Long-range Terms Research Articles

Low temperature dynamics of H + HeH+→ H2+ + He reaction: On the importance of long-range interaction.

While the growing realization of the importance of long-range interactions is being demonstrated in cold and ultracold bimolecular collision experiments, their influence on one of the most critical ion-neutral reactions has been overlooked. Here, we address the non-Langevin abrupt decrease observed earlier in the low-energy integral cross-sections and rate coefficients of the astrochemically important H + HeH+→ H2+ + He reaction. We attribute this to the presence of artificial barriers on existing potential energy surfaces (PESs). By incorporating precise long-range interaction terms, we introduce a new refined barrierless PES for the electronic ground state of HeH2+ reactive system, aligning closely with high-level abinitio electronic energies. Our findings, supported by various classical, quantum, and statistical methods, underscore the significance of long-range terms in accurately modeling reactive PESs. The low-temperature rate coefficient on this new PES shows a substantial enhancement as compared to the previous results and aligns with the Langevin behavior. This enhancement could noticeably affect the prediction of HeH+ abundance in early Universe condition.

Collision rate coefficients for C7N− and C10H− with H2

ABSTRACT The anions C$_7$N$^-$ and C$_{10}$H$^-$ are the two longest of the linear (C,N)-bearing and (C,H)-bearing chains that have so far been detected in the interstellar medium (ISM). In order to glean information on their collision-induced rotational state-changing processes, we analyse the general features of new ab initio potentials describing the interaction of both linear anions with H$_2$, one of the most abundant partners in their ISM environment. We employ an artificial neural network fit of the reduced-dimensionality potential energy surface for C$_7$N$^-$...H$_2$ interaction and discuss in detail the spatial features in terms of multipolar radial coefficients. For the C$_{10}$H$^-$...H$_2$ interaction, we use the initial grid of two-dimensional raw points to generate by quadrature the Legendre expansion directly, further including the long-range terms as discussed in the main text. Quantum scattering calculations are employed to obtain rotationally inelastic cross-sections, for collision energies in the range of 10$^{-4}$ to 400 cm$^{-1}$. From them we generate the corresponding inelastic rate coefficients as a function of temperature covering the range from 10 to 50 K. The results for the rate coefficients for the longest cyanopolyyne are compared with the earlier results obtained for the smaller terms of the same series, also in collision with H$_2$. We obtain that the inelastic rate coefficients for the long linear anions are all fairly large compared with the earlier systems. The consequences of such findings on their non-equilibrium rotational populations in interstellar environments are illustrated in our conclusions.

Topological phase transitions in the non-Hermitian SSH model with long-range hopping terms induced by gains and losses

The latest progress in the one-dimensional chain SSH model provide the basic understanding of non-Hermitian topological phases. By periodically introducing the gains and losses of imaginary potential ig,-ig,-ig,ig with anti-PT symmetry, we have investigated the topological property of non-Hermitian SSH model with long-range hopping terms. We find that the gains and losses of imaginary potential causes the model to exhibit non-Hermiticity, and the non-Hermiticity induces system to undergo topological phase transitions from topologically trivial phase with non-Hermitian winding number 0 to topologically nontrivial phase with non-Hermitian winding number 1 and −1. The introduction of gains and losses greatly broadens the topological non-trivial region and play a non-trivial role in the model. We fully characterize the topological phase transitions by the band gap closing-reopening, the non-Hermitian winding numbers v and the hidden Chern number C.

Wave-Function Tomography of Topological Dimer Chains with Long-Range Couplings.

The ability to tailor with a high accuracy the intersite connectivity in a lattice is a crucial tool for realizing novel topological phases of matter. Here, we report the experimental realization of photonic dimer chains with long-range hopping terms of arbitrary strength and phase, providing a rich generalization of the Su-Schrieffer-Heeger model which, in its conventional form, is limited to nearest-neighbor couplings only. Our experiment is based on a synthetic dimension scheme involving the frequency modes of an optical fiber loop platform. This setup provides direct access to both the band dispersion and the geometry of the Bloch wave functions throughout the entire Brillouin zone allowing us to extract the winding number for any possible configuration. Finally, we highlight a topological phase transition solely driven by a time-reversal-breaking synthetic gauge field associated with the phase of the long-range hopping, providing a route for engineering topological bands in photonic lattices belonging to the AIII symmetry class.

