Fast vibrational relaxation for a dipolar molecule in a polar solvent

Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation (GLE), which can be rigorously derived by means of a linear projection (LP) technique. Within this framework a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here we discuss that this task is most naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic underestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom. INTRODUCTIONStudying complex dynamics of many-particle systems has become one of the main goals in modern molecular physics. The fundamental understanding of the underlying microscopical processes requires the interplay of elaborate experimental techniques and sophisticated theoretical approaches. Experimentally, (non-)linear spectroscopy revealed itself as a powerful tool for probing the dynamics and for determining the characteristic timescales, such as dephasing/relaxation times and reaction rates to name but two. For interpreting the experimental spectra theoretical models are needed which can give insight into the atomistic dynamics. Often, a reduction of the description to few variables is convenient in many cases since this can not only ease the interpretation, but enable the identification of key properties [1]. Such a reduced description can formally be obtained from the so-called system-bath partitioning, where only a small subset of degrees of freedom (DOFs), referred to as system, is considered as important for describing a physical process under study. All the other DOFs, referred to as bath, are regarded as irrelevant in the sense that they might influence the time evolution of the system but do not explicitly enter any dynamical variable of interest. Practically, such a separation is often natural, for instance, when studying a reaction with a clearly defined reaction center or solute dynamics in a solvent environment. Further, reduced equations of motion (EOMs) for the system DOFs can be derived in which the influence of the bath is limited to dissipation and fluctuations.The most simple formulation of this idea is provided by the Markovian Langevin equation, where dissipation and fluctuations take the form of static friction and stochastic white noise, respectively [2][3][4]. Sit...

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“…in studies of vibrational relaxation [8,11,43], is based on approximating ξ LP (t) by ξ RB (t) calculated as…”

Section: Berne and Harp Methodsmentioning

confidence: 99%

Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

Gottwald

Karsten

Ivanov

et al. 2015

The Journal of Chemical Physics

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“…This approximate model has been employed to study, among other systems (44)(45)(46), dioxygen relaxation in a rare gas solvent (38), and relaxation of a polar solute (methyl chloride) in a polar solvent (water) (41). The latter study found the Landau-Teller theory to be valid in that the simulation result of the vibrational energy relaxation was exponential in time and in good agreement with the Landau-Teller theoretical prediction.…”

mentioning

confidence: 85%

Vibrational population relaxation of carbon monoxide in the heme pocket of photolyzed carbonmonoxy myoglobin: Comparison of time-resolved mid-IR absorbance experiments and molecular dynamics simulations

Sagnella

Straub

Jackson

et al. 1999

Proc. Natl. Acad. Sci. U.S.A.

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The vibrational energy relaxation of carbon monoxide in the heme pocket of sperm whale myoglobin was studied by using molecular dynamics simulation and normal mode analysis methods. Molecular dynamics trajectories of solvated myoglobin were run at 300 K for both the ␦-and -tautomers of the distal His-64. Vibrational population relaxation times of 335 ؎ 115 ps for the ␦-tautomer and 640 ؎ 185 ps for the -tautomer were estimated by using the Landau-Teller model. Normal mode analysis was used to identify those protein residues that act as the primary ''doorway'' modes in the vibrational relaxation of the oscillator. Although the CO relaxation rates in both the -and ␦-tautomers are similar in magnitude, the simulations predict that the vibrational relaxation of the CO is faster in the ␦-tautomer with the distal His playing an important role in the energy relaxation mechanism. Time-resolved mid-IR absorbance measurements were performed on photolyzed carbonmonoxy hemoglobin (Hb 13 CO). From these measurements, a T1 time of 600 ؎ 150 ps was determined. The simulation and experimental estimates are compared and discussed. Since the pioneering efforts of Landau and Teller (1), the problem of vibrational energy redistribution has attracted much theoretical attention (2-6). With the advent of ultrafast time-resolved IR spectroscopy, there is renewed interest in this problem as researchers can now probe directly the lifetimes of specific vibrational modes and, therefore, explore mechanisms of vibrational relaxation (7). In particular, the vibrational relaxation of metal carbonyl compounds has received considerable attention with CO population relaxation times (T 1 ) found to range from the picosecond to nanosecond time scales, depending on the metal carbonyl and its surroundings (8). In that study, both chemical bonding and surrounding solvent were found to influence the vibrational relaxation time of the carbonyl. In addition to this seminal work, there have been several experimental probes of CO relaxation when bound to model heme compounds and heme proteins (9-11).The vibrational relaxation of bound CO in heme proteins was found to be very fast (Ϸ20 ps) compared to other CO ligated compounds. In addition, Fayer and coworkers found that (i) the T 1 population relaxation time for the carbonyl ligand stretch is largely independent of temperature from 20 to 300 K (12); (ii) the vibrational lifetimes vary among different vibrational substates of the same protein (13); (iii) changes in the vibrational lifetime of bound CO are highly correlated with a change in the vibrational frequency of CO (13); and (iv) intermolecular transfer of vibrational energy is relatively unimportant in the relaxation process of bound CO (13).Vibrational relaxation tends to be more efficient through strong covalent interactions, yet there is only one such interaction between the CO and the heme. To explain the fast relaxation of bound CO in heme proteins, it has been suggested that the manifold of vibrational states within the heme is responsible.The...

