Vibrational Degrees Of Freedom Research Articles

Relaxation of excited molecules in a medium with memory at short and long times

Two qualitatively different approaches to the dynamics of vibrational wave packets in the presence of medium-induced relaxation, with taking into account relaxation memory effects and without taking them into account (Makovian approximation) were compared for a molecular system with one vibrational degree of freedom (the Morse oscillator) in a medium. The time evolution of the populations of levels, mean system energy, and response of “pumping-probing” experiments were calculated. It was found that, as distinct from the Markovian approximation, the approach including memory effects can predict the evolution of a molecular system satisfying the detailed equilibrium principle. The two approaches specified also predict the existence of a qualitative difference of phase characteristics in the behavior of the system at short times.

The analytic model between effective heat capacity and relaxation time in gas acoustic relaxation process

The acoustic relaxation is one important nature of gas, which is caused by the sound propagation in the polyatomic molecule gas. It is the basic relaxation process, which arises from the translational-vibrational degree of freedom (V-T) and the molecular energy transfer between different vibrational degrees of freedom (V-V) separately. By studying the molecule energy transition model of the basic acoustic relaxation processes of gas, we propose an analytic model reflecting the correspondence between effective specific heat capacity and relaxation time in this paper. Compared with the existing relaxation model, the analytic model provides the corresponding relationship between the vibrational specific heat capacity and the relaxation time in V-T and V-V. The solution procedure of the analytic model illustrates that the higher vibrational energy level is the determinant of the basic relaxation process. The effective heat capacity is the foundation of acoustic relaxation attenuation spectrum of gas. The relaxation attenuation spectra result from the analytic model in this paper, which is modified by fine-tuning the collision diameter of the gas molecule, are more consistent with the experiment data than with the existing theoretical value. It proves the correctness and validity of the analytic model.

Water binding energies of [Pb(amino acid-H)H2O]+ complexes determined by blackbody infrared radiative dissociation

The water binding energies (E(0)) of eight deprotonated Pb(2+)-amino acid (Aa) complexes of the form [Pb(Aa-H)H(2)O](+) (Aa = Gly, Ala, Val, Leu, Ile, Phe, Glu, and Lys) were determined using blackbody infrared radiative dissociation (BIRD). A Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer was used to trap ions generated by electrospray ionization (ESI) in a "zero"-pressure (~10(-10) torr) cell where dissociation can only occur by absorption of thermally generated photons. Since the [Pb(Aa-H)H(2)O](+) complexes have relatively few vibrational degrees of freedom (36-78) and are within the slow-exchange kinetic limit, the master equation was solved to extract meaningful threshold dissociation energies and thermal unimolecular dissociation rate constants (k(uni)). The master equation analysis uses variable reaction coordinate transition state theory (VRC-TST) to minimize the Rice-Ramsperger-Kassel-Marcus (RRKM) dissociation rate constants. The determined water binding energies range from 76.6 to 113.6 kJ mol(-1), and agree well with 0 K dissociation energies calculated using the B3LYP/6-31+G(d,p) and MP2(full)/6-311++G(2d,2p)//B3LYP/6-31+G(d,p) methods. The relative strengths of the binding energies reflect the known structural isomers (A-, B-, C-, and D-type) of these [Pb(Aa-H)H(2)O](+) complexes.

Water–protein dynamic coupling and new opportunities for probing it at low to physiological temperatures in aqueous solutions

Both the structure and dynamics of biomolecules are known to be essential for their biological function. In the dehydrated state, the function of biomolecules, such as proteins, is severely impeded, so hydration is required for bioactivity. The dynamics of the hydrated biomolecules and their hydration water are related - but how closely? The problem involves several layers of complexity. Even for water in the bulk state, the contribution from various dynamic components to the overall dynamics is not fully understood. In biological systems, the effects of confinement on the hydration water further complicate the picture. Even if the various components of the hydration water dynamics are properly understood, which of them are coupled to the protein dynamics, and how? The studies of protein dynamics over the wide temperature range, from physiological to low temperatures, provide some answers to these question. At low temperatures, both the protein and its hydration water behave as solids, with only vibrational degrees of freedom. As the temperature is increased, non-vibrational dynamic components start contributing to the measurable dynamics and eventually become dominant at physiological temperatures. Thus, the temperature dependence of the dynamics of protein and its hydration water may allow probing various dynamic components separately. In order to suppress the water freezing, the low-temperature studies of protein rely on either low-hydrated samples (essentially, hydrated protein powders), or cryo-protective solutions. Both approaches introduce the hydration environments not characteristic of the protein environments in living systems, which are typically aqueous protein solutions of various concentrations. In this paper, we discuss the coupling between the dynamic components of the protein and its hydration water by critical examining of the existing literature, and then propose that proteins can be studied in an aqueous solution that is remarkably similar in its dynamic properties to pure water, yet does not freeze down to about 200 K, even in the bulk form. The first experiment of this kind using quasielastic neutron scattering is discussed, and more experiments are proposed.

