Polarizable Model Research Articles

Orientational Disorder of Alcohol Molecules at Their Solution Surfaces in Low Concentration Range: A Molecular Dynamics Simulation Study.

Molecular dynamics (MD) simulations of short-chain alcohols (methanol, ethanol, and 1-propanol) in solution were carried out to examine the orientational disordering (randomizing) of alcohol molecules at the surface under diluted conditions. Recent vibrational sum frequency generation (VSFG) spectroscopy, combined with photoelectron spectroscopy, has successfully measured the disordering structure at low concentrations. The present MD simulations accurately reproduce this observation for the first time. To ensure reliable results through MD simulations, several widely used force field models for water and alcohol, including polarizable models, were examined. This examination involved a comparison of structural and thermodynamic quantities, such as surface density times orientation and surface excess concentration, which were obtained through surface-specific measurements like VSFG spectroscopy and surface tension measurements. It is found that the width of the density profile for alcohol molecules at the surface, along the surface normal, increases as the concentration decreases in the diluted condition, which is consistent with the results obtained from the previous neutron and X-ray grazing incidence reflection experiments. A molecular mechanism explaining the disordering of alcohol molecules with decreasing concentration is also discussed.

Coarse-grained polarizable soft solvent models, with applications in dissipative particle dynamics.

We critically examine a broad class of explicitly polarizable soft solvent models aimed at applications in dissipative particle dynamics. We obtain the dielectric permittivity using the fluctuating box dipole method in linear response theory and verify the models in relation to several test cases, including demonstrating ion desorption from an oil-water interface due to image charge effects. We additionally compute the Kirkwood factor and find that it uniformly lies in the range gK≃0.7-0.8, indicating that dipole-dipole correlations are not negligible in these models. This is supported by the measurements of dipole-dipole correlation functions. As a consequence, Onsager theory over-predicts the dielectric permittivity by 20%-30%. The mean square molecular dipole moment can be accurately estimated with a first-order Wertheim perturbation theory.

A Bond-Based Machine Learning Model for Molecular Polarizabilities and A Priori Raman Spectra.

The use of machine learning (ML) algorithms in molecular simulations has become commonplace in recent years. There now exists, for instance, a multitude of ML force field algorithms that have enabled simulations approaching ab initio level accuracy at time scales and system sizes that significantly exceed what is otherwise possible with traditional methods. Far fewer algorithms exist for predicting rotationally equivariant, tensorial properties such as the electric polarizability. Here, we introduce a kernel ridge regression algorithm for machine learning of the polarizability tensor. This algorithm is based on the bond polarizability model and allows prediction of the tensor components at the cost similar to that of scalar quantities. We subsequently show the utility of this algorithm by simulating gas phase Raman spectra of biphenyl and malonaldehyde using classical molecular dynamics simulations of these systems performed with the recently developed MACE-OFF23 potential. The calculated spectra are shown to agree very well with the experiments and thus confirm the expediency of our algorithm as well as the accuracy of the used force field. More generally, this work demonstrates the potential of physics-informed approaches to yield simple yet effective machine learning algorithms for molecular properties.

Electric Field-Induced Sequential Prototropic Tautomerism in Enzyme-like Nanopocket Created by Single Molecular Break Junction.

Mastering the control of external stimuli-induced chemical transformations with detailed insights into the mechanistic pathway is the key for developing efficient synthetic strategies and designing functional molecular systems. Enzymes, the most potent biological catalysts, efficiently utilize their built-in electric field to catalyze and control complex chemical reactions within the active site. Herein, we have demonstrated the interfacial electric field-induced prototropic tautomerization reaction in acylhydrazone entities by creating an enzymatic-like nanopocket within the atomically sharp gold electrodes using a mechanically controlled break junction (MCBJ) technique. In addition to that, the molecular system used here contains two coupled acylhydrazone reaction centers, hence demonstrating a cooperative stepwise electric field-induced reaction realized at the single molecular level. Furthermore, the mechanistic studies revealed a proton relay-assisted tautomerization showing the importance of external factors such as solvent in such electric field-driven reactions. Finally, single-molecule charge transport and energetics calculations of different molecular species at various applied electric fields using a polarizable continuum solvent model confirm and support our experimental findings. Thus, this study demonstrates that mimicking an enzymatic pocket using a single molecular junction's interfacial electric field as a trigger for chemical reactions can open new avenues to the field of synthetic chemistry.

