Juxtaposing density matrix and classical path-based wave packet dynamics

In many physical, chemical, and biological systems energy and charge transfer processes are of utmost importance. To determine the influence of the environment on these transport processes, equilibrium molecular dynamics simulations become more and more popular. From these simulations, one usually determines the thermal fluctuations of certain energy gaps, which are then either used to perform ensemble-averaged wave packet simulations, also called Ehrenfest dynamics, or to employ a density matrix approach via spectral densities. These two approaches are analyzed through energy gap fluctuations that are generated to correspond to a predetermined spectral density. Subsequently, density matrix and wave packet simulations are compared through population dynamics and absorption spectra for different parameter regimes. Furthermore, a previously proposed approach to enforce the correct long-time behavior in the wave packet simulations is probed and an improvement is proposed.     

Temperature- and solvation-dependent dynamics of liquid sulfur dioxide studied through the ultrafast optical Kerr effect

The ultrafast dynamics of liquid sulphur dioxide have been studied over a wide temperature range and in solution. The optically heterodyne-detected and spatially masked optical Kerr effect (OKE) has been used to record the anisotropic and isotropic third-order responses, respectively. Analysis of the anisotropic response reveals two components, an ultrafast nonexponential relaxation and a slower exponential relaxation. The slower component is well described by the Stokes-Einstein-Debye equation for diffusive orientational relaxation. The simple form of the temperature dependence and the agreement between collective (OKE) and single molecule (e.g., NMR) measurements of the orientational relaxation time suggests that orientational pair correlation is not significant in this liquid. The relative contributions of intermolecular interaction-induced and single-molecule orientational dynamics to the ultrafast part of the spectral density are discussed. Single-molecule librational-orientational dynamics appear to dominate the ultrafast OKE response of liquid SO2. The temperature-dependent OKE data are transformed to the frequency domain to yield the Raman spectral density for the low-frequency intermolecular modes. These are bimodal with the lowest-frequency component arising from diffusive orientational relaxation and a higher-frequency component connected with the ultrafast time-domain response. This component is characterized by a shift to higher frequency at lower temperature. This result is analyzed in terms of a harmonic librational oscillator model, which describes the data accurately. The observed spectral shifts with temperature are ascribed to increasing intermolecular interactions with increasing liquid density. Overall, the dynamics of liquid SO2 are found to be well described in terms of molecular orientational relaxation which is controlled over every relevant time range by intermolecular interactions.     

Component dynamics in polyvinylpyrrolidone concentrated aqueous solutions

(2)H-nuclear magnetic resonance (NMR) and neutron scattering (NS) on isotopically labelled samples have been combined to investigate the structure and dynamics of polyvinylpyrrolidone (PVP) aqueous solutions (4 water molecules/monomeric unit). Neutron diffraction evidences the nanosegregation of polymer main-chains and water molecules leading to the presence of water clusters. NMR reveals the same characteristic times and spectral shape as those of the slower process observed by broadband dielectric spectroscopy in this system [S. Cerveny et al., J. Chem. Phys. 128, 044901 (2008)]. The temperature dependence of such relaxation time crosses over from a cooperative-like behavior at high temperatures to an Arrhenius behavior at lower temperatures. Below the crossover, NMR features the spectral shape as due to a symmetric distribution of relaxation times and the underlying motions as isotropic. NS results on the structural relaxation of both components-isolated via H/D labeling-show (i) anomalously stretched and non-Gaussian functional forms of the intermediate scattering functions and (ii) a strong dynamic asymmetry between the components that increases with decreasing temperature. Strong heterogeneities associated to the nanosegregated structure and the dynamic asymmetry are invoked to explain the observed anomalies. On the other hand, at short times the atomic displacements are strongly coupled for PVP and water, presumably due to H-bond formation and densification of the sample upon hydration.     