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Section: Vibrational Relaxationmentioning

confidence: 99%

“…[3][4][5][6][7][8][9] Various approaches exist, perhaps the most intuitive of which uses non-equilibrium MD simulations to explicitly excite the bond(s) of interest and measure relaxation times. [3] By averaging over a number of non-equilibrium trajectories, the cooling time T 1 is obtained according to Eqn. (1) [10,11] quantum mechanical methods to compute the intermolecular interactio ever, due to the computational effort involved in such calculations, it is o for small systems or in conjunction with mixed quantum mechanics/m mechanics (QM/MM) calculations.…”

Section: Vibrational Relaxationmentioning

confidence: 99%

Computational Spectroscopy and Reaction Dynamics

Cazade

Lütz²,

Lee³

et al. 2011

Chimia

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Physico- and bio-chemical processes on the femto- to picosecond time scale are ideally suited to be investigated with all-atom simulations. They include, amongst others, vibrational relaxation, ligand migration in sterically demanding environments (proteins, ices), or vibrational spectra. By comparing with experimental data, the results can be used to obtain an understanding of the mechanisms underlying the observations. Furthermore, most of these processes are sensitive to the intermolecular interactions. Therefore, detailed refinement of such interaction potentials is possible. Keywords: Computational spectroscopy · Molecular dynamics simulations · Reaction dynamicsThe classification of fast and ultrafast time scales in atoms and molecules depends to some extent on the process and property considered. For example, the electronic degrees of freedom change on considerably more rapid time scales than the nuclear motions. This is the basis of the Born-Oppenheimer approximation which is valid in many cases. In proteins, on the other hand, vibrations are much more rapid than changes in the secondary structure. Typical time scales for electronic motion in molecules are attoseconds, whereas vibrations are associated with femto-and pico-second time scales. In the following, ultrafast time scales in molecular systems -which are at the focus of the NCCR Molecular and Ultrafast Science and Technology (MUST) -will be associated with atto-to picosecond processes.Understanding ultrafast processes in molecular systems requires multi-faceted approaches, including experiment, theory and computation. A typical example is the vibrational relaxation of a solvated diatomic molecule, e.g. cyanide (CN − ) in water. [1,2] Although time scales of vibrational relaxation can be reliably measured using modern laser techniques, understanding the relaxation mechanism in molecular detail is much more difficult as it includes coupling and energy transfer to solvent modes. Another example is allostery which is the regulation of a protein by binding a small molecule at the allosteric site. An allosteric activator will enhance the activity of the protein. The most widely known but still incompletely understood allosteric protein is hemoglobin. Here, four binding sites for the ligand (O 2 ) exist. Binding of the first O 2 molecule increases the protein's affinity for binding the second O 2 molecule, etc. However, the molecular details underlying the enhanced affinity for subsequent O 2 ligands is still unexplained. Finally, one purpose of high-resolution spectroscopy is to understand the bonding pattern and geometrical details of a molecule by recording and analyzing spectroscopic signatures. As the size of the molecule grows, directly determining the structure of the molecule from the spectroscopic data becomes increasingly difficult. Even more difficult is the situation in proteins where spectroscopic features of small probe molecules such as CO or NO can be recorded but the splitting patterns of the vibrational spectra are difficult ...

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Fast vibrational relaxation for a dipolar molecule in a polar solvent

Cited by 180 publications

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Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

Vibrational population relaxation of carbon monoxide in the heme pocket of photolyzed carbonmonoxy myoglobin: Comparison of time-resolved mid-IR absorbance experiments and molecular dynamics simulations

Computational Spectroscopy and Reaction Dynamics

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