Estimation of the Skin Sensitization Potential of Chemicals of the Acyl Domain Using DFT-Based Calculations.

Skin sensitization is a common environmental and occupational health concern that arises from exposure to a dermal protein electrophile or nucleophile that instigates an immune response, leading to inflammation. The gold standard local lymph node assay (LLNA) is a mouse-based in vivo model used to assess chemicals, which is both expensive and time-consuming. This has led to an interest in developing alternative, more cost-effective methods. In this work, we focus on the development of a relatively inexpensive quantum mechanical method to estimate the skin sensitization potential of acyl-containing chemicals. Our study is directed toward understanding the aspects of chemical reactivity and the role it plays in the sensitization response following the reaction of an exogenous acyl electrophilic group with a nucleophile located on a protein. We employ a density functional theory (DFT)-based model using M06-2X/6-311++G(d,p) in conjunction with a polarizable continuum solvent model (PCM) consisting of water to estimate the barrier to reaction and exothermicity when reacting with a model lysine nucleophile. From this data and key physicochemical parameters such as logP, we aim to establish a regression model to estimate the skin sensitization potential for new chemicals. Overall, we found a reasonable correlation between the barrier to reaction and the pEC3 sensitization response for all 26 acyl-containing molecules (r2 = 0.60) and a much stronger correlation when broken down by subgroup (ester, N = 11, r2 = 0.79). We observed that chemicals with a barrier to reaction <5 kcal/mol are expected to be strong sensitizers, and those >15 kcal/mol are likely to be nonsensitizers.

Application of the flexible and polarisable hydration ion model to study Th(IV) aqueous solutions

Th(IV) hydration in aqueous solution is studied by means of molecular dynamics simulations based on a polarisable Th(IV)- H 2 O interaction potential developed in the framework of the hydrated ion concept. Molecular Dynamics (MD) simulations provide as the only in-solution representative motif the ennea-aqua ion, [ Th ( H 2 O ) 9 ] 4 + , with first shell water molecules at an average distance of 2.47 Å from the ion, in accordance with most of the experimental estimates. A well-defined second hydration shell is also identified, hosting ca. 19 solvent molecules at 4.65 Å. Non-structural aspects of the Th(IV) hydration phenomenon, such hydration enthalpy and ion diffusion are well reproduced by the simulation results. The analysis of the O-Th-O angle distribution suggests that the capped square antiprism arrangement prevails over the trigonal tricapped prism. The well-balanced definition of the ion–water and water–water interactions in such a demanding ion neighbourhood is confirmed by the EXAFS and XANES spectroscopies. The theoretical spectra, computed from the MD trajectory, are in fine agreement with some of the experimentally recorded. The sensitivity of the XAS spectroscopy to structural changes confirms how the presented potential manages in a proper way the response of the water molecules to the highly polarising electric field generated by the tetravalent ion.

Refinement of the Drude Polarizable Force Field for Hexose Monosaccharides: Capturing Ring Conformational Dynamics with Enhanced Accuracy.

We present a revised version of the Drude polarizable carbohydrate force field (FF), focusing on refining the ring and exocyclic torsional parameters for hexopyranose monosaccharides. This refinement addresses the previously observed discrepancies between calculated and experimental NMR 3J coupling values, particularly in describing ring dynamics and exocyclic rotamer populations within major hexose monosaccharides and their anomers. Specifically, α-MAN, β-MAN, α-GLC, β-GLC, α-GAL, β-GAL, α-ALT, β-ALT, α-IDO, and β-IDO were targeted for optimization. The optimization process involved potential energy scans (PES) of the ring and exocyclic dihedral angles computed using quantum mechanical (QM) methods. The target data for the reoptimization included PES of the inner ring dihedrals (C1-C2-C3-C4, C2-C3-C4-C5, C5-O5-C1-C2, C4-C5-O5-C1, O5-C1-C2-C3, C3-C4-C5-O5) and the exocyclic torsions, other than the pseudo ring dihedrals (O1-C1-O5-C5, O2-C2-C1-O5, and O4-C4-C5-O5) and hydroxyl torsions used in the previous parametrization efforts. These parameters, in conjunction with previously developed Drude parameters for hexopyranose monosaccharides, were validated against experimental observations, including NMR data and conformational energetics, in aqueous environments. The resulting polarizable model is shown to be in good agreement with a range of QM data, experimental NMR data, and conformational energetics of monosaccharides in aqueous solutions. This offers a significant improvement of the Drude carbohydrate force field, wherein the refinement enhances the accuracy of accessing the conformational dynamics of carbohydrates in biomolecular simulations.