Ion and polymer dynamics in polymer electrolytes PPO-LiClO4. I. Insights from NMR line-shape analysis

We investigate ion and polymer dynamics in polymer electrolytes PPO-LiClO4 performing 2H and 7Li NMR line-shape analysis. Comparison of temperature dependent 7Li and 2H NMR spectra gives evidence for a coupling of ion and polymer dynamics. 2H NMR spectra for various salt concentrations reveal a strong slowdown of the polymer segmental motion when the salt content is increased. The 2H NMR line shape further indicates that the segmental motion is governed by dynamical heterogeneities. While the width of the distribution of correlation times G(log tau) is moderate for low and high salt content, an extremely broad distribution exists for an intermediate salt concentration of 15:1 PPO-LiClO4. For the latter composition, a weighted superposition of two spectral components, reflecting the fast and the slow polymer segments of the distribution, describes the 2H NMR line shape over a broad temperature range. Analysis of the temperature dependent relative intensity of both spectral components indicates the existence of a continuous rather than a discontinuous distribution G(log tau). Such continuous distribution is consistent with gradual fluctuations of the local salt concentration and, hence, of the local environments of the polymer segments, whereas it is at variance with the existence of large salt-depleted and salt-rich domains featuring fast and slow polymer dynamics, respectively. Finally, for all studied PPO-LiClO4 mixtures, the 2H NMR line shape strongly depends on the echo delay in the applied echo-pulse sequence, indicating that the structural relaxation of the polymer segments involves successive rotational jumps about small angles gamma < 20 degrees .     

Thermal history effects and methyl tunneling dynamics in a supramolecular complex of calixarene and para-xylene

The low-temperature structure and dynamics of guest molecules of p-xylene incorporated in the isopropyl-calix[4] arene(2:1) p-xylene complex have been investigated by solid state nuclear magnetic resonance (NMR). Using one-dimensional 1H-decoupled 13C cross-polarization magic-angle-spinning (MAS) NMR and two-dimensional 1H-13C correlation spectroscopy, a full assignment of the 13C and 1H chemical shifts has been made. Using 1H NMR relaxometry, the effects of thermal history on the structure of the system have been investigated. Rapidly cooled samples have 1H spin-lattice relaxation times T1, which at low temperature (T<60 K) are typically two orders of magnitude faster than those observed in annealed samples which have been cooled slowly over many hours. In both forms, the low-temperature relaxation is driven by the dynamics of the weakly hindered methyl rotors of the p-xylene guest. The substantial difference in T1 is attributed in the rapidly cooled sample to disorder in the structure of the complex leading to a wide distribution of correlation times and methyl barrier heights. A comparison of the linewidths and splittings in the high resolution 13C MAS spectra of the two forms provides structural insight into the nature of the disorder. Using 1H field-cycling NMR relaxometry, the methyl dynamics of the p-xylene guest in the annealed sample have been fully characterized. The B-field dependence of the 1H T1 maps out the spectral density from which the correlation times are directly measured. The methyl barrier heights are determined from an analysis of the temperature dependence.     

Diluting the hydrogen bonds in viscous solutions of n-butanol with n-bromobutane: a dielectric study

Glass-forming monohydroxy alcohols exhibit not only a structural relaxation but also a slower, single-exponential Debye-type relaxation process which already freezes in the liquid phase. By using dielectric spectroscopy, we study how these relaxations evolve when the aprotic alkyl halide n-bromobutane is added to n-butanol, thereby diluting the hydrogen-bond network. The structural relaxation times smoothly vary over the concentration range of this completely miscible binary system. The Debye process remains unaffected by the dilution of the OH groups up to n-bromobutane mole fractions of about 50%. For larger hydroxy dilutions, it turns rather abruptly into a feature which develops significant spectral broadening and it becomes faster. In the dilute limit, the decoupling between the time scale of the Debye process and that of the structural relaxation amounts to almost 6 decades when extrapolated to the glass transition temperature. This relatively large, strongly concentration dependent decoupling is interpreted in analogy to normal modes in polymers. The present results suggest that the structural and the Debye-like responses of monohydroxy alcohols are unrelated.     

Dynamics of glass-forming liquids. XI. Fluctuating environments by dielectric spectroscopy

The dielectric relaxation of a 1 wt % mixture of di-n-butylether in 3-methylpentane has been measured across a range of eight decades, in which the characteristic relaxation time varies from 5 s to 50 ns. Each loss spectrum is a superposition of the dispersive solvent peak and a Debye peak which is one decade slower and readily assigned to the larger and more dipolar solute molecules. Fluctuating environments or rate exchange is made responsible for the Debye nature of probe rotation, implying that the environmental relaxation times fluctuate on time scales which are faster than the rotational correlation decay of the probe molecule. Within the experimental range from 2.2 s to 42 ns regarding the mean alpha-relaxation time, the results are consistent with the exchange time matching the upper limit of structural relaxation times or two to three times their average value. As T(g) is approached, no indication for a variation in exchange behavior or for slower environmental fluctuations is found.     

