Long-range Coulomb Potential Research Articles

Molecular dynamics of liquid-electrode interface by integrating Coulomb interaction into universal neural network potential.

Computational understanding of the liquid-electrode interface faces challenges in efficiently incorporating reactive force fields and electrostatic potentials within reasonable computational costs. Although universal neural network potentials (UNNPs), representing pretrained machine learning interatomic potentials, are emerging, current UNNP models lack explicit treatment of Coulomb potentials, and methods for integrating additional charges on the electrode remain to be established. We propose a method to analyze liquid-electrode interfaces by integrating a UNNP, known as the preferred potential, with Coulomb potentials using the ONIOM method. This approach extends the applicability of UNNPs to electrode-liquid interface systems. Through molecular dynamics simulations of graphene-water and graphene oxide (GO)-water interfaces, we demonstrate the effectiveness of our method. Our findings emphasize the necessity of incorporating long-range Coulomb potentials into the water potential to accurately describe water polarization at the interface. Furthermore, we observe that functional groups on the GO electrode influence both polarization and capacitance.

Electron scattering beyond the independent atom model: Quantum fluctuation of the Coulomb potential.

In the past century, electron scattering has mostly served as a powerful tool to measure the microscopic structure of gases, liquids, and solids in either a static or time-resolved manner. One common basis for these works is the independent atom model, which directly relates electron scattering signals to the atomic structure of matter. In this perspective, we explore the information content of electron scattering that goes beyond the independent atom model. We show that the small-angle limit of the electron scattering signal encodes the quantum mechanical fluctuation of the long-range Coulomb potential. This quantum fluctuation, described by the second moment of the dipole operator, is the root cause of the intermolecular van der Waals forces.

Construction of Multiscale Dissipative Particle Dynamics (DPD) Models from Other Coarse-Grained Models.

We present a general scheme for converting coarse-grained models into Dissipative Particle Dynamics (DPD) models. We build the corresponding DPD models by analogy with the de novo DPD coarse-graining scheme suggested by Groot and Warren (J. Chem. Phys., 1997). Electrostatic interactions between charged DPD particles are represented though the addition of a long-range Slater Coulomb potential as suggested by González-Melchor et al. (J. Chem. Phys., 2006). The construction is illustrated by converting MARTINI models for various proteins into a DPD representation, but it not restricted to the usual potential form in the MARTINI model-viz., Lennard-Jones potentials. We further extended the DPD scheme away from the typical use of homogeneous particle sizes, therefore faithfully representing the variations in the particle sizes seen in the underlying MARTINI model. The accuracy of the resulting construction of our generalized DPD models with respect to several structural observables has been benchmarked favorably against all-atom and MARTINI models for a selected set of peptides and proteins, and variations in the scales of the coarse-graining of the water solvent.

Efficient Hartree–Fock exchange algorithm with Coulomb range separation and long-range density fitting

Separating the Coulomb potential into short-range and long-range components enables the use of different electron repulsion integral algorithms for each component. The short-range part can be efficiently computed using the analytical algorithm due to the locality in both the Gaussian-type orbital basis and the short-range Coulomb potentials. The integrals for the long-range Coulomb potential can be approximated with the density fitting method. A very small auxiliary basis is sufficient for the density fitting method to accurately approximate the long-range integrals. This feature significantly reduces the computational efforts associated with the N4 scaling in density fitting algorithms. For large molecules, the range separation and long-range density fitting method outperforms the conventional analytical integral evaluation scheme employed in Hartree–Fock calculations and provides more than twice the overall performance. In addition, this method offers a higher accuracy compared to conventional density fitting methods. The error in the Hartree–Fock energy can be easily reduced to 0.1 μEh per atom or smaller.

Structure formation by electrostatic interactions in strongly coupled medium.

