Coulomb Terms Research Articles

Coulomb phase in high harmonic generation

We derive a regularized expression for the Coulomb term in the phase of high order harmonics emitted in the interaction of intense laser pulses with atoms. The calculation is based on the formalism of quantum orbits and on the imaginary time method and allows one to match the initially divergent Coulomb integral with the phases of the atomic wave function at the instants of ionization and recombination, leading to a finite and closed analytic formula. This complex-valued Coulomb phase can considerably modify both the yield and the interference structure of high harmonic spectra. Its possible implications for numerical calculations of the high harmonic signal are discussed.

Phase diagram and re-entrant fermionic entanglement in a hybrid Ising-Hubbard ladder.

The degree of fermionic entanglement is examined in an exactly solvable Ising-Hubbard ladder, which involves interacting electrons on the ladder's rungs described by Hubbard dimers at half-filling on each rung, accounting for intrarung hopping and Coulomb terms. The coupling between neighboring Hubbard dimers is assumed to have an Ising-like nature. The ground-state phase diagram consists of four distinct regions corresponding to the saturated paramagnetic, the classical antiferromagnetic, the quantum antiferromagnetic, and the mixed classical-quantum phase. We have exactly computed the fermionic concurrence, which measures the degree of quantum entanglement between the pair of electrons on the ladder rungs. The effects of the hopping amplitude, the Coulomb term, temperature, and magnetic fields on the fermionic entanglement are explored in detail. It is shown that the fermionic concurrence displays a re-entrant behavior when quantum entanglement is being generated at moderate temperatures above the classical saturated paramagnetic ground state.

Size-dependent disproportionation (in ~ 2–20 nm regime) and hybrid Bond Valence derived interatomic potentials for BaTaO2N

Interatomic potentials for complex materials (like ceramic systems) are important for realistic molecular dynamics (MD) simulations. Such simulations are relevant for understanding equilibrium, transport and dynamical properties of materials, especially in the nanoregime. Here we derive a hybrid interatomic potential (based on bond valence (BV) derived Morse and Coulomb terms), for modeling a complex ceramic, barium tantalum oxynitride (BaTaO2N). This material has been chosen due to its relevance for capacitive and photoactive applications. However, the material presents processing challenges such as the emergence of non-stoichiometric phases during processing, demonstrating complex processing–property correlations. This makes MD investigations of this material both scientifically and technologically relevant. The BV based hybrid potential presented here has been used for simulating sintering of BaTaO2N nanoparticles (~ 2–20 nm) under different conditions (using the relevant canonical ensemble). Notably, we show that sintering of particles of diameter 10 nm in size results in the formation of a cluster of tantalum and oxygen atoms at the interface of the BaTaO2N particles. This is in agreement with the experimental reports. The results presented here suggest that the potential proposed can be used to explore dynamical properties of BaTaO2N and related systems. This work will also open avenues for development of nanoscience-enabled aid-free sintering approaches to this and related materials.

Molecular dynamics simulations of the local structures and thermodynamic properties on molten alkali carbonate K2CO3

Molten carbonate salts have received particular attention for high-temperature thermal energy storage and heat transfer applications due to desirable thermal characteristics, such as wide operating temperature range, low causticity and excellent thermal stability. In this study, molecular dynamics (MD) simulations were performed on molten alkali carbonate K2CO3 based on an effective pair potential model, a Born-Mayer type combined with a Coulomb term. The radial distribution functions (RDF) and coordination number curves of the molten salt were characterized to explore the temperature dependences of macroscopic properties from microscopic view. The results suggest that the distance between K2CO3 particles is getting larger with temperature increasing, resulting in the increase of molar volume and the diminished ability of resistance to shear deformation and heat transfer by vibration between ions. Besides, it can be concluded that the structure of CO32− is inferred reasonably to be ortho-triangular pyramid from the comprehensive analysis of local structures including the angular distribution functions (ADF). Moreover, the thermodynamic properties were simulated in detail from 1200 to 1600 K including the density, thermal expansion coefficient, specific heat capacity, sheer viscosity, thermal conductivity and ion self-diffusion coefficient, which was hard to be measured from experiments under high-temperature extreme conditions. All the simulation results are in satisfactory agreement with available experimental data with high accuracy, and the minimum simulation error is as low as 1.42%.