Rotational dynamics of benzene and water in an ionic liquid explored via molecular dynamics simulations and NMR T1 measurements

The rotational dynamics of benzene and water in the ionic liquid (IL) 1-butyl-3-methylimidazolium chloride are studied using molecular dynamics (MD) simulation and NMR T(1) measurements. MD trajectories based on an effective potential are used to calculate the (2)H NMR relaxation time, T(1) via Fourier transform of the relevant rotational time correlation function, C(2R)(t). To compensate for the lack of polarization in the standard fixed-charge modeling of the IL, an effective ionic charge, which is smaller than the elementary charge is employed. The simulation results are in closest agreement with NMR experiments with respect to the temperature and Larmor frequency dependencies of T(1) when an effective charge of ±0.5e is used for the anion and the cation, respectively. The computed C(2R)(t) of both solutes shows a bi-modal nature, comprised of an initial non-diffusive ps relaxation plus a long-time ns tail extending to the diffusive regime. Due to the latter component, the solute dynamics is not under the motional narrowing condition with respect to the prevalent Larmor frequency. It is shown that the diffusive tail of the C(2R)(t) is most important to understand frequency and temperature dependencies of T(1) in ILs. On the other hand, the effect of the initial ps relaxation is an increase of T(1) by a constant factor. This is equivalent to an "effective" reduction of the quadrupolar coupling constant (QCC). Thus, in the NMR T(1) analysis, the rotational time correlation function can be modeled analytically in the form of aexp (-t/τ) (Lipari-Szabo model), where the constant a, the Lipari-Szabo factor, contains the integrated contribution of the short-time relaxation and τ represents the relaxation time of the exponential (diffusive) tail. The Debye model is a special case of the Lipari-Szabo model with a = 1, and turns out to be inappropriate to represent benzene and water dynamics in ILs since a is as small as 0.1. The use of the Debye model would result in an underestimation of the QCC by a factor of 2-3 as a compensation for the neglect of the Lipari-Szabo factor.     

Ideal mixing behavior of the debye process in supercooled monohydroxy alcohols

Glass-forming monohydroxy alcohols exhibit two dielectric relaxation signals with super-Arrhenius temperature dependence: a Debye peak and an asymmetrically broadened alpha-process. We explore the behavior of these distinct relaxation features in mixtures of such liquids by dielectric measurements. The study focuses on the viscous regime of two binary systems: 2-methyl-1-butanol with 2-ethyl-1-hexanol and 1-propanol with 3,7-dimethyl-1-octanol. We find that the logarithmic relaxation time, log(tau), of the Debye peak follows an ideal mixing law (linear change with mole fraction), even in the case of mixing structurally dissimilar components. By contrast, the log(tau) versus mole fraction curve for the alpha-process is nonlinear, indicative of slower structural relaxation relative to the expectation on the basis of ideal mixing behavior. The latter observation is analogous to the effect of composition on viscosity, heat of mixing, and glass-transition temperature, whereas the ideal mixing of log(tau) seen for the Debye peak is the exception. We conclude that the unusual ideal mixing behavior of dielectric relaxation in monohydroxy alcohols is not a result of structural similarity, but rather yet more evidence of the Debye process being decoupled from other dynamic and thermodynamic properties.     

Identification of dielectric and structural relaxations in glass-forming secondary amides

Dielectric relaxation dynamics of secondary amides is explored in their supercooled state near the glass transition temperature Tg by investigating N-ethylacetamide and its mixtures with N-methylformamide. All the samples are found to exhibit giant dielectric permittivities, reaching over 500 in N-methylformamide-rich mixtures around Tg. For both the neat and binary systems, the predominant relaxation peak is of the Debye-type throughout the viscous regime, which is an unexpected feature for a glass former with intermediate fragility. The present results combined with the earlier reported high-temperature data reveal that the dielectric strength delta epsilon(D) of the Debye relaxation extrapolates to zero at frequencies of 10(10)-10(11) Hz, which is about two orders of magnitude lower than the phonon frequency limit typical of the structural relaxation. This Debye process is remarkably similar to the dielectric behavior of many monohydroxy alcohols, which implies a common nature of purely exponential relaxation dynamics in these liquids. Based on the dielectric properties, we conclude that the Debye relaxation in the secondary amides is not a direct signature of the primary or alpha-relaxation, the latter being obscured at low temperatures due to the relatively low permittivity and close spectral proximity to the Debye peak. As in the case of monohydroxy alcohols, dielectric polarization and structure fluctuate on different time scales in secondary amides. The Kirkwood-Fr?hlich correlation factors for Debye-type liquids are also discussed.     

