Vibrational Degrees Of Freedom Research Articles

Triaxiality in the proton emitter I109

We study the role of triaxial deformation in the proton-emitting nucleus $^{109}\mathrm{I}$. We analyze the rotational spectrum as well as the decay width within the nonadiabatic quasiparticle approach. The parent nuclear wave functions are calculated using a modified rotation-particle coupling where the matrix elements of the Hamiltonian representing the rotational states of the parent nucleus are written in terms of the rotational energies of the daughter nucleus. The measured spectrum of the daughter nucleus $^{108}\mathrm{Te}$ suggests a strong role of either triaxial or vibrational degrees of freedom which is applicable for $^{109}\mathrm{I}$ also. With these results we successfully explain the spectra of the parent and daughter and also the decay width in a unified way which enables us to establish the configuration of the rotational bands and the decaying state.

Collisional Intermolecular Energy Transfer from a N2 Bath at Room Temperature to a Vibrationlly “Cold” C6F6 Molecule Using Chemical Dynamics Simulations

Chemical dynamics simulations were performed to study collisional intermolecular energy transfer from a thermalized N2 bath at 300 K to vibrationally "cold" C6F6. The vibrational temperature of C6F6 is taken as 50 K, which corresponds to a classical vibrational energy of 2.98 kcal/mol. The temperature ratio between C6F6 and the bath is 1/6, the reciprocal of the same ratio for previous "hot" C6F6 simulations (J. Chem. Phys. 2014, 140, 194103). Simulations were also done for a C6F6 vibrational temperature of 0 K. The average energy of C6F6 versus time is well fit by a biexponential function which gives a slightly larger short time rate component, k1, but a four times smaller long time rate component, k2, compared to those obtained from the "hot" C6F6 simulations. The average energy transferred per collision depends on the difference between the average energy of C6F6 and the final C6F6 energy after equilibration with the bath, but not on the temperature ratio of C6F6 and the bath. The translational and rotational degrees of freedom of the N2 bath transfer their energies to the vibrational degrees of freedom of C6F6. The energies of the N2 vibrational mode and translational and rotational modes of C6F6 remain unchanged during the energy transfer. It is also found that the energy distribution of C6F6 broadens as energy is transferred from the bath, with an almost linear increase in the deviation of the C6F6 energies from the average C6F6 energy as the average energy of C6F6 increases.

Vibronic exciton theory of singlet fission. I. Linear absorption and the anatomy of the correlated triplet pair state.

Recent time-resolved spectroscopic experiments have indicated that vibronic coupling plays a vital role in facilitating the process of singlet fission. In this work, which forms the first article of a series, we set out to unravel the mechanisms underlying singlet fission through a vibronic exciton theory. We formulate a model in which both electronic and vibrational degrees of freedom are treated microscopically and non-perturbatively. Using pentacene as a prototypical material for singlet fission, we subject our theory to comparison with measurements on polarization-resolved absorption of single crystals, and employ our model to characterize the excited states underlying the absorption band. Special attention is given to the convergence of photophysical observables with respect to the basis size employed, through which we determine the optimal basis for more expensive calculations to be presented in subsequent work. We furthermore evaluate the energetic separation between the optically prepared singlet excited state and the correlated triplet pair state, as well as provide a real-space characterization of the latter, both of which are of key importance in the discussion of fission dynamics. We discuss our results in the context of recent experimental studies.

Fine-tuning the Mott metal–insulator transition and critical charge carrier dynamics in molecular conductors

The unique possibilities of fine-tuning their physical properties in the vicinity of the Mott metal–insulator transition make the quasi-two-dimensional organic charge-transfer salts -(BEDT-TTF)X unprecedented model systems for studying the fundamentals of electron–electron correlations and the coupling between charge, spin and lattice degrees of freedom in reduced dimensions. The critical properties and the universality class of the Mott transition, however, are controversially debated for these materials, and information on the low-frequency dynamical properties of the correlated electrons is rather limited. By introducing fluctuation (noise) spectroscopy as a powerful new tool for studying the slow dynamics of charge carriers, in the past years we have been able to extract spectroscopic information on the coupling of charge carriers to the vibrational degrees of freedom of the crystal lattice. This is related to a glassy freezing of the BEDT-TTF molecules’ ethylene end-group (EEG) rotations at elevated temperatures, which (i) results in a small amount of (intrinsic) disorder and (ii) crucially influences the ratio of bandwidth to on-site Coulomb repulsion (W / U) and therefore the samples’ position in the phase diagram, i.e. the electronic ground state. The low-frequency resistance fluctuations show a dramatic enhancement and divergent behaviour when tuning the sample close to the critical point of the Mott transition, accompanied by a strong shift of spectral weight to low frequencies and the onset of non-Gaussian behaviour. This indicates the critical slowing down of the order-parameter (doublon density) fluctuations and suggests a collective dynamics of the correlated electrons. In order to enable detailed investigations of this hypothesis in future experiments, by exploiting the structural EEG relaxation, a ‘warming cycle’ protocol can be established that allows for fine-tuning the sample across the Mott transition and therefore precisely accessing the finite-temperature critical endpoint. We ‘calibrate’ this procedure by a comparison to pressure-tuning experiments on the same sample. This method will allow to map out the region of ergodicity breaking around the critical endpoint and its dependence on disorder.

