Abstract Peptides at biological interfaces often encode function through preferential compatibility with chemical environments rather than through binding to a single molecular target. We report a physically motivated, knowledge-based Hamiltonian for programming such preferences in α-helical peptides. The model maps amino-acid sequences onto a normalized energy landscape that combines helix propensity, local sequence context, residue contacts, solvent exposure, membrane charge coupling, and electrostatic screening. Random-reference Z-scores place different lengths, residue sets, and environments on a common scale. In homogeneous benchmarks, the Hamiltonian separates experimentally characterized alanine-rich Glu/Lys water-soluble helices from WALP/GWALP transmembrane model helices. In interfacial benchmarks, it recognizes canonical membrane-active antimicrobial peptides as preferentially stabilized at anionic interfaces over neutral, cationic, aqueous, and apolar alternatives, while rejecting non-antimicrobial helical controls. The same score generates sequence libraries for environment-specific compatibility, polar–apolar robustness, and one-vs-rest anionic selectivity. Low-energy ensembles display amphipathic segregation, charge regulation, and hydrophobicity periodicity at sequence separations of 3 and 4 residues, linking the designed sequences to interpretable chemical organization. Because the objective is a discrete Hamiltonian, it can be explored by exact search, classical heuristics, and binary-encoded quantum-compatible workflows without changing the scoring function. This framework provides a transparent route to design α-helical peptides whose environmental preferences are specified directly in the molecular objective.
Abstract This study presents the relativistic prolapse-free Gaussian basis sets of double- and triple-ζ quality (RPF-2Z and RPF-3Z, respectively) developed for f-block elements. Thus, RPF-2Z and RPF-3Z are achieved after the augmentation of small- and medium-size sets of primitive functions previously generated, respectively, by correlation/polarization (C/P) functions obtained by relying on the power of a polynomial version of the Generator-Coordinate Dirac-Fock method aiming a description of the valence space. These C/P functions are selected based on the results of multi-reference configuration interaction calculations and also considering consistency arguments when compared to the already proposed RPF-4Z set for the same elements. Versions of these new sets containing extra diffuse functions (aug-RPF-2Z and aug-RPF-3Z) are promptly defined as well. Calculations of fundamental molecular properties show that these new basis sets constitute reliable alternatives to well-known sets of similar quality. Finally, due to the absence of variational prolapse, the new sets must show advantages in investigations of properties that are more strongly affected by the distribution of the innermost electrons.
Abstract The orbital cluster expansion (OCE) matches neural-network potentials on biomolecular benchmarks at linear-regression cost, but its topology-only basis is blind to geometric variation at fixed connectivity and fails on out-of-distribution rings. We add three geometric feature classes─distance-binned pair counts (CT2F), distance-binned electrostatics (Madelung-CT2F), and angular triplets (CT3F)─a bootstrap-variance active-learning protocol with a basis-adequacy filter, and a Δ-learning extension against a GFN2-xTB baseline. The recommended Wave-1.5 basis is 1F + 2F + 3F + CT2F + MADCT2F + CT3F; where partial charges are unavailable (peptides), a GFN2-xTB single-point supplies per-conformer Mulliken charges for MADCT2F at ≈ 28 ms per conformer. Validation: (i) carbon allotrope out-of-distribution RMSE 596 → 97 meV per atom (−84%) with 26 features, against 87 meV per atom for a 12-feature Behler–Parrinello symmetry-function baseline that lacks OCE’s multielement transferability and partial-charge channel; (ii) PEPCONF within-parent ranking ⟨ρ⟩ on tripeptides 0.10 → 0.38 → 0.54 under CT2F → full Wave-1.5 (×5.4 cumulative) and disulfides 0.24 → 0.57, with 15–33% intra-parent RMSE drops in four of five categories; (iii) halide perovskites RMSE 172 → 63 ± 10 meV per atom under Wave-1.5 (mean ± s.d., 20 resplits, −63%; better than the 1F + 2F baseline on 20/20 splits), strain held-out 577 → 181 meV per atom (ρ 0.19 → 0.87), and 152 meV per atom (ρ = 0.91) under Δ-learning, the Cs/K family disparity resolved by Madelung-CT2F, and an active-learning loop converging from 210 to 116 meV per atom; (iv) QMOF metal–organic frameworks total-energy RMSE 74 → 60 meV per atom (−19%) and band gap RMSE 0.623 → 0.552 eV (R2 0.61 → 0.69), establishing band gap as a screening target. Inference remains microsecond-scale, three to 5 orders of magnitude faster than GFN2-xTB, DFTB+, and DFT.
