Dipole Moment Fluctuations Research Articles

Polar fluctuations in proteins: molecular-dynamic studies of cytochrome c in aqueous solution.

The equilibrium fluctuations (the polar fluctuations), of yeast cytochrome c are studied using nanosecond molecular-dynamic simulations in a spherical droplet of water, with a particular emphasis on the fluctuations of the total dipole moment, which determine the average relative permittivity. These fluctuations follow a simple probability distribution, predicted by continuum electrostatics, and already observed in simulations of several polar liquids. An important component consists of diffusive, mutually independent, motions of the charged side chains at the protein surface. A quasiharmonic normal mode analysis of the trajectory shows that while motions covering a large range of frequencies contribute to the polar fluctuations, the four lowest frequency modes account for 50% of the overall static relative permittivity of ca. 25. The fluctuations of the protein bulk, i.e. parts other than the charged side chains, are distributed over a larger number of modes. Modes up to at least 60 cm-1 contribute to the average relative permittivity of the protein interior of ca. 4. The water surrounding the protein, despite the structural perturbation represented by the protein, has fluctuations similar to pure water, consistent with the idea of a linear solvent response to the protein charges. The relationship between the microscopic fluctuations seen in the simulations and simple continuum models is discussed.

Dipole moment noise in the hydrogen atom in the Bohm quantum-mechanical theory

In the Bohm theory of quantum mechanics, particles move in well-defined paths. The probability distribution (at a single time) is exactly what would be computed from the Schrodinger equation. Here we consider two-time probabilities in the Bohm theory, and compute dipole moment fluctuation spectra for the hydrogen atom. The resulting dipole fluctuations differ from those which can be obtained from conventional quantum mechanics.

Molecular dynamics study of the dielectric constant of water under high pressure and temperature conditions

AbstractThe static dielectric constant of a water model (extended simple point charges, SPC/E) was evaluated by molecular dynamics simulations in the (N, V, E) ensemble for temperatures ranging from T = 324 K to 1278 K and densities from 0.257 g/cm3 to 1.1108 g/cm3. The dielectric constants calculated from fluctuations of the total dipole moment of the simulation box in the absence of an external field, and those obtained from the polarization response to an applied field were demonstrated to be consistent. Simulations within the pressure‐temperature range (up to 500 MPa and 823 K) of available experimental data yield dielectric constant in very good agreement with experiment. It appears therefore that the SPC/E potential model can be used for the simulation of the dielectric properties of supercritical water and of aqueous solutions under supercritical conditions.

The dielectric constant of polar fluids and the distribution of the total dipole moment

This article examines the distribution of fluctuations of the total dipole moment M in polar fluids. Detailed results, including average energies, pressures, and dielectric constants, are reported from molecular dynamics simulations of a dipolar soft-sphere system in reaction field (RF) and periodic boundary conditions (PBC). Both cubic and truncated octahedral simulation cells are employed and we demonstrate that the properties of interest are insensitive to our choice of cell geometry. Some dependence upon RF cutoff is observed, particularly in results for the static dielectric constant. The distribution of instantaneous values of M shows no anisotropy, and we argue that the isotropic probability distribution function P(g), where g is the Kirkwood correlation factor and depends only upon the magnitude of M, is sufficient to fully characterize the fluctuations in the total moment for a large sample of a polar liquid. We demonstrate that the functional form for P(g) previously tested for a dipolar fluid in PBC [P. G. Kusalik, Mol. Phys. 80, 225 (1993)] holds for RF boundary conditions; we also find that this form is obeyed by other polar liquids such as water and methanol. The distribution function P(g) is found to be particularly effective at detecting finite size effects in simulations of polar liquids. We also show how knowledge of the functional form for P(g) can be efficaciously used to achieve significant reductions in the computational resources required to determine a static dielectric constant for a polar liquid.