Quantum entanglement between electronic and vibrational degrees of freedom in molecules

We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potential-energy surfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.

Preparation and Relaxation of Very Stable Glassy States of a Simulated Liquid

We prepare metastable glassy states in a model glass former made of Lennard-Jones particles by sampling biased ensembles of trajectories with low dynamical activity. These trajectories form an inactive dynamical phase whose "fast" vibrational degrees of freedom are maintained at thermal equilibrium by contact with a heat bath, while the "slow" structural degrees of freedom are located in deep valleys of the energy landscape. We examine the relaxation to equilibrium and the vibrational properties of these metastable states. The glassy states we prepare by our trajectory sampling method are very stable to thermal fluctuations and also more mechanically rigid than low-temperature equilibrated configurations.

On the Effect of Nonequilibrium Plasma on the Minimum Ignition Energy: Part 2

A mathematical model for the calculation of the minimum ignition energy (MIE) of the nanosecond-pulsed discharge ignition is presented. The model is based on the kinetic and transport equations for a multicomponent reacting mixture combined with the equations for translational and vibrational temperatures. The analysis of the influence of a pulsewidth, the reduced electric field of the discharge, the energy stored in the vibrational degrees of freedom, and the mixture composition on the MIE is conducted.

Polaron transport in organic crystals: Temperature tuning of disorder effects

We explore polaronic quantum transport in three-dimensional models of disordered organic crystals with strong coupling between electronic and vibrational degrees of freedom. By studying the polaron dynamics in a static disorder environment, temperature dependent mobilities are extracted and found to exhibit different fingerprints depending on the strength of the disorder potential. At low temperatures and for strong enough disorder, coherence effects induce weak localization of polarons. These effects are reduced with increasing temperature (thermal disorder) resulting in mobility increase. However at a transition temperature, phonon-assisted contributions driven by polaron-phonon scattering prevail, provoking a downturn of the mobility. The results provide an alternative scenario to discuss controversial experimental features in molecular crystals.

Electronic excitation dynamics in multichromophoric systems described via a polaron-representation master equation

We derive a many-site version of the non-Markovian time-convolutionless polaron master equation [Jang et al., J. Chem Phys. 129, 101104 (2008)] to describe electronic excitation dynamics in multichromophoric systems. By treating electronic and vibrational degrees of freedom in a combined frame (polaron frame), this theory is capable of interpolating between weak and strong exciton-phonon coupling and is able to account for initial non-equilibrium bath states and spatially correlated environments. Besides outlining a general expression for the expected value of any electronic system observable in the original frame, we also discuss implications of the Markovian and Secular approximations highlighting that they need not hold in the untransformed frame despite being strictly satisfied in the polaron frame. The key features of the theory are illustrated using as an example a four-site subsystem of the Fenna-Mathews-Olson light-harvesting complex. For a spectral density including a localised mode, we show that oscillations of site populations may only be observed when non-equilibrium bath effects are taken into account. Furthermore, we illustrate how this formalism allows us to identify the electronic and vibrational components of the oscillatory dynamics.

Transport through molecular junctions

Transport through molecular junctions

Cotunneling, current blockade, and backaction forces in nanobeams close to the Euler buckling instability

Single-electron transistors embedded in a vibrating nanoresonator such as a doubly-clamped carbon nanotube exhibit effects stemming from the coupling between electronic and vibrational degrees of freedom. In particular, a capacitive electromechanical coupling induces a blockade of the current at low bias voltage. It has been recently shown theoretically within a sequential-tunneling approximation that this current blockade can be enhanced by orders of magnitude when the suspended structure is brought to the Euler buckling instability. Here, we investigate the role of cotunneling on the predicted enhancement and show that the latter is not suppressed by cotunneling effects. We further demonstrate that despite the fact that the current blockade is difficult to measure far from the Euler instability, the backaction of the current flow on the nanobeam frequency may be easier to observe.

Inelastic transport through double quantum dot systems

Inelastic transport through double quantum dot systems with coupling between electronic and vibrational degrees of freedom is examined by means of a master equation approach. The current and the conductance are analyzed for both weak and strong interdot couplings. The results show that an asymmetry in the current–voltage characteristic and appearance of negative differential conductance due to electron–phonon interaction. The influence of temperature on the current is studied and found that increasing temperature gives rise to eliminating the current blockade and, thus, removing the Coulomb diamonds in the conductance spectra.