The formation of correlated structures is of importance in many diverse contexts such as strongly coupled plasmas, soft matter, and even biological mediums. In all these contexts the dynamics are mainly governed by electrostatic interactions and result in the formation of a variety of structures. In this study, the process of formation of structures is investigated with the help of molecular dynamics (MD) simulations in two and three dimensions. The overall medium has been modeled with an equal number of positive and negatively charged particles interacting via long-range pair Coulomb potential. A repulsive short-range Lennard-Jones (LJ) potential is added to take care of the blowing up of attractive Coulomb interaction between unlike charges. In the strongly coupled regime, a variety of classical bound states form. However, complete crystallization of the system, as typically observed in the context of one-component strongly coupled plasmas, does not occur. The influence of localized perturbation in the system has also been studied. The formation of a crystalline pattern of shielding clouds around this disturbance is observed. The spatial properties of the shielding structure have been analyzed using the radial distribution function and Voronoi diagram. The process of accumulation of oppositely charged particles around the disturbance triggers a lot of dynamic activity in the bulk of the medium. As a result of this, close encounters are possible even between those particles/clusters which were initially and/or at some point of time widely separated. This leads to the formation of a larger number of bigger clusters. There are, however, also instances when bound pairs break up and the electrons from bound pairs contribute to the shielding cloud, whereas ions bounce back into the bulk. A detailed discussion of these features has been provided in the manuscript.

Superconductivity from electronic interactions and spin-orbit enhancement in bilayer and trilayer graphene

What drives superconductivity in non-moir\'e graphene? Here, an electron-electron mechanism is applied to the continuum framework of Bernal bilayer and rhombohedral trilayer graphene. Within a Kohn-Luttinger-like approach, the internal screening of the long-range Coulomb potential leads to an effective attraction between carriers, enabling the formation of Cooper pairs. The calculations provide a filling-dependent critical temperature that is remarkably enhanced due to Ising spin-orbit coupling, and determine the spin-triplet valley-singlet symmetry of the superconducting order parameter, in line with recent experimental advances.

Coherent-control phase lag across doubly excited atomic strontium resonances in an ω−2ω interference scheme

Accurate calculations of phase lag associated with coherent control where an excited system decays into more than one product channel have recently been reported for atomic barium in Wang and Greene [Y. Wang and C. H. Greene, Phys. Rev. A 105, 013113 (2022)]. The present study extends the calculations to make predictions of that observable for another alkaline-earth-metal atom, strontium, with a discussion of its spectrum and phase lag for energies between the ${\mathrm{Sr}}^{+}\phantom{\rule{4pt}{0ex}}4{d}_{3/2}$ and $4{d}_{5/2}$ thresholds. We explore the physics influenced by the electron correlations of strontium and the long-range Coulomb potential. The behavior of the phase lag cannot be simply addressed by a time-delay analysis, although the latter is often used to address the prominent channel of resonance decay of doubly excited states.

Electron attachment to interstellar grains

ABSTRACT We have performed quantum mechanical calculations of cross-sections and rate coefficients for electron attachment to small, neutral, and positively charged grains. In addition to the polarization potential and – for charged grains – the Coulomb potential, we considered the influence of the interaction between the charge of the electron and a possible permanent electric dipole on the grain. We found large discrepancies between the predictions of classical and quantal models of electron scattering on neutral grains at low energies (temperatures) in the absence of a permanent dipole moment, but much closer agreement when a dipole moment was present. The presence of the long-range Coulomb potential also leads to better agreement between classical and quantal models.

Bound states in the continuum (BIC) protected by self-sustained potential barriers in a flat band system

In this work, we investigate the bound states in the continuum (BIC) of a one-dimensional spin-1 flat band system. It is found that, when the potential is sufficiently strong, there exists an effective attractive potential well surrounded by infinitely high self-sustained barriers. Consequently, there exist some BIC in the effective potential well. These bound states are protected by the infinitely high potential barriers, which could not decay into the continuum. Taking a long-ranged Coulomb potential and a short-ranged exponential potential as two examples, the bound state energies are obtained. For a Coulomb potential, there exists a series of critical potential strengths, near which the bound state energy can go to infinity. For a sufficiently strong exponential potential, there exist two different bound states with a same number of wave function nodes. The existence of BIC protected by the self-sustained potential barriers is quite a universal phenomenon in the flat band system under a strong potential. A necessary condition for the existence of BIC is that the maximum of potential is larger than two times band gap.