Long-Range Effects in Topologically Defective Arm-Chair Graphene Nanoribbons.

The electronic structure of 7/9-AGNR superlattices with up to eight unit cells has been studied by means of state-of-the-art Density Functional Theory (DFT) and also by two model Hamiltonians, the first one including only local interactions (Hubbard model, Hu) while the second one is extended to allow long-range Coulomb interactions (Pariser, Parr and Pople model, PPP). Both are solved within mean field approximation. At this approximation level, our calculations show that 7/9 interfaces are better described by spin non-polarized solutions than by spin-polarized wavefunctions. Consequently, both Hu and PPP Hamiltonians lead to electronic structures characterized by a gap at the Fermi level that diminishes as the size of the system increases. DFT results show similar trends although a detailed analysis of the density of states around the Fermi level shows quantitative differences with both Hu and PPP models. Before improving model Hamiltonians, we interpret the electronic structure obtained by DFT in terms of bands of topological states: topological states localized at the system edges and extended bulk topological states that interact between them due to the long-range Coulomb terms of Hamiltonian. After careful analysis of the interaction among topological states, we find that the discrepancy between ab initio and model Hamiltonians can be resolved considering a screened long-range interaction that is implemented by adding an exponential cutoff to the interaction term of the PPP model. In this way, an adjusted cutoff distance λ=2 allows a good recovery of DFT results. In view of this, we conclude that the correct description of the density of states around the Fermi level (Dirac point) needs the inclusion of long-range interactions well beyond the Hubbard model but not completely unscreened as is the case for the PPP model.

Topological semimetal phase in non-Hermitian Su–Schrieffer–Heeger model

We explore the non-Hermitian Su–Schrieffer–Heeger model with long-range hopping and off-diagonal disorders. In the non-Hermitian clean limit, we find that the phase diagram holds topological semimetal phase with exceptional points except the normal insulator phase and the topological insulator phase. Interestingly, it is found that the topological semimetal phase is induced by long-range nonreciprocal term when the long-range hopping is not equal to the intercell hopping. Especially, we show the existence of topological semimetal phase with exceptional points and determine the transition point analytically and numerically under the Hermitian clean limit when the long-range hopping is equal to the intercell hopping. Furthermore, we also investigate the effects of the disorders on topological semimetal phase, and show that the disorders can enhance the region of topological semimetal phase in contrast to the case of non-Hermitian clean limit, indicating that it is beneficial to topological semimetal phase whether there is one disorder or two disorders in the system, that is, the topological semimetal phase is stable against the disorders in this one-dimensional non-Hermitian system. Our work provides an alternative avenue for studying topological semimetal phase in non-Hermitian lattice systems.

The Interplay between Protein Frustration and Hotspot Formation

Hotspots situated at protein-protein interfaces, allosteric and orthosteric binding sites, traditionally play a crucial role in the initial phases of drug discovery, as they are useful to identify druggable targets and guide the optimization of fragments into lead compounds. Despite the high level of protein frustration, which can be thought of as the percentage of residues that cannot independently achieve minimum energy due to tridimensional restraints, observed at those locations, limited efforts have been made to investigate any potential connection between the localized frustration and hotspots in proteins. This review paper aims to partially address this knowledge gap by proposing that the origin of hotspots is, at least in part, due to localized frustration in proteins. While there is no hard evidence to support this hypothesis, the results obtained by integrating in silico tools predicting hot spot locations, with those calculating localized protein frustration, suggest that druggable hotspots are surrounded by residues involved in frustrated contacts. Additionally, the inclusion of long-range electrostatic terms in the protein frustration calculation enables the identification of an equal to a higher number of frustrated residues. These observations indirectly suggest that localized protein frustration around druggable hotspots could guide the development of more potent leads.

High-accuracy DMBE potential energy surface for CNO(A''4) and the rate coefficients for the C + NO reaction in the A'2, A''2, and A''4 states.

