Soft-core Potential Research Articles

Coulomb-induced asymmetry on photoelectron momentum distributions in orthogonal two-color laser fields

By numerically solving the time-dependent Schr\"odinger equation, we study the ionization of helium atoms with different forms of the atomic potential, including the soft-core potential, the model potential, and the short-range potential, in orthogonally polarized two-color laser fields. We show that in the case of the long-range atomic potentials (the soft-core potential and the model potential), the photoelectron momentum distributions exhibit asymmetric structures, while for the short-range potential, they present nearly symmetric structures. Besides, the asymmetric structures are sensitive to the specific forms of the atomic potential. We find that the asymmetric structures are more pronounced for the lower laser intensity and/or the shorter laser wavelength. Our results may provide a reference for further analytical studies of strong-field ionization of complex atoms and molecules, where the Coulomb effects are included for quantitative descriptions.

Two-Step Discontinuous Shear Thickening of Dilute Inertial Suspensions Having Soft-Core Potential

Kinetic theory for dilute inertial suspension having soft-core potential is theoretically investigated. From the analysis of the scattering process, the expression of the scattering angle is analytically obtained. We derive the flow curve between the viscosity and the shear rate, which shows two-step discontinuous shear thickening when we change the softness of the particles. The molecular dynamics simulation shows that our theoretical results are consistent with the numerical ones.

An Alternative to Conventional λ-Intermediate States in Alchemical Free Energy Calculations: λ-Enveloping Distribution Sampling

Alchemical free energy calculations typically rely on intermediate states to bridge between the relevant phase spaces of the two end states. These intermediate states are usually created by mixing the energies or parameters of the end states according to a coupling parameter λ. The choice of the procedure has a strong impact on the efficiency of the calculation, as it affects both the encountered energy barriers and the phase space overlap between the states. The present work builds on the connection between the minimum variance pathway (MVP) and enveloping distribution sampling (EDS). It is shown that both methods can be regarded as special cases of a common scheme referred to as λ-EDS, which can also reproduce the behavior of conventional λ-intermediate states. A particularly attractive feature of λ-EDS is its ability to emulate the use of soft core potentials (SCP) while avoiding the associated computational overhead when applying efficient free energy estimators such as the multistate Bennett's acceptance ratio (MBAR). The method is illustrated for both relative and absolute free energy calculations considering five benchmark systems. The first two systems (charge inversion and cavity creation in a dipolar solvent) demonstrate the use of λ-EDS as an alternative coupling scheme in the context of thermodynamic integration (TI). The three other systems (change of bond length, change of dihedral angles, and cavity creation in water) investigate the efficiency and optimal choice of parameters in the context of free energy perturbation (FEP) and Bennett's acceptance ratio (BAR). It is shown that λ-EDS allows larger steps along the alchemical pathway than conventional intermediate states.

Improved Alchemical Free Energy Calculations with Optimized Smoothstep Softcore Potentials.

Progress in the development of GPU-accelerated free energy simulation software has enabled practical applications on complex biological systems and fueled efforts to develop more accurate and robust predictive methods. In particular, this work re-examines concerted (a.k.a., one-step or unified) alchemical transformations commonly used in the prediction of hydration and relative binding free energies (RBFEs). We first classify several known challenges in these calculations into three categories: endpoint catastrophes, particle collapse, and large gradient-jumps. While endpoint catastrophes have long been addressed using softcore potentials, the remaining two problems occur much more sporadically and can result in either numerical instability (i.e., complete failure of a simulation) or inconsistent estimation (i.e., stochastic convergence to an incorrect result). The particle collapse problem stems from an imbalance in short-range electrostatic and repulsive interactions and can, in principle, be solved by appropriately balancing the respective softcore parameters. However, the large gradient-jump problem itself arises from the sensitivity of the free energy to large values of the softcore parameters, as might be used in trying to solve the particle collapse issue. Often, no satisfactory compromise exists with the existing softcore potential form. As a framework for solving these problems, we developed a new family of smoothstep softcore (SSC) potentials motivated by an analysis of the derivatives along the alchemical path. The smoothstep polynomials generalize the monomial functions that are used in most implementations and provide an additional path-dependent smoothing parameter. The effectiveness of this approach is demonstrated on simple yet pathological cases that illustrate the three problems outlined. With appropriate parameter selection, we find that a second-order SSC(2) potential does at least as well as the conventional approach and provides vast improvement in terms of consistency across all cases. Last, we compare the concerted SSC(2) approach against the gold-standard stepwise (a.k.a., decoupled or multistep) scheme over a large set of RBFE calculations as might be encountered in drug discovery.