Movement behavior of residual oil droplets and CO2: insights from molecular dynamics simulations

After primary and secondary recovery of tight reservoirs, it becomes increasingly challenging to recover the remaining oil. Therefore, improving the recovery of the remaining oil is of great importance. Herein, molecular dynamics simulation (MD) of residual oil droplet movement behavior under CO2 displacement was conducted in a silica nanopores model. In this research, the movement behavior of CO2 in contact with residual oil droplets under different temperatures was analyzed, and the distribution of molecules number of CO2 and residual oil droplets was investigated. Then, the changes in pressure, kinetic energy, potential energy, van der Waals' force, Coulomb energy, long-range Coulomb potential, bond energy, and angular energy with time in the system after the contact between CO2 and residual oil droplets were studied. At last, the g(r) distribution of CO2–CO2, CO2-oil molecules, and oil molecules-oil molecules at different temperatures was deliberated. According to the results, the diffusion of CO2 can destroy residual oil droplets formed by the n-nonane and simultaneously peel off the n-nonane molecules that attach to SiO2 and graphene nanosheets (GN). The cutoff radius r of the CO2–CO2 is approximately 0.255 nm and that of the C–CO2 is 0.285 nm. The atomic force between CO2 and CO2 is relatively stronger. There is little effect caused by changing temperature on the radius where the maximum peak occurs in the radial distribution function (RDF)-g(r) of CO2–CO2 and C–CO2. The maximum peak of g(r) distribution of the CO2–CO2 in the system declines first and then rises with increasing temperature, while that of g(r) distribution of C–CO2 changes in the opposite way. At different temperatures, after the peak of g(r), its curve decreases with the increase in radius. The coordination number around C9H20 decreases, and the distribution of C9H20 becomes loose.

Probing tunneling dynamics of dissociative H2 molecules using two-color bicircularly polarized fields

Probing and manipulating the electronic motion in the ultrafast laser molecular interaction provides the pathways for quantum imaging and controlling chemical reactions. Recently, the emerging application of attosecond metrology of ultrafast electron dynamics has accessed the time scale of the most fundamental processes in molecular chemical reactions. Here, we probe the tunneling dynamics of internuclear-dependent dissociative reaction of ${\mathrm{H}}_{2}$ with angular streaking using two-color bicircularly polarized femtosecond laser pulses. By measuring high-resolution photoelectron spectroscopy, we disentangle the orientation and internuclear-distance dependent effect of the long-range Coulomb potential and the initial phase on molecular-frame photoelectron momentum distributions, and stereo extract the phase gradient of the tunneling electron wave packets and Wigner time delay during the dissociative ionization using two-color bicircular fields. The work has an insight into the clocking of ultrafast spatiotemporal photoelectron dynamics and the quantum control of molecular chemical processes via sculptured circular fields, which can be applied to polyatomic molecules.

Compound-tunable embedding potential method and its application to calcium niobate crystal CaNb2O6 with point defects containing tantalum and uranium

The compound-tunable embedding potential (CTEP) method developed for simulating the influence of environment on a fragment in the ionic-covalent crystal is presented in the form of a linear combination of particular short-range semilocal pseudopotentials for the atoms of nearest environment and the long-range Coulomb potentials from optimized fractional point charges centered on both nearest and more distant atoms of the environment. A pilot application of the CTEP method to calcium niobate crystal, ${\mathrm{CaNb}}_{2}{\mathrm{O}}_{6}$, is performed. A very good agreement of the electronic density and interatomic distances within the relaxed fragment with those of the original periodic crystal calculation is attained. Calcium niobate crystal can be considered as an idealized fersmite $({\mathrm{CaNb}}_{2\ensuremath{-}x}{\mathrm{Ta}}_{x}{\mathrm{O}}_{6},x\ensuremath{\approx}0.3)$ mineral when neglecting the contributions of the impurities with smaller molar fractions, and substitution $\mathrm{Nb}\ensuremath{\rightarrow}\mathrm{Ta}$ is considered here as a point Ta defect in ${\mathrm{CaNb}}_{2}{\mathrm{O}}_{6}$. Besides, uranium-containing point defects are also studied since the euxenite group minerals, to which fersmite belongs, are considered as prospective matrices for long-term immobilization of high-level waste. The chemical shifts of ${K}_{{\ensuremath{\alpha}}_{1,2}}$ and ${K}_{{\ensuremath{\beta}}_{1,2}}$ lines of x-ray emission (fluorescence) spectra in niobium are evaluated to analyze its chemical state in the crystal. Potential of CTEP for studying properties of point defects containing $f$ and heavy $d$ elements with relativistic effects, extended basis set, and broken crystal symmetry taken into account is discussed.

