Dipole Correlation Function Research Articles

On the efficient and accurate short-ranged simulations of uniform polar molecular liquids

We show that spherical truncations of the 1/r interactions in models for water and acetonitrile yield very accurate results in bulk simulations for all site–site pair correlation functions as well as dipole–dipole correlation functions. This good performance in bulk simulations contrasts with the generally poor results found with the use of such truncations in nonuniform molecular systems. We argue that Local Molecular Field (LMF) theory provides a general theoretical framework that gives the necessary corrections to simple truncations in most nonuniform environments and explains the accuracy of spherical truncations in uniform environments by showing that these corrections are very small. LMF theory is derived from the exact Yvon–Born–Green (YBG) hierarchy by making physically-motivated and well-founded approximations. New and technically interesting derivations of both the YBG hierarchy and LMF theory for a variety of site–site molecular models are presented in appendices. The main paper focuses on understanding the accuracy of these spherical truncations in uniform systems both phenomenologically and quantitatively using LMF theory.

Inertial and bias effects in the rotational Brownian motion of rodlike molecules in a uniaxial potential

Inertial effects in the rotational brownian motion in space of a rigid dipolar rotator (needle) in a uniaxial potential biased by an external field giving rise to asymmetry are treated via the infinite hierarchy of differential-recurrence relations for the statistical moments (orientational correlation functions) obtained by averaging the Euler-Langevin equation over its realizations in phase space. The solutions of this infinite hierarchy for the dipole correlation function and its characteristic times are obtained using matrix continued fractions showing that the model simultaneously predicts both slow overbarrier (or interwell) relaxation at low frequencies accompanied by intermediate frequency Debye relaxation due to fast near-degenerate motion in the wells of the potential (intrawell relaxation) as well as the high frequency resonance (Poley) absorption due to librations of the dipole moments. It is further shown that the escape rate of a brownian particle from a potential well as extended to the Kramers turnover problem via the depopulation factor yields a close approximation to the longest (overbarrier) relaxation time of the system. For zero and small values of the bias field parameter h, both the dipole moment correlation time and the longest relaxation time have Arrhenius behavior (exponential increase with increasing barrier height). While at values of h in excess of a critical value however far less than that required to achieve nucleation, the Arrhenius behavior of the correlation time disappears.

Second‐order collision‐induced light scattering: a spherical tensor approach

AbstractCollision‐induced light scattering (CILS) is a rotational–translational Raman scattering occurring in pairs or larger clusters of interacting molecules. A general explicit expression for the dipole correlation function relevant to second‐order CILS is derived in the spherical tensor formalism. A Mathematica program is given to calculate this autocorrelation function and hence the scattered intensity and depolarization ratio. Some examples are given for interacting atoms and tetrahedral molecules. These developments will aid in the interpretation of the weak, high‐frequency wings of induced spectra. Copyright © 2011 John Wiley & Sons, Ltd.

Multidimensional phase-sensitive single-molecule spectroscopy with time-and-frequency-gated fluorescence detection

($n$ $+$ 1)-dimensional gated fluorescence signals induced by $n$ impulsive pulses are calculated using a superoperator formalism. The signals are given by a time-and-frequency convolution of a bare signal, expressed in terms of multipoint dipole correlation functions, with a gating spectrogram. Different groups of quantum pathways can be separated by their variation with the phases of the pulses (phase cycling), as is commonly done in nuclear magnetic resonance. Comparison is made with heterodyne-detected coherent signals.

Outer-Sphere Investigation of MRI Relaxation Contrast Agents. Example of a Cyclodecapeptide Gadolinium Complex with Second-Sphere Water

We show how the purely outer-sphere (OS) relaxivity of a probe solute due to a Gd(3+) complex can help characterize the outer (O), inner (I), and second (2) sphere (S) contributions to the water proton relaxivity. Because of the difficulties of accurate theoretical predictions, we propose an experimental determination of the OS dipolar time correlation function (OS-DTCF) of the relative position of Gd(3+) with respect to any of the equivalent protons of the purely OS probe p-dioxane, which moves around the complex without binding to it. The method is illustrated by the GdPA complex with PA = c(AspArgGluProGlyGluTrpAspProGly). The experimental DTCF for dioxane is obtained by a model-free analysis of the high-field relaxivity of its protons. The time-modulation of the dioxane DTCF by the Gd(3+) electronic spin relaxation yields a measurable quenching of the longitudinal relaxivity at low-to-medium field, which serves us to deduce the fluctuating zero-field splitting (ZFS) Hamiltonian causing this electronic relaxation. The DTCF for water is derived from that for dioxane by appropriate scaling of the geometry of collision and relative diffusion coefficients of these molecules with respect to GdPA. The information obtained on the OS motion for water and the ZFS Hamiltonian together with an independent characterization of the IS contribution allows us to disentangle the OS, IS, and 2S mechanisms and interpret the relaxivity profile of the water protons from 2.35 mT to 18.8 T. The presence of a large 2S contribution is confirmed.