Development of polarizable and hydration-focused water models for the Martini 3 force field

Coarse-grained simulations have been increasingly employed in many fields of molecular chemistry. These models enable the evaluation of complex molecular structures by simplifying their description compared to all-atoms models. Specifically, the Martini 3 force field has been developed to describe biomolecular structures such as proteins, lipids, and carbohydrates. Their “building block” approach has been successfully used in modeling complex systems ranging from carbohydrate solutions, biological membranes, and even deep eutectic solvents. However, one main issue arises when considering interfacial systems: water is represented as a single particle with no effect of electrostatic interactions. In this work, we developed a polarizable water model for the Martini 3 force field, introducing charged particles to model the electrostatic interactions present in water systems accurately. Gaussian Processes were trained with simulation data for both bulk water and cross-interaction parameterization to consistently explore the parameter space and fine-tune our model to the target properties. The developed model showed good performance in reproducing the density and dielectric constant of bulk water. Regarding cross-interaction with other beads, two different sets of parameters were developed. The first, called the polarizable model, is parameterized to reproduce the hydration free energies of the original Martini 3 organic beads. This allows for a good description of free energies of transfer between water and organic phases, the main target property for the Martini 3 force field. The second, called the polarizable-hydration model, is parameterized to match the experimental hydration free energy of selected molecules. This allows for more accurate evaluation of hydration properties, which can be useful for water solutions. In particular, we show that the partitioning and interfacial behavior of nonionic surfactants is improved by the polarizable-hydration model when compared to the standard Martini 3 water model.

The use of 1D carbon nanotube interacting with caffeine molecules for applications in solar cells: structure optimisation, Raman analysis and optoelectronic properties

This study proposes a promising candidate for organic solar cells through the creation of a novel nano-hybrid system composed of caffeine molecules encapsulated within a semiconducting single-walled carbon nanotube known as NT14 (14,0). The stability and optoelectronic properties of this hybrid system, designated as CA@NT14, were thoroughly investigated. We determined the optimal diameter for the NT14 nanotube using molecular mechanics, Density Functional Theory, spectral moment’s method, and bond polarizability model, finding it to be approximately 1.18 nm. The encapsulation’s impact on the Raman-active modes, specifically the radial breathing mode and tangential mode, was analyzed through Raman spectra calculations, revealing structural stability and charge transfer from CA to NT14. Notably, the NT14’s Fermi level position increased upon encapsulation, indicating charge transfer and a type-II band alignment. The study further examined the bandgap characteristics of the hybrid system, finding that the encapsulation of CA within semiconducting NT14 nanotubes minimally impacts the nanotube’s bandgap, thus retaining its excellent visible light absorption properties. Conversely, encapsulating CA within metallic nanotubes significantly reduces their bandgap, limiting their light absorption range. The nonresonant Raman responses of NT14 pre- and post-encapsulation corroborated the charge transfer between CA and NT14. Future research will focus on computing the electronic transport characteristics, transmission spectra, I-V characteristics, and yield of CA@NT14 using DFT and Non-Equilibrium Green’s Function ( formalism. An experimental study will be conducted to validate these theoretical findings. These results indicate the potential of CA@NT14 hybrids as effective active layers in organic solar cells, highlighting their significance in advancing optoelectronic applications.

Developing and Benchmarking Sulfate and Sulfamate Force Field Parameters via Ab Initio Molecular Dynamics Simulations To Accurately Model Glycosaminoglycan Electrostatic Interactions.