Towards a self-consistent dynamical nuclear model

Density functional theory (DFT) is a powerful and accurate tool, exploited in nuclear physics to investigate the ground-state and some of the collective properties of nuclei along the whole nuclear chart. Models based on DFT are not, however, suitable for the description of single-particle dynamics in nuclei. Following the field theoretical approach by A Bohr and B R Mottelson to describe nuclear interactions between single-particle and vibrational degrees of freedom, we have taken important steps towards the building of a microscopic dynamic nuclear model. In connection with this, one important issue that needs to be better understood is the renormalization of the effective interaction in the particle-vibration approach. One possible way to renormalize the interaction is by the so-called subtraction method. In this contribution, we will implement the subtraction method in our model for the first time and study its consequences.

Validation and analysis of gas-kinetic unified algorithm for solving Boltzmann model equation with vibrational energy excitation

With the increase of temperature in flow field,gas molecules possess not only rotational degree of freedom,but also vibrational energy excitation.In order to simulate and study the influence of internal energy excitation on polyatomic gas flow with high temperature and high Mach number,according to the general Boltzmann equation,we consider the rotational and vibrational energy modes as the independent variables of gas molecular velocity distribution function.It is assumed that the rotational and vibrational energy modes are described by continuous distribution with degree of freedom and temperature.Based on the Borgnakke-Larsen collision model used in direct simulation Monte Carlo (DSMC) method, the collision term of Boltzmann equation with internal energy excitation is divided into elastic and inelastic collision terms.The inelastic collision is decomposed into translational-rotational energy relaxation and translational-rotationalvibrational energy relaxation according to a certain relaxation rate obtained from the reciprocalities of rotational and vibrational collisions numbers per one elastic collision.Then a kind of Boltzmann model equation considering the excitation of vibrational energy is constructed.For showing the consistency between the present model equation and Boltzmann equation,the conservation of summational invariants and the H-theorem of this model are proved.When solving the present model equation with numerical methods,because of the continuous energy modes,it is difficult to simulate this model equation directly.In this paper,three control equations are derived and solved by the LU-SGS (lower-upper symmetric Gauss-Seidel) method,and the cell-centered finite volume method with multi-block patched grid technique in physical space.As a result,these gas-kinetic unified algorithm (GKUA) with vibrational energy excitation has been developed.Results are presented for N2 with different Knudsen numbers around cylinder from continuum to rarefied gas flow by using the present Boltzmann model equation,GKUA with simple gas model,and DSMC method. Very good agreement between the present model and DSMC results is obtained,which shows that the accuracy and reliability of the present model.Comparing the translational,rotational,vibrational,and total temperatures computed by different methods,the effects of the rotational and vibrational degrees of freedom are demonstrated.For the simple gas model,the translational temperature is much higher than those for the other two models with internal energy excitation. At the same time,the distance from shock wave to wall for the simple gas model is about twice those for the other two models.On the other hand,the obtained aerodynamic force coefficients of the cylinder are increasing according to the sequence from the simple gas model to the rotational energy excitation model to the vibrational energy excitation model, but the variation range is very small.By reducing the gas characteristic vibrational temperature,the temperature after the shock wave is much lower,and the heat flux declines evidently at the stagnation point with the same temperature as the wall temperature.This implies that with the wall temperature increasing the heat flux declines.

Accurate schemes for calculation of thermodynamic properties of liquid mixtures from molecular dynamics simulations.