The development of accurate and transferable force fields for metal-organic frameworks (MOFs) remains a significant challenge. Here, we introduce MODEX, a modular and extensible force field for MOFs. MODEX employs a building block approach in which the inorganometallic node and organic linker are parametrized separately and subsequently combined. Currently, MODEX is parametrized for ten representative Zr-based MOFs. Zr-based MOFs represent an important class of MOFs with a wide range of applications; however, limited transferable force fields have been developed exclusively for this family. The parametrization is driven by a custom multiobjective particle swarm optimization (PSO) algorithm implemented in our Force Field Factory program, enabling simultaneous fitting to multiple types of quantum chemistry reference data. The resulting force field accurately reproduces the structural, phonon, and mechanical properties of the ten target Zr-based MOFs. Furthermore, MODEX accurately captures the rotational dynamics of the linker in UiO-66, reproducing both the rotational barrier and the thermally accessible conformational space obtained from quantum chemistry calculations. MODEX is designed for continuous expansion; new building blocks can be readily parametrized using Force Field Factory. This work establishes MODEX as a robust force field for large-scale simulations of the ten Zr-based MOFs studied here and provides a platform for future extension to new frameworks.
Accurate reaction energetics in complex environments require correlated electronic-structure accuracy in the reactive region while retaining the influence of the surrounding system. Density functional embedding theory (DFET) enables this balance by introducing a local embedding potential that makes the cluster and environment densities reproduce the full-system Kohn-Sham density. However, obtaining this potential through optimized effective potential (OEP) or Wu-Yang optimization can be expensive, especially for metallic systems where dense frontier orbital manifolds make direct second-order optimization difficult. Here, we introduce a gradient-enhanced surrogate strategy for DFET embedding-potential optimization. The method builds a kernel-based surrogate of the Wu-Yang objective from previously evaluated functional values and gradients, optimizes this surrogate within a trust region and adaptive Newton subspace, and evaluates the true Wu-Yang functional only for selected trial potentials. The resulting surrogate-optimized embedding potentials are used in embedded correlated wave function (ECW) calculations and benchmarked against trust-exact OEP potentials and all-atom NEVPT2 reaction energies. Across representative metallic and molecular reaction benchmarks, the surrogate approach produces embedding potentials comparable to trust-exact baselines while reducing the number of expensive true OEP evaluations for challenging metallic systems. ECW energies driven by surrogate-optimized embedding potentials closely reproduce all-atom NEVPT2 reaction profiles and improve over parent KS-DFT. These results show that surrogate OEP provides a practical and accurate route to DFET embedding potentials for large and electronically complex systems.
Antimicrobial peptide (AMP) design is commonly guided by sequence-level descriptors such as cationicity, hydrophobicity, and amphipathicity. However, this design paradigm often relies on empirical intervention or machine-learning prediction, lacks direct support from rigorous quantitative thermodynamic data, and remains difficult to apply to the optimization of known AMP sequences. Here, using the recently proposed WTM-λABF method, we develop an alchemical free-energy framework that incorporates peptide-membrane affinity calculations into sequence reoptimization. Owing to the enhanced sampling efficiency of WTM-λABF, this framework can efficiently handle densely discretized alchemical pathways required for cooperative multiresidue mutations, thereby enabling simultaneous multiresidue substitutions to be evaluated within a single alchemical transformation in each environment, without decomposition into separate single-residue transformations. Following the empirical proposal of candidate mutations, mutation-induced ΔΔG values are used as a membrane-affinity thermodynamic criterion for their interpretation, classification, and prioritization prior to experimental validation. We first validate the framework using a literature-reported membrane-active peptide series, where the calculated ΔΔG values are interpreted together with experimental activity trends and physicochemical descriptors. We then apply the framework to the iterative reoptimization of AMP sequences identified in our previous work. Stepwise multiresidue mutations are first proposed based on empirical design principles and subsequently evaluated using WTM-λABF, thereby identifying mutations that provide favorable contributions to relative membrane affinity and yielding new candidate AMP sequences for subsequent experimental screening. By extending the previously developed WTM-λABF method to mutation-dependent membrane-insertion thermodynamics in medium-length AMP-membrane systems, this work establishes a physically grounded framework that integrates empirical AMP redesign with free-energy-based thermodynamic evaluation of multiresidue reoptimization.
