Hydrogen Bond Networks: Structure and Evolution after Hydrogen Bond Breaking

Spectroscopic investigation of proton bonding at sub-kelvin temperatures

The proton bond is a pivotal chemical motif in many areas of science and technology. Its quantum chemical description is remarkably challenged by nuclear and charge delocalization effects and the fluxional perturbation that it induces on molecular substrates. This work seeks insights into proton bonding at sub-kelvin temperatures. In this way, intrinsic features of the proton bond are exposed, essentially free from thermal fluctuations of the molecular frame. To this end, a proton is bound within the molecular ring cavity provided by the 12-crown-4 ether. The resulting ion is isolated in a He-droplet at ∼0.4 K, where it is interrogated by infrared laser spectroscopy. The recorded spectrum features narrow vibrational bands, consistent with a robust proton bond bridging ether sites across the cavity of the essentially frozen crown ether. The potential energy surface sustaining the proton bond is broad and markedly anharmonic. In consequence, common modeling methods within the harmonic approximation fail to capture the observed band positions, whose accurate description seems to be even beyond perturbative anharmonic approaches. Calculations show that at elevated temperatures, the crown ether backbone is highly fluxional and that the distance between the oxygen atoms fluctuates in time, modulating the potential that the proton or deuteron is exposed to, and yielding dynamic inhomogeneous broadening and blue shifts with respect to the cryogenic spectra. These observations call for novel computational developments, for which the vibrational signatures outlined in this work should provide a valuable benchmark.

Molecular Simulation-Guided Spectroscopy of Imidazolium-Based Ionic Liquids and Effects of Methylation on Ion-Cage and -Pair Dynamics

Classical molecular dynamics simulations were performed to assess an atomistic interpretation of the ion-probe structural interactions in two typical ionic liquids (ILs), 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [BMIm][NTf₂] and 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide [BDimIm][NTf₂] through computational ultrafast spectroscopy. The nitrile stretching vibrations of the thiocyanate anion, [SCN]^-, serve as the local mode of the ultrafast system dynamics within the imidazolium-based ionic liquid environment. The wavelet transform of classical trajectories determines the time-varying fluctuating frequencies and the stretch spectral signatures of SCN^- in the normalized distribution. However, computational modeling of the two-dimensional (2D) spectra from the wavelet-derived vibrational frequencies yields time evolution of the local molecular structure along with the varied time-dependent dynamics of the spectral diffusion process. We calculated the frequency-frequency correlation functions (FFCFs), time correlations associated with the ion-pair and -cage dynamics, and mean square displacements as a function of time, depicting diffusive dynamics. The calculated results based on the pair correlation functions and the distribution of atomic density suggest that the hydrogen and methylated carbon at the two-position of the imidazolium ring of [BMIm] and [BDimIm] cations, respectively, strongly interact with the probe through the N of the thiocyanate anion rather than the S atom. The center-of-mass center-of-mass (COM-COM) cation-probe radial distribution functions (RDFs) in conjunction with the site-specific structural analysis further reveal well-structured interactions of the thiocyanate ion and [BMIm]⁺ cation rather than the [BDimIm] cation. In contrast, the anion-probe COM-COM RDFs depict weak interactive associations within the vibrational probe [SCN]^- and [NTf₂]^- ions. Methylation at the two-position of the imidazolium ring predicts slower structural reorganization and breaking and reformation dynamics of the ion pairs and cages within the ionic liquid framework.

Multiple Ensembles of the Hydrogen-bonded Network in Ethylammonium Nitrate versus Water from Vibrational Spectral Dynamics of SCN- Probe

We performed classical molecular dynamics simulations to monitor the structural interactions and ultrafast dynamical and spectral response in the protic ionic liquid, ethylammonium nitrate (EAN) and water using the nitrile stretching mode of thiocyanate ion (SCN-) as the vibrational probe. The normalized stretch frequency distribution of nitrile stretch of SCN- attains an asymmetric shape in EAN, indicating the existence of more than one hydrogen-bonding environment in EAN. We computed the 2D IR spectrum from classical trajectories, applying the response function formalism. Spectral diffusion dynamics in EAN undergo an initial rattling of the SCN - inside the local ion-cage occurring at a timescale of 0.10 ps, followed by the breakup of the ion-cage activating molecular diffusion at 7.86 ps timescale. In contrast, the dynamics of structural reorganization occur at a timescale of 0.58 ps in H 2 O. Hence, the time dependence of the frequency-frequency correlation function decay hints at the local molecular structure and ultrafast ion dynamics of the SCN - probe. The loss of frequency correlation read from the peak shape changes in the 2D correlation spectrum as a function of waiting time is faster in H 2 O than in EAN due to the enhanced structural ordering and higher viscosity of the latter. We provide an atomic-level interpretation of the solvation environment around SCN - in EAN and water, which indicates the multiple ensembles of the hydrogen bond network in EAN.