An accurate potential energy surface (PES) for the lowest lying A''4 state of the CNO system is presented based on explicitly correlated multi-reference configuration interaction calculations with quadruple zeta basis set (MRCI-F12/cc-pVQZ-F12). The abinitio energies are fitted using the double many-body expansion method, thus incorporating long-range energy terms that can accurately describe the electrostatic and dispersion interactions with physically motivated decaying functions. Together with the previously fitted lowest A'2 and A''2 states using the same theoretical framework, this constitutes a new set of PESs that are suitable to predict rate coefficients for all atom-diatom reactions of the CNO system. We use this set of PESs to calculate thermal rate coefficients for the C(P3) + NO(Π2) reaction and compare the temperature dependence and product branching ratios with experimental results. The comparison between theory and experiment is shown to be improved over previous theoretical studies. We highlight the importance of the long-range interactions for low-temperature rate coefficients.

Quantum geometric tensor and the topological characterization of the extended Su–Schrieffer–Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su–Schrieffer–Heeger (SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss–Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. However, some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric, which leads to ill-defined non-integer topological Euler numbers. Nevertheless, the non-integer “Euler number” provides valuable insights and an upper bound for the absolute values of the Chern numbers.

Dual-band higher-order topological states and four-wave mixing in plasmonic valley-Hall metasurfaces

Higher-order topological states in plasmonic metasurfaces are of great importance in practice for their tight confinements and high field enhancements, providing many promising nonlinear applications such as robust quantum light source through four-wave mixing (FWM). However, previous works are limited to single-band modes and FWM processes based on second-order topological corner states have still not been revealed. In this work, we propose a plasmonic valley-Hall topological metasurface, which is modelled based on coupled dipole approximation with dyadic Green's functions containing retarded long-range interaction terms. Simultaneous lifting of Dirac degeneracies in two bandgaps due to inversion-symmetry breaking results in dual-band second-order topological states, which are robust against structural disorder. We present a theoretical approach for considering the nonlinear interaction in dipole arrays and numerically show nonlinear generation of corner mode at signal frequency via the FWM process by pumping with edge modes. The results presented in this work will pave a broad way towards the wide applications of topological plasmonic metasurfaces.

Robust light bullets in Rydberg gases with moiré lattice

Rydberg electromagnetically-induced transparency has been widely studied as a medium supporting light propagation under the action of nonlocal nonlinearities. Recently, optical potentials based on moiré lattices (MLs) were introduced for exploring unconventional physical states. Here, we predict a possibility of creating fully three-dimensional (3D) light bullets (LBs) in cold Rydberg gases under the action of ML potentials. The nonlinearity includes local self-defocusing and long-range focusing terms, the latter one induced by the Rydberg-Rydberg interaction. We produce zero-vorticity LB families of the fundamental, dipole, and quadrupole types, as well as vortex LBs. They all are gap solitons populating finite bandgaps of the underlying ML spectrum. Stable subfamilies are identified utilizing the combination of the anti-Vakhitov-Kolokolov criterion, computation of eigenvalues for small perturbations, and direct simulations.

Uniform bound on the number of partitions for optimal configurations of the Ohta–Kawasaki energy in 3D

AbstractWe study a 3D ternary system which combines an interface energy with a long-range interaction term. Several such systems were derived as a sharp-interface limit of the Nakazawa–Ohta density functional theory of triblock copolymers. Both the binary case in 2D and 3D, and the ternary case in 2D, are quite well understood, whereas very little is known about the ternary case in 3D. In particular, it is even unclear whether minimizers are made of finitely many components. In this paper, we provide a positive answer to this, by proving that the number of components in a minimizer is bounded from above by a computable quantity depending only on the total masses and the interaction coefficients. There are two key difficulties, namely, the impossibility to decouple the long-range interaction from the perimeter term, and the absence of a quantitative isoperimetric inequality with two mass constraints in 3D. Therefore, the actual shape of minimizers is unknown, even for small masses, making the construction of suitable competing configurations significantly more delicate.

Modeling Concentration-dependent Phase Separation Processes Involving Peptides and RNA via Residue-Based Coarse-Graining.