Exploring the effect of important parameters on decomposition of gas hydrate structure I: A molecular dynamics simulation study

The aim of this study was to investigate the stability of methane hydrate in the NPT ensemble using MD simulation. Methane hydrate at 6 different cage occupancies ranging from 75 to 100% was placed arbitrarily in a cubic cell. Methane hydrate decomposition was explored at the equilibrium pressure for varied temperatures (T = 290, 300, and 310 K). The effect of cage occupancy of the hydrate structure – ranging from fully hydrate to empty small cage structures – on the hydrate stability and decomposition rate was examined. Simulation results showed that at constant temperatures, the decomposing process was accelerated at lower cage occupancy. Decomposition process increased the total energy of the system and enhanced the diffusion coefficient. When hydrate structure decomposed, the coulombic energy term was increase about 18% while LJ potential energy decreased about 33%. In stable hydrate crystal, diffusion coefficient of water oxygen in hydrate had an order of magnitude of 10−15 m2/s while in decomposed hydrate structure, the diffusion coefficient order of magnitude was changed to 10−9 m2/s. This changed the RDF curve of the system from solid to liquid-like structure by reducing the number of peaks versus distance. In addition, the value of coordination number of water-water molecules at a distance of 1 nm in the system during the decomposing process enhanced about 20% which confirmed changing the structure from solid state to liquid. Also, after dissociation of hydrate structure, the number of hydrogen bonding were decreased. Finally, results suggested that each of these parameters could be successfully applied to predict the decomposition of gas hydrate structure from ice-like stable phase to liquid-like structure.

The exact solution of a four-body Coulomb problem

The elastic collision between two H-like atoms utilizing an ab initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly, is studied thoroughly. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. The new SEM code [Ray, Pramana 83, 907 (2014)] in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude using partial wave analysis, is utilized to study the s-, p-, d-wave elastic phase shifts and the corresponding partial cross sections. An augmented-Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross sections. The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The systems studied are Ps–Ps, Ps–Mu, Ps–H, Ps–D, Ps–T, Mu–Mu, Mu–H, Mu–D, Mu–T, H–H, H–D, H–T, D–D, D–T, T–T. The SEM includes the non-adiabatic short-range effects due to exchange. The MSEM code [Ray, Pramana 83, 907 (2014)] is used to study the effect of the long-range van der Waals interaction due to induced dipole polarizabilities of the atoms in H(1s)–H(1s) elastic collision. The dependence of scattering length on the reduced mass of the system and the dependence of scattering length on the strength of long-range van der Waals interaction that varies with the minimum interatomic distance are observed.

Effective masses, lifetimes, and optical conductivity in Sr2RuO4 and Sr3Ru2O7 : Interplay of spin-orbit, crystal-field, and Coulomb tetragonal tensor interactions

By using the local-density approximation + dynamical mean-field theory approach, we study the low-energy electronic properties and the optical conductivity of the layered ruthenates ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ and ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$. We study the interplay of spin-orbit, crystal-field, and Coulomb interactions, including the tetragonal terms of the Coulomb tensor. We show that the spin-orbit interaction is multifaced; depending on the parameter regime, filling, and temperature, it can either enhance or reduce the effective strength of correlations. We compare the results based on the two common approximations for the screened Coulomb parameters, the constrained random-phase approximation (cRPA) and the constrained local-density approximation. We show that the experimental Drude peak is better reproduced by the cRPA parameters, hinting to relatively small mass renormalizations. We find that including the spin-orbit interaction is, however, important, for a realistic description. We show that Coulomb terms with tetragonal ${D}_{4h}$ symmetry have a strong effect on the mass-enhancement anisotropy, but they do not affect sizably the total spectral function or the in-plane conductivity.

Large-Scale Functional Group Symmetry-Adapted Perturbation Theory on Graphical Processing Units.

Symmetry-adapted perturbation theory (SAPT) is a valuable method for analyzing intermolecular interactions. The functional group SAPT partition (F-SAPT) has been introduced to provide additional insight into the origins of noncovalent interactions. Until now, SAPT analysis has been too costly for large ligand-protein complexes where it could provide key insights for chemical modifications that might improve ligand binding. In this paper, we present a large-scale implementation of a variant of F-SAPT. Two pragmatic choices are made from the outset to render the problem tractable: (1) Ab initio computation of dispersion and exchange-dispersion is replaced with Grimme's empirical dispersion correction. (2) Basis sets with augmented functions are avoided to allow for efficient integral screening. These choices allow the F-SAPT analysis to be written largely in terms of Coulomb and exchange matrix builds which have been implemented efficiently on graphical processing units (GPUs). Our formulation of F-SAPT is routinely applicable to molecules with well over 3000 atoms and 25,000 basis functions and is particularly optimized for the case where one monomer is significantly larger than the other. This is demonstrated explicitly with results from F-SAPT analysis of the full indinavir @ HIV-II protease complex (PDB ID 1HSG ) in a polarized double-ζ basis.

