Anharmonic vibrational probe for N-methylacetamide in different micro-environments

In the present study, anharmonic vibrational properties of the amide modes in N-methylacetamide (NMA), a model molecule for peptide vibrational spectroscopy, are examined by DFT calculations. The 3N-6 normal mode frequencies, diagonal and off-diagonal anharmonicities are evaluated by means of the second order vibrational perturbation theory (VPT2). Good performance of B3LYP/6-31+G** is found for predicting vibrational frequencies in comparison with gas phase experimental data. The amide vibrational modes are assigned through potential energy distribution analysis (PED). The solvation effect on the amide vibrational modes is modeled within the PCM method. From gas phase to polar solvents, red shifts are observed for both harmonic and anharmonic vibrational frequency of amide I mode while the CO bond length increases upon the solvent polarity. Cubic and quartic force constants are further calculated to evaluate the origin of the anharmonicity for the amide I mode of NMA in different micro-environments.     

Simulations of vibrational spectra from classical trajectories: calibration with ab initio force fields

An algorithm allowing simulating vibrational spectra from classical time-dependent trajectories was applied for infrared absorption, vibrational circular dichroism, Raman, and Raman optical activity of model harmonic systems. The implementation of the theory within the TINKER molecular dynamics (MD) program package was tested with ab initio harmonic force fields in order to determine the feasibility for more extended MD simulations. The results suggest that sufficiently accurate frequencies can be simulated with integration time steps shorter than about 0.5 fs. For a given integration time step, lower vibrational frequencies ( approximately 0-2000 cm(-1)) could be reproduced with a higher accuracy than higher-frequency vibrational modes (e.g., O-H and C-H stretching). In principle, the algorithm also provides correct intensities for ideal systems. In applied simulations, however, the intensity profiles are affected by an unrealistic energy distribution between normal modes and a slow energy relaxation. Additionally, the energy fluctuations may cause weakening of the intensities on average. For ab initio force fields, these obstacles could be overcome by an arbitrary normal mode energy correction. For general MD simulations, averaging of many shorter MD trajectories started with randomly distributed atomic velocities provided the best spectral shapes. alpha-pinene, D-gluconic acid, formaldehyde dimer, and the acetylprolineamide molecule were used in the tests.     

Solvation pressure in chloroform

Molecular dynamics (MD) simulations of chloroform vapor and liquid at normal temperature and pressure and liquid under hydrostatic pressure are presented, giving bond lengths and vibrational frequencies as functions of pressure. The change in bond lengths between vapor and liquid at normal temperature and pressure is consistent with a pressure equivalent to the cohesive energy density (CED) of the liquid, supporting the solvation pressure model which predicts that solvated molecules or nanoparticles experience a pressure equal to the CED of the liquid. Experimental data for certain Raman frequencies of chloroform in the vapor phase, in the liquid, and in the liquid under pressure are presented and compared to MD. Results for C-Cl vibrational modes are in general agreement with the solvation pressure model whereas frequencies associated with the C-H bond are not. The results demonstrate that masking interactions exist in the real liquid that can be reduced or eliminated in simplified simulations.     

Harmonic analysis of large systems. III. Comparison with molecular dynamics

Atomic motions in bovine pancreatic trypsin inhibitor (BPTI), derived from molecular dynamics, harmonic analysis, and quasiharmonic analysis, are compared when a single protein model, energy parameters, and environment are employed. Molecular dynamics (MD) was carried out for 2 nanoseconds. An average structure was determined from the last nanosecond of the MD simulation, when no major structural changes were observed. This structure was used for several harmonic analysis calculations as well as for a reference structure for the quasiharmonic analysis, for both full basis and reduced basis sets. In contrast to the harmonic analysis results, the quasiharmonic reduced basis calculation using a spherical harmonics reduced basis provided good agreement with the full basis calculation, suggesting that when anharmonic effects are considered, BPTI can behave as a homogeneous object. An extensive analysis of the normal modes from a diverse set of 201 minimized MD simulation frames was performed. On only the sub-picosecond time scale were energy minima revisited after a transition to another state. This analysis shows that the dynamics average structure is not representative of the simulation frames in terms of energy and vibrational frequencies. For this model of BPTI, 42% of the motion (mean-squared fluctuation) can be attributed to harmonic limit behavior. A spectral analysis of the correlation function of deformation for a particular normal mode or quasiharmonic mode can be used to determine the time scales of motions which correspond to harmonic vibration, large-scale drift, or sharp transitions between local substrates. © 1995 John Wiley & Sons, Inc.     

