Soft-core Potential Research Articles

Self-assembly and phase behavior of Janus rods: Competition between shape and potential anisotropy

We characterize the self-assembly and phase behavior of Janus rods over a broad range of temperatures and volume fractions, using Langevin dynamics simulations and free energy calculations. The Janus rods consist of a line of fused overlapping spheres that interact via a soft-core repulsive potential, with the addition of an attractive pseudo-square-well tail to a fraction of the spheres (the coverage) ranging from 5% to 100% of sites. Competition between the stability of liquid crystal phases originating from shape anisotropy and assembly driven by directional interactions gives rise to a rich polymorphism that depends on the coverage. At low densities near the Boyle temperature, we observe the formation of spherical and tubular micelles at low coverages, while at higher coverages, randomly oriented monolayers form as the attractive parts of the rods overlap. At higher densities, bilayer structures appear and merge to form smectic and crystalline lamellar phases. All these structures gradually become unstable as the temperature is increased until eventually regular nematic and smectic phases appear, consistent with the hard rod limit. Our results indicate that the intermediate regime where shape-entropic effects compete with anisotropic attractions provided by site specificity is rich in structural possibilities and should help guide the design of rod-like colloids for specific applications.

Influence of catastrophes and hidden dynamical symmetries on ultrafast backscattered photoelectrons

We discuss the effect of using potentials with a Coulomb tail and different degrees of softening in photoelectron momentum distributions (PMDs) using the recently implemented hybrid forward-boundary CQSFA (H-CQSFA). We show that introducing a softening in the Coulomb interaction influences the ridges observed in the PMDs associated with backscattered electron trajectories. In the limit of a hard-core Coulomb interaction, the rescattering ridges close along the polarization axis, while for a soft-core potential, they are interrupted at ridge-specific angles. We analyze the momentum mapping of the different orbits leading to the ridges. For the hard-core potential, there exist two types of saddle-point solutions that coalesce at the ridge. By increasing the softening, we show that two additional solutions emerge as the result of breaking a hidden dynamical symmetry associated exclusively with the Coulomb potential. Further signatures of this symmetry breaking are encountered in subsets of momentum-space trajectories. Finally, we use scattering theory to show how the softening affects the maximal scattering angle and provide estimates that agree with our observations from the CQSFA. This implies that, in the presence of residual binding potentials in the electron's continuum propagation, the distinction between purely kinematic and dynamic caustics becomes blurred. Published by the American Physical Society 2024

Alchemical Enhanced Sampling with Optimized Phase Space Overlap.

An alchemical enhanced sampling (ACES) method has recently been introduced to facilitate importance sampling in free energy simulations. The method achieves enhanced sampling from Hamiltonian replica exchange within a dual topology framework while utilizing new smoothstep softcore potentials. A common sampling problem encountered in lead optimization is the functionalization of aromatic rings that exhibit distinct conformational preferences when interacting with the protein. It is difficult to converge the distribution of ring conformations due to the long time scale of ring flipping events; however, the ACES method addresses this issue by modeling the syn and anti ring conformations within a dual topology. ACES thereby samples the conformer distributions by alchemically tunneling between states, as opposed to traversing a physical pathway with a high rotational barrier. We demonstrate the use of ACES to overcome conformational sampling issues involving ring flipping in ML300-derived noncovalent inhibitors of SARS-CoV-2 Main Protease (Mpro). The demonstrations explore how the use of replica exchange and the choice of softcore selection affects the convergence of the ring conformation distributions. Furthermore, we examine how the accuracy of the calculated free energies is affected by the degree of phase space overlap (PSO) between adjacent states (i.e., between neighboring λ-windows) and the Hamiltonian replica exchange acceptance ratios. Both of these factors are sensitive to the spacing between the intermediate states. We introduce a new method for choosing a schedule of λ values. The method analyzes short "burn-in" simulations to construct a 2D map of the nonlocal PSO. The schedule is obtained by optimizing an alchemical pathway on the 2D map that equalizes the PSO between the λ intervals. The optimized phase space overlap λ-spacing method (Opt-PSO) leads to more numerous end-to-end single passes and round trips due to the correlation between PSO and Hamiltonian replica exchange acceptance ratios. The improved exchange statistics enhance the efficiency of ACES method. The method has been implemented into the FE-ToolKit software package, which is freely available.

Enhancing torsional sampling using fully adaptive simulated tempering.