Dynamics of Ionic Liquid through Intrinsic Vibrational Probes Using the Dispersion-Corrected DFT Functionals

First principles molecular dynamics simulations have been utilized to study the spectral properties of the protic ionic liquid, methylammonium formate (MAF). All simulations were performed using density functional theory (DFT) and various van der Waals-corrected exchange-correlation functionals. We calculated the vibrational stretch frequency distributions, determined the time-frequency correlations of the intrinsic vibrational probes, the N-H and C-O modes in MAF, and the frequency-structure correlations. We also estimated the average hydrogen-bond lifetimes and orientation dynamics to capture the ultrafast spectral response. The spectroscopic signature of the N-H stretching vibrations using the Becke-Lee-Yang-Parr (BLYP) and Perdew-Burke-Ernzerhof (PBE) functionals displays a spectral shift in the lower frequency side, suggesting stronger hydrogen-bonding interactions represented by the gradient approximation functionals than the van der Waals (vdW)-corrected simulations. The carboxylate frequency profiles with the dispersion-corrected representations are almost similar without a significant difference in the normalized distributions. Besides, the COO stretching frequencies at the peak maxima positions of the PBE functionals exhibit a lesser deviation from the experimental data. Spectral diffusion dynamics of the intrinsic vibrational probes on the cationic and anionic sites of the ionic liquid proceed through a short time relaxation of the intact hydrogen bonds followed by an intermediate time constant and a longer time decay indicating the switchover of hydrogen bonds. Dispersion-corrected atom-centered one-electron potential (DCACP) correction added to the BLYP system slows down the picosecond time scales of frequency correlation and the time constants of rotational motion, lengthening the overall system dynamics. The observed trends in the time-dependent decays of frequency fluctuations and the orientation autocorrelation functions correlate with the structural interactions in liquid MAF and hydrogen-bond dynamics. In this study, we examine the predictions made by different density functional treatments comparing the results of the uncorrected BLYP and PBE representations with the semiempirical vdW methods of Grimme and matching our calculated data with the experimental observations.

Intramolecular O-H⋯S hydrogen bonding in threefold symmetry: Line broadening dynamics from ultrafast 2DIR-spectroscopy and ab initio calculations

The dynamics of intramolecular hydrogen-bonding involving sulfur atoms as acceptors is studied using two-dimensional infrared (2DIR) spectroscopy. The molecular system is a tertiary alcohol whose donating hydroxy group is embedded in a hydrogen-bond potential with torsional C₃-symmetry about the carbon-oxygen bond. The linear and 2DIR-spectra recorded in the OH-stretching region of the alcohol can be simulated very well using Kubo's line shape theory based on the cumulant expansion for evaluating the linear and nonlinear optical response functions. The correlation function for OH-stretching frequency fluctuations reveals an ultrafast component decaying with a time constant of 700 fs, which is in line with the apparent decay of the center line slopes averaged over absorption and bleach/emission signals. In addition, a quasi-static inhomogeneity is detected, which prevents the 2DIR line shape to fully homogenize within the observation window of 4 ps. The experimental data were then analyzed in more detail using a full ab initio approach that merges time-dependent structural information from classical molecular dynamics (MD) simulations with an OH-stretching frequency map derived from density functional theory (DFT). The latter method was also used to obtain a complementary transition dipole map to account for non-Condon effects. The 2DIR-spectra obtained from the MD/DFT method are in good agreement with the experimental data at early waiting delays, thereby corroborating an assignment of the fast decay of the correlation function to the dynamics of hydrogen-bond breakage and formation.