Nonempirical intermolecular potentials for urea–water systems

In this work, we present ab initio derived intermolecular potentials for the urea–water system. Our method of calculation, which is termed NEMO, is based on intermolecular perturbation theory. Dipole moment fluctuations as well as many-body effects in an assembly of molecules are described by including atomic polarizabilities in the potential. For the urea dimer we found a cyclic minimum with an energy of −21.9 kcal/mol and two equivalent hydrogen bonds of length 1.77 Å. Noteworthy is that this interaction energy is more than four times larger than the water dimer minimum energy. To be able to satisfactorily model the interaction between two urea molecules we have improved the NEMO approach in the description of the repulsion energy and we have also included a more accurate damping on the dispersion energy. With this improved model we reinvestigated the water dimer and urea–water potentials and found good agreement with earlier potentials derived with similar approaches. From simulations of liquid water we investigated the sensitivity of structural properties resulting from small changes in repulsion parameters. Qualitative changes of the tetrahedral hydrogen bonding may occur for inappropriate parameter choices of the same potential surface.

The distribution of fluctuations of the total dipole moment in polar liquids

By P. G. KUSALIK Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, B3H 4J3, Canada {Received 21 June 1993; accepted 12 July 1993) The distribution of fluctuations o f the total dipole moment in polar liquids is characterized. The functional form of the probability distribution function, P(g), where g is proportional to the square of the total moment and its average value is directly related to the static dielectric constant, is empirically deter­mined. A formal justification of the functional form is then developed and impli­cations to the calculation of the dielectric constant in computer simulations are discussed. The dielectric properties of polar liquids, particularly the static dielectric constant e, are fundamental characteristics of these systems [1]. Unfortunately, the deter­mination of these properties by computer simulation has presented both conceptual [2-7] and computational difficultie [7-16] Man.sy of the problems associated with the treatment of the boundary conditions have now been resolved, yet many impor­tant questions concerning the influences of the boundary conditions and finite-size samples have remained at least partially unanswered [14-16]. Furthermore, although reasonably precise values for e for highly polar liquids (such as water) can be determined with rather long simulations, the results obtained may still contain non-trivial systematic errors due to the effects of system size and boundary con­ditions (for examples, see [13-15]). Clearly, there is a need for more computationally efficient routes to e and for an increased understanding of the influences of sample size and boundary conditions upon the dielectric properties of polar liquids. The traditional means of obtaining the static dielectric constant from a computer simulation has been from the average fluctuations in the total dipole moment of the system, M, through the standard relationship (valid for both reaction-field and periodic boundary conditions [3, 5]) (

On statistical thermodynamics of the ideal polarizable interface

The fundamentals of the statistical mechanical theory of the electric double layer are discussed in relation to the choice of the independent electric variable. It is shown that the grand canonical ensemble theory implies the use of the potential as the independent electric variable. The notion of a constant charge ensemble is then introduced as a particular case of the grand canonical ensemble. The differential capacity is expressed unambiguously by charge fluctuation in the grand canonical ensemble theory, while the analogous formula in the constant charge ensemble theory can be interpreted as a surface excess of polarizability, which cannot be resolved unambiguously into absolute quantities: dipole moment fluctuation and thickness of the interface. The implication of the choice of the independent electric variable for the so-called polarization catastrophe is discussed.

Dielectric properties of trypsin inhibitor and lysozyme calculated from molecular dynamics simulations

The static and frequency dependent dielectric properties of trypsin inhibitor and hen egg white lysozyme have been calculated from the fluctuations in the total dipole moment of the two proteins. Total dipole moment fluctuations were obtained from long molecular dynamics simulations of both proteins in an explicit solvent environment. Despite differences in the total charge, volume, shape and secondary structure composition of the two proteins, consistent values for the dielectric constant were obtained. The static dielectric constant of trypsin inhibitor was calculated to be 36, compared with a value of 30 for hen egg white lysozyme. Convergence in the calculations required 1 ns of simulation. The calculated frequency dependent dielectric constant was also consistent with known experimental dielectric dispersion curves for proteins in aqueous solution. The implications for free energy calculations involving significant charge redistribution are also discussed.