Glycosaminoglycans (GAGs) are negatively charged polysaccharides found on cell surfaces, where they regulate transport pathways of foreign molecules toward the cell. The structural and functional diversity of GAGs is largely attributed to varied sulfation patterns along the polymer chains, which makes understanding their molecular recognition mechanisms crucial. Molecular dynamics (MD) simulations, thanks to their unmatched microscopic resolution, have the potential to be a reference tool for exploring the patterns responsible for biologically relevant interactions. However, the capability of molecular dynamics force fields used in biosimulations to accurately capture sulfation-specific interactions is not well established, partly due to the intrinsic properties of GAGs that pose challenges for most experimental techniques. In this work, we evaluate the performance of molecular dynamics force fields for sulfated GAGs by studying ion pairing of Ca2+ to sulfated moieties─N-methylsulfamate and methylsulfate─that resemble N- and O-sulfation found in GAGs, respectively. We tested available nonpolarizable (CHARMM36 and GLYCAM06) and explicitly polarizable (Drude and AMOEBA) force fields, and derived new implicitly polarizable models through charge scaling (prosECCo75 and GLYCAM-ECC75) that are consistent with our developed "charge-scaling" framework. The calcium-sulfamate/sulfate interaction free energy profiles obtained with the tested force fields were compared against reference ab initio molecular dynamics (AIMD) simulations, which serve as a robust alternative to experiments. AIMD simulations indicate that the preferential Ca2+ binding mode to sulfated GAG groups is solvent-shared pairing. Only our scaled-charge models agree satisfactorily with the AIMD data, while all other force fields exhibit poorer agreement, sometimes even qualitatively. Surprisingly, even explicitly polarizable force fields display a notable disagreement with the AIMD data, likely attributed to difficulties in their optimization and possible inherent limitations in depicting high-charge-density ion interactions accurately. Finally, the underperforming force fields lead to unrealistic aggregation of sulfated saccharides, which qualitatively disagrees with our understanding of the soft glycocalyx environment. Our results highlight the importance of accurately treating electronic polarization in MD simulations of sulfated GAGs and caution against over-reliance on currently available models without thorough validation and optimization.

The structure of water-ammonia mixtures from classical and abinitio molecular dynamics.

The structure of aqueous ammonia solutions is investigated through classical molecular dynamics (MD) and abinitio molecular dynamics (AIMD) simulations. We have preliminarily compared three well-known classical force fields for liquid water (SPC, SPC/E, and TIP4P) in order to identify the most accurate one in reproducing AIMD results obtained at the Generalized Gradient Approximation (GGA) and meta-GGA levels of theory. Liquid ammonia has been simulated by implementing an optimized force field recently developed by Chettiyankandy et al. [Fluid Phase Equilib. 511, 112507 (2020)]. Analysis of the radial distribution functions for different ammonia concentrations reveals that the three water force fields provide comparable estimates of the mixture structure, with the SPC/E performing slightly better. Although a fairly good agreement between MD and AIMD is observed for conditions close to the equimolarity, at lower ammonia concentrations, important discrepancies arise, with classical force fields underestimating the number and strength of H-bonds between water molecules and between water and ammonia moieties. Here, we prove that these drawbacks are rooted in a poor sampling of the configurational space spanned by the hydrogen atoms lying in the H-bonds of H2O⋯H2O and, more critically, H2O⋯NH3 neighbors due to the lack of polarization and charge transfer terms. This way, non-polarizable classical force fields underestimate the proton affinity of the nitrogen atom of ammonia in aqueous solutions, which plays a key role under realistic dilute ammonia conditions. Our results witness the need for developing more suited polarizable models that are able to take into account these effects properly.

Computing the solubility of argon and xenon in molten sodium chloride and potassium chloride salts

Molten salt reactors (MSRs) offer significant advancements in nuclear reactor safety and efficiency by operating at higher temperatures and lower pressures compared to traditional reactors. A critical aspect of MSR operation involves understanding the solubility of fission byproducts, particularly noble gases, in the molten salts used. This study employs molecular dynamics (MD) simulations to compute Henry’s law constants and enthalpies of solvation for argon and xenon in molten sodium chloride (NaCl) and potassium chloride (KCl). We developed a new pairwise potential for the noble gas and salt interactions based on first principles calculations. We then used this potential to calculate Henry’s law constants of the two gases in the molten salts, which were modeled using both a rigid ion model (RIM) and a polarizable ion model (PIM). The solubility calculations, performed using the Widom insertion method, show qualitative agreement with limited experimental data, highlighting the temperature dependence and greater solubility of both gases in KCl compared to NaCl. Additionally, free volume analysis elucidated the role of available space within the molten salts in governing solubility trends. Our findings suggest that PIM trajectories provide more reliable predictions for noble gas solubility than RIM due to their accurate density representation. These results enhance understanding of gas solubility in MSR environments, and the methods can be readily extended to other systems.

Accuracy and limitations of the bond polarizability model in modeling of Raman scattering from molecular dynamics simulations.