Universal time delays in the inelastic core level photoemission of metals

Proposing a theoretical model of the core level photoemission of metals, we investigate the plasmon-driven inelastic photoemission delays based on a nonperturbative treatment of many-electron responses due to the long-range Coulomb potential. Being irrelevant to the plasmon coupling strength as well as the plasmon frequency, the emission delays $\mathrm{\ensuremath{\Delta}}{\ensuremath{\tau}}_{n}$ of the $n\mathrm{th}$-order plasmon satellites ($n=1,2,3,...$) are found to be universal order by order among the metals in the core level photoemission where the recoil-less approximation would be valid. In particular, for a main line with its weight ${e}^{\ensuremath{-}\ensuremath{\gamma}}$, where $\ensuremath{\gamma}$ quantifies the plasmon coupling strength, the average inelastic photoemission delay $\ensuremath{\langle}\mathrm{\ensuremath{\Delta}}\ensuremath{\tau}\ensuremath{\rangle}$ is found to be $\ensuremath{\gamma}{(1\ensuremath{-}{e}^{\ensuremath{-}\ensuremath{\gamma}})}^{\ensuremath{-}1}\mathrm{\ensuremath{\Delta}}{\ensuremath{\tau}}_{1}$ and thus is simply scaled by a universal time delay $\mathrm{\ensuremath{\Delta}}{\ensuremath{\tau}}_{1}$. This finding is sharply contrasted with the emission delays under the localized potential, which indicates a fundamental difference in the emission process between extended and localized screenings.

Jost matrices for some analytically solvable potential models

A family of analytically solvable potential models for the one- and two-channel problems is considered within the Jost matrix approach. The potentials are chosen to be constant in the interior region and to have different asymptotic behavior (tails) at large distances. The migration of the $S$-matrix poles on the Riemann surface of the energy, caused by variations of the potential strength, is studied. It is demonstrated that the long-range ($\ensuremath{\sim}1/{r}^{2}$) tails and Coulomb potential ($\ensuremath{\sim}1/r$) cause an unusual behavior of the $S$-matrix poles. It is found that in the two-channel problem with the long-range potentials the $S$-matrix poles may appear at complex energies on the physical Riemann sheet. The Coulomb tail not only changes the topology of the Riemann surface, but also breaks down the so-called mirror symmetry of the poles in both the single-channel and the two-channel problems.

Ultrafast electron cooling in an expanding ultracold plasma

Plasma dynamics critically depends on density and temperature, thus well-controlled experimental realizations are essential benchmarks for theoretical models. The formation of an ultracold plasma can be triggered by ionizing a tunable number of atoms in a micrometer-sized volume of a 87Rb Bose-Einstein condensate (BEC) by a single femtosecond laser pulse. The large density combined with the low temperature of the BEC give rise to an initially strongly coupled plasma in a so far unexplored regime bridging ultracold neutral plasma and ionized nanoclusters. Here, we report on ultrafast cooling of electrons, trapped on orbital trajectories in the long-range Coulomb potential of the dense ionic core, with a cooling rate of 400 K ps−1. Furthermore, our experimental setup grants direct access to the electron temperature that relaxes from 5250 K to below 10 K in less than 500 ns.