Distinctive behavior and two-dimensional vibrational dynamics of water molecules inside glycine solvation shell

We present a first principles molecular dynamics study of a deuterated aqueous solution of a single glycine moiety to explore the structure, dynamics, and two-dimensional infrared spectra of water molecules found in the solvation shell of glycine.

Dynamic multiple-scattering treatment of X-ray absorption: Parameterization of a new molecular dynamics force field for myoglobin

We present a detailed analysis of the X-ray absorption near-edge structure (XANES) data on the Fe K-edge of CO Myoglobin based on a combined procedure of Molecular Dynamics (MD) calculations and MXAN (Minuit XANes) data analysis that we call D-MXAN. The ability of performing quantitative XANES data analysis allows us to refine classical force field MD parameters, thus obtaining a reliable tool for the atomic investigation of this important model system for biological macromolecules. The iterative procedure here applied corrects the greatest part of the structural discrepancy between classical MD sampling and experimental determinations. Our procedure, moreover, is able to discriminate between different heme conformational basins visited during the MD simulation, thus demonstrating the necessity of a sampling on the order of tens of nanoseconds, even for an application such X-ray absorption spectroscopy data analysis.

Energy Transfer to the Hydrogen Bond in the (H2O)2 + H2O Collision

Trajectory procedures are used to study the collision between the vibrationally excited H₂O and the ground-state (H₂O)₂ with particular reference to energy transfer to the hydrogen bond through the inter- and intramolecular pathways. In nearly 98% of the trajectories, energy transfer processes occur on a subpicosecond scale (≤0.7 ps). The H₂O transfers approximately three-quarters of its excitation energy to the OH stretches of the dimer. The first step of the intramolecular pathway in the dimer involves a near-resonant first overtone transition from the OH stretch to the bending mode. The energy transfer probability in the presence of the 1:2 resonance is 0.61 at 300 K. The bending mode then redistributes its energy to low-frequency intermolecular vibrations in a series of small excitation steps, with the pathway which results in the hydrogen-bonding modes gaining most of the available energy. The hydrogen bonding in ∼50% of the trajectories ruptures on vibrational excitation, leaving one quantum in the bend of the monomer fragment. In a small fraction of trajectories, the duration of collision is longer than 1 ps, during which the dimer and H₂O form a short-lived complex through a secondary hydrogen bond, which undergoes large amplitude oscillations.

Hydrogen bond and lifetime dynamics in diluted alcohols

Hydrogen-bonding plays a crucial role in many chemical and biochemical reactions.

Capturing the Ultrafast Vibrational Decoherence of Hydrogen Bonding in Interfacial Water

Vibrational sum-frequency generation (vSFG) measurements in the frequency and time domains reveal that the interfacial hydrogen bonded OH stretch at the water/calcium fluoride interface is composed of two populations oriented oppositely. The time-resolved vSFG free-induction decay suggested that, whereas the strongly hydrogen bonded OH vibrational stretches, centered near 3140 ± 11 cm^-1, are oriented toward bulk water and lose their collective coherence within ∼70 ± 7 fs, the weakly hydrogen bonded OH species, centered near 3410 ± 12 cm^-1, are pointed toward the interface and dephase within ∼50 ± 6 fs.

Concentration-dependent dynamics of hydrogen bonding between acetonitrile and methanol as determined by 1D vibrational spectroscopy

Solutions of acetonitrile (MeCN) in methanol (MeOH) at various concentrations have been investigated by variable temperature Raman spectroscopy. In the ν(CN) region of the spectrum, the variable temperature spectra at each concentration show two overlapping bands from hydrogen bound and free MeCN. These two species undergo dynamic exchange that gives rise to increasing coalescence of the two bands with increasing temperature. By simulation of the band shape, the rate of exchange was determined at each temperature. Arrhenius plots yielded values for the activation energy, Ea, and the natural log of the pre-exponential factor, ln[A/s(-1)], for the hydrogen bond formation/cleavage. Both of these dynamic parameters were found to depend on the relative amounts of MeCN and MeOH in the solutions. In particular, two different concentration regimes of dynamic hydrogen bonding were observed. First, at low MeCN concentration, the dynamics are largely independent of changes in MeCN concentration. Second, at higher MeCN concentration (above ∼0.2 MeCN mole fraction) the dynamics are strongly dependent on further increases of MeCN content. Over the range of MeCN mole fractions that we studied (0.03-0.5), the ln[A/s(-1)] changes from 32.5 ± 0.1 to 30.1 ± 0.2 and Ea changes from 3.73 ± 0.08 to 2.7 ± 0.1 kcal/mol. We suggest the observed changes in dynamics arise from changes in the local solvent microstructure that occur above a critical mole fraction of MeCN.

