Long-range Coulomb Forces Research Articles

Revisiting the Hammond Postulate: The Role of Reactant and Product Ionic States in Regulating Barrier Heights, Locations, and Transition State Frequencies

Radical−molecule reaction barriers are often the product of an avoided curve crossing between two states: the reactant ground state, which ultimately correlates with a product ionic state, and a reactant ionic state, which ultimately correlates with the product ground state. The energy, location, and loose-mode frequencies of the transition state are controlled by this interaction. The curve crossing itself is constrained by long-range Coulombic forces acting primarily on the ionic states as the reactants approach each other. The crossing height is in essence a geometric mean of the ionic surface heights; a low ionic state energy in either the reactants or the products will force a low reaction barrier. The crossing location is controlled primarily by any asymmetry in the reactant and product ionic heights, while the interaction distance of the transition state is controlled by a balance in gradients on the ground and ionic states. The frequencies related to translation of the separated reagents within the center of mass frame of reference are controlled by the same physics controlling the barrier height, as is the imaginary frequency associated with the reaction itself. This drives a tight correlation between barrier heights, transition state frequencies (and thus preexponential terms), and the imaginary frequency (and thus the tunneling term). This is demonatrated by analyzing a series of H atom transfers from a mainfold of alkanes to a mainfold of atoms. The Hammond postulatereaction enthalpy controls transition state locationdoes not correspond to the mechanism controlling either barrier height or location, but rather appears to work in cases where ionization potential correlates with bond strengths.

Temperature dependence of dielectric and phonon properties in superionic conductor CuI

Roles of interionic ( I) forces on the mobile defects are investigated by measuring far-infrared reflectivity (FIR) spectra of sintered CuI as a function of temperature ( T) below 300 K. Anomalous increase was observed for the phonon damping constant γ ph and long-range Coulomb force f L. From this T-dependence and small increase of effective charge with T, we point out the effective role of the ionic character of the I force on ionic conduction.

Structure anddynamics of a model glass: influence of long-range forces

We vary the amplitude of the long-range Coulomb forces within aclassical potential describing a model silica glass and study theconsequences on the structure and dynamics of the glass, viamolecular dynamics simulations. This model allows us to follow thevariation of specific features such as the first sharp diffractionpeak and the boson peak in a system going continuously from afragile (no Coulomb forces) to a strong (with Coulomb forces) glass.In particular we show that the characteristic features of a strongglass (existence of medium-range order, bell-shaped ring sizedistribution, sharp boson peak) appear as soon as tetrahedral unitsare formed.

Wannier threshold law and the classical-quantum correspondence in three-body Coulomb breakup

We derive the classical threshold law for the breakup of three charged particles interacting via long-range Coulomb forces for the case of a charge ratio of $1/4$ between the particles involved. The Wannier exponent in canonical Wannier theory is known to diverge in this case. We find that the classical threshold law, which is proportional to $\mathrm{exp}(\ensuremath{-}\ensuremath{\lambda}/\sqrt{E}),$ shows exponential suppression of the ionization probability at threshold. We thus identify the possibility that exponential behavior in breakup processes, typically attributed to quantum-mechanical tunneling, can arise as a completely classical dynamical effect. We show that in the limit of zero energy, the behavior of the cross section is characterized by a classical to quantum transition. We discuss the regime of parameters in which this transition occurs and the possibility of an experimental observation of this transition.

Momentum space integral equations for three charged particles: Nondiagonal kernels

Standard solution methods are known to be applicable to Faddeev-type momentum space integral equations for three-body transition amplitudes, not only for purely short-range interactions but also, after suitable modifications, for potentials possessing Coulomb tails provided the total energy is below the three-body threshold. For energies above that threshold, however, long-range Coulomb forces have been suspected to give rise to such severe singularities in the kernels, even of the modified equations, that their compactness properties are lost. Using the rigorously equivalent formulation in terms of an effective-two-body theory we prove that, for all energies, the nondiagonal kernels occurring in the integral equations which determine the transition amplitudes for all binary collision processes, possess on and off the energy shell only integrable singularities, provided all three particles have charges of the same sign, i.e., all Coulomb interactions are purely repulsive. Hence, after a few iterations these kernels become compact. The case of the diagonal kernels is dealt with in a subsequent paper.

