Dipole Correlation Function Research Articles

A molecular dynamics simulation of interaction-induced FIR absorption spectra of liquid CS2

A molecular dynamics simulation of liquid CS2 was carried out using site-site Lennard-Jones potentials. The total interaction-induced dipole correlation function was calculated by analysing the intermolecular interactions in self and cross terms as well as in different many-body correlation functions. The calculated correlation functions display large static and dynamic cancellation effects showing that a careful study of the various individual correlation functions is a necessary prerequisite for the understanding of the molecular dynamics of liquids. The present data display not perfect, but improved agreement with experimental far infrared absorption spectra as compared to previous simulations.

Atomic fluorescence in a mode-hopping laser field

The authors apply the recently developed theory of multiplicative stochastic correlation functions with Markovian random jumps to the problem of resonance fluorescence from a two-level atom in a strong laser field. The finite bandwidth of a single-mode laser or the appearance of distinct lines in a multimode laser is considered to be brought about by a random mode-switching process. The two-time dipole correlation functions, which determine the spectral distribution of the fluorescence and the temporal correlations between the emitted photons are averaged exactly over the stochastics of the driving field. The authors' explicit expressions only involve single-time averages, which can be easily evaluated for a given probability distribution. These results generalise and modify earlier results. The authors obtain closed expressions, rather than implicit differential equations, which can handle the continuous case as well, and take into account the initial correlations, which always arise when the laser coherence time is finite. They illustrate the dependence on the stochastics of the laser model by comparing the multimode description with the phase-diffusion process and the Lorentz wave, which all give rise to the same laser profile, but to a different fluorescence spectrum.

Interaction-induced far infrared spectra of liquid CS 2-CCl 4 mixtures

The far infrared absorption spectra of pure liquid CS 2 and CCl 4 and of their mixtures at three different mole fractions have been obtained at room temperature. The integrated absorption, the effective dipole moments and the dipole correlation functions have been calculated. The results indicate that these quantities of the mixtures cannot be calculated as a sum of additive contributions of the pure components. The applicability of two different models, an isolated binary interaction model and a concentration fluctuation model, is discussed. The changes of the spectra and of the induced dipole autocorrelation functions with composition are interpreted in terms of a time-dependent cancellation of molecular dipoles by local fluctuations of density, concentration and molecular orientation.

The far infrared absorption spectrum of liquid nitrogen

The interaction quadrupole-induced dipole correlation function and the corresponding absorption spectrum of liquid nitrogen have been simulated in a site-site molecular dynamics calculation at atmospheric pressure and 66 K. Two models were used: an anisotropic and an isotropic molecular polarizability model. The differences between the two models are significant, but small. The results were compared to the published absorption spectra and reasonable agreement was obtained. The differences between simulation and experiment are discussed in terms of the properties of the model used. The total dipole correlation function was analysed in terms of a self-term and a cross-term. The contribution of the latter, which is negative, is quite large. Furthermore, a number of correlation functions describing the details of the molecular motion in the liquid have been calculated and are discussed in view of a possible discrimination between rotational/translational motions and/or single-molecule/collective motions.

Effects of an arbitrary laser lineshape on fluorescence radiation, redistributed by collisions

The authors investigate collisional redistribution in a laser field with arbitrary lineshape. The phase diffusion model cannot be correct in general due to its inherent assumption of zero correlation times. The authors give general expressions for the state of the atom, the dipole correlation function and the steady-state fluorescence spectrum in the presence of collisions and phase fluctuations with finite correlation times. It turns out that collisional effects decouple from the free-atom stochastic problem to a good approximation and that modifications due to the laser bandwidth can be quite different from collisional effects, although they are additive on a microscopic level. They evaluate the fluorescence spectrum explicitly in the limit where the three lines are well separated and show that the spectrum is determined by simple field correlation functions. The arbitrary phase fluctuations do not affect the line strengths but only the lineshapes. Collisions, on the other hand, can transfer intensity between the lines, due to the very small collision time. For free atoms and strong driving fields, the fluorescence spectrum becomes a convolution of the normalised laser spectrum with the fluorescence spectrum at monochromatic irradiation, but this does not hold any more when collisions are present.

Some Comments and Corrections on the Defect Diffusion Models of Dielectric Relaxation

AbstractAn attempt is made to improve the “defect‐diffusion model” initially proposed by Glarum. Some of the basic ideas underlying the model and assessing its success and rationality as applied to polymer relaxation are discussed. The model is generalized by developing a new one‐dimensional “molecular chain‐defect diffusion model”, namely, extending the single dipole relaxation to a linear chain molecular system. A dipole correlation function derived from this new model under various physical conditions, appears in the form of the Williams‐Watts empirical decay function φ(t) = exp [−(t/τ)γ] with 0 < γ ≦ 1. The results obtained lead to a molecular interpretation of this “universal” non‐exponential decay function.