High-Performance Solution of Hierarchical Equations of Motion for Studying Energy Transfer in Light-Harvesting Complexes.

Excitonic models of light-harvesting complexes, where the vibrational degrees of freedom are treated as a bath, are commonly used to describe the motion of the electronic excitation through a molecule. Recent experiments point toward the possibility of memory effects in this process and require one to consider time nonlocal propagation techniques. The hierarchical equations of motion (HEOM) were proposed by Ishizaki and Fleming to describe the site-dependent reorganization dynamics of protein environments ( J. Chem. Phys. 2009 , 130 , 234111 ), which plays a significant role in photosynthetic electronic energy transfer. HEOM are often used as a reference for other approximate methods but have been implemented only for small systems due to their adverse computational scaling with the system size. Here, we show that HEOM are also solvable for larger systems, since the underlying algorithm is ideally suited for the usage of graphics processing units (GPU). The tremendous reduction in computational time due to the GPU allows us to perform a systematic study of the energy-transfer efficiency in the Fenna-Matthews-Olson (FMO) light-harvesting complex at physiological temperature under full consideration of memory effects. We find that approximative methods differ qualitatively and quantitatively from the HEOM results and discuss the importance of finite temperature to achieving high energy-transfer efficiencies.

MOLECULE MODEL FOR KAONIC NUCLEAR CLUSTER $\bar{K}NN$

We analyze the properties of the kaonic nuclear cluster (KNC) [Formula: see text] with the structure [Formula: see text], having the quantum numbers [Formula: see text], and treated as a quasi-bound hadronic molecule state. We describe the properties of the hadronic molecule, or the KNC [Formula: see text], in terms of vibrational degrees of freedom with oscillator wave functions and chiral dynamics. These wave functions, having the meaning of trial wave functions of variational calculations, are parametrized by the frequency of oscillations of the [Formula: see text] pair, which is fixed in terms of the binding energy of the strange baryon resonance Λ(1405), treated as a quasi-bound [Formula: see text] state. The binding energies BX and widths ΓX of the states [Formula: see text] and [Formula: see text], respectively, are calculated in the heavy-baryon approximation by using chiral Lagrangians with meson–baryon derivative couplings invariant under chiral SU (3)× SU (3) symmetry at the tree-level approximation. The results are [Formula: see text] and [Formula: see text] and, where [Formula: see text] and [Formula: see text] are the widths of non-pionic [Formula: see text], NΣ and pionic [Formula: see text] decay modes, calculated for [Formula: see text] and [Formula: see text], respectively.

Franck–Condon physics in a single trapped ion

We propose a way to explore the Franck–Condon (FC) physics using a single ion confined in a spin-dependent potential, formed by the combination of a Paul trap and a magnetic field gradient. A correlation between electronic and vibrational degrees of freedom, called electron–vibron coupling, is induced by a non-zero gradient. In the case of a sufficiently strong electron–vibron coupling, FC blockade of low-lying vibronic transitions takes place. We examine the feasibility of observing FC physics in a single trapped ion and demonstrate many potential applications of ionic FC physics in quantum state engineering and quantum information processing.

Ab initio rovibronic states of the thioketenyl radical in its X2Π electronic ground state

We present an ab initio study of the thioketenyl (HCCS) radical in its degenerate X(2)Π electronic ground state. All rotational and vibrational degrees of freedom are taken into account including the electronic orbital and spin angular momenta. The structure of the rovibronic levels and the nature of the corresponding wave functions show resonances even at very low energies due to strong couplings between the bending, rotation, and spin terms in the Hamiltonian. Assignments from the dominant contributions of the eigenvectors are discussed in parallel with previously published data. The rotational structures for the first excited vibronic states are computed as well as transition intensities for the fundamental one.

Communication: Exciton–phonon information flow in the energy transfer process of photosynthetic complexes

Non-Markovian and nonequilibrium phonon effects are believed to be key ingredients in the energy transfer in photosynthetic complexes, especially in complexes which exhibit a regime of intermediate exciton-phonon coupling. In this work, we utilize a recently developed measure for non-Markovianity to elucidate the exciton-phonon dynamics in terms of the information flow between electronic and vibrational degrees of freedom. We study the measure in the hierarchical equation of motion approach which captures strong coupling effects and nonequilibrium molecular reorganization. We propose an additional trace distance measure for the information flow that could be extended to other master equations. We find that for a model dimer system and for the Fenna-Matthews-Olson complex the non-Markovianity is significant under physiological conditions.