Repulsive Soft-Core Potentials for Efficient Alchemical Free Energy Calculations.

In alchemical free energy (FE) simulations, annihilation and creation of atoms are generally achieved with the soft-core potential that shifts the interparticle separations. While this soft-core potential eliminates the numerical instability occurring near the two end states of the transformation, it makes the hybrid Hamiltonian vary nonlinearly with respect to the parameter λ, which interpolates between the Hamiltonians representing the two end states. This complicates FE estimation by Bennett acceptance ratio (BAR), free energy perturbation (FEP), and thermodynamic integration (TI) methods, thus reducing their calculation efficiency. In this work, we develop a new type of repulsive soft-core potential, called Gaussian soft-core (GSC) potential, with two parameters controlling its maximum and width. The main advantage of this potential is the linearity of the hybrid Hamiltonian with respect to λ, thus permitting the direct application of BAR, FEP, TI, and other variant FE methods. The accuracy and efficiency of the GSC potential are demonstrated by comparing the free energies of annihilation determined for 13 small molecules and an alchemical mutation of a protein side chain. In addition, in combination with a TI integrand (∂H/∂λ) estimation strategy, we show that GSC can considerably reduce the number of λ simulations compared to the commonly used separation-shifted soft-core potential.

Role of quantum paths in generation of attosecond pulses

We investigate the role of core potential in high ionization potential systems on high harmonic generation (HHG) spectra and obtain attosecond pulses. In our scheme, we use a standard soft core potential to model high ionization potential systems and irradiated these systems with fixed laser parameters. We observe the role of these systems on all the three steps involved in HHG process including ionization, propagation and recombination. In our study, the results illustrate that for high ionization potential systems, the HHG process is more sensitive to the ionization probability compared to the recombination amplitude. We also observe that due to the stronger core potential, small oscillations of the electrons during the propagation do not contribute to the HHG spectrum, which implies the dominance of only long quantum paths in the HHG spectrum. Our results, for attosecond pulse generation, show that long quantum path electrons are responsible for the supercontinuum region near the cutoff, which is suitable for the extraction of a single attosecond pulse in this region.

Confining Liquids inside Carbon Nanotubes: Accelerated Molecular Dynamics with Spliced, Soft-Core Potentials and Simulated Annealing.

Understanding emergent phenomena of fluids under physical confinement requires the development of advanced tools for rapid and accurate simulation of their physiochemical properties. Simulating liquid molecules commensurate in size with the nanoscale enclosures that confine them is a key challenge. We demonstrate an accelerated molecular dynamics simulation technique that combines soft-core potentials (SCP) and simulated annealing (SA) to analyze confined liquids. This integrated SCP/SA method relies on a new spliced soft-core potential (SSCP), which enables tunable accuracy with respect to the target hard-core potential (HCP). SCP/SA enables the packing of enclosures with bulk material in a controlled, thermodynamically consistent manner. The enhanced SSCP accuracy is a critical feature of SCP/SA, enabling a smooth transition between the SCP and the HCP at a desired SCP hardness. We applied SCP/SA to the problem of filling a carbon nanotube (CNT) in periodic boundary conditions with a popular ionic liquid (IL), 1-butyl-3-methylimidazolium hexafluorophosphate [BMIM+][PF6-]. We performed a series of triplicate simulations on systems with varying CNT diameter and charge to demonstrate SCP/SA's versatility. Beyond this IL/CNT system, the SCP/SA simulation framework has a broad range of potential applications, not limited to nanoscale enclosures and interfaces, including both solid-state and biological systems.

Stabilization Mechanism for a Nonfibrillar Amyloid β Oligomer Based on Formation of a Hydrophobic Core Determined by Dissipative Particle Dynamics.