Dynamics of proton transfer and vibrational relaxation in dilute hydrofluoric acid

The molecular mechanisms in both vibrational relaxation and proton transfer (PT) associated with infrared (IR)-induced PT in a dilute hydrofluoric acid solution at ambient temperature are studied by molecular dynamics (MD) simulations with the multistate empirical valence bond model. To investigate the solvation dynamics, a collective solvent coordinate and its perpendicular bath modes are defined from the diabatic energy gap and their motions are examined by the generalized Langevin equation (GLE) formalism. The GLE analysis using the equilibrium MD simulation shows that the major solvent reorganizations in the PT are represented by the libration and hindered translation. In particular, the libration gives the stronger coupling to the solvent reorganization and the faster relaxation. The nonequilibrium MD simulation demonstrated that both the HF stretching vibration and the solvent reorganization relax on a similar time scale and thus compete in the PT. It also supported the "presolvation mechanism" for the PT in this system.     

Vibrational analysis of small species in the liquid phase by a combined density functional theory and polarizable continuum method

The vibrational frequencies of small organic molecules and inorganic ions were predicted both in vacuum and in the liquid phase at the B3LYP/6-311G++(d,p) level of theory, within the harmonic approximation. The solvent effect was introduced as an electrostatic influence of the bulk by means of the integral equation formalism of the polarizable continuum model. The results show that the application of this continuum solvation model can reduce the overall error in the theoretical predictions. In order to improve the quality of the results, two different scaling procedures were applied. The frequencies obtained for the continuum, when compared with vacuum calculations, show a better linear correlation with experimental data, which increases the efficiency of the scaling procedures. A further reduction of the errors is obtained by partitioning the overall set of frequencies according to the nature of the normal modes and the charge of the solutes. The quality of the theoretical predictions, especially for the stretching modes of vibration of nonionic chemical species, is here noteworthy.     

Hierarchical structure of the energy landscape of proteins revisited by time series analysis. II. Investigation of explicit solvent effects

Time series analysis tools are employed on the principal modes obtained from the C(alpha) trajectories from two independent molecular-dynamics simulations of alpha-amylase inhibitor (tendamistat). Fluctuations inside an energy minimum (intraminimum motions), transitions between minima (interminimum motions), and relaxations in different hierarchical energy levels are investigated and compared with those encountered in vacuum by using different sampling window sizes and intervals. The low-frequency low-indexed mode relationship, established in vacuum, is also encountered in water, which shows the reliability of the important dynamics information offered by principal components analysis in water. It has been shown that examining a short data collection period (100 ps) may result in a high population of overdamped modes, while some of the low-frequency oscillations (<10 cm(-1)) can be captured in water by using a longer data collection period (1200 ps). Simultaneous analysis of short and long sampling window sizes gives the following picture of the effect of water on protein dynamics. Water makes the protein lose its memory: future conformations are less dependent on previous conformations due to the lowering of energy barriers in hierarchical levels of the energy landscape. In short-time dynamics (<10 ps), damping factors extracted from time series model parameters are lowered. For tendamistat, the friction coefficient in the Langevin equation is found to be around 40-60 cm(-1) for the low-indexed modes, compatible with literature. The fact that water has increased the friction and that on the other hand has lubrication effect at first sight contradicts. However, this comes about because water enhances the transitions between minima and forces the protein to reduce its already inherent inability to maintain oscillations observed in vacuum. Some of the frequencies lower than 10 cm(-1) are found to be overdamped, while those higher than 20 cm(-1) are slightly increased. As for the long-time dynamics in water, it is found that random-walk motion is maintained for approximately 200 ps (about five times of that in vacuum) in the low-indexed modes, showing the lowering of energy barriers between the higher-level minima.     