Charge-charge correlation functions in the Emery three-band model

The influence of the long-range Coulomb forces on the charge-charge correlation functions has been examined in the Emery three-band model. The ${U}_{d}=0$ limit and the mean-field approximation of the ${U}_{d}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit have been studied. The intraband and interband contributions to the dynamically screened correlation functions are found both for the intercell (monopole) and intracell (quadrupole) charge fluctuations. It appears that the interband monopole processes are responsible for the optical interband transitions. For strong local correlations ${(U}_{d}\ensuremath{\rightarrow}\ensuremath{\infty}),$ the threshold energy of these processes is found to be only slightly dependent on the bare hybridization parameter ${t}_{\mathrm{pd}}^{0}/{\ensuremath{\Delta}}_{\mathrm{pd}}^{0}.$ The value of the threshold energy is comparable with the bare first-neighbor overlap energy ${t}_{\mathrm{pd}}^{0}.$ As expected from experimental observations and previous static, symmetry-based theoretical considerations, the oxygen-oxygen charge correlation function is not screened in the tetragonal lattices, in contrast to the oxygen-copper $(\mathrm{pd})$ charge correlation function. The intraband coupling of the Raman-active phonons to the $\mathrm{pd}$ intracell charge fluctuations becomes thus substantially screened, but does not vanish, at variance with the predictions of the static-screening models. It is also found that the mean-field approximation of the ${U}_{d}\ensuremath{\rightarrow}\ensuremath{\infty}$ case can explain the measured magnitude of the plasma frequency, as well as its dependence on doping, but only in the overdoped high-${T}_{c}$ superconductors.

Long-range Coulomb forces and localized bonds

The ionic model is shown to be applicable to all compounds in which the atoms carry a net charge and their electron density is spherically symmetric regardless of the covalent character of the bonding. By examining the electric field generated by an array of point charges placed at the positions of the ions in over 40 inorganic compounds, we show that the Coulomb field naturally partitions itself into localized regions (bonds) which are characterized by the electric flux that links neighbouring ions of opposite charge. This flux is identified with the bond valence, and Gauss' law with the valence-sum rule, providing a secure theoretical foundation for the bond-valence model. The localization of the Coulomb field provides an unambiguous definition of coordination number and our calculations show that, in addition to the expected primary coordination sphere, there are a number of weak bonds between cations and the anions in the second coordination sphere. Long-range Coulomb interactions are transmitted through the crystal by the application of Gauss' law at each of the intermediate atoms. Bond fluxes have also been calculated for compounds containing ions with non-spherical electron densities (e.g. cations with stereoactive lone electron pairs). In these cases the point-charge model continues to describe the distant field, but multipoles must be added to the point charges to give the correct local field.

Ewald summation for systems with slab geometry

We propose a modification in the three-dimensional Ewald summation technique for calculations of long-range Coulombic forces for systems with a slab geometry that are periodic in two dimensions and have a finite length in the third dimension. The proposed method adds a correction term to the standard Ewald summation formula. To test the current method, molecular dynamics simulations on water between Pt(111) walls have been carried out. For a more direct test, the calculation of the pair forces between two point charges has been also performed. An excellent agreement with the results from simulations using the rigorous two dimensional Ewald summation technique were obtained. We observed that a significant reduction in computing time can be achieved when the proposed modification is used.

Dielectric constant of water at high electric fields: Molecular dynamics study

Molecular dynamics computer simulations have been carried out for water enclosed between Pt(111) surfaces at high external electric fields. The dielectric constant of water as a function of electric fields has been calculated. Two-dimensional Ewald summation technique has been used for the calculation of long-range Coulombic forces. Simulations with a larger distance between walls, different surfaces, and bulk water have been done to confirm the macroscopic nature of the dielectric constant. Calculated dielectric constants have been compared with those obtained by a theoretical prediction and a recent simulation study.