Neurotoxicity caused by nonfibrillar amyloid β (Aβ) oligomers in the brain is suggested to be associated with the onset of Alzheimer's disease (AD). Elucidating the structural features of Aβ oligomers is critical for promoting drug discovery research for AD. One of the Aβ oligomers, known as Aβ*56, is a dodecamer that impairs memory when injected into healthy rats, suggesting that Aβ*56 may contribute to cognitive deficits in AD patients. Another dodecamer structure, formed by 20-residue peptide segments derived from the Aβ peptide (Aβ17-36), has been revealed by X-ray crystallography. The structure of the Aβ17-36 dodecamer is composed of trimer units and shows the oligomer antibody A11 reactivity, which are characteristic of Aβ*56, indicating that Aβ*56 and the Aβ17-36 dodecamer share a similar structure. However, the structure of the C-terminal regions (Aβ37-42) remains unclear. The C-terminal region, which is abundant in hydrophobic residues, is thought to play a key role in stabilizing the oligomer structure by forming a hydrophobic core. In this study, we employed dissipative particle dynamics, a coarse-grained simulation method with soft core potentials, utilizing the crystal structure information to unravel Aβ dodecamer structures with C-terminal regions. The simulation results were validated by the reported experimental data. Hence, an analysis of the simulation results can provide structural insights into Aβ oligomers. Our simulations revealed the stabilization mechanism of the dodecamer structure at the molecular level. We showed that C-terminal regions spontaneously form a hydrophobic core in the central cavity, contributing to stabilizing the dodecamer structure. Furthermore, four consecutive hydrophobic residues in the C-terminal region (i.e., Val39-Ala42) are important for core formation.

LOCV calculation for nuclear and neutron matter with the Nijmegen potential

The lowest order constrained variational (LOCV) formalism is formulated for the Nijmegen soft-core potential, which is fitted by the proton-proton (pp) scattering phase shift. The calculations are performed for the equation of state (EOS) of both nuclear and neutron matter. The state-dependent correlation functions are calculated by the minimization of two-body cluster energy, and the resulting Euler Lagrange equations are solved for this kind of potential. It is shown that LOCV calculations can work with this kind of interaction as well as other interactions in configuration space. The state-dependent correlation functions are calculated by minimization of two-body cluster energy for each channel with various JLSTMT, by using Nijmegen interaction. The correlation functions are compared with those coming from UV14 interaction in LOCV formalism. It is shown that unlike UV14, AV14, and AV18 potentials, the binding energy obtained from Nijmegen in the LOCV framework is −16.81 MeV that is close to the experimental value. Finally, it is recognized our LOCV results with Nijmegen interaction are similar to calculations with different interactions and different many-body methods.

Intense VUV–xenon-cluster interaction revisited

During the inaugural experiment at FLASH, the first vacuum ultraviolet (VUV) free-electron laser facility, Wabnitz et al. [Nature 420, 482 (2002)] irradiated xenon clusters and sparked a concerted theoretical and experimental effort to understand how dense, finite plasmas behave under intense irradiation. In this work, we revisit this experiment with a model that is based only on well-established atomic processes. We find that the experimental results can be explained by hybrid quantum-classical molecular-dynamics simulations if collisional excitation, recombination, and a sufficiently deep soft-core potential is used. Our recent theoretical model for inverse bremsstrahlung heating (IBH) is used to show that the measured energy absorbed by the cluster in the experiment is well predicted by our model.

Grid-Based Ehrenfest Model To Study Electron-Nuclear Processes.

The two-dimensional electron-nuclear Schrödinger equation using soft-core Coulomb potentials has been a cornerstone for modeling and predicting the behavior of one-active-electron diatomic molecules, particularly for processes where both bound and continuum states are important. The model, however, is computationally expensive to extend to more electron or nuclear coordinates. Here we propose use of the Ehrenfest approach to treat the nuclear motion, while the electronic motion is still solved by quantum propagation on a grid. In this work, we present results for a one-dimensional treatment of H2+, where the quantum and semiclassical dynamics can be directly compared, showing remarkably good agreement for a variety of situations. The advantage of the Ehrenfest approach is that it can be easily extended to treat as many nuclear degrees of freedom as needed.