Two-particle random walk simulation of outer-sphere nuclear relaxation

We present a two-particle Monte Carlo method for computing the outer-sphere (OS) dipolar time correlation function (DTCF) of the relative position of a nuclear spin I on a diamagnetic molecule M(I) with respect to a nuclear or electronic spin S on a molecule M(S) when both molecules are anisotropic and undergo translational and rotational diffusion. As a first application, we question the validity of the appealing interspin procedure [L. P. Hwang, Mol. Phys. 51, 1235 (1984); A. Borel et al., Chem. Eur. J. 7, 600 (2001)] based on the solutions of a Smoluchowski diffusion equation, which conserve the interspin radial distribution function in the course of time. We show that the true random spatial motion of the interspin vector obtained by simulation can be very different from that given by the Smoluchowski solutions and lead to notable retardation of the time decay of the OS-DTCF. Then, we explore the influence of the solvation properties of M(S) on the decay rate of the DTCF. When M(S) is significantly larger than M(I), its rotation accelerates the decay only weakly, even if M(I) follows M(S) in its Brownian tumbling. By contrast, viscous solvation layers in OS pockets of M(S) can yield an important local slowdown of the relative translational diffusion of M(I), leading to a decay retardation of the DTCF, which adds to that due to the shape anisotropy of M(S). When M(S) is a Gd(3+)-based contrast agent, this retardation leads to a notable increase of the OS contribution to relaxivity even at rather high imaging field.

A simulation model for dielectric relaxation based on defect diffusion model and waiting time problems

We propose a simulation model for dielectric relaxation based on defect diffusion. The defect diffusion model (DDM) has been used to interpret dielectric relaxation and other relaxation phenomena. The essential feature of the model is a cooperative interaction between the relaxing dipole and its nearest-neighbors, containing defects, and the relaxation can only occur when a defect encounters a dipole. In our model we have taken the motion of defect as a stochastic process characterized by successive waiting time problem rather than classical random walk motion. We present computer simulation result for a simple dipolar model system and the dipole correlation function obtained from this new model under various physical conditions appears to be in the form of a stretched exponential function.

Determination of outer-sphere dipolar time correlation functions from high-field NMR measurements. Example of a Gd3+ complex in a viscous solvent

We consider a diamagnetic species carrying a nuclear spin and having a purely outer-sphere dynamics with respect to a Gd(3+) complex. The maximal structural and dynamic information attainable from the paramagnetic relaxation (rate) enhancement (PRE) of this nuclear spin due to the Gd(3+) electronic spin is the outer-sphere dipolar time correlation function (OS-DTCF) of the relative position of these spins. We show how to determine this OS-DTCF by a model-free analysis of high-field PRE measurements, which accounts for the relative diffusion coefficient of the spin carrying species derived from pulsed-gradient spin-echo experiments. The method rests on the spectral characterization of the OS-DTCF through a PRE property, the "star" relaxivity, which can be measured over an unexpectedly large frequency range by combining multiple field and temperature NMR experiments. It is illustrated in the case of the (1)H spins on the three diamagnetic probes tert-butanol CHD(2)(CD(3))(2)COD and glycerol (CD(2)OD)(2)CHOD and CHDOD-CDOD-CD(2)OD interacting with Gddtpa(2-) (dtpa(5-)=diethylen triamin pentaacetate) in a viscous glycerol-d8/D(2)O solvent. The general usefulness of the OS-DTCF for the description of the liquid state and electronic spin relaxation is discussed.

IR spectrum of the O–H⋯O hydrogen bond of phthalic acid monomethylester in gas phase and in CCl 4 solution

The absorption spectrum of the title compound in the spectral range of the hydrogen-bonded OH-stretching vibration has been investigated using a five-dimensional gas phase model as well as a QM/MM classical molecular dynamics simulation in solution. The gas phase model predicts a Fermi-resonance between the OH-stretching fundamental and the first OH-bending overtone transition with considerable oscillator strength redistribution. The anharmonic coupling to a low-frequency vibration of the hydrogen bond leading to a vibrational progression is studied within a diabatic potential energy curve model. The condensed phase simulation of the dipole–dipole correlation function results in a broad band in the 3000 cm −1 region in good agreement with experimental data. Further, weaker absorption features around 2600 cm −1 have been identified as being due to motion of the hydrogen within the hydrogen bond.