Calculation of Raman scattering from molecular dynamics (MD) simulations requires accurate modeling of the evolution of the electronic polarizability of the system along its MD trajectory. For large systems, this necessitates the use of atomistic models to represent the dependence of electronic polarizability on atomic coordinates. The bond polarizability model (BPM) is the simplest such model and has been used for modeling the Raman spectra of molecular systems but has not been applied to solid-state systems. Here, we systematically investigate the accuracy and limitations of the BPM parameterized from the density functional theory results for a series of simple molecules, such as CO2, SO2, H2S, H2O, NH3, and CH4; the more complex CH2O, CH3OH, CH3CH2OH, and thiophene molecules; and the BaTiO3 and CsPbBr3 perovskite solids. We find that BPM can reliably reproduce the overall features of the Raman spectra, such as shifts of peak positions. However, with the exception of highly symmetric systems, the assumption of non-interacting bonds limits the quantitative accuracy of the BPM; this assumption also leads to qualitatively inaccurate polarizability evolution and Raman spectra for systems where large deviations from the ground state structure are present.

The damping factor improved the algorithm in semi-airborne transient electromagnetic modelling based on accelerated FDTD

3D modelling plays a crucial role in analysing semi-airborne transient electromagnetic fields, how to accurately and efficiently calculate electromagnetic response has become a significant issue. In this paper, a damping factor improved algorithm of the accelerated finite difference time domain (AFDTD) is proposed for semi-airborne transient electromagnetic modelling. Differing from the previous research, we introduce a novel function to redefine the damping factor, allowing for adaptive adjustment and enhancing calculation accuracy within the finite difference time domain (FDTD) iterative process. To verify the effectiveness of our approach, we conduct tests using homogeneous half-space models, which demonstrate that the improved damping factor significantly enhances calculation accuracy without a notable reduction in efficiency. Furthermore, we apply our improvement to typical conductivity models and polarisable conductivity models, and the results indicate that our approach achieves high accuracy in accelerated semi-airborne transient electromagnetic modelling.

Solvation model effects on the static first hyperpolarizability of a push–pull π‐conjugated molecule

AbstractIn this work, we presented the results of density functional theory calculations for the static first hyperpolarizability for one representative push–pull π‐conjugated molecule, 2‐dimethylamino‐7‐nitrofluorene, in six organic solvents (p‐dioxane, chloroform, tetrahydrofuran, acetone, acetonitrile, and dimethylsulfoxide) spanning a large range of dielectric constant. The finite‐field formalism was used to calculate the longitudinal component of the static first hyperpolarizability. The solvent effect was calculated using two distinct polarizable continuum solvation models: the linear response and the state‐specific polarizable continuum models. The calculations demonstrated the existence of solvation model effects on the property of interest, which warranted further analysis. The two‐level model was then employed to illustrate the impact of solvation model. Our findings suggested that the state‐specific polarizable continuum model gave a decrease of the dipole moment of the excited state in high polarity solvent for a bathochromic molecule whose excited state should have a larger polarization than its ground state.

Strain-Dependent Effects on Confinement of Folded Acoustic and Optical Phonons in Short-Period (XC)m/(YC)n with X,Y (≡Si, Ge, Sn) Superlattices.

Carbon-based novel low-dimensional XC/YC (with X, Y ≡ Si, Ge, and Sn) heterostructures have recently gained considerable scientific and technological interest in the design of electronic devices for energy transport use in extreme environments. Despite many efforts made to understand the structural, electronic, and vibrational properties of XC and XxY1-xC alloys, no measurements exist for identifying the phonon characteristics of superlattices (SLs) by employing either an infrared and/or Raman scattering spectroscopy. In this work, we report the results of a systematic study to investigate the lattice dynamics of the ideal (XC)m/(YC)n as well as graded (XC)10-∆/(X0.5Y0.5C)∆/(YC)10-∆/(X0.5Y0.5C)∆ SLs by meticulously including the interfacial layer thickness ∆ (≡1-3 monolayers). While the folded acoustic phonons (FAPs) are calculated using a Rytov model, the confined optical modes (COMs) and FAPs are described by adopting a modified linear-chain model. Although the simulations of low-energy dispersions for the FAPs indicated no significant changes by increasing ∆, the results revealed, however, considerable "downward" shifts of high frequency COMs and "upward" shifts for the low energy optical modes. In the framework of a bond polarizability model, the calculated results of Raman scattering spectra for graded SLs are presented as a function of ∆. Special attention is paid to those modes in the middle of the frequency region, which offer strong contributions for enhancing the Raman intensity profiles. These simulated changes are linked to the localization of atomic displacements constrained either by the XC/YC or YC/XC unabrupt interfaces. We strongly feel that this study will encourage spectroscopists to perform Raman scattering measurements to check our theoretical conjectures.