Effects of resolution and friction in the interpretation of QHAS measurements

We use Langevin molecular dynamics (MD) simulations to improve the picture of the processes that contribute to QHAS broadening, as a function of momentum transfer at the crystal. We use a simulation of realistic damped vibrational motion in a harmonic well to establish the contributions to QHAS measurements due to both vibrational motion and intracell diffusion (usually referred to as vibrational dephasing). We demonstrate the experimental conditions under which such contributions are likely to be important. These results are compared with those from a simulation of thermal diffusion over a sinusoidally corrugated potential. We show that resolution and atom-surface "friction" play an important role in determining the form of QHAS measurements and we demonstrate that there is no simple relationship between the "activation energy" derived from an Arrhenius plot of QHAS data and the adiabatic potential barrier height. MD simulations are therefore necessary to perform a complete analysis of the data. Finally, we discuss the application of our results to more sophisticated potentials, particularly those with multiple adsorption sites.     

Heat flow in proteins: computation of thermal transport coefficients

The rate of vibrational energy transfer and thermal transport coefficients are computed for two structurally distinct proteins, green fluorescent protein (GFP) and myoglobin. The computation of thermal transport coefficients exploits the scaling of the energy diffusion coefficient with the vibrational mode frequency of a protein. Near 300 K we find that vibrational energy transfer due to anharmonicity contributes substantially to thermal transport because of the localization of many thermally accessible normal modes. The thermal diffusivity for the beta-barrel GFP is larger than that for myoglobin, particularly at low temperature due to a mean free path for vibrational energy propagation that is twice as large at low frequency. Vibrational energy transfer is also faster in GFP than in myoglobin for most vibrational modes.     

Normal mode partitioning of Langevin dynamics for biomolecules

We propose a novel normal mode multiple time stepping Langevin dynamics integrator called NML. The aim is to approximate the kinetics or thermodynamics of a biomolecule by a reduced model based on a normal mode decomposition of the dynamical space. Our basis set uses the eigenvectors of a mass reweighted Hessian matrix calculated with a biomolecular force field. This particular choice has the advantage of an ordering according to the eigenvalues, which have a physical meaning of being the square of the mode frequency. Low frequency eigenvalues correspond to more collective motions, whereas the highest frequency eigenvalues are the limiting factor for the stability of the integrator. In NML, the higher frequency modes are overdamped and relaxed near their energy minimum while respecting the subspace of low frequency dynamical modes. Our numerical results confirm that both sampling and rates are conserved for an implicitly solvated alanine dipeptide model, with only 30% of the modes propagated, when compared to the full model. For implicitly solvated systems, NML gives a twofold improvement in efficiency over plain Langevin dynamics for sampling a small 22 atom (alanine dipeptide) model and in excess of an order of magnitude for sampling an 882 atom (bovine pancreatic trypsin inhibitor) model, with good scaling with system size subject to the number of modes propagated. NML has been implemented in the open source software PROTOMOL.     

Exploring the effect of anharmonicity of molecular vibrations on thermodynamic properties

Thermodynamic properties of selected small and medium size molecules were calculated using harmonic and anharmonic vibrational frequencies. Harmonic vibrational frequencies were obtained by normal mode analysis, whereas anharmonic ones were calculated using the vibrational self-consistent field (VSCF) method. The calculated and available experimental thermodynamic data for zero point energy, enthalpy, entropy, and heat capacity are compared. It is found that the anharmonicity and coupling of molecular vibrations can play a significant role in predicting accurate thermodynamic quantities. Limitations of the current VSCF method for low frequency modes have been partially removed by following normal mode displacements in internal, rather than Cartesian, coordinates.     