Orbital rotations induced by charges of polarons and defects in doped vanadates

We explore the competiton of doped holes and defects that leads to the loss of orbital order in vanadate perovskites. In compounds such as La$_{1-{\sf x}}$Ca$_{\,\sf x}$VO$_3$ spin and orbital order result from super-exchange interactions described by an extended three-orbital degenerate Hubbard-Hund model for the vanadium $t_{2g}$ electrons. Long-range Coulomb potentials of charged Ca$^{2+}$ defects and $e$-$e$ interactions control the emergence of defect states inside the Mott gap. The quadrupolar components of the Coulomb fields of doped holes induce anisotropic orbital rotations of degenerate orbitals. These rotations modify the spin-orbital polaron clouds and compete with orbital rotations induced by defects. Both mechanisms lead to a mixing of orbitals, and cause the suppression of the asymmetry of kinetic energy in the $C$-type magnetic phase. We find that the gradual decline of orbital order with doping, a characteristic feature of the vanadates, however, has its origin not predominantly in the charge carriers, but in the off-diagonal couplings of orbital rotations induced by the charges of the doped ions.

Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure of Fourth Order

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The fourth order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second and third order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Differentiative Study of Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure of Third and Fourth Order

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The second order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Dependence of Surface Tension of a Droplet Formed on the Molecular Condensation Nucleus or Ion on the Droplet Radius

Abstract—The dependence of the thermodynamic surface tension of a small droplet formed on a molecular-size condensation nucleus on the droplet size, nucleus size, molecular field parameters, and nuclear charge in the case of an ion is investigated. Calculations have been performed for molecules of supersaturated argon vapor at different values of the chemical potential of the molecules in the framework of the gradient density functional theory (DFT) and the Carnahan–Starling model to take into account the contribution of hard spheres. The interaction of argon molecules with an uncharged condensation nucleus has been described by the Lennard–Jones potential. In the case of an ion, the long-range Coulomb potential of electric forces is additionally taken into account. The dielectric constant is defined as a function of the local density of the number of argon molecules. As a variable describing the size of the droplet, the radius of the equimolecular surface of the droplet is chosen. The obtained dependences of the surface tension of the droplets have been compared with the dependence of the surface tension on the size of droplet without a condensation nucleus. When the effect of the solvation layer is discarded, the dependence of the surface tension on the radius of the equimolecular surface of a small droplet with a condensation nucleus exhibits similar behavior as in the absence of the nucleus with almost the same negative Tolman correction. The effect of the rigidity constant, however, is clearly influenced by the existence of a condensation nucleus. It is shown that when the first solvation layer is divided around the condensation nucleus, the dependence of surface tension on the radius of the equimolecular surface of a small droplet with a condensation nucleus exhibits similar behavior with almost the same negative Tolman correction as in the absence of a nucleus, but with a different correction, namely, with effective rigidity constant for the surface layer.

Effect of Projectile Charge State on Electron Emission Spectra from He Atom

The single ionization of He atom by the impact of highly charged dressed projectile nucleus is investigated by applying the three-body formalism of three-Coulomb wave (3CW) model and the first Born approximation (FBA). In the 3CW formalism, the interaction between the dressed projectile and the active electron is represented by a model potential containing both the long-range and short-range part of the Coulomb potential. The target is treated as a one-electron atom, where the interaction of the active electron with the rest of the target is represented by a similar type of model potential. The correlated motion of each pair of particles, interacting through long-range Coulomb potential, is taken into account in the final state. In addition, an independent particle model and a single-zeta Roothaan-Hartree-Fock 1s wavefunction, describing helium in its ground state, is used to carry out the calculations, where the effective charge of the target nuclei is obtained from the initial orbital energy. The energy distributions of the double-differential cross sections (DDCS) at low and intermediate energy electron emission from helium atom have been investigated. Our theoretical results are compared with both the available experimental measurements and theoretical calculations using other methods. There is good overall agreement of the present calculations with experimental data except for low-energy electron emission (less than 10 eV). For target ionization by a dressed projectile, we find that the cross sections depend on the projectile charge. For distant collisions involving high energy ions, the primary effect of bound projectile electrons is to screen the projectile nuclear charge, thereby reducing the strength of the interaction potential. Finally, the energy distribution of DDCS ratio at different angles has also been studied.