Signatures of nanoconfinement on the linear and nonlinear vibrational spectroscopy of a model hydrogen-bonded complex dissolved in a polar solvent

The one-dimensional IR (1D-IR) absorption and IR pump-probe spectra of a hydrogen stretch in a model hydrogen-bonded complex dissolved in a polar solvent confined in spherical hydrophobic cavities of different sizes were simulated using ground-state mixed quantum-classical dynamics. Due to a thorough analysis of key properties of the complex and solvent from equilibrium trajectory data, we were able to gain insight into the microscopic details underlying the spectra. Both the 1D-IR and IR pump-probe spectra manifested the effects of confinement on the relative stabilities of the covalent and ionic forms of the complex through pronounced changes in their peak intensities and numbers. However, in contrast to the 1D-IR spectra, the time-resolved pump-probe spectra were found to be uniquely sensitive to the changes in the molecular dynamics as the cavity size is varied. In particular, it was found that the variations in the time evolutions of the peak intensities in the pump-probe spectra reflect the differences in the solvation dynamics associated with the various forms of the complex in different locations within the cavities. The ability to detect these differences underscores the advantage of using pump-probe spectroscopy for studying nanoconfined systems.

Intramolecular vibrational coupling contribution to temperature dependence of vibrational mode frequencies

High-frequency vibrational modes in molecules in solution are sensitive to temperature and shift either to lower or higher frequencies with the temperature increase. These frequency shifts are often attributed to specific interactions of the molecule and to the solvent polarization effect. We found that a substantial and often dominant contribution to sensitivity of vibrational high-frequency modes to temperature originates from anharmonic interactions with other modes in the molecule. The temperature dependencies were measured for several modes in ortho-, meta-, and para-isomers of acetylbenzonitrile in solution and in a solid matrix and compared to the theoretical predictions originated from the intramolecular vibrational coupling (IVC) evaluated using anharmonic density functional theory calculations. It is found that the IVC contribution is essential for temperature dependencies of all high-frequency vibrational modes and is dominant for many modes. As such, the IVC contribution alone permits predicting the main trend in the temperature dependencies, especially for vibrational modes with smaller transition dipoles. In addition, an Onsager reaction field theory was used to describe the solvent contribution to the temperature dependencies.

Mixed quantum-classical molecular dynamics study of the hydroxyl stretch in methanol/carbon-tetrachloride mixtures II: excited state hydrogen bonding structure and dynamics, infrared emission spectrum, and excited state lifetime

We present a mixed quantum-classical molecular dynamics study of the hydrogen-bonding structure and dynamics of a vibrationally excited hydroxyl stretch in methanol/carbon-tetrachloride mixtures. The adiabatic Hamiltonian of the quantum-mechanical hydroxyl is diagonalized on-the-fly to obtain the ground and first-excited adiabatic energy levels and wave functions which depend parametrically on the instantaneous configuration of the classical degrees of freedom. The dynamics of the classical degrees of freedom are determined by Hellmann-Feynman forces obtained by taking the expectation value of the force with respect to the ground or excited vibrational wave functions. Polarizable force fields are used which were previously shown to reproduce the experimental infrared absorption spectrum rather well, for different isotopomers and over a wide composition range [Kwac, K.; Geva, E. J. Phys. Chem. B 2011, 115, 9184]. We show that the agreement of the absorption spectra with experiment can be further improved by accounting for the dependence of the dipole moment derivatives on the configuration of the classical degrees of freedom. We find that the propensity of a methanol molecule to form hydrogen bonds increases upon photoexcitation of its hydroxyl stretch, thereby leading to a sizable red-shift of the corresponding emission spectrum relative to the absorption spectrum. Treating the relaxation from the first excited to the ground state as a nonadiabatic process, and calculating its rate within the framework of Fermi's golden rule and the harmonic-Schofield quantum correction factor, we were able to predict a lifetime which is of the same order of magnitude as the experimental value. The experimental dependence of the lifetime on the transition frequency is also reproduced. Nonlinear mapping relations between the hydroxyl transition frequency and bond length in the excited state and the electric field along the hydroxyl bond axis are established. These mapping relations make it possible to reduce the computational cost of the mixed quantum-classical treatment to that of a fully classical treatment.