Phase Behaviors of Soft-core Particle Systems

This paper reviews some of our recent works on phase behaviors of particulate systems with a soft-core interaction potential. The potential is purely repulsive and bounded, i.e., it is finite even when two particles completely overlap. The one-sided linear spring (harmonic) potential is one of the representatives. This model system has been successively employed to study the jamming transition, i.e., the formation of rigid and disordered packings of hard particles, and establish the jamming physics. This is actually based on the “hard” aspect of the potential, because at low densities and when particle overlap is tiny the potential resembles the hard sphere limit. At high densities, the potential exhibits its “soft” aspect: with the increase of density, there are successive reentrant crystallizations with many types of solid phases. Taking advantage of the dual nature of the potential, we investigate the criticality of the jamming transition from different perspectives, extend the jamming scenario to high densities, reveal the novel density evolution of two-dimensional melting, and find unexpected formation of quasicrystals. It is surprising that such a simple potential can exhibit so rich and unexpected phenomena in phase transitions. The phase behaviors discussed in this paper are also highly regarded in polymer science, which may thus shed light on our understanding of polymeric systems or inspire new ideas in studies of polymers.

Nucleonic 1S0 Superfluidity Induced by a Soft Pion in Neutron Star Matter with Antikaon Condensations**Supported by the Open Foundation of Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, the Youth Innovation Promotion Association of the Chinese Academy of Sciences under Grant No 2016056, the Development Project of Science and Technology of Jilin Province under Grant No 20180520077JH, and

The nucleonic 1S0 superfluidity is investigated by solving the gap equation for the Reid soft-core potential as the nucleon–nucleon interaction in neutron star (NS) matter which is considered to be made up of n, p, e, μ and condensed antikaon matter. We mainly study the influence of the soft pion-induced potential on the nucleonic 1S0 pairing gaps in the above NS matter. It is found that the intensities of the nucleonic 1S0 pairing gaps including the soft pion-induced potential are smaller than those calculated in the case of not including the soft pion-induced potential. Furthermore, the nucleonic 1S0 pairing gaps with the soft pion-induced potential fall into decline with the deepening of the optical potential of antikaons in the above NS matter, whereas they increase with the parameter η for the fixed optical potential of antikaons. Due to the appearance of the soft pion-induced potential, the maximum values of nucleonic 1S0 pairing gaps at parameter η = 0.20, 0.55 are suppressed by 1.7%–6.8% with respect to the case without soft pion-induced potential in the above NS matter.

Statistical theory of fluids with a complex electric structure: Application to solutions of soft-core dipolar particles

Based on the thermodynamic perturbation theory (TPT) and the random phase approximation (RPA), we present a statistical theory of solutions of electrically neutral soft molecules, every of which is modelled as a set of sites that interact with each other through the potentials, presented as the sum of the Coulomb potential and arbitrary soft-core potential. As an application of our formalism, we formulate a general statistical theory of solution of the soft-core dipolar particles. For the latter, we obtain a new analytical relation for the screening function. As a special case, we apply this theory to describing the phase behavior of a solution of the dipolar particles interacting with each other in addition to the electrostatic potential through the repulsive Gaussian potential – Gaussian core dipolar model (GCDM). Using the obtained analytic expression for the total free energy of the GCDM, we obtain the liquid-liquid phase separation with an upper critical point. The developed formalism could be used as a general framework for the coarse-grained description of thermodynamic properties of solutions of macromolecules, such as proteins, betaines, polypeptides, etc.

Properties of 4He Nucleus in the Mean Field Approximation with Compression

Constrained spherical Hartree–Fock approximations are used to investigate nuclear system of closed shell $$^{4}{\hbox {He}}$$ nucleus. Two potentials were used: Reid soft core (RSC) and Nijmegen potentials. Moreover, the dependence of the nuclear properties was studied for the degree of compression. It was seen that it is possible to compress the nucleus into a smaller volume. This means that nuclear equation of state becomes softer for the compressed nucleus. Also, the nucleus becomes more bounded using RSC than Nijmegen potential. The $$E_{{\mathrm{HF}}}$$ increases steeply toward zero binding energy under compression for both potentials. In the case of using Nijmegen potential, the curve increases to zero binding energy more than RSC potential. In addition to that the spectrum of single particle increases more rapidly for Nijmegen than for RSC potential under compression. For the compressed nucleus, the energy spectrum also clearly shows the gaps between single-particle energy shells. In addition, it is preserved the ordering of the energy spectrum levels and the gaps among them. Finally, except in the interior region, the radial density distribution remains constant, while it is larger with RSC than with Nijmegen potential. At large compression, it becomes larger than that in the interior region when RSC potential is used.