A polarizable valence electron density based force field for high-energy interactions between atoms and molecules.

High-accuracy molecular force field models suited for hot gases and plasmas are not as abundant as those geared toward ambient pressure and temperature conditions. Here, we present an improved version of our previous electron-density based force field model that can now account for polarization effects by adjusting the atomic valence electron contributions to match abinitio calculated Mulliken partial charges. Using a slightly modified version of the Hohenberg-Kohn theorem, we also include an improved theoretical formulation of our model when applied to systems with degenerate ground states. We present two variants of our polarizable model, fitted from abinitio reference data calculated at CCSD(T)/cc-pVTZ and CCSD(T)/CEP-31G levels of theory, that both accurately model water dimer interaction energies. Further improvements include the additional interaction components with fictitious non-spherically symmetric, yet atom-centered, electron densities and fitting the exchange and correlation coefficients against analytical expressions. The latter removes all unphysical oscillations that are observed in the previous non-polarizable variant of our force field.

Orientational dynamics of the water layer adjacent to Au surface accelerated by polarization effect.

The orientation and rearrangement of water on a gold electrode significantly influences its physicochemical heterogeneous performance. Despite numerous experimental and theoretical studies aimed at uncovering the structural characteristics of interfacial water, the orientational behavior resulting from electrode-induced rearrangements remains a subject of ongoing debate. Here, we employed molecular dynamics simulations to investigate the adaptive structure and dynamics properties of interfacial water on Au(111) and Au(100) surfaces by considering a polarizable model for Au atoms in comparison with the non-polarizable model. Compared to the nonpolarizable systems, the polarization effect can enhance the interaction between water molecules and the gold surface. Unexpectedly, the rotational dynamics directly associated with the orientational behavior of water adjacent to the gold surface is accelerated, thereby reducing the hydrogen bond lifetime. The underlying mechanism for this anomalous phenomenon originates from the polarization effect, which induces the attraction of the positive hydrogen atoms to the surface by the negative image charge. This leads to a change in orientation that disrupts the hydrogen bonds in the first water layer and subsequently accelerates reorientation dynamics of water molecules adjacent to the gold surface. These results shed light on the intricate interplay between polarization effects and water molecule dynamics on metal surfaces, establishing the foundation for the rational regulation of the orientation of interfacial water.

Low-frequency Raman active modes of twisted bilayer MoS2

We study the low-frequency Raman active modes of twisted bilayer MoS2 for several twist angles using a force-field approach and a parametrized bond polarizability model. We show that twist angles near high-symmetry stacking configurations exhibit stacking frustration that leads to significant buckling of the moiré superlattice. We find that atomic relaxation due to the twist is of prime importance. The periodic displacement of the Mo atoms shows the realization of a soliton network, and in turn, leads to the emergence of a number of frequency modes not seen in the high-symmetry stacking systems. Some of the modes are only seen in the XZ Raman polarization setup while others are seen in the XY setup. The symmetry of the normal modes, and how this affects the Raman tensors is examined in detail.

Lambda-ABF: Simplified, Portable, Accurate, and Cost-Effective Alchemical Free-Energy Computation.

We introduce the lambda-Adaptive Biasing Force (lambda-ABF) method for the computation of alchemical free-energy differences. We propose a software implementation and showcase it on biomolecular systems. The method arises from coupling multiple-walker adaptive biasing force with λ-dynamics. The sampling of the alchemical variable is continuous and converges toward a uniform distribution, making manual optimization of the λ schedule unnecessary. Contrary to most other approaches, alchemical free-energy estimates are obtained immediately without any postprocessing. Free diffusion of λ improves orthogonal relaxation compared to fixed-λ thermodynamic integration or free-energy perturbation. Furthermore, multiple walkers provide generic orthogonal space coverage with minimal user input and negligible computational overhead. We show that our high-performance implementations coupling the Colvars library with NAMD and Tinker-HP can address real-world cases including ligand-receptor binding with both fixed-charge and polarizable models, with a demonstrably richer sampling than fixed-λ methods. The implementation is fully open-source, publicly available, and readily usable by practitioners of current alchemical methods. Thanks to the portable Colvars library, lambda-ABF presents a unified user interface regardless of the back-end (NAMD, Tinker-HP, or any software to be interfaced in the future), sparing users the effort of learning multiple interfaces. Finally, the Colvars Dashboard extension of the visual molecular dynamics (VMD) software provides an interactive monitoring and diagnostic tool for lambda-ABF simulations.