Unified Impact Theory for Velocity-Changing Effects and Speed Dependencies in Neutral Species Lineshapes

A dipole correlation function which incorporates velocity-changing (motional narrowing) effects and the effects of speed-dependent Lorentz relaxation rates into otherwise Voigt profile correlation functions is developed, based partly upon previous work by the author. For the first time simple closed expressions, which lend themselves to elementary calculation beginning only with the relevant parts of intermolecular interaction energies, are developed for the cubic time-dependent term within the exponent describing the decay of the correlation function. This term is of first order in perturber number density, as are the Lorentz parameters, and is complex, thereby allowing for narrowing, changing in shape and asymmetry in the line profile. “Soft” and “hard” collisions play no explicit role, though both are variously present for each line. Quartic time dependencies are also discussed, though they are thought to be negligible in nonhydrogen molecular spectroscopy. Finally, some comments are added about a relevant technique for hydrogen spectra.

The nonlinear dielectric behavior of water: Comparisons of various approaches to the nonlinear dielectric increment

A number of connections between the first nonlinear dielectric increment and dipole correlation functions have been proposed over a large span of years. These range from the Langevin-Debye approach, the use of cavity and reaction fields, a cavity free formulation, to modified Langevin-Debye approaches. Comparisons of the predictions of a number of these approaches, together with results of molecular dynamics simulations and an experimental result, are given. The relations include those by Booth and by Kielich based on the use of cavity and reaction fields as traditionally used in the determination of such connections but also including a partial correction by Booth for some ignored nonlinear effects, those by Sandberg and Edholm and by Jha and Freed based on the use of a Langevin-Debye type of approach, and one based on a cavity free non-Langevin-Debye formulation that automatically includes all nonlinear effects to the appropriate order. The local structures of water used for the determination of the pertinent correlation functions are chosen to be given by the Bernal-Fowler model, by a modification of the Berna-Fowler model, and by the Onsager approximation. In the limit of epsilon>>epsilon(infinity), the cavity free connection gives results for the first nonlinear decrements 36% larger than the decrement obtained by Booth, irrespective of the model used for the dipole correlation functions. The inclusion of epsilon(infinity) is found to decrease the decrements by about 4%. Using parameters deduced from the requirement that the Kirkwood-Frohlich connection give the experimental value of epsilon, the Booth uncorrected expression for the dielectric decrement using the modified Bernal-Fowler model is found to give good agreement with the simulations of Yeh and Berkowitz, while the cavity free result is too large. Using the Bernal-Fowler model for the local structure of water, the cavity free expression gives good agreement with the simulation results, the partially corrected Booth expression gives reasonable agreement, while the Booth uncorrected expression is too small. Comparisons to the experimental value of the nonlinear coefficient of (1.00+/-0.15)x10(-15) m(2)/V(2) as found by Kołodziej et al. are also made. Using the Bernal-Fowler model, the calculated nonlinear coefficients divided by 10(-15) m(2)/V(2) are as follows: Booth, 0.82; Booth including partial corrections for nonlinear effects on the cavity and reaction fields, 0.99; Kielich, 0.83; cavity free, 1.12; and modified Langevin-Debye, 2.93. The partially corrected Booth value shows the best fit, with the cavity free value next best but still within the cited error range. If the slope of the line given by Kołodziej et al. is used as the measure of the nonlinear increment, the experimental value is 1.10x10(-15) m(2)/V(2), similar to the corrected Booth and remarkably similar to the cavity free result.