The d-dimensional softcore Coulomb potential and the generalized confluent Heun equation

An analysis of the generalized confluent Heun equation (α2r2 + α1r) y″ + (β2r2 + β1r + β0) y′ − (ε1r + ε0) y = 0 in d-dimensional space, where {αi, βi, εi} are real parameters, is presented. With the aid of these general results, the quasi-exact solvability of the Schrödinger eigenproblem generated by the softcore Coulomb potential V(r) = −e2Z/(r + b), b > 0, is explicitly resolved. Necessary and sufficient conditions for polynomial solvability are given. A three-term recurrence relation is provided to generate the coefficients of polynomial solutions explicitly. We prove that these polynomial solutions are sources of finite sequences of orthogonal polynomials. Properties such as the recurrence relations, Christoffel-Darboux formulas, and moments of the weight function are discussed. We also reveal a factorization property of these polynomials which permits the construction of other interesting related sequences of orthogonal polynomials.

GPU-Accelerated Molecular Dynamics and Free Energy Methods in Amber18: Performance Enhancements and New Features.

We report progress in graphics processing unit (GPU)-accelerated molecular dynamics and free energy methods in Amber18. Of particular interest is the development of alchemical free energy algorithms, including free energy perturbation and thermodynamic integration methods with support for nonlinear soft-core potential and parameter interpolation transformation pathways. These methods can be used in conjunction with enhanced sampling techniques such as replica exchange, constant-pH molecular dynamics, and new 12-6-4 potentials for metal ions. Additional performance enhancements have been made that enable appreciable speed-up on GPUs relative to the previous software release.

Meson–baryon coupling constants of the SU(3) baryons with flavor SU(3) symmetry breaking

We investigate the strong coupling constants for the baryon octet–octet, decuplet–octet, and decuplet–decuplet vertices with pseudoscalar mesons within a general framework of the chiral quark-soliton model, taking into account the effects of flavor SU(3) symmetry breaking to linear order in the expansion of the strange current quark mass. All relevant dynamical parameters are fixed by using the experimental data on hyperon semileptonic decays and the singlet axial-vector constant of the nucleon. The results of the strong coupling constants for the baryon octet and the pseudoscalar meson octet are compared with those determined from the Jülich–Bonn potential and the Nijmegen extended soft-core potential for hyperon–nucleon scattering. The results of the strong decay widths of the baryon decuplet are in good agreement with the experimental data. The effects of SUf(3) symmetry breaking are sizable on the η′ coupling constants. We predict also the strong coupling constants for the Ω baryons.

Soft-core Interaction for the 4,6He + 64Zn Fusion Reactions

In this paper, the cross section of the 4He + 64Zn and 6He + 64Zn reactions, at bombarding energies above and below the fusion barrier, has been investigated. Soft-core nucleon-nucleon interaction and the Monte Carlo method have been employed for studying the nuclear potential of the projectile-target system. One adjustable parameter has been chosen in this study. This parameter can change the depth of the soft-core potential. It has to be adjusted so that the calculated elastic scattering and fusion cross sections are in acceptable agreement with experimental data. Our results indicate that an increase in energy decreases the depth parameter of the soft-core nucleon-nucleon potential obtained from careful analysis the 4He + 64Zn and 6He + 64Zn reactions. Likewise, by comparing the results obtained from both reactions, one can observe that the calculated depth parameter for the reaction related to 6He is larger than that for 4He at the same energy, in particular at the sub-barrier energies. We try to explain this behavior.

Effects of a soft-core coulomb potential on the dynamics of a hydrogen atom near a metal surface

The goal of this paper is to investigate the effects that the replacement of the Coulomb potential by a soft-core Coulomb potential produces in the classical dynamics of a perturbed Rydberg hydrogen atom. As example, we consider a Rydberg hydrogen atom near a metal surface subjected to a constant electric field in the electron-extraction regime. Thence, the dynamics of the real perturbed Coulomb system, studied by applying the Levi–Civita regularization, is compared with that of the softened one. The results of this study show that the global behavior of the system is significantly altered when the original Coulomb potential part is replaced by a soft-core potential.