bound colliding systems

This work systematically analyzed the fusion dynamics of the projectile-target combinations involving stable and loosely bound systems within the view of the energy-dependent Woods–Saxon potential model (EDWSP model) and the coupled channel approach. The different projectiles are bombarded onto series of Sm-isotopes, which possess the dominance of the different kinds of the nuclear structure degrees of freedom and with the increase of the neutron richness, the Sm-isotopes gradually shift from spherical shape to a statically deformed shape. In the fusion of [Formula: see text] reaction, the impacts of vibrational degrees of freedom of the colliding nuclei are dominant while in the case of [Formula: see text] systems, the rotational states of the deformed target isotopes have a strong impression on the below-barrier fusion data. The heavier target isotopes ([Formula: see text] also exhibit the higher order deformation such as [Formula: see text], [Formula: see text]-deformation parameter in its ground state and couplings to such channels must be incorporated in theoretical calculations in order to achieve close agreement with the sub-barrier fusion data. However, in the case of the loosely bound systems, the projectile breakup channel significantly affects the fusion excitation functions in the domain of the Coulomb barrier. To ensure the role of the projectile breakup channel, the fusion of the different loosely bound projectiles ([Formula: see text] and [Formula: see text] with Sm-isotopes are investigated, wherein the above-barrier fusion data of these reactions are suppressed with reference to the coupled channel calculations. This hindrance is the result of the projectile breakup effects that occur as a consequence of the breakup of the projectile before reaching the fusion barrier due to its low binding energy. However, in the EDWSP model calculations the magnitude of the hindrance of the above-barrier fusion data of [Formula: see text] and [Formula: see text] reactions is reduced by a factor varying from 7% to 13% with respect to a value reported in the literature. In contrast to this, the sub-barrier fusion enhancement of [Formula: see text] and [Formula: see text] reactions is the result of the dominance of the nuclear structure degrees of freedom of the colliding systems.

Vibronically coherent ultrafast triplet-pair formation and subsequent thermally activated dissociation control efficient endothermic singlet fission.

Singlet exciton fission (SF), the conversion of one spin-singlet exciton (S1) into two spin-triplet excitons (T1), could provide a means to overcome the Shockley-Queisser limit in photovoltaics. SF as measured by the decay of S1 has been shown to occur efficiently and independently of temperature, even when the energy of S1 is as much as 200 meV less than that of 2T1. Here we study films of triisopropylsilyltetracene using transient optical spectroscopy and show that the triplet pair state (TT), which has been proposed to mediate singlet fission, forms on ultrafast timescales (in 300 fs) and that its formation is mediated by the strong coupling of electronic and vibrational degrees of freedom. This is followed by a slower loss of singlet character as the excitation evolves to become only TT. We observe the TT to be thermally dissociated on 10-100 ns timescales to form free triplets. This provides a model for 'temperature-independent' efficient TT formation and thermally activated TT separation.

Signatures of vibronic coupling in two-dimensional electronic-vibrational and vibrational-electronic spectroscopies.

Two-Dimensional Electronic-Vibrational (2D EV) spectroscopy and Two-Dimensional Vibrational-Electronic (2D VE) spectroscopy are new coherent four-wave mixing spectroscopies that utilize both electronically resonant and vibrationally resonant field-matter interactions to elucidate couplings between electronic and vibrational degrees of freedom. A system Hamiltonian is developed here to lay a foundation for interpreting the 2D EV and 2D VE signals that arise from a vibronically coupled molecular system in the condensed phase. A molecular system consisting of one anharmonic vibration and two electronic states is modeled. Equilibrium displacement of the vibrational coordinate and vibrational frequency shifts upon excitation to the first electronic excited state are included in our Hamiltonian through linear and quadratic vibronic coupling terms. We explicitly consider the nuclear dependence of the electronic transition dipole moment and demonstrate that these spectroscopies are sensitive to non-Condon effects. A series of simulations of 2D EV and 2D VE spectra obtained by varying parameters of the system, system-bath, and interaction Hamiltonians demonstrate that one of the following conditions must be met to observe signals: (1) non-zero linear and/or quadratic vibronic coupling in the electronic excited state, (2) vibrational-coordinate dependence of the electronic transition dipole moment, or (3) electronic-state-dependent vibrational dephasing dynamics. We explore how these vibronic interactions are manifested in the positions, amplitudes, and line shapes of the peaks in 2D EV and 2D VE spectroscopies.

Unified gas-kinetic scheme for diatomic molecular flow with translational, rotational, and vibrational modes

The unified gas-kinetic scheme (UGKS) is a direct modeling method for both continuum and rarefied flow computations. In the previous study, the UGKS was developed for diatomic molecular simulations with translation and rotational motions. In this paper, a UGKS with non-equilibrium translational, rotational, and vibrational degrees of freedom, will be developed. The new scheme is based on the phenomenological gas dynamics model, where the translational, rotational, and vibrational modes get to the equilibrium with different time scales with the introduction of rotational and vibrational collision numbers. This new scheme is tested in a few cases, such as the homogeneous flow relaxation, shock structure, shock tube problem, and flow passing through a circular and semi-circular cylinders. The analytical and DSMC solutions are used for the validation of the UGKS, and reasonable agreements have been achieved.

Multilayer-MCTDH approach to the energy transfer dynamics in the LH2 antenna complex

The multilayer multiconfiguration time-dependent Hartree method is used to study the coupled exciton–vibrational dynamics in a high-dimensional nonameric model of the LH2 antenna complex of purple bacteria. The exciton–vibrational coupling is parametrized within the Huang–Rhys model according to phonon and intramolecular vibrational modes derived from an experimental bacteriochlorophyll spectral density. In contrast to reduced density matrix approaches, the Schrödinger equation is solved explicitly, giving access to the full wave function. This facilitates an unbiased analysis in terms of the coupled dynamics of excitonic and vibrational degrees of freedom. For the present system, we identify spectator modes for the B800 to B800 transfer and we find a non-additive effect of phonon and intramolecular vibrational modes on the B800 to B850 exciton transfer.

Modified particle-rotor model and low-lying rotational bands in odd-A triaxial nuclei

The low-lying rotational bands of triaxially deformed nuclei 137Pr, 137Pm and 139Eu are studied with a modified particle-rotor model following the nonadiabatic quasiparticle approach. The matrix elements of the odd-A nucleus are obtained in terms of a coupling matrix and the rotational energies of the even–even core. The spectra of the cores 136Ce, 136Nd and 138Sm indicate a strong influence of triaxial deformation and vibrational degrees of freedom. These properties are appropriately carried forward to the calculations for the odd-A nucleus. We demonstrate that the ground and side bands of the odd-A nucleus and its core can be explained with the same set of deformation parameters (, γ). We argue that this method could be useful in studying the low-lying states in exotic nuclei also.