Dielectric spectroscopy of hydrogen bond dynamics and microheterogenity of water + dioxane mixtures

Mixtures of water or D2O + 1,4-dioxane (DX) have been studied at 25 degrees C by dielectric relaxation spectroscopy over a wide range of frequencies (0.2 < or = nu/GHz < or = 89) for DX mole fractions 0 < or = x2 < or = 0.67. The spectra were best fitted by the sum of two Debye terms. The slower process was assigned to the cooperative relaxation of the hydrogen-bond network of water, whereas the faster mode reflects the dynamics of H2O molecules in a DX-rich environment. Analysis of the relaxation parameters revealed a largely microheterogeneous structure of the mixtures. The marked slowing-down of the cooperative mode on addition of DX is ascribed to the reduction of available H-bond acceptor sites and geometrical constraints on the H2O molecules in the water-rich regions.     

The influence of aqueous versus glassy solvents on protein dynamics: vibrational echo experiments and molecular dynamics simulations

Spectrally resolved infrared stimulated vibrational echo measurements are used to measure the vibrational dephasing of the CO stretching mode of carbonmonoxy-hemoglobin (HbCO), a myoglobin mutant (H64V), and a bacterial cytochrome c(552) mutant (Ht-M61A) in aqueous solution and trehalose glasses. The vibrational dephasing of the heme-bound CO is significantly slower for all three proteins embedded in trehalose glasses compared to that of aqueous protein solutions. All three proteins exhibit persistent but notably slower spectral diffusion when the protein surface is fixed by the glassy solvent. Frequency-frequency correlation functions (FFCFs) of the CO are extracted from the vibrational echo data to reveal that the structural dynamics, as sensed by the CO, of the three proteins in trehalose and aqueous solution are dominated by fast (tens of femtoseconds), motionally narrowed fluctuations. MD simulations of H64V in dynamic and "static" water are presented as models of the aqueous and glassy environments. FFCFs are calculated from the H64V simulations and qualitatively reproduce the important features of the experimentally extracted FFCFs. The suppression of long time scale (picoseconds to tens of picoseconds) frequency fluctuations (spectral diffusion) in the glassy solvent is the result of a damping of atomic displacements throughout the protein structure and is not limited to structural dynamics that occur only at the protein surface. The analysis provides evidence that some dynamics are coupled to the hydration shell of water, supporting the idea that the bioprotection offered by trehalose is due to its ability to immobilize the protein surface through a thin, constrained layer of water.     

Diluent effects on the Debye-type dielectric relaxation in viscous monohydroxy alcohols

With the recognition that the Debye-type dielectric relaxation of liquid monohydroxy alcohols does not reflect the structural relaxation dynamics associated with the viscous flow and the glass transition, its behavior upon dilution is expected to differ from that of real alpha-processes. We have investigated the Debye-type dielectric relaxation of binary alcohol/alkane mixtures across the entire concentration range in the supercooled regimes. The focus is on 2-ethyl-1-hexanol in two nonpolar liquids, 3-methylpentane and squalane, which are more fluid and more viscous than the alcohol, respectively. The Debye relaxation is found to occur only for alcohol mole fractions x > 0.2 and is always accompanied by a non-Debye relaxation originating from the alcohol component. Prior to its complete disappearance, the Debye relaxation is subject to broadening. We observe that the Debye dynamics of 2-ethyl-1-hexanol is accelerated in the more fluid 3-methylpentane, while the more viscous squalane leads to longer Debye relaxation times. The present experiments also provide evidence that the breakdown of the Debye relaxation amplitude does not imply the absence of hydrogen-bonded structures.     