Metal-organic frameworks (MOFs) are promising materials for adsorption and separation, but accurately predicting water adsorption remains a major challenge in molecular simulation. Classical force fields, such as UFF, often fail to capture the strong, directional hydrogen-bonding interactions between water and MOFs, while high-throughput density functional theory (DFT) calculations are computationally prohibitive. Here, we develop a transferable machine-learning potential (MLP) for water adsorption in Al-based MOFs by fine-tuning the pretrained MACE foundation model. Using a data set of 420 Al-MOFs with diverse chemical environments, we show that accurate prediction of water adsorption thermodynamics requires not only an improved description of water-framework interactions but also explicit treatment of framework flexibility. The resulting model reproduces experimental heats of adsorption and Henry coefficients for a series of benchmark Al-MOFs and achieves DFT-level accuracy across more than 400 Al-MOFs. Analysis of MIL-160 establishes practical accuracy requirements of approximately 10 kJ mol-1 in total energies and 40 meV Å-1 in atomic forces for reliable adsorption thermodynamics. Compared with DFT-level predictions, UFF underestimates water adsorption enthalpies by more than 10 kJ mol-1 for 74% of the materials studied. In addition, the MLP identifies lower-energy framework configurations than previously reported DFT-optimized structures, highlighting the importance of enhanced configurational sampling. These results demonstrate that foundation-model-based machine-learning potentials can enable DFT-accurate, high-throughput screening of water adsorption in flexible MOFs.
Computation of redox potential of cofactors in biological systems requires an accurate description of the interaction between the redox cofactors and the biomolecular environment and extensive conformational sampling. Seeking to achieve a quantitative leap in redox potential evaluation for flavoproteins, we report here the calibration of sets of parameters to describe flavin molecules in various redox states in the framework of AMOEBA, a multipolar and polarizable force field. We calibrate both the isoalloxazine ring in the five biologically relevant redox states and the polyol chain needed to describe riboflavin or flavin adenine dinucleotide molecules. We propose a delineated, step-by-step protocol to accurately account for the physical effects at play. We provide evidence that these parameters produce stable conformations in agreement with quantum chemistry (DFT) calculations. The newly derived AMOEBA force field allows to compute interaction energies of lumiflavin with water molecules and amino acids in very good agreement with quantum chemistry calculations, with a net improvement with respect to a monopolar nonpolarizable force field. Finally, as a first application, we compute redox free energy of half-reactions for two redox couples of lumiflavin in water. The values obtained are once again in better agreement with DFT values than those obtained with a standard classical force field.
Accurately predicting excited-state properties of heterogeneous systems remains a central challenge in computational chemistry and materials science. Dielectric-dependent hybrid functionals have achieved notable success for bulk semiconductors and insulators, but their reliance on a scalar macroscopic dielectric constant hampers their applicability to systems with spatially inhomogeneous screening environments. Here, we use hybrid functionals with spatially dependent screened exchange within linear-response time-dependent density functional theory (TDDFT), and we evaluate analytical excited-state forces, enabling geometry relaxation on excited-state potential-energy surfaces and the computation of adiabatic excitation energies. We first consider point defects in three-dimensional bulk hosts, including diamond, silicon carbide, and magnesium oxide, and we show that our approach preserves the accuracy of conventional dielectric-dependent hybrid functionals. For systems with strongly heterogeneous dielectric environments, including the Cr(o-tolyl)4 molecular qubit embedded in a Sn(o-tolyl)4 host matrix and the CBCN defect in monolayer h-BN, hybrid functionals with spatially dependent screened exchange yield substantially improved agreement with experiment and high-level many-body benchmarks, compared to conventional dielectric-dependent hybrid functionals. Our results establish hybrid-functional TDDFT with spatially dependent screened exchange as a broadly applicable and physically motivated strategy for excited-state simulations of complex, inhomogeneous environments.
We introduce spin-resolved dielectric bath embedding theory (SR-DBET), which incorporates a physics-informed embedding potential to describe attractive and repulsive interactions, a charge dielectric bath to capture charge polarization, and a spin dielectric bath to account for spin density fluctuations. We demonstrate the accuracy of SR-DBET through adsorption energy calculations on Cu surfaces. This embedding scheme is essential for extending embedded correlated wave function theory to spin-polarized quantum systems.
Machine learning potentials (MLPs) have emerged as game-changing tools for large-scale atomic simulations, overcoming the poor-scaling limitation intrinsic to traditional quantum mechanics (QM) methods. However, accurately incorporating electronic information remains a significant challenge for MLPs, particularly in efficiently computing the dynamic properties of matter under electric fields─a task central to topics such as infrared spectroscopy, interfaces under electric fields, and ferroelectric polarization. Herein, we report a physics-informed pairwise charge-transfer (PQT) theory to derive dynamic equations for macroscopic polarization that inherently conserve fundamental physical laws. Using the PQT theory, a Generalized Global Neural Network (GGNN) enhanced with the PQT mechanism is developed for the rapid prediction of dynamic properties under electric fields, applicable to both molecules and materials across the periodic table. Specifically, a generalized global data set comprising 3.18 million structures with atomic charges for 81 elements is utilized to pretrain a GGNN patched with PQT modules. Leveraging this pretrained GGNN-PQT potential, we can conveniently sample the potential energy surface under electric fields and fine-tune the potential using a small QM data set containing exact response properties at low cost. Our GGNN-PQT has linear scaling and introduces a low computational overhead compared to the standard GGNN, yet achieves both high speeds and low scaling. We demonstrate the performance of GGNN-PQT in computing dynamic response properties across a wide range of systems, including isolated molecules, adsorbed molecules, molecular crystals, liquid water, and ferroelectric materials.