Vibrational structure of vinyl chloride cation studied by using one-photon zero-kinetic energy photoelectron spectroscopy

The vibrational structure of vinyl chloride cation, CH(2)CHCl+ (X(2)A' '), has been studied by vacuum ultraviolet (VUV) zero-kinetic energy (ZEKE) photoelectron spectroscopy. Among nine symmetric vibrational modes, the fundamental frequencies of six modes have been determined. The first overtone of the out-of-plane CH(2) twist vibrational mode has been also measured. In addition to these, the combination and overtone bands of the above vibrational modes about 4500 cm(-1) above the ground state have been observed in the ZEKE spectrum. The vibrational band intensities of the ZEKE spectrum can be described approximately by the Franck-Condon factors with harmonic approximation. The ZEKE spectrum has been assigned based on the harmonic frequencies and Franck-Condon factors from theoretical calculations. The ionization energy (IE) of CH(2)CHCl is determined as 80705.5 +/- 2.5 (cm(-1)) or 10.0062 +/- 0.0003 (eV).     

Microscopic Investigation of Ethylene Carbonate Interface: A Molecular Dynamics and Vibrational Spectroscopic Study

Ethylene carbonate(EC) liquid and its vapor-liquid interface were investigated using a combination of molecular dynamics(MD)simulation and vibrational IR, Raman and sum frequency generation(SFG)spectroscopies. The MD simulation was performed with a flexible and polarizable model of the EC molecule newly developed for the computation of vibrational spectra. The internal vibration of the model was described on the basis of the harmonic couplings of vibrational modes, including the anharmonicity and Fermi resonance coupling of C=O stretching. The polarizable model was represented by the charge response kernel(CRK),which is based on ab initio molecular orbital calculations and can be readily applied to other systems. The flexible and polarizable model can also accurately reproduce the structural and thermodynamic properties of EC liquid. Meanwhile, a comprehensive set of vibrational spectra of EC liquid, including the IR and Raman spectra of the bulk liquid as well as the SFG spectra of the liquid interface, were experimentally measured and reported. The set of experimental vibrational spectra provided valuable information for validating the model, and the MD simulation using the model comprehensively elucidates the observed vibrational IR, Raman, and SFG spectra of EC liquid. Further MD analysis of the interface region revealed that EC molecules tend to orientate themselves with the C=O bond parallel to the interface. The MD simulation explains the positive Im[χ~((2))](ssp) band of the C=O stretching region in the SFG spectrum in terms of the preferential orientation of EC molecules at the interface. This work also elucidates the distinct lineshapes of the C=O stretching band in the IR, Raman, and SFG spectra. The lineshapes of the C=O band are split by the Fermi resonance of the C=O fundamental and the overtone of skeletal stretching. The Fermi resonance of C=O stretching was fully analyzed using the empirical potential parameter shift analysis(EPSA) method. The apparently different lineshapes of the C=O stretching band in the IR, Raman, and SFG spectra were attributed to the frequency shift of the C=O fundamental in different solvation environments in the bulk liquid and at the interface. This work proposes a systematic procedure for investigating the interface structure and SFG spectra, including general modeling procedure based on ab initio calculations, validation of the model using available experimental data, and simultaneous analysis of molecular orientation and SFG spectra through MD trajectories. The proposed procedure provides microscopic information on the EC interface in this study, and can be further applied to investigate other interface systems, such as liquid-liquid and solid-liquid interfaces.     

Langevin模方法研究溶剂粘度对18-冠醚-6性质的影响

本文在各种溶剂粘度下对18-冠醚-6的两种稳定构象C_i和D_3d进行了Langevin模分析。结果表明,溶剂的粘度对18-冠醚-6的性质,特别是对振动频率分布和键偶极矢量的摇摆角度有较大的影响。同时表明,Langevin模方法是解释溶液中分子运动情况的一种简捷有力的模型。     

On the nature of low-frequency vibrational modes in globular protein molecules immersed in water

Recent vibrational normal mode analysis of globular protein molecules (in vacuum) has shown that they have characteristic low-frequency (≈ 2–5 cm⁻¹) modes. It is shown that when the molecules are immerséd in water the modes are strongly red-shifted and damped. The implications of this result are briefly discussed.     