Phase space geometry of dynamics passing through saddle coupled with spatial rotation

Nonlinear reaction dynamics through a rank-one saddle is investigated for many-particle system with spatial rotation. Based on the recently developed theories of the phase space geometry in the saddle region, we present a theoretical framework to incorporate the spatial rotation which is dynamically coupled with the internal vibrational motions through centrifugal and Coriolis interactions. As an illustrative simple example, we apply it to isomerization reaction of HCN with some nonzero total angular momenta. It is found that no-return transition state (TS) and a set of impenetrable reaction boundaries to separate the "past" and "future" of trajectories can be identified analytically under rovibrational couplings. The three components of the angular momentum are found to have distinct effects on the migration of the "anchor" of the TS and the reaction boundaries through rovibrational couplings and anharmonicities in vibrational degrees of freedom. This method provides new insights in understanding the origin of a wide class of reactions with nonzero angular momentum.

Response signal in a femtosecond pump-probe experiment in a condensed medium with account of the memory induced by the relaxation medium

For a model molecular system with one vibrational degree of freedom and three electronic states coupled by pump and probe laser pulses in a condensed medium, the response signal in a femtosecond pump-probe experiment is calculated. The potential curves of all three states are described by the Morse potential. Calculations are performed using two qualitatively different approaches to describing the medium-induced relaxation: with memory of the relaxation process and without memory (Markovian approximation). The temporal evolution of the vibrational wave packet in the intermediate electronically excited state is described using a master equation for the density matrix of the molecular system, which is derived within the framework of the Nakajima-Zwanzig formalism. It is demonstrated that, at short delay times, when the proposed approach is applicable, taking into account memory effects can substantially change the form of the pump-probe experiment signal in comparison with the signal calculated in the Markovian approximation.

Approximate theoretical model for the five electronic states ( Ω = 5/2, 3/2, 3/2, 1/2, 1/2) arising from the ground 3d 9 configuration in nickel halide molecules and for rotational levels of the two Ω = 1/2 states in that manifold

In the first part of this paper an effective Hamiltonian for a non-rotating diatomic molecule containing only crystal-field and spin–orbit operators is set up to describe the energies of the five spin–orbit components that arise in the ground electronic configuration of the nickel monohalides. The model assumes that bonding in the nickel halides has the approximate form Ni +X −, with an electronic 3d 9 configuration plus closed shells on the Ni + moiety and a closed shell configuration on the X − moiety. From a crystal-field point of view, interactions of the positive d-hole with the cylindrically symmetrical electric charge distribution of the hypothetical NiX − closed-shell core can then be parameterized by three terms in a traditional expansion in spherical harmonics: C 0 + C 2 Y 20( θ, ϕ) + C 4 Y 40( θ, ϕ). Interaction of the hole with the magnetic field generated by its own orbital motion can be parameterized by a traditional spin–orbit interaction operator A L · S . The Hamiltonian matrix is set up in a basis set consisting of the 10 Hund’s case (a) basis functions | L, Λ; S , Σ〉 that arise when L = 2 and S = 1/2. Least-squares fits of the observed five spin–orbit components of the three lowest electronic states in NiF and NiCl are then carried out in terms of the four parameters C 0, C 2, C 4, and A which lead to good agreement, except for the two | Ω| = 1/2 states. The large equal and opposite residuals of the | Ω| = 1/2 states can be reduced to values comparable with those for the | Ω| = 3/2 and | Ω| = 5/2 states by fixing A to its value in Ni + and then introducing an empirical correction factor for one off-diagonal orbital matrix element. In the second part of this paper the usual effective Hamiltonian B( J – L – S ) 2 for a rotating diatomic molecule is used to derive expressions for the Ω-type doubling parameter p in the two | Ω| = 1/2 states. These expressions show (for certain sign conventions) that the sum of the two p values should be −2 B, but that their difference can vary between −10 B and +10 B. These theoretical results are in good agreement with the two observed p values for both NiF and NiCl. The present formalism should in principle be applicable to NiBr and NiI, and to the halides of palladium, since Pd + has a well isolated 4d 9 electronic ground configuration. Extension to metal halides having d n configurations with n < 9, or to platinum halides may present difficulties, since manifolds from the d n and d n −1 s configurations may be heavily mixed, thus requiring “too many” parameters in the electronic part of the problem. Application to linear triatomic molecules may also present problems because of the large number of vibronic perturbations made possible by their four vibrational degrees of freedom.