Low frequency phonon modes and ferroelectric phase transitions in nanocrystalline Pb1−x A x Ti1−y B y O3

Low frequency Micro-Raman scattering measurements as well as X-ray diffraction have been carried out on nanocrystalline PbZr1−y TiyO3, Pb1−x Sr x TiO3, Pb1−x LaxTiO3 and Pb1−x Ba x TiO3 system. Grain sizes-induced and different doping ions-induced phase transitions from the tetragonal ferroelectric phase to the cubic paraelectric phase were identified in these ABO3 systems. These phase transitions are closely concerned with the “softening” of the low frequency phonon modes. A lowest frequency phonon mode at 10c−1 is detected. The temperature dependence of Raman phonon modes for Pb0.8La0.2TiO3 with grain size of 58nm reveals a temperature-induced soft mode phase transition occurring at 375K. The “softening” of the low frequency modes with reducing grain size and increasing doping ion content and temperature is shown to arise from a delicate balance between long-range Coulomb forces and short-range repulsion. Investigations show that PbTiO3 has an adjustable Curie temperature depending on different dopants and different grain sizes which will be useful in sensor and actuator devices.

Localized excitations in diluted magnetic Cd 1− xMn xTe semiconductor ternary alloys and CdTe/Cd 1− xMn xTe superlattices

In terms of a long-wavelength optical response theory, we have analysed the far-infrared reflectivity spectra of Cd 1− x Mn x Te ternary alloys and predicted s- and p-polarized reflectance in CdTe/Cd 1− x Mn x Te thick multiple heterostructures. Lattice dynamics of bulk cubic CdTe, MnTe; folded phonons and anisotropy of optical modes in CdTe/Cd 1− x Mn x Te [0 0 1] SLs are investigated using a realistic rigid-ion-model (RIM). The short-range forces in CdTe and MnTe materials are optimized by incorporating neutron scattering and transformed Raman data of phonons and elastic constants. The long-range Coulombic forces are evaluated exactly by Ewald summation method. In CdTe/Cd 1− x Mn x Te SLs, the influence of composition and disorder in Cd 1− x Mn x Te ternary alloys is described within a modified random-element iso-displacement scheme generalized to layered structures with arbitrary wavevectors and composition profiles. Theoretical results are compared and discussed with the existing far infrared and Raman scattering data.

Anion-related variations in the phonon behavior of cubic Ga 1− xAl xY semiconductors and (GaY) m/(Ga 1− xAl xY, Y = As, N) n superlattices

We have reported a comprehensive theoretical study of anion-related variations in the phonon behavior of cubic Ga 1− x Al x Y semiconductors and (GaY) m /(Ga 1− x Al x Y,Y=As, N) n superlattices (SLs) using a microscopic rigid-ion model (RIM). The short range forces for the bulk GaAs and AIAs in the RIM are optimized by incorporating values of elastic constants, and phonons at critical points from the inelastic neutron scattering and/or Raman data. The force constants for cubic GaN, AlN are obtained from the transformed Raman scattering data of phonons for the wurtzite materials and the existing elastic constants. The long-range Coulomb forces are evaluated exactly via Ewald summation. To treat the alloying of barrier layers and disorder at the interfaces in (GaY) m /(Ga 1− x Al x Y) n SLs, we considered a generalized random-element iso-displacement model. For short period SLs, the dependence of phonons on wavevectors both parallel and perpendicular to the growth direction [0 0 1] is investigated. An interesting variation in the phonon behavior found in the two systems is explained in terms of the differences in the anion masses and effective ionic-charges.