Dipolar and Bond Vector Correlation Function of Linear Polymers Revealed by Field Cycling 1H NMR: Crossover from Rouse to Entanglement Regime

We apply field cycling NMR to study segmental reorientation dynamics in melts of linear 1,4-polybutadiene (PB) in the entanglement regime (M ≥ Me). Dispersion data of the spin−lattice relaxation time T1(ω) are transformed to the susceptibility representation χ′′(ω) = ω/T1(ω), and using frequency temperature superposition master curves χ′′(ωτs) are constructed which reflect spectral contributions from glassy as well as polymer specific dynamics. The correlation time τs is determined by glassy dynamics. Transforming χ′′(ωτs) into the time domain and studying the crossover from Rouse to entanglement regime, the full dipolar or segmental reorientational correlation function F2(t/τs) is presented covering six decades in amplitude and 8 decades in time. Assuming F2(t) ≅ ⟨ub(t)ub(0)⟩2 the bond vector correlation function ϕb(t) = ⟨ub(t)ub(0)⟩ is obtained. Reaching Z = M/Me ≤ 9, comparison with theoretical predictions by the tube-reptation model as well as renormalized Rouse theory reveals significant discrepancie...

Inertial effects in the orientational relaxation of rodlike molecules in a uniaxial potential

The inertial rotational Brownian motion and dielectric relaxation of an assembly of noninteracting rodlike polar molecules in a uniaxial potential are studied. The infinite hierarchy of differential-recurrence relations for the equilibrium correlation functions is generated by averaging the governing inertial Langevin equation over its realizations in phase space. The solution of this hierarchy for the one-sided Fourier transforms of the relevant correlation functions is obtained using matrix continued fractions yielding the longitudinal dipole correlation function, the correlation time, and the complex polarizability, which are calculated for typical values of the model parameters. Pronounced inertial effects appear in these characteristics in the high-frequency region for low damping. The exact longitudinal correlation time is compared with the predictions of the Kramers theory of the escape rate of a Brownian particle from a potential well as extended by Mel'nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)]. In the low temperature limit, the universal Mel'nikov and Meshkov formula for the inverse of the escape rate provides a good estimate of the longitudinal correlation time for all values of the dissipation including the very low damping, very high damping, and Kramers turnover regimes. Moreover, the low-frequency part of the spectra of the longitudinal correlation function may be approximated by a single Lorentzian with a halfwidth determined by this universal escape rate formula.

A theoretical spin relaxation and molecular dynamics simulation study of the Gd(H2O)93+ complex

A theoretical analysis of the paramagnetically enhanced water proton spin-lattice relaxation of a hydrated Gd(3+) ion is combined with Molecular Dynamics (MD) simulations. The electron-proton dipole-dipole correlation function, C(p)(DD)(tau), as well as the pseudo-rotation (PR) model of the transient zero-field splitting (ZFS) are evaluated with the help of the data from MD simulations. The fast local water motion in the first hydration shell, i.e. the wagging and rocking motions, is found not to change the mono exponential character of the dipole correlation function C(p)(DD)(tau), but is important in the time dependence of the transient ZFS interaction. The dynamics of the transient ZFS interaction is modeled as the water-induced electric field gradient tensor at the site of the metal ion. This approach follows the ideas of the pseudo-rotation model, describing the fluctuating zero-field interaction as a constant amplitude in the principal frame but reorienting according to a rotational diffusion equation of motion. The MD results indicate that the pseudo-rotation model gives a multi-exponential correlation function which oscillates at short times and is described by three exponential terms. The time scale is shorter than previously assumed but contain an intermediate time constant (1-2 ps). The electron spin resonance (ESR) spectral width at half height at frequencies of X-band, Q-band, 75 MHz, 150 MHz and 225 MHz can be reproduced at 320 K without any contributions from 4th or 6th rank ZFS interactions. Consequently, there are two mutually inconsistent dynamic models of the ZFS interaction which can describe the water proton T(1)-NMRD (nuclear magnetic resonance dispersion) profile and the field dependent ESR spectra of the hydrated Gd(III) complex equally well.

Probing dynamics of single molecules: Nonlinear spectroscopy approach

A two level model of a single molecule undergoing spectral diffusion dynamics and interacting with a sequence of two short laser pulses is investigated. Analytical solution for the probability of n=0,1,2 photon emission events for the telegraph and Gaussian processes is obtained. We examine under what circumstances the photon statistics emerging from such pump-probe setup provides new information on the stochastic process parameters and what are the measurement limitations of this technique. The impulsive and selective limits, the semiclassical approximation, and the fast modulation limit exhibit general behaviors of this new type of spectroscopy. We show that in the fast modulation limit, where one has to use impulsive pulses in order to obtain meaningful results, the information on the photon statistics is contained in the molecule's dipole correlation function, equivalently to continuous wave experiments. In contrast, the photon statistics obtained within the selective limit depends on the both spectral shifts and rates and exhibits oscillations, which are not found in the corresponding line shape.