Dynamics of fragment formation in neutron-rich matter

Background: Neutron stars are astronomical systems with nucleons submitted to extreme conditions. Due to the longer range coulomb repulsion between protons, the system has structural inhomogeneities. Several interactions tailored to reproduce nuclear matter plus screened Coulomb term reproduce these inhomogeneities known as nuclear pasta. These structural inhomogeneities, located in the crust of neutron stars, can also arise in expanding systems depending on the thermodynamic conditions (temperature, proton fraction, ...) and the expansion velocity. Purpose: We aim to find the dynamics of the fragments formation for expanding systems simulated according to the little big bang model. This expansion resembles the evolution of neutron stars merger. Method: We study the dynamics of the nucleons with semiclassical molecular dynamics models. Starting with an equilibrium configuration, we expand the system homogeneously until we arrive to an asymptotic configuration (i. e. very low final densities). We study, with four different cluster recognition algorithms, the fragment distribution throughout this expansion and the dynamics of the cluster formation. Results: Studying the topology of the equilibrium states, before the expansion, we reproduced the known pasta phases plus a novel phase we called pregnocchi, consisting of proton aggregates embedded in a neutron sea. We have identified different fragmentation regimes, depending on the initial temperature and fragment velocity. In particular, for the already mentioned pregnocchi, a neutron cloud surrounds the clusters during the early stages of the expansion, resulting in systems that give rise to configurations compatibles with the emergence of r-proccess. Conclusions: These calculations pave the way to a comparision between Earth experiments and neutron star studies.

Isospin-symmetry breaking in masses of N ≃ Z nuclei

Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the N=Z line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton–neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the T=12 doublets and T=1 triplets, and TDEs for the T=1 triplets. Relative strengths of the obtained isospin-symmetry-breaking terms are not consistent with the differences in the NN scattering lengths, ann, app, and anp. Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections.

Confinement-driven electronic and topological phases in corundum-derived 3d -oxide honeycomb lattices

Using density functional theory calculations including an on-site Coulomb term, we explore electronic and possibly topologically nontrivial phases in $3d$ transition metal oxide honeycomb layers confined in the corundum structure ($\alpha$-Al$_2$O$_3$) along the [0001] direction. In most cases the ground state is a trivial antiferromagnetic Mott insulator, often with distinct orbital or spin states compared to the bulk phases. With imposed symmetry of the two sublattices the ferromagnetic phases of Ti, Mn, Co and Ni exhibit a characteristic set of four bands, two relatively flat and two with a Dirac crossing at K, associated with the single electron occupation of $e_{g}'$ (Ti) or $e_{g}$ (Mn, Co, Ni) orbitals. Our results indicate that the Dirac point can be tuned to the Fermi level using strain. Applying spin-orbit coupling (SOC) leads to a substantial anomalous Hall conductivity with values up to 0.94 $e^2/h$. Moreover, at $a_{Al_2O_3}$=4.81\AA\ we identify a particularly strong effect of SOC with out-of-plane easy axis for ($Ti_2$O$_3$)$_1$/(Al$_2$O$_3$)$_5$(0001) which stabilizes dynamically the system. Due to the unusually high orbital moment of -0.88$\mu_{\rm B}$ that nearly compensates the spin moment of 1.01$\mu_{\rm B}$, this system emerges as a candidate for the realization of the topological Haldane model of spinless fermions. Parallels to the perovskite analogs (La$X$O$_3$)$_2$/(LaAlO$_3$)$_4$(111) are discussed.