Peptides in ionic solutions: A comparison of the Ewald and switching function techniques

The methodological dependence of observed ion–peptide associations in molecular dynamics simulations is investigated. We compare the results from several simulations of a pentapeptide in explicit solvent and salt ions which differ in the their treatment of the long ranged electrostatic interactions. Results for both the Ewald and switching function techniques are presented. It was found that there were important differences between the two methods for the water dipole–dipole temporal and spatial correlations, total dipole moment fluctuations, and self-diffusion constants. Electrostatic potentials calculated in the region of the peptide are also used to illustrate the large differences that can arise from different treatments of the electrostatic interactions. It appears that the switching function distorts the molecular electrostatic potential experienced by the salt ions to such a degree that their behaviour becomes highly dependent on the initial conditions. In summary, the use of a switching function is not recommended for the simulation of ions and their interactions with biomolecules.

On the computer simulation of highly polar fluids using large systems

The determination of the dielectric properties of polar liquids by computer simulation has, in the past, presented both conceptual and computational difficulties. Many of the conceptual problems have now been at least partially resolved, yet the accurate calculation of the dielectric response for a highly polar liquid remains a major computational task. The usual means of obtaining the static dielectric constant, ϵ, is through the fluctuations in the total dipole moment of the system. In this paper we describe an alternate approach which relies upon the long-range asymptotic behaviour of the dipole-dipole correlations in order to determine ϵ. It requires that a rather large simulation cell be employed, in the present case samples of 4000 particles. Molecular dynamics simulations have been performed for a highly polar fluid composed of dipolar soft spheres in which the dipole-dipole interactions have been evaluated using the Ewald summation technique. Results for the static dielectric constant are reported...

Ergodic measures for the simulation of dialectric properties of water

We determine the time interval, t obs, required for effective ergodic convergence of the fluctuations in dipole moment which are needed for the computation of the dialectric properties of water. It is established that the value of t obs can be computed from the scaling relations obeyed by the fluctuation metric, Ω μ( t) associated with the time-average values of the dipole moment of the individual water molecules. The theoretical ideas behind Ω μ( t) are used to compute t obs at several temperatures for the simple point-charge model of water. It is found that t obs increases exponentially with decreasing temperature, the barrier being associated with the difficulty in making collective orientational rearrangements. For the simple point-charge model considered in this paper the barrier for these collective motion is estimated to be 3.5 kcal/mole. This study provides a firm basis for obtaining reliable values of the dielectric properties of dipolar fluids using molecular dynamics simulations.

Dynamical properties of molecules physisorbed on a metal particle

The response potential of a small metallic sphere to a fluctuating dipole moment is determined from spherical-tensor theory. The non-local character of the electron response is included by using the random-phase approximation and by introducing a jellium model. The response field obtained from this calculation allows us to define a new expression of the effective linear polarisability of a molecule physisorbed on a metal particle. Two limiting cases are then considered: the dielectric approximation and the non-local homogeneous one.

Superconductivity in the liquid-dimer valence-bond state.

Introducing an unambiguous prescription which converts singlet dimers into quasidipoles, we describe the low-energy excitations in the liquid-dimer state as fluctuations of the average dipole moment. The exchange of these fluctuations leads to a long-range interaction between holes in this state. This interaction favors the two-particle Bose condensate and destroys the order parameter of the one-particle Bose condensate even at zero temperature.

Computer simulations of the dielectric properties of water: Studies of the simple point charge and transferrable intermolecular potential models

A series of very long molecular dynamics simulations has been completed for the rigid simple point charge (SPC) and transferrable intermolecular potential 4P (TIP4P) water models with reaction field boundary conditions. The dielectric constant corresponding to these models was evaluated in two ways: (1) by calculating the fluctuations in the mean square dipole moment of the system in the absence of an applied field and (2) by evaluating the polarization response of the system to an applied field. Consistent values for the dielectric constant are obtained by the two methods. For the TIP4P water model, the dielectric constant ε0 is calculated to be ∼50 at 293 K, in agreement with previously published results. For the rigid SPC model, ε0 is calculated to be ∼68 at 300 K and ∼59 at 350 K. The calculated dielectric constant is shown to be very sensitive to the way in which the truncation of long-range forces is treated, although the short-range liquid properties are insensitive to the truncation procedure. The effects on the dielectric response of system size, cutoff radius, and the smoothing of long range interactions at the cutoff boundary are examined. It is found that the introduction of a smoothing function causes perturbations of the water–water angular orientation correlation functions which can result in large errors in the calculated dielectric constant.