Enhanced sampling algorithms are indispensable when working with highly disconnected multimodal distributions. An important application of these is the conformational exploration of particular internal degrees of freedom of molecular systems. However, despite the existence of many commonly used enhanced sampling algorithms to explore these internal motions, they often rely on system-dependent parameters, which negatively impact efficiency and reproducibility. Here, we present fully adaptive simulated tempering (FAST), a variation of the irreversible simulated tempering algorithm, which continuously optimizes the number, parameters, and weights of intermediate distributions to achieve maximally fast traversal over a space defined by the change in a predefined thermodynamic control variable such as temperature or an alchemical smoothing parameter. This work builds on a number of previously published methods, such as sequential Monte Carlo, and introduces a novel parameter optimization procedure that can, in principle, be used in any expanded ensemble algorithms. This method is validated by being applied on a number of different molecular systems with high torsional kinetic barriers. We also consider two different soft-core potentials during the interpolation procedure and compare their performance. We conclude that FAST is a highly efficient algorithm, which improves simulation reproducibility and can be successfully used in a variety of settings with the same initial hyperparameters.

Hartree-Fock Calculations of 12C Nucleus at Equilibrium and Under Static Compression

Abstract: The ground state features of the semi-doubly magic 12C nucleus (i.e. binding energy, nuclear radius, radial density distribution, and single particle energies) are estimated using ab initio calculations at equilibrium and under high static compression. Nijmegen and Reid soft-core (RSC) potentials are used as input nucleon-nucleon interactions. Within the framework of the constrained spherical Hartree-Fock approximations, we do the calculations in no-core shell-model space, which consists of six major oscillator shells (i.e. 21 single particle orbitals). The sensitivity of the ground state features of the 12C nucleus to the degree of compression and the sensitivity of the equation of state to the two potentials are investigated. We also discovered that the nuclear binding energy calculated using the Nijmegen potential is higher than that calculated using the RSC potential. When utilizing the Nijmegen potential, the curve reaches zero binding energy faster than when using the RSC potential. Besides, in the case of Nijmegen, the spectrum of single-particle energies increases more quickly than in the case of RSC potential under compression. The space between single-particle energy shells is also visible in the energy spectrum. At high compression, the radial density distribution becomes higher than that in the interior zone when the RSC potential is applied. Keywords: Nijmegen potential, RSC potential, Ab-initio calculations model, Radial density distribution, Ground state, 12C nucleus.

Enhancing spin squeezing using soft-core interactions

Ising interactions in the form of a soft-core potential, such as the ones experienced by Rydberg dressed atoms, can be combined with a strong coherent drive to help preserve collective spin coherences even in systems much larger than the range of the soft-core interactions. As a result, they can lead to the robust generation of metrologically useful spin-squeezed states in optical tweezer clocks.

ACES: Optimized Alchemically Enhanced Sampling.

We present an alchemical enhanced sampling (ACES) method implemented in the GPU-accelerated AMBER free energy MD engine. The methods hinges on the creation of an "enhanced sampling state" by reducing or eliminating selected potential energy terms and interactions that lead to kinetic traps and conformational barriers while maintaining those terms that curtail the need to otherwise sample large volumes of phase space. For example, the enhanced sampling state might involve transforming regions of a ligand and/or protein side chain into a noninteracting "dummy state" with internal electrostatics and torsion angle terms turned off. The enhanced sampling state is connected to a real-state end point through a Hamiltonian replica exchange (HREMD) framework that is facilitated by newly developed alchemical transformation pathways and smoothstep softcore potentials. This creates a counterdiffusion of real and enhanced-sampling states along the HREMD network. The effect of a differential response of the environment to the real and enhanced-sampling states is minimized by leveraging the dual topology framework in AMBER to construct a counterbalancing HREMD network in the opposite alchemical direction with the same (or similar) real and enhanced sampling states at inverted end points. The method has been demonstrated in a series of test cases of increasing complexity where traditional MD, and in several cases alternative REST2-like enhanced sampling methods, are shown to fail. The hydration free energy for acetic acid was shown to be independent of the starting conformation, and the values for four additional edge case molecules from the FreeSolv database were shown to have a significantly closer agreement with experiment using ACES. The method was further able to handle different rotamer states in a Cdk2 ligand identified as fractionally occupied in crystal structures. Finally, ACES was applied to T4-lysozyme and demonstrated that the side chain distribution of V111χ1 could be reliably reproduced for the apo state, bound to p-xylene, and in p-xylene→ benzene transformations. In these cases, the ACES method is shown to be highly robust and superior to a REST2-like enhanced sampling implementation alone.