Polaron Crystallization and the Metal–Insulator Transition

The Crystallization of polarons at finite density, due to the long-range Coulomb forces — when no bipolarons can be formed — is discussed close to the metal–insulator transition (MIT). As a function of the density, the melting is examined at zero temperature. By calculating the quantum fluctuations of both the electron and the polarization, we show that at strong electron–phonon coupling the dissociation of the polarons at the MIT is favored, rather than the melting towards a polaron liquid. In this regime, we demonstrate, that an instability of the transverse vibrational modes of the polaron crystal occurs as the density increases. This provides a new physical mechanism for the MIT in polar materials, for which an experimental signature is predicted.

Electrostatic Contributions to the Binding Free Energy of the λcI Repressor to DNA

A model based on the nonlinear Poisson-Boltzmann (NLPB) equation is used to study the electrostatic contribution to the binding free energy of the λcI repressor to its operator DNA. In particular, we use the Poisson-Boltzmann model to calculate the pK a shift of individual ionizable amino acids upon binding. We find that three residues on each monomer, Glu 34, Glu 83, and the amino terminus, have significant changes in their pK a and titrate between pH 4 and 9. This information is then used to calculate the pH dependence of the binding free energy. We find that the calculated pH dependence of binding accurately reproduces the available experimental data over a range of physiological pH values. The NLPB equation is then used to develop an overall picture of the electrostatics of the λcI repressor–operator interaction. We find that long-range Coulombic forces associated with the highly charged nucleic acid provide a strong driving force for the interaction of the protein with the DNA. These favorable electrostatic interactions are opposed, however, by unfavorable changes in the solvation of both the protein and the DNA upon binding. Specifically, the formation of a protein-DNA complex removes both charged and polar groups at the binding interface from solvent while it displaces salt from around the nucleic acid. As a result, the electrostatic contribution to the λcI repressor–operator interaction opposes binding by ∼73 kcal/mol at physiological salt concentrations and neutral pH. A variety of entropic terms also oppose binding. The major force driving the binding process appears to be release of interfacial water from the protein and DNA surfaces upon complexation and, possibly, enhanced packing interactions between the protein and DNA in the interface. When the various nonelectrostatic terms are described with simple models that have been applied previously to other binding processes, a general picture of protein/DNA association emerges in which binding is driven by the nonpolar interactions, whereas specificity results from electrostatic interactions that weaken binding but are necessary components of any protein/DNA complex.

Direct photon–phonon coupling at (001) surfaces of zinc-blende structure crystals

The loss of translational symmetry at solid surfaces relaxes the momentum conservation constraints in photon–phonon coupling processes. We study this coupling at polar crystal surfaces and its manifestation in far-infrared reflection anisotropy spectra (RAS). We apply the Keating valence force potential to describe short-range mechanical interactions together with long-range Coulomb forces and radiation fields, and we solve analytically the ensuing system of coupled equations for the electromagnetic field and the lattice vibrations. We calculate the far-infrared normal reflectance spectra of (001) surfaces of semi-infinite zinc-blende crystals. They display a resonance structure associated with the excitation of surface and bulk phonon modes which might be observed with far-infrared RAS.

Dispersion of optical and acoustical phonons in the zinc-blende group III-nitride superlattices

A comprehensive theoretical study of phonons in cubic GaN, AlN, Ga1−xAlxN, and (GaN)m/(AlN)n superlattices (SLs) is reported using both simple and microscopic models. The new periodicity introduced by the SL structure causes zone folding of the acoustical modes allowing phonons with large q vectors, normally inactive in light scattering, to become Raman active. We predicted the frequencies of such modes in GaN/AlN SLs using elastic continuum, diatomic linear-chain, and rigid-ion models. In the rigid-ion model (RIM), the short range forces are optimized in terms of elastic constants and phonon energies at critical points while the long-range Coulomb forces are evaluated exactly via Ewald summation. The advantage of using RIM is that it permits the construction of a dynamical matrix entering into the secular equation for the SL vibrations of a given wavevector directly from the dynamical matrices of the bulk materials. For short period (GaN)m/(AlN)n SLs, the dependence of phonons on wavevectors both parallel and perpendicular to the growth direction [001] is investigated. Theoretical results for the GaN/AlN superlattices are compared and discussed with the GaAs/AlAs system as well as with the existing model calculation of Grille and Bechstedt. Unlike GaAs/AlAs, the larger optical phonon values and partially changed confinement characteristics in GaN/AlN superlattices are believed to have significant affects on the relaxation properties of electrons in group III-nitride material systems.