Giant resonances in hot nuclei

The spectrum of gamma-radiation emitted by a highly excited nucleus can be calculated in two ways. In the first method the transition probability for gamma emission is related to the photon absorption cross-section by detailed balance. The second method relies on the fact that an excited hot nucleus has thermal fluctuations. In particular it has a fluctuating dipole moment which produces thermal radiation. The two methods are closely related and in both cases the spectrum of the radiation emitted is dominated by the giant dipole resonance. The equivalence of the detailed balance and thermal radiation theories can be demonstrated explicitly for a coupled oscillator model of the giant resonance.

Theory of the transient electric birefringence of rod-like polyions: Coupling of rotational and counterion dynamics

Expressions constructed by applying statistical mechanics to a molecular model of polyion–counterion rod assemblies are used to find values for two phenomenological parameters in the stochastic theory of Szabo, Haleem, and Eden for the transient electric birefringence of rod-like polyions. These parameters are the polyion electric polarizability and the decay rate of fluctuations in macroion dipole moment. The range of system parameters over which the model of Szabo et al. applies is delineated.

A molecular dynamics simulation of a water model with intramolecular degrees of freedom

Simulations of water models with and without intramolecular degrees of freedom have been performed within the classical approximation. Three H2O simulations with interaction parameters taken from a simple point charge model due to Berendsen et al. are reported: (i) with rigid water molecules, (ii) with flexible water molecules and (iii) with rigid water molecules and polarized bond lengths and bond angles obtained from the second simulation. The most important effect of the inclusion of intramolecular vibrations is seen on transport properties, which in general become a foctor of 2-3 faster. The internal vibrations lead to a small but significant lowering of the potential energy and also reduce the structure, as seen from atom-atom distribution functions. The dipole moment fluctuations are affected by the nuclear polarization caused by the intermolecular interactions. Two D2O simulation have been performed in order to assess the effects of isotope substitution, one with rigid molecules and the other with ...

On the calculation of the frequency-dependent dielectric constant in computer simulations

An equation is derived which relates, for all boundary conditions currently used, the dipole moment fluctuations observed in computer simulations of polar systems to the frequency-dependent dielectric constant. Provided that the modified dipolar interactions do not explicitly depend upon time, the resulting formula is of a generalized Glarum type.

Dipole moment fluctuation formulas in computer simulations of polar systems

The fundamental equation of electrostatics, i.e. the integral equation for the polarization of a macroscopic dielectric in an arbitrary external field, is written in a form that allows explicit inclusion of the toroidal boundary conditions as well as the cutoff of dipolar interactions often used in the computer simulation of polar systems. The toroidal boundary conditions are accounted for in a natural way if the integral equation is formulated (and solved) in Fourier space. Rigorous expressions for the polarization induced by a homogeneous field as well as for the equilibrium dipole moment fluctuations, both as a function of the dielectric constant, are then easily derived for general systems in two and three dimensions. The equations obtained for spherical cutoff geometry with reaction field are identical to those valid for an infinite periodic system (Ewald sum plus reaction field). When applied to the case of a highly polar Stockmayer system (μ*2=3·0, θ*=0·822, T*=1·15) the formulas lead to a consiste...

Boundary conditions for Monte Carlo simulation of charged systems

We investigate the effects of a change in external dielectric constant e′ on the properties of a system of charges in periodic boundary conditions. The mean square dipole moment fluctuations of a configuration are shown to depend strongly on e′ in the thermodynamic limit. Simulations of 216 restricted primitive electrolyte particles with e′ = 1 and e′ = ∞ at η = 0·35 and Γ = 2, 5 and 10 are reported and obey the formula for the change in mean square dipole moment fluctuations rather well.