A new approach for the equation of state of pure neutron matter using the quantum second virial coefficient with the Reid-93 soft-core potential

In this work, a new approach is presented for determining the equation of state for pure neutron matter. This is valid in the temperature- and density-regime where the system behaves like a nonideal gas. Further, the calculations involved are confined to the nonrelativistic and low-energy ([Formula: see text] 150 MeV) regime. The approach is based on evaluating the quantum second virial coefficient [Formula: see text] of the system, where the input potential is the Reid-93 soft-core potential for [Formula: see text], together with the one-pion-exchange potential (OPEP) for higher [Formula: see text]. The many-body phase shifts are determined within the framework of a generalized scattering theory, taken here as the Galitskii–Migdal–Feynman formalism. The integral equations involved are solved using a highly-accurate matrix-inversion method. These medium phase shifts are then inserted in the Beth–Uhlenbeck formula to determine [Formula: see text]. Once this coefficient has been calculated, other thermophysical properties of the system can be readily computed according to standard expressions. Specifically, these properties include the equation of state (pressure–temperature–density relations), Helmholtz (free) energy, entropy, mean internal energy, specific heat capacity and chemical potential. Our results are compared, whenever possible, to those of previous calculations. The agreement is, on the whole, fair considering that the available calculations vary considerably among themselves.

Disentangling interferences in the photoelectron momentum distribution from strong-field ionization

Using the semiclassical two-step model for strong-field ionization, we theoretically investigate subcycle interference structures in the photoelectron momentum distribution. Specifically, we focus on the low-momentum fanlike interference structure. Employing a time-variable soft-core Coulomb potential, we demonstrate that the low-momentum interference arises from the interference between drifted and undrifted electrons from opposite direct quarter cycles. We also find that the main scattering in the nuclear Coulomb potential occurs just after ionization. Our findings suggest that the low-momentum region of the photoelectron spectrum is particularly sensitive to the ion potential and thereby offers another path to probe ultrafast electronic structure dynamics.

A unified approach for calculating free energies of liquid and defective crystals based on thermodynamic integration.

Free energy calculation is fundamentally important in the research of physics, chemistry, and materials. Thermodynamic integration is the most common way to estimate free energies. In the research, we proposed a unified approach using atomic simulations to calculate the free energies of liquid and defective crystals. The new approach is based on thermodynamic integration using two alchemical pathways. Softcore potentials are developed for three-body interatomic potentials to realize the alchemical pathways. Employing the new approach, the free energy of the liquid can be calculated without requiring another reference system. The free energy of the defective crystal can be calculated directly at high temperatures. It avoids the singularity at the integration endpoint caused by the defect diffusion, which is a serious problem in the widely used Einstein crystal method. In addition, the new approach can capture the whole free energy of the defective crystal including the contribution of anharmonic and configurational entropy, which are particularly important at high temperatures. The new method is simple yet effective and can be extended to different materials and more complex liquid and defective crystal systems.

Dynamics of position-disordered Ising spins with a soft-core potential

We theoretically study the magnetization relaxation of Ising spins distributed randomly in a $d$-dimension homogeneous and Gaussian profile under a soft-core two-body interaction potential $\ensuremath{\propto}1/[1+{(r/{R}_{c})}^{\ensuremath{\alpha}}]$ $(\ensuremath{\alpha}\ensuremath{\ge}d)$, where $r$ is the interspin distance and ${R}_{c}$ is the soft-core radius. The dynamics starts with all spins polarized in the transverse direction. In the homogeneous case, an analytic expression is derived at the thermodynamic limit, which starts as $\ensuremath{\propto}exp(\ensuremath{-}k{t}^{2})$ with a constant $k$ and follows a stretched-exponential law at long time with an exponent $\ensuremath{\beta}=d/\ensuremath{\alpha}$. In between an oscillating behavior is observed with a damping amplitude. For Gaussian samples, the degree of disorder in the system can be controlled by the ratio ${l}_{\ensuremath{\rho}}/{R}_{c}$, with ${l}_{\ensuremath{\rho}}$ the mean interspin distance and the magnetization dynamics is investigated numerically. In the limit of ${l}_{\ensuremath{\rho}}/{R}_{c}\ensuremath{\ll}1$, a coherent many-body dynamics is recovered for the total magnetization despite the position disorder of spins. In the opposite limit of ${l}_{\ensuremath{\rho}}/{R}_{c}\ensuremath{\gg}1$, a similar dynamics as that in the homogeneous case emerges at a later time after a initial fast decay of the magnetization. We obtain a stretched exponent of $\ensuremath{\beta}\ensuremath{\approx}0.18$ for the asymptotic evolution with $d=3,\ensuremath{\alpha}=6$, which is different from that in the homogeneous case $(\ensuremath{\beta}=0.5)$.