We explore different schemes for improved accuracy of entropy calculations in aqueous liquid mixtures from molecular dynamics (MD) simulations. We build upon the two-phase thermodynamic (2PT) model of Lin et al. [J. Chem. Phys. 119, 11792 (2003)] and explore new ways to obtain the partition between the gas-like and solid-like parts of the density of states, as well as the effect of the chosen ideal "combinatorial" entropy of mixing, both of which have a large impact on the results. We also propose a first-order correction to the issue of kinetic energy transfer between degrees of freedom (DoF). This problem arises when the effective temperatures of translational, rotational, and vibrational DoF are not equal, either due to poor equilibration or reduced system size/time sampling, which are typical problems for ab initio MD. The new scheme enables improved convergence of the results with respect to configurational sampling, by up to one order of magnitude, for short MD runs. To ensure a meaningful assessment, we perform MD simulations of liquid mixtures of water with several other molecules of varying sizes: methanol, acetonitrile, N, N-dimethylformamide, and n-butanol. Our analysis shows that results in excellent agreement with experiment can be obtained with little computational effort for some systems. However, the ability of the 2PT method to succeed in these calculations is strongly influenced by the choice of force field, the fluidicity (hard-sphere) formalism employed to obtain the solid/gas partition, and the assumed combinatorial entropy of mixing. We tested two popular force fields, GAFF and OPLS with SPC/E water. For the mixtures studied, the GAFF force field seems to perform as a slightly better "all-around" force field when compared to OPLS+SPC/E.

Predicting the thermal conductivity in a graphene nanoflake from its response to a thermal impulse

Inspired by pulsed laser-assisted thermal relaxation experiments, we simulated the response of a nanometer-size monolayer graphene sample to thermal impulses by means of nonequilibrium molecular dynamics. By following the time evolution of the temperature profile until equilibrium is eventually reached, we obtain a direct estimation of the thermal conductivity of the excited graphene sample. It is shown that the predicted thermal conductivity depends on which vibrational degrees of freedom are in fact excited by the thermal impulse, suggesting that its determination depends, among many other issues, on the actual phonon population generated in the sample. The situation here explored is typically found in experiments or simulations addressing a transient regime of approach to equilibrium.

Temperature Dependence of HeBr2 Isomers' Stability through Rovibrational Multiconfiguration Time-Dependent Hartree Calculations.

The multiconfiguration time-dependent Hartree (MCTDH) method using a six-dimensional Hamiltonian that includes all rotational and vibrational degrees of freedom and an ab initio potential energy surface was employed to calculate the rovibronic states of the HeBr2 van der Waals complex. All rotational states of energies within 7 cm -1 with respect to the energy of the linear ground state were calculated without restriction of the total angular momentum. In total, we obtained 500 and 320 rotationally excited states of the ground vibrational T-shaped and linear isomers of the HeBr2, respectively, and compared them with those predicted by the rigid rotor model. A thermodynamic model was then introduced to determine the relative stability of the two conformers as a function of the temperature. On the basis of the present results, the linear conformers were found to be energetically more stable than the T-shaped ones by 1.14 cm-1 at T = 0 K, whereas conversion from linear to T-shaped complexes was observed at temperatures above 2.87 K.

Optical absorption spectra of the Bi+ impurity center in CsCdBr3 ternary bromide

Optical absorption spectra of the Bi+ impurity center isomorphically substituting Cs+ in CsCdBr3 are recorded over a wide temperature range (from 3.2 to 300 K). An analysis of the vibrational degrees of freedom of the impurity center within the framework of the model of a single effective phonon mode yields various spectroscopic parameters of the optical transition in the Bi+ ion, such as the zero-phonon transition energy, Huang–Rhys parameter, and effective phonon energy. The results are used to compare the properties of the Bi+ center in various crystalline matrices.

A Unified Picture of S* in Carotenoids.

In π-conjugated chain molecules such as carotenoids, coupling between electronic and vibrational degrees of freedom is of central importance. It governs both dynamic and static properties, such as the time scales of excited state relaxation as well as absorption spectra. In this work, we treat vibronic dynamics in carotenoids on four electronic states (|S0⟩, |S1⟩, |S2⟩, and |Sn⟩) in a physically rigorous framework. This model explains all features previously associated with the intensely debated S* state. Besides successfully fitting transient absorption data of a zeaxanthin homologue, this model also accounts for previous results from global target analysis and chain length-dependent studies. Additionally, we are able to incorporate findings from pump-deplete-probe experiments, which were incompatible to any pre-existing model. Thus, we present the first comprehensive and unified interpretation of S*-related features, explaining them by vibronic transitions on either S1, S0, or both, depending on the chain length of the investigated carotenoid.