A mixed quantum-classical molecular dynamics study of the hydroxyl stretch in methanol/carbon tetrachloride mixtures: equilibrium hydrogen-bond structure and dynamics at the ground state and the infrared absorption spectrum

We present a mixed quantum-classical molecular dynamics study of the structure and dynamics of the hydroxyl stretch in methanol/carbon tetrachloride mixtures. One of the methanol molecules is tagged, and its hydroxyl stretch is treated quantum-mechanically, while the remaining degrees of freedom are treated classically. The adiabatic Hamiltonian of the quantum-mechanical hydroxyl is diagonalized on-the-fly to obtain the corresponding adiabatic energy levels and wave functions which depend parametrically on the instantaneous configuration of the classical degrees of freedom. The dynamics of the classical degrees of freedom are in turn affected by the quantum-mechanical state of the tagged hydroxyl stretch via the corresponding Hellmann-Feynman forces. The ability of five different force-field combinations to reproduce the experimental absorption infrared spectrum of the hydroxyl stretch is examined for different isotopomers and on a wide range of compositions. It is found that, in addition to accounting for the anharmonic nature of the hydroxyl stretch, one also has to employ polarizable force fields and account for the damping of the polarizability at short distances. The equilibrium ground-state hydrogen-bonding structure and dynamics is analyzed, and its signature on the absorption infrared spectrum of the hydroxyl stretch is investigated in detail. Five different hydroxyl stretch subpopulations are identified and spectrally assigned: monomers (α), hydrogen-bond acceptors (β), hydrogen-bond donors (γ), simultaneous hydrogen-bond donors and acceptors (δ), and simultaneous hydrogen-bond donors and double-acceptors (ε). The fundamental transition frequencies of the α and β subpopulations are found to be narrowly distributed and to overlap, thereby giving rise to a single narrow band whose intensity is significantly diminished by rotational relaxation. The fundamental transition frequency distributions of the γ, δ, and ε subpopulations are found to be broader and to partially overlap, thereby giving rise to a single broad band which is red-shifted relative to the αβ band. The γδε band is also found to be inhomogeneously broadened and unaffected by rotational relaxation. The exchange rates between the different subpopulations and corresponding branching ratios are reported and explained. Finally, nonlinear mapping relations between the hydroxyl transition frequency and bond length and the electric field along the hydroxyl bond axis are established, which can be used to reduce the computational cost of the mixed quantum-classical treatment to that of a purely classical molecular dynamics simulation.

OH and NH Stretching Vibrational Relaxation of Liquid Ethanolamine

Femtosecond mid-infrared pump-probe spectroscopy was carried out to obtain information about the dynamics of vibrational energy relaxation in liquid ethanolamine at room temperature and ambient pressure. Through partial deuteration it was possible to disentangle the dynamics resulting from the OH and the NH stretching modes that proceed independently and simultaneously in the hydrogen-bonded liquid following an ultrafast vibrational excitation by a resonant mid-infrared pulse. The OH-stretching vibrational lifetime was determined to be 450 fs while the NH-stretching lifetime was found to be 1.2 ps. This large difference in lifetimes highlights the importance of the hydrogen-donating and the hydrogen-accepting character of the vibrating groups that are engaged in hydrogen-bonding.

Solvent-dependent spectral diffusion in a hydrogen bonded "vibrational aggregate"