Vibrational modes of metal nanoshells and bimetallic core-shell nanoparticles

We theoretically study the spectrum of radial vibrational modes in composite metal nanostructures such as bimetallic core-shell particles and metal nanoshells with dielectric core in an environment. We calculate frequencies and damping rates of fundamental (breathing) modes for these nanostructures along with those of two higher-order modes. For metal nanoshells, we find that the breathing mode frequency is always lower than the one for solid particles of the same size, while the damping is higher and increases with a reduction in the shell thickness. We identify two regimes that can be characterized as weakly damped and overdamped vibrations in the presence of external medium. For bimetallic particles, we find periodic dependence of frequency and damping rate on the shell thickness with period being determined by the mode number. For both types of nanostructures, the frequency of higher modes is nearly independent of the environment, while the damping rate shows a strong sensitivity to the outside medium.     

Influence of the solvent representation on vibrational entropy calculations: Generalized born versus distance‐dependent dielectric model

The harmonic model is the most popular approximation for estimating the “configurational” entropy of a solute in molecular mechanics/Poisson‐Boltzmann solvent accessible surface area (MM/PBSA)‐type binding free energy calculations. Here, we investigate the influence of the solvent representation in the harmonic model by comparing estimates of changes in the vibrational entropies for 30 trypsin/ligand complexes on ligand binding. Second derivatives of Amber generalized Born (GB) solvation models are available in the nucleic acid builder code. They allow one to use these models for the calculation of vibrational entropies instead of using a simpler solvation model based on a distance‐dependent dielectric (DDD) constant. Estimates of changes in the vibrational entropies obtained with a DDD model are systematically and significantly larger, by on average, 6 kcal mol^?1 (at T = 300 K), than estimates obtained with a GB model and so are more favorable for complex formation. The difference becomes larger the more the vibrational entropy contribution disfavors complex formation, that is, the larger the ligand is (for the complexes considered here). A structural decomposition of the estimates into per‐residue contributions reveals polar interactions between the ligand and the surrounding protein, in particular involving charged nitrogens, as a main source of the differences. Snapshots minimized with the DDD model showed a structural deviation from snapshots minimized in explicit water that is larger by, on average, 0.5 Å RMSD compared to snapshots that were minimized with GB^HCT. As experimental vibrational entropies of biomacromolecules are elusive, there is no direct way to establish a solvent model's superiority. Thus, we can only recommend using the GB harmonic model for vibrational entropy calculations based on the reasoning that smaller structural deviations should point to the implicit solvent model that closer approximates the energy landscape of the solute in explicit solvent. © 2012 Wiley Periodicals, Inc.     

Vibrational energy relaxation of large-amplitude vibrations in liquids

Given the limited intermolecular spaces available in dense liquids, the large amplitudes of highly excited, low frequency vibrational modes pose an interesting dilemma for large molecules in solution. We carry out molecular dynamics calculations of the lowest frequency ("warping") mode of perylene dissolved in liquid argon, and demonstrate that vibrational excitation of this mode should cause identifiable changes in local solvation shell structure. But while the same kinds of solvent structural rearrangements can cause the non-equilibrium relaxation dynamics of highly excited diatomic rotors in liquids to differ substantially from equilibrium dynamics, our simulations also indicate that the non-equilibrium vibrational energy relaxation of large-amplitude vibrational overtones in liquids should show no such deviations from linear response. This observation seems to be a generic feature of large-moment-arm vibrational degrees of freedom and is therefore probably not specific to our choice of model system: The lowest frequency (largest amplitude) cases probably dissipate energy too quickly and the higher frequency (more slowly relaxing) cases most likely have solvent displacements too small to generate significant nonlinearities in simple nonpolar solvents. Vibrational kinetic energy relaxation, in particular, seems to be especially and surprisingly linear.