Grain size effect on ferroelectric phase transition in Pb1 − xBaxTiO3 ceramics

Micro-Raman scattering measurements in the frequency range of 5–1000 cm −1 as well as X-ray diffraction have been carried out on nanocrystalline Pb 1 − x Ba x TiO 3 system. A grain size and Ba ion-induced phase transition from the tetragonal ferroelectric phase of PbTiO 3 to the cubic paraelectric phase of BaTiO 3 is found to occur at x~0.7 and it is associated with the “softening” of the mode at 74 cm −1 ( x = O) which arises from a delicate balance between long-range Coulomb forces and short-range repulsion. A lowest frequency phonon mode at 10 cm −1 is detected and its grain size, Ba composition and temperature dependence appears to be correlated with structures for ABO 3 oxides. The temperature dependence of Raman phonon modes for Pb 0.66Ba 0.4TiO 3 with grain size of 60 nm reveals a temperature-induced soft mode phase transition occurring at 360K.

Semiclassical S-matrix theory for atomic fragmentation

A semiclassical scattering approach is developed which can handle long-range (Coulomb) forces without the knowledge of the asymptotic wave function for multiple charged fragments in the continuum. The classical cross section for potential and inelastic scattering including fragmentation (ionization) is derived from first principles in a form which allows for a simple extension to semiclassical scattering amplitudes as a sum over classical orbits and their associated actions. The object of primary importance is the classical deflection function which can show regular and chaotic behavior. Applications to electron impact ionization of hydrogen and electron–atom scattering in general are discussed in a reduced phase space, motivated by partial fixed points of the respective scattering systems. Special emphasis, also in connection with chaotic scattering, is put on threshold ionization. Finally, motivated by the reflection principle for molecules, a semiclassical hybrid approach is introduced for photoabsorption cross sections of atoms where the time-dependent propagator is approximated semiclassically in a short-time limit with the Baker–Hausdorff formula. Applications to one- and two-electron atoms are followed by a presentation of double photoionization of helium, treated in combination with the semiclassical S-matrix for scattering.

Classical molecular simulations of complex, industrially-important systems on the intel paragon

Advances in parallel supercomputing now make possible molecular-based engineering and science calculations that will soon revolutionize many technologies, such as those involving polymers and those involving aqueous electrolytes. We have developed a suite of message-passing codes for classical molecular simulation of these industrially-important systems on the Intel Paragon and summarize some of the results. Nonequilibrium, multiple time step molecular dynamics lets us investigate the rheology of molecular fluids. Chain molecule Monte Carlo simulations in the Gibbs ensemble permit calculation of phase equilibrium of long-chain molecular systems. Complementary equilibrium molecular dynamics yields fundamental insight into the technologically-important problem of liquid-liquid phase separation in polymer blends. Parallel codes for quaternion dynamics using techniques for handling long-range Coulombic forces allow study of ion pairing in supercritical aqueous electrolyte solutions.

Coulomb Interactions and Mesoscopic Effects in Carbon Nanotubes

We argue that long-range Coulomb forces convert an isolated (N,N) armchair carbon nanotube into a strongly-renormalized *Luttinger liquid*. At high temperatures, we find anomalous temperature dependences for the interaction and impurity contributions to the resistivity, and similar power-law dependences for the local tunneling density of states. At low temperatures, the nanotube exhibits spin-charge separation, visible as an extra energy scale in the discrete tunneling density of states (for which we give an analytic form), signaling a departure from the orthodox theory of Coulomb blockade.