Role of dipolar correlations in the infrared spectra of water and ice

We report simulated infrared (IR) spectra of deuterated water and ice using Car--Parrinello molecular dynamics with maximally localized Wannier functions. Experimental features are accurately reproduced within the harmonic approximation. By decomposing the line shapes in terms of intramolecular and intermolecular dipole correlation functions, we find that short-range intermolecular dynamic charge fluctuations associated to hydrogen bonds are prominent over the entire spectral range. Our analysis reveals the origin of several spectral features and identifies network bending modes in the far IR range.

Photon Statistics for Single-Molecule Nonlinear Spectroscopy

We develop the theory of nonlinear spectroscopy for a single molecule undergoing stochastic dynamics and interacting with a sequence of two laser pulses. We find general expressions for the photon counting statistics and the exact solution to the problem for the Kubo-Anderson process. In the limit of impulsive pulses the information on the photon statistics is contained in the molecule's dipole correlation function. The selective limit, the semiclassical approximation, and the fast modulation limit exhibit rich general behaviors of this new type of spectroscopy. We show how the design of external fields leads to insights on ultrafast dynamics of individual molecules that are different from those found for an ensemble.

Structure, Dynamics, and the Free Energy of Solute Adsorption at Liquid−Vapor Interfaces of Simple Dipolar Systems: Molecular Dynamics Results for Pure and Mixed Stockmayer Fluids

We have performed molecular dynamics simulation studies of the structural, thermodynamic, and dynamical properties of liquid-vapor interfaces of pure and binary Stockmayer fluids of different polarity. The density profiles, the width of the liquid-vapor interface, and the orientational structure of the interfaces are calculated to characterize the structural aspects of the interfaces. Among the thermodynamic properties, we have computed the surface tension and also the free energy of transfer of a charged solute across the liquid-vapor interface for both pure and mixed fluids. Among the dynamical properties of the interfaces, we have calculated the time dependence of the velocity and angular velocity autocorrelation functions, continuous and intermittent survival probabilities, mean square displacements, diffusion coefficients, and also the dipole correlation functions and orientational relaxation times of interfacial solvent molecules. It is found that the width of the interfaces decreases with increase of concentration of the more polar component. The dipole vectors of the interfacial molecules tend to align parallel to the surfaces and this alignment is enhanced with increasing dipole moment of the fluid molecules. Also, the surface tension shows an increasing trend with increase of dipole moment of the molecules. The dynamical properties of the interfaces are found to be different from those of the corresponding bulk liquid phases. In general, the molecules at the interfaces are found to rotate and translate in the parallel direction at a somewhat faster rate than the bulk molecules. Also, on increase of concentration of the more polar component, the diffusion and orientational relaxation of interfacial molecules are found to show a weaker slowing down than those of the bulk molecules, which can be attributed to the preferential presence of the more polar component in the bulk liquid regions. The temporal behavior of the interfacial survival probabilities reveals a decrease of the survival times with increasing polarity, which can be attributed to a corresponding decrease in the interfacial thickness. Results are presented for both continuous and intermittent survival times and the origins of their differences are discussed. The free energy calculations reveal no minimum at the interfaces for adsorption of a charged solute, which shows that the ions would prefer to stay in the interior of the liquid phases, rather than at interfaces, for these model dipolar systems.

Molecular orientational and dipolar correlation in the liquid crystal mixture E7: a molecular dynamics simulation study at a fully atomistic level

Molecular dynamics simulations are reported for the four component nematic liquid crystal mixture E7, which is used commercially. We are able to show the growth of a nematic phase directly from an isotropic liquid over a 100 ns period for an all-atom model, and study orientational and dipole order within the nematic phase. The simulations show that the cyanoterphenyl component of the mixture, 5CT, is more ordered than the three cyanobiphenyl components. The simulations show also that both parallel and anti-parallel dipole correlation take place in E7 but that the strong anti-parallel dipole correlation is localised to particular arrangements of molecules. It is possible to identify two key preferred configurations for molecular pairs in the fluid, which explain the form of the dipole correlation function, g(1)(r).

Two-time correlation functions: stochastic and conventional quantum mechanics

An investigation of two-time correlation functions is reported within the framework of (i) Stochastic Quantum Mechanics and (ii) conventional Heisenberg-Schr\"odinger Quantum Mechanics. The spectral functions associated with the two-time electric dipole correlation functions are worked out in detail for the case of the hydrogen atom. While the single time averages are identical for stochastic and conventional quantum mechanics, differences arise in the two approaches for multiple time correlation functions.