Dynamics of end-grafted polystyrene brushes in theta solvents

The dynamics of the concentration fluctuations in end-grafted polystyrene brushes in a theta solvent (cyclohexane) are probed by evanescent wave dynamic light scattering at different wavevectors q and temperatures. When the solvent quality changes from marginal to poor, the relaxation function C(q, t) exhibits strong effects as compared with the smooth variation of the brush density profile. From a single exponential above 50 °C, C(q, t) becomes a two-step decay function. The fast decay is still assigned to the cooperative diffusion albeit slower than in the good solvent regime whereas the slow nonexponential and nondiffusive process might relate to microsegragated and/or chain dynamics in the present polydisperse brush. The relaxation function of the present three brushes with different grafting density reveals similarities and disparities between wet brushes and semidilute polymer solutions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3590–3597, 2006     

A first principles simulation study of fluctuations of hydrogen bonds and vibrational frequencies of water at liquid-vapor interface

We present a theoretical study of the structure and dynamics of water-vapor interface by means of ab initio molecular dynamics simulations. The inhomogeneous density, hydrogen bond and orientational profiles, voids and vibrational frequency distributions are investigated. We have also studied various dynamical properties of the interface such as diffusion, orientational relaxation, hydrogen bond dynamics and vibrational frequency fluctuations. The diffusion and orientational relaxation of water molecules are found to be faster at the interface which can be correlated with the voids present in the system. The hydrogen bond dynamics, however, is found to be slightly slower at the interface than that in bulk water. The correlations of hydrogen bond relaxation with the dynamics of vibrational frequency fluctuations are also discussed.     

Isotope effects associated with tunneling and double proton transfer in the hydrogen bonds of benzoic acid

The isotope effects associated with double proton transfer in the hydrogen bonds of benzoic acid (BA) dimers have been measured using field-cycling (1)H NMR relaxometry and quasielastic neutron scattering. By studying mixed isotope (hydrogen and deuterium) samples, the dynamics of three isotopologues, BA-HH, BA-HD, and BA-DD, have been investigated. Low temperature measurements provide accurate measurements of the incoherent tunneling rate, k(0). This parameter scales accurately with the mass number, m, according to the formula k(0)=(E/m)e(-Fm) providing conclusive evidence that the proton transfer process is a strongly correlated motion of two hydrons. Furthermore, we conclude that the tunneling pathway is the same for the three isotopologue species. Measurements at higher temperatures illuminate the through barrier processes that are mediated via intermediate or excited vibrational states. In parallel with the investigation of proton transfer dynamics, the theoretical and experimental aspects of studying spin-lattice relaxation in single crystals of mixed isotope samples are investigated in depth. Heteronuclear dipolar interactions between (1)H and (2)H isotopes contribute significantly to the overall proton spin-lattice relaxation and it is shown that these must be modeled correctly to obtain accurate values for the proton transfer rates. Since the sample used in the NMR measurements was a single crystal, full account of the orientation dependence of the spin-lattice relaxation with respect to the applied B field was incorporated into the data analysis.     

Water dynamics--the effects of ions and nanoconfinement

Hydrogen bond dynamics of water in highly concentrated NaBr salt solutions and reverse micelles are studied using ultrafast 2D-IR vibrational echo spectroscopy and polarization-selective IR pump-probe experiments performed on the OD hydroxyl stretch of dilute HOD in H(2)O. The vibrational echo experiments measure spectral diffusion, and the pump-probe experiments measure orientational relaxation. Both experimental observables are directly related to the structural dynamics of water's hydrogen bond network. The measurements performed on NaBr solutions as a function of concentration show that the hydrogen bond dynamics slow as the NaBr concentration increases. The most pronounced change is in the longest time scale dynamics which are related to the global rearrangement of the hydrogen bond structure. Complete hydrogen bond network randomization slows by a factor of approximately 3 in approximately 6 M NaBr solution compared to that in bulk water. The hydrogen bond dynamics of water in nanoscopically confined environments are studied by encapsulating water molecules in ionic head group (AOT) and nonionic head group (Igepal CO 520) reverse micelles. Water dynamics in the nanopools of AOT reverse micelles are studied as a function of size by observing orientational relaxation. Orientational relaxation dynamics deviate significantly from bulk water when the size of the reverse micelles is smaller than several nm and become nonexponential and slower as the size of the reverse micelles decreases. In the smallest reverse micelles, orientational relaxation (hydrogen bond structural randomization) is almost 20 times slower than that in bulk water. To determine if the changes in dynamics from bulk water are caused by the influence of the ionic head groups of AOT or the nanoconfinement, the water dynamics in 4 nm nanopools in AOT reverse micelles (ionic) and Igepal reverse micelles (nonionic) are compared. It is found that the water orientational relaxation in the 4 nm diameter nanopools of the two types of reverse micelles is almost identical, which indicates that confinement by an interface to form a nanoscopic water pool is a primary factor governing the dynamics of nanoscopic water rather than the presence of charged groups at the interface.     