Relative Binding Free Energy Calculations for Ligands with Diverse Scaffolds with the Alchemical Transfer Method.

We present an extension of the alchemical transfer method (ATM) for the estimation of relative binding free energies of molecular complexes applicable to conventional, as well as scaffold-hopping, alchemical transformations. Named ATM-RBFE, the method is implemented in the free and open-source OpenMM molecular simulation package and aims to provide a simpler and more generally applicable route to the calculation of relative binding free energies than what is currently available. ATM-RBFE is based on sound statistical mechanics theory and a novel coordinate perturbation scheme designed to swap the positions of a pair of ligands such that one is transferred from the bulk solvent to the receptor binding site while the other moves simultaneously in the opposite direction. The calculation is conducted directly in a single solvent box with a system prepared with conventional setup tools, without splitting of electrostatic and nonelectrostatic transformations, and without pairwise soft-core potentials. ATM-RBFE is validated here against the absolute binding free energies of the SAMPL8 GDCC host-guest benchmark set and against protein-ligand benchmark sets that include complexes of the estrogen receptor ERα and those of the methyltransferase EZH2. In each case the method yields self-consistent and converged relative binding free energy estimates in agreement with absolute binding free energies and reference literature values, as well as experimental measurements.

Driven transport of soft Brownian particles through pore-like structures: Effective size method

Single-file transport in pore-like structures constitutes an important topic for both theory and experiment. For hardcore interacting particles, a good understanding of the collective dynamics has been achieved recently. Here, we study how softness in the particle interaction affects the emergent transport behavior. To this end, we investigate the driven Brownian motion of particles in a periodic potential. The particles interact via a repulsive softcore potential with a shape corresponding to a smoothed rectangular barrier. This shape allows us to elucidate effects of mutual particle penetration and particle crossing in a controlled manner. We find that even weak deviations from the hardcore case can have a strong impact on the particle current. Despite this fact, knowledge about the transport in a corresponding hardcore system is shown to be useful to describe and interpret our findings for the softcore case. This is achieved by assigning a thermodynamic effective size to the particles based on the equilibrium density functional of hard spheres.

Bayesian learning of thermodynamic integration and numerical convergence for accurate phase diagrams

Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free energy functions using data of various origin. Our framework allows for propagating statistical uncertainty from finite molecular dynamics trajectories to the phase diagram and automatically performing convergence with respect to simulation parameters. Furthermore, our approach provides a way for automatic optimal sampling in the simulation parameter space based on Bayesian optimization approach. We validate our methodology by constructing phase diagrams of two model systems, the Lennard-Jones and soft-core potential, and compare the results with existing works studies and our coexistence simulations. Finally, we construct the phase diagram of lithium at temperatures above 300 K and pressures below 30 GPa from a machine-learning potential trained on ab initio data. Our approach performs well when compared to coexistence simulations and experimental results.

Efficient Alchemical Intermediate States in Free Energy Calculations Using λ-Enveloping Distribution Sampling.

Alchemical free energy calculations generally require intermediate states along a coupling parameter λ to establish sufficient phase space overlap for obtaining converged results. Such intermediate states can also be engineered to lower the energy barriers and, consequently, reduce the required sampling time. The recently introduced λ-enveloping distribution sampling (λ-EDS) scheme combines the properties of the minimum variance pathway and the EDS methods to improve sampling and allow for larger steps along the alchemical pathway compared to conventional approaches. This scheme also eliminates the need for soft-core potentials and retains the behavior of conventional λ-intermediate states as a limiting case. In this study, an automated procedure is developed to select the parameters of λ-EDS for optimal performance. The underlying theory is illustrated based on simulations of simple test systems (bond length changes in harmonic oscillators, mutations of dihedral angles, and charge creation in water), as well as on the calculation of the absolute hydration free energies of 12 small organic molecules.

DynaBiS: A hierarchical sampling algorithm to identify flexible binding sites for large ligands and peptides.