Collision-induced absorption in molecular gases: an analytical solution

An analytic solution for the translational two-body contribution to the quadrupole-induced dipole correlation function is presented. It allows one to evaluate the far-infrared collision-induced absorption spectra of molecular systems, composed of quasi-spherical molecules at low density from the knowledge of few parameters derived from different experiments. The comparison with a translational correlation function extracted from the absorption spectrum of gaseous N 2, under the same approximations, is also discussed.

A molecular dynamics simulation of interaction-induced dipole correlation functions in liquid CS2

The interaction-induced dipole correlation function for liquid CS2 was calculated by molecular dynamics simulation. This correlation function was separated into components parallel and normal to the molecular symmetry axis, and the shape of these, as well as of the tensorial P 2 orientational correlation function, were calculated and compared. The discussion shows that we can obtain information on the environment anisotropy fluctuations contributing to the time dependence of the induced dipoles. The comparative discussion of several of these correlation functions can be useful in obtaining a differentiated, but still partial picture of the molecular dynamics in liquid CS2.

Dynamics of helical worm-like chains. IV. Dielectric relaxation

Dielectric relaxation of both flexible and stiff chain polymers in dilute solution is studied on the basis of the discrete helical worm-like chain such that an electric dipole moment is attached rigidly or with a rotational degree of freedom to each of the subbodies composing the chain. The complex dielectric constant is formulated with the dipole correlation function, which may be expressed in terms of the L=1 time-correlation functions derived previously. Then, dielectrically active branches of the eigenvalue spectrum are identified for a given type of dipoles, and a mode analysis of them is made in order to inquire into the interaction between global and local modes. The decay behavior of the dipole correlation function is also examined numerically for various chains. A comparison of theory with experiment is made with respect to the dispersion and loss, and also the dielectric correlation time τD as determined from the loss peak. The theory cannot always well explain the asymmetry of the loss curve, especially for flexible chains without side chain motions. For flexible chains, however, the calculated values of τD agree rather well with the observed values, although the former are somewhat smaller than the latter. Furthermore, it is found that there is strong correlation between the static stiffness parameter λ−1 and the dynamic stiffness as defined as the ratio of τD to that of the isolated subbody (monomer unit). For stiff chains, an interpolation formula for τD is constructed, and it is shown to explain well the molecular weight dependence of τD. Finally, a possible direction toward improvement of the theory is suggested.

Dielectric behavior and multibody orientational correlations of dipolar molecular liquids

Computer simulation studies of dipolar two center Lennard-Jones molecular liquids are reported. The dielectric constant, Kirkwood factor, two and three body orientational correlation functions are given as a function of molecular elongation for a series of approximately corresponding states. The packing of linear molecules in dense dipolar liquids is found to reduce the dielectric constant by between 50% and 60% (l>0.2) from that of an equivalent Stockmayer fluid. The Kirkwood factor is found to be <1 for elongated molecules as suggested by Buckingham. These changes are explained in terms of a local structure which also predicts the qualitative features of the two and three body dipole correlation functions.

Relaxation of siloxanes observed by FIR absorption

The FIR spectra of liquid dimethyl siloxanes of different molecular weight, from the monomer to the polymer with 1000 monomer units, have been measured and interpreted in terms of the calculated dipole correlation functions. Evidence for a fast localized motion in the siloxane chain is presented.

A computer simulation study of the dielectric properties of a model of methyl cyanide

The dielectric permittivity of a model fluid representing methyl cyanide has been studied with a view to testing a recently developed theory of the frequency dependent dielectric permittivity. Although there are large correlations between the orientations of dipoles the Kirkwood g factor is close to the trivial value of unity; this contrasts with the behaviour of Stockmayer and similar model fluids and is a consequence of the molecular shape. The time dependence of both the longitudinal and transverse components of the dipole density is obtained and related to the relaxation of the single molecule dipole correlation function. The applicability of the ‘dipolaron’ description to the oscillation observed in the relaxation of the longitudinal component is examined.

Modeling noise by jump processes in strong laser-atom interactions

In this paper, a practical scheme for computing time-dependent properties, such as excitation probabilities and dipole correlation functions of a multilevel atom strongly excited by a laser in the presence of noise, is described in detail. The method, which is based on the notion of randomly interrupted, multivalued jump processes, can be used to treat laser phase, amplitude, and/or frequency noise, and fluctuating microfields. The method provides analytic expressions, which are based on eigenvalues and eigenvectors of a finite-dimensional matrix, for time dependence and spectral dependence, and it permits computation of time-dependent fluorescence emitted from atoms excited by a noisy laser. The method is illustrated by application to time-dependent spectra.