Scaled effective on-site Coulomb interaction in the DFT+ U method for correlated materials

The first-principles calculation of correlated materials within density functional theory remains challenging, but the inclusion of a Hubbard-type effective on-site Coulomb term $({U}_{\mathrm{eff}})$ often provides a computationally tractable and physically reasonable approach. However, the reported values of ${U}_{\mathrm{eff}}$ vary widely, even for the same ionic state and the same material. Since the final physical results can depend critically on the choice of parameter and the computational details, there is a need to have a consistent procedure to choose an appropriate one. We revisit this issue from constraint density functional theory, using the full-potential linearized augmented plane wave method. The calculated ${U}_{\mathrm{eff}}$ parameters for the prototypical transition-metal monoxides---MnO, FeO, CoO, and NiO---are found to depend significantly on the muffin-tin radius ${R}_{\mathrm{MT}}$, with variations of more than 2--3 eV as ${R}_{\mathrm{MT}}$ changes from 2.0 to 2.$7{a}_{B}$. Despite this large variation in ${U}_{\mathrm{eff}}$, the calculated valence bands differ only slightly. Moreover, we find an approximately linear relationship between ${U}_{\mathrm{eff}}({R}_{\mathrm{MT}})$ and the number of occupied localized electrons within the sphere, and give a simple scaling argument for ${U}_{\mathrm{eff}}$; these results provide a rationalization for the large variation in reported values. Although our results imply that ${U}_{\mathrm{eff}}$ values are not directly transferable among different calculation methods (or even the same one with different input parameters such as ${R}_{\mathrm{MT}})$, use of this scaling relationship should help simplify the choice of ${U}_{\mathrm{eff}}$.

Efficient Treatment of Local Meta-generalized Gradient Density Functionals via Auxiliary Density Expansion: The Density Fitting J + X Approximation.

We report an efficient technique to treat density functionals of the meta-generalized gradient approximation (mGGA) class in conjunction with density fitting of Coulomb terms (DF-J) and exchange-correlation terms (DF-X). While the kinetic energy density τ cannot be computed in the context of a DF-JX calculation, we show that the Laplacian of the density υ can be computed with almost no extra cost. With this technique, υ-form mGGAs become only slightly more expensive (10%-20%) than GGAs in DF-JX treatment-and several times faster than regular τ-based mGGA calculations with DF-J and regular treatment of the density functional. We investigate the translation of υ-form mGGAs into τ-form mGGAs by employing a kinetic energy functional but find this insufficiently reliable at this moment. However, υ and τ are believed to carry essentially equivalent information beyond ρ and ||∇ρ|| ( Phys. Rev. B 2007 , 75 , 155109 , DOI: 10.1103/PhysRevB.75.155109 ), so a reparametrization of accurate mGGAs from the τ-form into the υ-form should be possible. Once such functionals become available, we expect the presented technique to become a powerful tool in the computation of reaction paths, intermediates, and transition states of medium sized molecules.

The Mechanism of Erythrocytes Aggregation in EDTA-Blood of Ovarian Cancer Patients Viewed by Coulomb’s Law

The objective of this research is to assess the application of Coulomb’s law in complex systems. The observed erythrocyte interaction is erythrocytes in the EDTA-blood. The detection of the erythrocyte interaction uses a spectrophotometer with λ = 560 nm. The EDTA-blood in the cuvette is irradiated on the lower surface of the EDTA-blood. Data were analyzed using deterministic and stochastic approaches. Based on the data analysis, three deterministic and three stochastic parameters are obtained. The differences in the values of both deterministic and stochastic parameters of ovarian cancer and normal subject patients were analyzed using Mann-Whitney for non-normally distributed data, while normally distributed data were analyzed using t-test. The results of this calculation show that the parameters in both groups are not significantly different. The mechanism of absorbance pattern in terms of Coulomb’s law cannot distinguish the patterns of erythrocyte interactions as living cells with the complexity of EDTA-blood composition in both normal and ovarian cancer subjects.

Water dissociation at the Au/α-Fe2O3(0001) interface

The dissociative adsorption of water on a model catalyst formed by a Au5 cluster attached to the Fe-terminated (0001) surface of hematite (α-Fe2O3) was investigated within the density functional theory including an on-site Coulomb term (DFT + U). A flattened 2D-like structure was employed as supported gold particle. On clean hematite, the water molecule interacts with its O atom directly bound to a surface Fe ion. Conversely, in the most stable adsorption mode on Au5/hematite, it adsorbs in a multi-coordinated fashion at the metal-oxide interface and with one H atom oriented downward. Regarding the dissociative process, the isolated Au5 particle has a poor performance to activate one of the OH bonds (H2O → OH + H). However, when supported on hematite it becomes very active, having an activation barrier of only 0.09 eV. This process is even more favorable than on clean hematite. Thus, a very reactive site emerges at the metal-support interface. In this distinctive site, the water molecule is able to adsorb in a configuration (H-down) wherein one OH bond is strongly activated. An adsorbate-induced modification on the way that the flattened Au5 is anchored to the surface was observed, accompanied with changes in Au charges.