On the role of collective and local molecular fluctuations in the relaxation of proton intrapair dipolar order in nematic 5CB

We investigate the role that local motions and slow cooperative fluctuations have on the relaxation of the intrapair dipolar order in the nematic 5CB. With this purpose we present a theoretical and experimental systematic study which allow us to quantify the contribution from each type of molecular fluctuation to the intrapair dipolar order relaxation time, T(1D). The experimental work includes measurements of Zeeman and intrapair dipolar order relaxation times (T(1Z) and T(1D)) as a function of temperature at conventional NMR frequencies, in three complementary samples: normal and chain deuterated 4-n-pentyl-4(')-cyanobiphenyl (5CB and 5CB(d11)) and a mixture of normal 5CB and fully deuterated 4-n-pentyl-4'-cyanobiphenyl (5CB(d19)), 50% in weight. Additionally we perform T(1Z) field-cycling Larmor frequency-dependent measurements to obtain the spectral density of the cooperative fluctuations. The obtained results are as follows. (a) The cooperative molecular fluctuations have a strong relative weight in the relaxation of the intrapair dipolar order state, even at Larmor frequencies in the range of conventional NMR. (b) Alkyl chain rotations are an important relaxation mechanism of the intrapair dipolar order at megahertz frequencies. (c) Intermolecular fluctuations mediated by translational self-diffusion of the molecules is not an efficient mechanism of relaxation of the intrapair dipolar order.     

Multidimensional infrared spectroscopy of water. I. Vibrational dynamics in two-dimensional IR line shapes

In this and the following paper, we describe the ultrafast structural fluctuations and rearrangements of the hydrogen bonding network of water using two-dimensional (2D) infrared spectroscopy. 2D IR spectra covering all the relevant time scales of molecular dynamics of the hydrogen bonding network of water were studied for the OH stretching absorption of HOD in D2O. Time-dependent evolution of the 2D IR line shape serves as a spectroscopic observable that tracks how different hydrogen bonding environments interconvert while changes in spectral intensity result from vibrational relaxation and molecular reorientation of the OH dipole. For waiting times up to the vibrational lifetime of 700 fs, changes in the 2D line shape reflect the spectral evolution of OH oscillators induced by hydrogen bond dynamics. These dynamics, characterized through a set of 2D line shape analysis metrics, show a rapid 60 fs decay, an underdamped oscillation on a 130 fs time scale induced by hydrogen bond stretching, and a long time decay constant of 1.4 ps. 2D surfaces for waiting times larger than 700 fs are dominated by the effects of vibrational relaxation and the thermalization of this excess energy by the solvent bath. Our modeling based on fluctuations with Gaussian statistics is able to reproduce the changes in dispersed pump-probe and 2D IR spectra induced by these relaxation processes, but misses the asymmetry resulting from frequency-dependent spectral diffusion. The dynamical origin of this asymmetry is discussed in the companion paper.     

Parameterization of peptide 13C carbonyl chemical shielding anisotropy in molecular dynamics simulations.

NMR chemical shielding anisotropy (CSA) relaxation is an important tool in the study of dynamical processes in proteins and nucleic acids in solution. Herein, we investigate how dynamical variations in local geometry affect the chemical shielding anisotropy relaxation of the carbonyl carbon nucleus, using the following protocol: 1) Using density functional theory, the carbonyl (13)C' CSA is computed for 103 conformations of the model peptide group N-methylacetamide (NMA). 2) The variations in computed (13)C' CSA parameters are fitted against quadratic hypersurfaces containing cross terms between the variables. 3) The predictive quality of the CSA hypersurfaces is validated by comparing the predicted and de novo calculated (13)C' CSAs for 20 molecular dynamics snapshots. 4) The CSA fluctuations and their autocorrelation and cross correlation functions due to bond-length and bond-angle distortions are predicted for a chemistry Harvard molecular mechanics (CHARMM) molecular dynamics trajectory of Ca(2+)-saturated calmodulin and GB3 from the hypersurfaces, as well as for a molecular dynamics (MD) simulation of an NMA trimer using a quantum mechanically correct forcefield. We find that the fluctuations can be represented by a 0.93 scaling factor of the CSA tensor for both R(1) and R(2) relaxations for residues in helix, coil, and sheet alike. This result is important, as it establishes that (13)C' relaxation is a valid tool for measurement of interesting dynamical events in proteins.