Biomolecular condensation, especially liquid-liquid phase separation, is an important physical process with relevance for a number of different aspects of biological functions. Key questions of what drives such condensation, especially in terms of molecular composition, can be addressed via computer simulations, but the development of computationally efficient yet physically realistic models has been challenging. Here, the coarse-grained model COCOMO is introduced that balances the polymer behavior of peptides and RNA chains with their propensity to phase separate as a function of composition and concentration. COCOMO is a residue-based model that combines bonded terms with short- and long-range terms, including a Debye-Hückel solvation term. The model is highly predictive of experimental data on phase-separating model systems. It is also computationally efficient and can reach the spatial and temporal scales on which biomolecular condensation is observed with moderate computational resources.

An extended solvation theory for electrolyte osmotic and activity coefficients. Application to 1:1, 1:2, 1:3, 1:4, 2:1, 2:2, 3:1, 3:2 and 4:1 aqueous electrolyte solutions

In this work, we have used two models (DH-MS and PDH-MS) based upon the extended solvation theory to correlate osmotic and activity coefficients of electrolyte aqueous solutions. These models contain the long-range term of the Debye-Hückel (DH) theory or the Pitzer-Debye-Hückel (PDH) modification and a short-range term based upon a modified solvation (MS) theory. We have used literature experimental data of mean ionic activity and osmotic coefficients of 338 aqueous solutions. The electrolytes included in this work are type 1:1, 1:2, 1:3, 1:4, 2:1, 2:2, 3:1, 3:2, and 4:1 at 298.15 K. The results show that the DH-MS and PDH-MS models effectively correlate the experimental data within an average absolute percentage deviation of 0.588% and 0.688%, respectively. We have compared our results with those obtained from the Archer model. This model agrees within 0.769% with the literature data.

High-energy Landau levels in graphene beyond nearest-neighbor hopping processes: Corrections to the effective Dirac Hamiltonian

We study the Landau level spectrum of bulk graphene monolayers beyond the Dirac Hamiltonian with linear dispersion. We consider an effective Wannier-like tight-binding model obtained from ab initio calculations that includes long-range electronic hopping integral terms. We employ the Haydock-Heine-Kelly recursive method to numerically compute the Landau level spectrum of bulk graphene in the quantum Hall regime and demonstrate that this method is both accurate and computationally much faster than the standard numerical approaches used for this kind of study. The Landau level energies are also obtained analytically for an effective Hamiltonian that accounts for up to third-nearest-neighbor hopping processes. We find an excellent agreement between both approaches. We also study the effect of disorder on the electronic spectrum. Our analysis helps to elucidate the discrepancy between theory and experiment for the high-energy Landau level energies.

Dielectric effects, crystal field, and shape anisotropy tuning of the exciton fine structure of halide perovskite nanocrystals

We present a theoretical study of the excitonic band edge states applied to the more commonly studied inorganic perovskite nanocrystals: ${\mathrm{CsPbBr}}_{3}$. We highlight the key role played by the electron-hole exchange interaction, including long-range and short range terms, in the positioning and splitting of dark and bright exciton sublevels, and discuss the influence of dielectric confinement, crystal field and shape anisotropy effects on the excitonic fine structure. The electron-hole exchange interaction splits the four excitonic states into three bright excitonic states at higher energy and a singlet dark state at lower energy. We find that, whatever the crystal phase, the bright-dark splitting is weakly sensitive to shape anisotropy. However, a strong enhancement, of about 50%, is obtained at the maximum of the dielectric contrast. For two crystalline symmetries, we particularly analyze how the bright exciton triplet energies vary, taking into account the states polarizations and considering the directions along which shape elongation/contraction applies. The main effect of the dielectric contrast is to increase significantly the exciton energies, for all the configurations. For a cubic crystal---${\mathrm{O}}_{h}$ symmetry---the bright exciton triplet degeneracy can be partially or fully lifted with anisotropic shape along one or two directions, respectively. For a tetragonal crystal---${\mathrm{D}}_{4h}$ symmetry---the partial triplet degeneracy can be completely lifted by a single distortion from the cubic shape along a direction perpendicular to the tetragonal axis but a partial degeneracy is maintained for small distortions along the tetragonal axis. The amplitude of bright exciton splittings are basically driven by the shape anisotropy and is almost insensitive to the dielectric contrast. On the basis of this model, we discuss recent results on ${\mathrm{CsPbBr}}_{3}$ nanocrystals photoluminescence.