Molecular dynamics of some crotonates using infrared band shapes

The dipole correlation function of three esters of crotonic acid have been computed from the infrared absorption bands. Both short-time and long-time behaviour of the correlation functions are computed and discussed. The correlation times are also calculated. The short-time behaviour was compared with the correlation functions generated as an even-power series with second and fourth moments. They were also compared with the correlation functions of the freely rotating molecule.

Dipole correlation functions and intermolecular torques in nematic phase of EBBA and PAA

A new method for separation of the orientational contribution from the vibrational relaxation part in the IR absorption bands of ordered liquid crystals is suggested. The pure rotational relaxation times and intermolecular torques acting on PAA molecules in nematic phase have been calculated from the experimental results.

Dipole correlation functions and Kirkwood g(1) factor in liquid chlorobenzene

The Kirkwood g(1) factor for room temperature liquid chlorobenzene has been measured from (a) the integrated intensity of the far IR rotation-translation band, and (b) the long time slopes of the single-particle and total-particle dipole correlation functions, using the Keyes–Kivelson rotational diffusion model. The values are 1.13±0.11 and 1.18±0.10, respectively, and do not agree with the Kirkwood–Frohlich theory, which predicts 0.83. The vibrational and far IR band shapes are presented, along with their second moments and the dipole correlation functions. The vibrational band second moment is within experimental error of the theoretical value; the far IR band second moment is in excess by 153%.

Dielectric behavior of polyelectrolytes

The role of the Coulomb forces between the counterions on the surface of polyelectrolytes on the dielectric response is analyzed. An estimate of the maximum dielectric increment (as a function of the number of counterions) is found as a function of the molecular length. The minimum-energy configuration of the counterions on a cylinder is found to be a double helix, suggesting the fundamental importance of electrostatic interactions in determining structure. Solutions of the dynamical equations for a few counterions indicate that a single mode dominates the relaxation which is enhanced by the inter-ion repulsions. A lower bound is found for this mode based on analysis of the system response for short lengths. Sum rules for the rates and amplitudes of the dipolar correlation function are derived and lead to an upper bound for the rate of the dominant mode. These bounds approach one another for the parameters characteristic of restriction fragments of DNA. This permits a prediction of the magnitude and time scale of the dielectric response.

Dipolar correlation function and motional narrowing in finite two-dimensional spin systems

A statistical treatment is used to describe the dipole–dipole relaxation processes of spins S=1/2 diffusing on finite two-dimensional (2D) surfaces. This leads to a general expression for the dipolar correlation function G(τ) including pairwise autocorrelation and cross-correlation terms. We show that for a finite 2D planar surface, G(τ) decays faster than that for an infinite planar surface. For finite 2D planar surfaces, dipolar translational correlation times, τ̄c are expressed in terms of the diffusion coefficient, the distance of closest approach between spins, and the area of the surface. It is shown that there is rapid motional line shape narrowing for sufficiently small two-dimensional surfaces. The calculation of resonance line shapes for the infinite 2D surface is discussed, but remains an unsolved problem when the only relaxation processes are those that arise from intermolecular dipolar interactions.

Angular-dependent rotational friction in anisotropic liquids

Hydrodynamical arguments are used to derive an expression for the angular-dependent rotational friction, appropriate for the description of the rotational dynamics of molecules in liquid-crystal phases characterized by anisotropic viscosities and orientational torques. The solutions of the corresponding Fokker—Planck equation, obtained under conditions of diffusional motion, show significant variations in the time dependence of the dipole correlation functions.

On the semiclassical calculation of molecular absorption and fluorescence spectra

A semiclassical expansion is developed for the direct calculation of molecular electronic (absorption and fluorescence) spectra without having to calculate the molecular vibrational eigenstates. The expansion is based on expressing the necessary dipole correlation functions (which do not have a straightforward classical analog) in terms of a hierarchy of other intramolecular correlation functions which do have a simple semiclassical expansion. To lowest order in h/ the spectra may be calculated by running classical trajectories on a zero-order Hamiltonian Hc. The present semiclassical expansion is not unique and depends on our choice of Hc. This arises since the spectra are not analytic functions of h/. Applications are made to the absorption and to the fluorescence spectra of polyatomic molecules (single- and two-photon processes). The present method may be easily generalized to other multiphoton processes.