Many-body theory and Energy Density Functionals

In this paper a method is first presented to construct an Energy Density Functional on a microscopic basis. The approach is based on the Kohn-Sham method, where one introduces explicitly the Nuclear Matter Equation of State, which can be obtained by an accurate many-body calculation. In this way it connects the functional to the bare nucleon-nucleon interaction. It is shown that the resulting functional can be performing as the best Gogny force functional. In the second part of the paper it is shown how one can go beyond the mean-field level and the difficulty that can appear. The method is based on the particle-vibration coupling scheme and a formalism is presented that can handle the correct use of the vibrational degrees of freedom within a microscopic approach.

Rate constants of chemical reactions from semiclassical transition state theory in full and one dimension.

Semiclassical Transition State Theory (SCTST), a method for calculating rate constants of chemical reactions, offers gains in computational efficiency relative to more accurate quantum scattering methods. In full-dimensional (FD) SCTST, reaction probabilities are calculated from third and fourth potential derivatives along all vibrational degrees of freedom. However, the computational cost of FD SCTST scales unfavorably with system size, which prohibits its application to larger systems. In this study, the accuracy and efficiency of 1-D SCTST, in which only third and fourth derivatives along the reaction mode are used, are investigated in comparison to those of FD SCTST. Potential derivatives are obtained from numerical ab initio Hessian matrix calculations at the MP2/cc-pVTZ level of theory, and Richardson extrapolation is applied to improve the accuracy of these derivatives. Reaction barriers are calculated at the CCSD(T)/cc-pVTZ level. Results from FD SCTST agree with results from previous theoretical and experimental studies when Richardson extrapolation is applied. Results from our implementation of 1-D SCTST, which uses only 4 single-point MP2/cc-pVTZ energy calculations in addition to those for conventional TST, agree with FD results to within a factor of 5 at 250 K. This degree of agreement and the efficiency of the 1-D method suggest its potential as a means of approximating rate constants for systems too large for existing quantum scattering methods.

Long-range energy transport in photosystem II.

We simulate the long-range inter-complex electronic energy transfer in photosystem II-from the antenna complex, via a core complex, to the reaction center-using a non-Markovian (ZOFE) quantum master equation description that allows the electronic coherence involved in the energy transfer to be explicitly included at all length scales. This allows us to identify all locations where coherence is manifested and to further identify the pathways of the energy transfer in the full network of coupled chromophores using a description based on excitation probability currents. We investigate how the energy transfer depends on the initial excitation-localized, coherent initial excitation versus delocalized, incoherent initial excitation-and find that the overall energy transfer is remarkably robust with respect to such strong variations of the initial condition. To explore the importance of vibrationally enhanced transfer and to address the question of optimization in the system parameters, we systematically vary the strength of the coupling between the electronic and the vibrational degrees of freedom. We find that the natural parameters lie in a (broad) region that enables optimal transfer efficiency and that the overall long-range energy transfer on a ns time scale appears to be very robust with respect to variations in the vibronic coupling of up to an order of magnitude. Nevertheless, vibrationally enhanced transfer appears to be crucial to obtain a high transfer efficiency, with the latter falling sharply for couplings outside the optimal range. Comparison of our full quantum simulations to results obtained with a "classical" rate equation based on a modified-Redfield/generalized-Förster description previously used to simulate energy transfer dynamics in the entire photosystem II complex shows good agreement for the overall time scales of excitation energy transport.

Quantum dynamics of a vibronically coupled linear chain using a surrogate Hamiltonian approach.

Vibronic coupling between the electronic and vibrational degrees of freedom has been reported to play an important role in charge and exciton transport in organic photovoltaic materials, molecular aggregates, and light-harvesting complexes. Explicitly accounting for effective vibrational modes rather than treating them as a thermal environment has been shown to be crucial to describe the effect of vibronic coupling. We present a methodology to study dissipative quantum dynamics of vibronically coupled systems based on a surrogate Hamiltonian approach, which is in principle not limited by Markov approximation or weak system-bath interaction, using a vibronic basis. We apply vibronic surrogate Hamiltonian method to a linear chain system and discuss how different types of relaxation process, intramolecular vibrational relaxation and intermolecular vibronic relaxation, influence population dynamics of dissipative vibronic systems.

Multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach to the correlated exciton-vibrational dynamics in the FMO complex.

The coupled quantum dynamics of excitonic and vibrational degrees of freedom is investigated for high-dimensional models of the Fenna-Matthews-Olson complex. This includes a seven- and an eight-site model with 518 and 592 harmonic vibrational modes, respectively. The coupling between local electronic transitions and vibrations is described within the Huang-Rhys model using parameters that are obtained by discretization of an experimental spectral density. Different pathways of excitation energy flow are analyzed in terms of the reduced one-exciton density matrix, focussing on the role of vibrational and vibronic excitations. Distinct features due to both competing time scales of vibrational and exciton motion and vibronically assisted transfer are observed. The question of the effect of initial state preparation is addressed by comparing the case of an instantaneous Franck-Condon excitation at a single site with that of a laser field excitation.

Thermal-light-induced dynamics: Coherence and revivals inV-type and molecular Jaynes-Cummings systems

We examine the interaction of thermal light with matter with emphasis on two aspects that have not been considered before. By employing a fully quantized Jaynes-Cummings--type interaction model on a $V$-type three-level system, we show that multimode thermal light induces coherence in the excited material states. This is in contrast to previous studies that suggest thermal light cannot induce coherence in material systems. We also show that the ratio between the field detuning and the interaction constant has a significant influence on the characteristic time-dependent dynamics. In particular, for some ratio regimes, the thermal light induces dynamics with a ``coherentlike'' collapse and revivals pattern rather than the familiar pattern. We then extend the Jaynes-Cummings model to a two-state Born-Oppenheimer potential energy surface molecular system where the internal vibrational degrees of freedom are fully taken into account. The matter-field bipartite system is represented, and propagated, in the full electronic bond-coordinate Fock product space. We show that single-mode thermal light induces extensive excited-state vibrational coherence in the molecule that, when observed in coordinate space, exhibits wave-packet-like dynamics. The molecular Jaynes-Cummings model we propose is useful for cavity molecular dynamics simulations.

Excitonic spectral features in strongly coupled organic polaritons

Starting from a microscopic model, we investigate the optical spectra of molecules in strongly-coupled organic microcavities examining how they might self-consistently adapt their coupling to light. We consider both rotational and vibrational degrees of freedom, focusing on features which can be seen in the peak in the center of the spectrum at the bare excitonic frequency. In both cases we find that the matter-light coupling can lead to a self-consistent change of the molecular states, with consequent temperature-dependent signatures in the absorption spectrum. However, for typical parameters, these effects are much too weak to explain recent measurements. We show that another mechanism which naturally arises from our model of vibrationally dressed polaritons has the right magnitude and temperature dependence to be at the origin of the observed data.

Slow relaxation of kinetic energy of a spring-chain model in solvent

The distribution and relaxation of kinetic energy in a chain is investigated. The chain is composed of masses serially connected by springs. When the chain is at rest and surrounded with solvent, masses in the chain receive energy by collisions with solvent particles. If the spring constant k is large, the distribution of time-averaged energy of each particle is not uniform for some time; it is larger near the ends of the chain. The non-uniform distribution of kinetic energy is transient, and the system relaxes to the equipartition state. The relaxation time obeys for large k, which is a typical feature of Boltzmann–Jeans-type relaxation. The non-uniformity in energy distribution is due to the fact that when the spring constant k is large, the vibrational degrees of freedom in the chain are frozen. In that case, the system is dominated by rotational motion and the system behaves as if the masses are connected with rigid links, instead of springs.

Abinitio Prediction of Martensitic and Intermartensitic Phase Boundaries in Ni-Mn-Ga.

Despite the importance of martensitic transformations of Ni-Mn-Ga Heusler alloys for their magnetocaloric and shape-memory properties, the martensitic part of their phase diagrams is not well determined. Using an abinitio approach that includes the interplay of lattice and vibrational degrees of freedom we identify an intermartensitic transformation between a modulated and a nonmodulated phase as a function of excess Ni and Mn content. Based on an evaluation of the theoretical findings and experimental x-ray diffraction data for Mn-rich alloys, we are able to predict the phase diagram for Ni-rich alloys. In contrast to other mechanisms discussed for various material systems in the literature, we herewith show that the intermartensitic transformation can be understood solely using thermodynamic concepts.