Investigation of the monopole magneto-chemical potential in spin ices using capacitive torque magnetometry

The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength (Jeff) determines the relative energies of the different spin-ice states. With this work, we display the capability of capacitive torque magnetometry in characterizing the magneto-chemical potential associated with monopole formation. We build a magnetic phase diagram of Ho2Ti2O7, and show that the magneto-chemical potential depends on the spin sublattice (α or β), i.e., the Pauling state, involved in the transition. Monte Carlo simulations using the dipolar-spin-ice Hamiltonian support our findings of a sublattice-dependent magneto-chemical potential, but the model underestimates the Jeff for the β-sublattice. Additional simulations, including next-nearest neighbor interactions (J2), show that long-range exchange terms in the Hamiltonian are needed to describe the measurements. This demonstrates that torque magnetometry provides a sensitive test for Jeff and the spin-spin interactions that contribute to it.

Second-order topological insulator in periodically driven optical lattices.

The higher-order topological insulator (HOTI) is a new type of topological system which has special bulk-edge correspondence compared with conventional topological insulators. In this work, we propose a scheme to realize Floquet HOTI with ultracold atoms in optical lattices. With the combination of periodically spin-dependent driving of the superlattices and a long-range coupling term, a Floquet second-order topological insulator with four zero-energy corner states emerges, whose Wannier bands are gapless and exhibit interesting bulk topology. Furthermore, the nearest-neighbor anisotropic coupling term also induced other intriguing topological phenomena, e.g. non-topologically protected corner states and topological semimetal for two different types of lattice structures respectively. Our scheme may give insight into the construction of different types of higher-order topological insulators in synthetic systems. It also provides an experimentally feasible platform to research the relations between different types of topological states and may have a wide range of applications in future.

Covariant Evolution of Gravitoelectromagnetism

The long-range gravitational terms associated with tidal forces, frame-dragging effects, and gravitational waves are described by the Weyl conformal tensor, the traceless part of the Riemann curvature that is not locally affected by the matter field. The Ricci and Bianchi identities provide a set of dynamical and kinematic equations governing the matter coupling and evolution of the electric and magnetic parts of the Weyl tensor, so-called gravitoelectric and gravitomagnetic fields. A detailed analysis of the Weyl gravitoelectromagnetic fields can be conducted using a number of algebraic and differential identities prescribed by the 1+3 covariant formalism. In this review, we consider the dynamical constraints and propagation equations of the gravitoelectric/-magnetic fields and covariantly debate their analytic properties. We discuss the special conditions under which gravitational waves can propagate, the inconsistency of a Newtonian-like model without gravitomagnetism, the nonlinear generalization to multi-fluid models with different matter species, as well as observational effects caused by the Weyl fields via the kinematic quantities. The 1+3 tetrad and 1+1+2 semi-covariant methods, which can equally be used for gravitoelectromagnetism, are briefly explained, along with their correspondence with the covariant formulations.

Quasiclassical Trajectory Study of the Si + SH Reaction on an Accurate Double Many-Body Expansion Potential Energy Surface

An accurate potential energy surface (PES) for the HSiS system based on MRCI+Q calculations extrapolated to the complete basis set limit is presented. Modeled with the double many-body expansion (DMBE) method, the PES provides an accurate description of the long-range interactions, including electrostatic and dispersion terms decaying as R-4, R-5, R-6, R-8, R-10 that are predicted from dipole moments, quadrupole moments, and dipolar polarizabilities, which are also calculated at the MRCI+Q level. The novel PES is then used in quasiclassical trajectory calculations to predict the rate coefficients of the Si + SH → SiS + H reaction, which has been shown to be a major source of the SiS in certain regions of the interstellar medium. An account of the zero-point energy leakage based on various nonactive models is also given. It is shown that the reaction is dominated by long-range forces, with the mechanism Si + SH → SiSH → SSiH → SiS + H being the most important one for all temperatures studied. Although SSiH corresponds to the global minimum of the PES, the contribution from the direct reaction Si + SH → SSiH → SiS + H is less than 0.5% for temperatures higher than 500 K. The rovibrational distributions of the products are calculated using the momentum Gaussian binning method and show that as the temperature is increased the average vibrational quantum number decreases while the rotational distribution spreads up to larger values.