Knowing the ligand or peptide binding site in proteins is highly important to guide drug discovery, but experimental elucidation of the binding site is difficult. Therefore, various computational approaches have been developed to identify potential binding sites in protein structures. However, protein and ligand flexibility are often neglected in these methods due to efficiency considerations despite the recognition that protein-ligand interactions can be strongly affected by mutual structural adaptations. This is particularly true if the binding site is unknown, as the screening will typically be performed based on an unbound protein structure. Herein we present DynaBiS, a hierarchical sampling algorithm to identify flexible binding sites for a target ligand with explicit consideration of protein and ligand flexibility, inspired by our previously presented flexible docking algorithm DynaDock. DynaBiS applies soft-core potentials between the ligand and the protein, thereby allowing a certain protein-ligand overlap resulting in efficient sampling of conformational adaptation effects. We evaluated DynaBiS and other commonly used binding site identification algorithms against a diverse evaluation set consisting of 26 proteins featuring peptide as well as small ligand binding sites. We show that DynaBiS outperforms the other evaluated methods for the identification of protein binding sites for large and highly flexible ligands such as peptides, both with a holo or apo structure used as input.

Binary mixtures of locally coupled mobile oscillators.

Synchronized behavior in a system of coupled dynamic objects is a fascinating example of an emerged cooperative phenomena which has been observed in systems as diverse as a group of insects, neural networks, or networks of computers. In many instances, however, the synchronization is undesired because it may lead to system malfunctioning, as in the case of Alzheimer's and Parkinson's diseases, for example. Recent studies of static networks of oscillators have shown that the presence of a small fraction of so-called contrarian oscillators can suppress the undesired network synchronization. On the other hand, it is also known that the mobility of the oscillators can significantly impact their synchronization dynamics. Here, we combine these two ideas-the oscillator mobility and the presence of heterogeneous interactions-and study numerically binary mixtures of phase oscillators performing two-dimensional random walks. Within the framework of a generalized Kuramoto model, we introduce two phase-coupling schemes. The first one is invariant when the types of any two oscillators are swapped, while the second model is not. We demonstrate that the symmetric model does not allow for a complete suppression of the synchronized state. However, it provides means for a robust control of the synchronization timescale by varying the overall number density and the composition of the mixture and the strength of the off-diagonal Kuramoto coupling constant. Instead, the asymmetric model predicts that the coherent state can be eliminated within a subpopulation of normal oscillators and evoked within a subpopulation of the contrarians.

STATIC PROPERTIES OF THE 6Li NUCLEUS IN THE THREE-CLUSTER MODEL

This scientific work is devoted to a deep study of the structure of the weakly bound light 6Li nucleus in the framework of the three-cluster α+p+n-model. The realistic Reid soft core potential (RSC-potential) have been utilized as the nucleon-nucleon interaction. The potential with even-odd splitting in waves is used for describing the interaction of the alpha-particle and nucleons. The spectrum of low-lying energy levels of the 6Li nucleus has been calculated, and realistic wave functions of the relative motion of the clusters in this nucleus have been defined. The matrix elements and operators of the main static characteristics of the 6Li nucleus are presented. In particular, the root-mean-square charge and material radii, magnetic dipole and electric quadrupole moments of the 6Li nucleus have been calculated.

Strong-field triple ionisation of atoms with p 3 valence shell

The interaction of strong pulsed femtosecond laser field with atoms having three equivalent electrons in the outer shell (p 3 configuration, e.g. nitrogen) is studied via numerical integration of a time-dependent Schrödinger equation on a spatial grid. Single ionisation, double ionisation (DI) and triple ionisation (TI) yields originating from a completely antisymmetric wave function are calculated and extracted using a restricted-geometry model with the soft-core potential and three active electrons. The observed suppression of the ionisation yields for the non-sequential processes, in both DI and TI cases, is attributed to the action of the Pauli principle. Compared against earlier results investigating the s 2 p 1 configuration, we propose that the differences found here might in fact be accessible through electron’s momentum distribution.

Alchemical Transfer Approach to Absolute Binding Free Energy Estimation.

The alchemical transfer method (ATM) for the calculation of standard binding free energies of noncovalent molecular complexes is presented. The method is based on a coordinate displacement perturbation of the ligand between the receptor binding site and the explicit solvent bulk and a thermodynamic cycle connected by a symmetric intermediate in which the ligand interacts with the receptor and solvent environments with equal strength. While the approach is alchemical, the implementation of the ATM is as straightforward as that for physical pathway methods of binding. The method is applicable, in principle, with any force field, as it does not require splitting the alchemical transformations into electrostatic and nonelectrostatic steps, and it does not require soft-core pair potentials. We have implemented the ATM as a freely available and open-source plugin of the OpenMM molecular dynamics library. The method and its implementation are validated on the SAMPL6 SAMPLing host-guest benchmark set. The work paves the way to streamlined alchemical relative and absolute binding free energy implementations on many molecular simulation packages and with arbitrary energy functions including polarizable, quantum-mechanical, and artificial neural network potentials.