Hybrid grid/basis set discretizations of the Schrödinger equation.

We present a new kind of basis function for discretizing the Schrödinger equation in electronic structure calculations, called a gausslet, which has wavelet-like features but is composed of a sum of Gaussians. Gausslets are placed on a grid and combine advantages of both grid and basis set approaches. They are orthogonal, infinitely smooth, symmetric, polynomially complete, and with a high degree of locality. Because they are formed from Gaussians, they are easily combined with traditional atom-centered Gaussian bases. We also introduce diagonal approximations that dramatically reduce the computational scaling of two-electron Coulomb terms in the Hamiltonian.

Study of $$^{14}\hbox {C}$$ 14 C Cluster Decay Half-Lives of Heavy Deformed Nuclei

A theoretical model based on deformed Woods–Saxon, Coulomb and centrifugal terms are constructed to evaluate the half-lives for the cluster radioactivity of various super heavy nuclei. Deformation have been applied on all parts of their potential containing nuclear barrier for cluster decay. Also, both parent and daughter nuclei are considered to be deformed. The calculated results of $$^{14}\hbox {C}$$ cluster radioactivity half-lives are compared with available experimental data. A satisfactory agreement between theoretical and measured data is achieved. Also, obtained half-lives for each decay family is agreed with Geiger–Nuttall law.

Molecular dynamics simulations on the binary eutectic system Na2CO3-K2CO3

Molten carbonate salts as phase change materials have received particular attention for high-temperature thermal energy storage and heat transfer applications due to desirable thermal characteristics such as wide operating temperature range, low causticity and excellent thermal stability. In this study, molecular dynamics (MD) simulations were performed on the binary carbonate salt Na2CO3-K2CO3 (58-42 mol%) based on an effective pair potential model, a Born-Mayer type combined with a Coulomb term. The temperature dependences of thermodynamic properties including the density, sheer viscosity and thermal conductivity were simulated in detail from 1000 to 1400 K, which were all difficult to achieve from experiments on account of high-temperature extreme conditions. Moreover, the radial distribution functions (RDF) and coordination number curves of the binary carbonate salt were characterized to explore the mechanisms of their temperature dependences from microscopic view. The simulation results suggested that the changes of thermodynamic properties with temperature were induced by the distance changes between ions. Besides, it can be concluded that the high bond energy in the strong covalent bond C-O of molten carbonate salts must contribute to the large specific heat capacity in comparison with that of molten un-oxyacid salts.

The Elastic Collision of Two H-Like Atoms Including the Exotic Ps and Mu

The elastic collision between two H-like atoms utilizing an ab-initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly, is studied thoroughly. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. The new SEM code [1-5] in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude using partial wave analysis, is utilized to study the s-, p-, d- wave elastic phase shifts and the corresponding partial cross sections. An augmented-Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross sections. The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The systems studied are Ps-Ps, Ps-Mu, Ps-H, Ps-D, Ps-T, Mu-Mu, Mu-H, Mu-D, Mu-T, H-H, H-D, H-T, D-D, D-T, T-T. The SEM includes the non-adiabatic short-range effects due to exchange. The MSEM code [1] is used to study the effect of the long-range van der Waals interaction due to induced dipole polarizabilities of the atoms in H(1s)-H(1s) elastic collision. The dependence of scattering length on the reduced mass of the system and the dependence of scattering length on the strength of long-range van der Waals interaction that varies with the minimum interatomic distance are observed [3].

Molecular dynamics simulation of ZnO wurtzite phase under high and low pressures and temperatures

Isothermal and isobaric ensembles behaviours of ZnO wurtzite phase have been investigated, by parallel molecular dynamics method and using Buckingham potential, which contains long-range Coulomb, repulsive exponential, and attractive dispersion terms. To conduct our calculations, we have used dl_poly 4 software, under which the method is implemented. We have examined the influence of the temperature and pressure on molar volume in the ranges of 300–3000 K and 0–200 GPa. Isothermal-isobaric relationships, fluctuations, standard error, equilibrium time, molar volume and its variation versus time are predicted and analyzed. Our results are close to available experimental data and theoretical results.