Two-dimensional infrared spectroscopy (2DIR) is used to measure the viscosity-dependent spectral diffusion of a model vibrational probe, Mn(2)(CO)(10) (dimanganese decacarbonyl, DMDC), in a series of alcohols with time scales ranging from 2.67 ps in methanol to 5.33 ps in 1-hexanol. Alcohol-alkane solvent mixtures were found to produce indistinguishable linear IR spectra, while still demonstrating viscosity-dependent spectral diffusion. Using a vibrational exciton model to characterize the inhomogeneous energy landscape, several analogies emerge with multichromophoric electronic systems, such as J-aggregates and light-harvesting protein complexes. An excitonic, local vibrational mode Hamiltonian parametrized to reproduce the vibrational structure of DMDC serves as a starting point from which site energies (i.e., local carbonyl frequencies) are given Gaussian distributed disorder. The model gives excellent agreement with both the linear IR spectrum and the inhomogeneous widths extracted from 2DIR, indicating the system can be considered to be a "vibrational aggregate." This model naturally leads to exchange narrowing due to disorder-induced exciton localization, producing line widths consistent with our 1D and 2D measurements. Further, the diagonal disorder alone effectively reduces the molecular symmetry, leading to the appearance of Raman bands in the IR spectrum in accord with the measurements. Here, we show that the static inhomogeneity of the excitonic model with disorder successfully captures the essential details of the 1D spectrum while predicting the degree of IR activity of forbidden modes as well as the inhomogeneous widths and relative magnitudes of the transition moments.

Hydrophobic solvation: a 2D IR spectroscopic inquest

For decades, the enigma of the hydrophobic force has captured the imagination of scientists. In particular, Frank and Evans' idea that the hydrophobic effect was mainly due to some kind of "iceberg" formation around a hydrophobic solute stimulated many experiments and molecular dynamics simulation studies. A better understanding of hydrophobic interactions will aid understanding in many contexts including protein structural dynamics and functioning in biological systems. In this Account, we present results of two-dimensional infrared (2D IR) spectroscopy experiments on the OH-stretch vibrational mode of water molecules near hydrophobic groups in concentrated solutions with tetramethylurea (TMU). The frequency of the OH vibration is a sensitive probe for environmental dynamics and, in particular, for the strength of the hydrogen bond. Two-dimensional IR spectroscopy can trace time correlations of the vibrational frequency at the scale of hundreds of femtoseconds and thus provides valuable insight into the effect of hydrophobic solutes on the dynamics of a hydrogen-bond network. We compare the 2D spectroscopic results with molecular dynamics (MD) simulations to obtain a microscopic picture of hydrophobic solvation. We observe two different types of hydrogen-bond dynamics in the water/TMU mixtures. We attribute the "fast" ( approximately 100 fs) dynamics to highly coordinated water molecular-jump reorientations and assigned the "slow" (>1 ps) dynamics to water translational motions that are strongly suppressed by the TMU molecules. Molecular dynamics simulations demonstrate a clear correlation between the slowed dynamics and the translational mobility of water. This finding indicates that the molecular-jump reorientations are switched off near hydrophobic groups. The fifth water molecule, which is required to form a defect state in the tetrahedral surroundings, cannot approach the hydrogen-bonded pair to initiate the molecular jump. As a result, the rate of the jumping events sharply decreases, which, in turn, strongly slows the rotation of the water molecules. Our findings suggest that water molecules in the hydrophobic solvation shell do not exhibit an increased tetrahedral ordering compared with the bulk but that the hydrogen-bond dynamics in the two cases are different. This result also indicates that consideration of a hydrogen bond's dynamics could be critical for its definition.

C-D modes of deuterated side chain of leucine as structural reporters via dual-frequency two-dimensional infrared spectroscopy

Perdeuteration of the side chains of amino acids such as leucine results in appearance of reasonably strong absorption peaks around 2050-2220 cm(-1) that belong to the CD stretching modes and exhibit extinction coefficients of up to 120 M(-1) cm(-1). The properties of the CD stretching transitions in leucine-d(10) as structural labels are studied via the methods of two-dimensional infrared (2DIR) spectroscopy. The cross peaks caused by interactions of the CD stretching modes with amide I (Am-I), CO, and amide II (Am-II) modes are obtained by the dual-frequency 2DIR method. The CD stretching peaks in leucine-d(10) are characterized using DFT computational modeling as well as relaxation-assisted 2DIR (RA 2DIR) measurements. The RA 2DIR measurements showed different enhancements and different energy transport times (arrival times) for different CD/Am-II and CD/CO cross peaks; a correlation between the intermode distance, the arrival time, and the amplification factor is reported. We demonstrated that the CD transitions of leucine-d(10) amino acid can serve as convenient structural reporters via the dual-frequency 2DIR methods and discussed the potential of leucine-d(10) and other amino acids with deuterium-labeled side chains as probes of protein structure and dynamics.