Understanding the structure of the electrical double layer (EDL) at the electrode-electrolyte interface is crucial for electrocatalytic and charge storage processes. The EDL structure is strongly influenced by electrode polarization, highlighting the need for accurate modeling of polarization effects. This study introduces a novel simulation method known as dynamic mirror image molecular dynamics (DMI-MD) to incorporate electrode polarization within classical molecular dynamics (MD) simulations. DMI-MD employs a dynamically varying mirror plane whose position depends on the locations of the electrolyte charges. Within the image-charge framework, this approach reproduces the ab initio linear-response electrostatic polarization of the slab, thereby providing a simplified yet accurate representation of complex electrode polarization. Comparative analysis demonstrates the superior performance of this approach over other MD polarization methods, effectively capturing the characteristic camel-shaped double-hump behavior of EDL capacitance. DMI-MD is poised to be a valuable tool for computationally efficient modeling of polarization effects at diverse interfaces within classical MD frameworks.
An analytic nuclear energy gradient for multicomponent coupled-cluster theory with single and double excitations (CCSD) is introduced along with the corresponding Z-vector equations, assuming that the wave function of the quantum nuclei is a Hartree product and no proton-proton double excitation operators are included in the cluster operator. The analytic gradient is used to optimize molecular geometries to determine vibrationally averaged bond distances and angles, from which rotational constants are calculated. The Z-vector methodology is used to calculate relaxed protonic densities and dipole moments at vibrationally averaged geometries. Due to the essential role that analytic energy gradients play in electronic structure theory, we expect the analytic nuclear energy gradient to enable many applications for including nuclear quantum effects in coupled-cluster calculations.
Abstract The mechanisms underlying critical energy-gap fluctuations and nonadiabatic dynamics in disordered condensed phases remain elusive, and their accurate simulation poses a challenge due to the inherent complexity of these systems. In this study, we make the first attempt to leverage highly efficient coarse-grained (CG) models to investigate these fundamental mechanisms. Employing a rigorous bottom-up parameterization approach, we construct CG models for two prototypical systems: a carotenoid–porphyrin–fullerene triad in tetrahydrofuran and a perylene diimide dimer in acetonitrile. Using nonadiabatic semiclassical mapping dynamics, we evaluate a hierarchy of representations spanning fully atomistic explicit-molecule simulations, intermediate CG resolutions, and highly reduced multistate harmonic (MSH) models to assess their impact on energy-gap fluctuations and nonadiabatic properties. A distinct advantage of these explicit-molecule simulations is their ability to yield time-dependent radial distribution functions, revealing the detailed molecular picture of localized solvent rearrangement upon photoinduced charge transfer. Our results confirm that with appropriate coarse-graining of the solvent and solute, the resulting CG models faithfully preserve the structural responses, pairwise reorganization energies, and electronic population dynamics of the atomistic benchmark. Conversely, aggressive 2-heavy-atom solute mapping severely distorts local nonbonded environments. Importantly, MSH models parameterized from structurally valid CG simulations successfully reproduce explicit-molecule dynamics while discarding tens of thousands of degrees of freedom. This work provides a new, highly efficient theoretical foundation for scaling nonadiabatic dynamics simulations to larger and more complex condensed-phase systems.
Abstract Machine learning electron densities enabled fast quantum chemistry but suffered from a fidelity gap in downstream tasks due to integration errors and unbalance on uniform grids. We introduce MARGR, an adaptive framework that refines the grid only in the critical regions. We analyze its efficiency through theory and benchmark it on molecular property calculations, demonstrating that adaptive grid refinement achieves an accuracy comparable to high-resolution uniform grids at substantially reduced computational cost.
Abstract In this work, we have extended the existing “sol-3c” composite methods to meta-GGA XC functionals using the r2SCAN one. The corresponding r2SCAN-based composite methods in their pure and hybrid HF/DFT variants have been developed in combination with double-ζ (sol-def2-mSVP) and triple-ζ (pob-TZVP-rev2) quality basis sets specifically adapted to solids. The r2SCAN “sol-3c/pob-3c” methods are validated and tested on benchmark sets containing both intermolecular adducts (S66 × 7), molecular crystals (X23, DMC8) and simple inorganic solids (SS20). They are then applied to selected applications of relevance for solid-state calculations such as the study of the energetic and structural properties of layered materials, the mechanical, electronic and vibrational properties of α-quartz, relative stability of all-silica zeolite polymorphs, α-quartz vs stishovite phase transition and the adsorption of small molecules on the surface of inorganic solids and in the pore of metal–organic frameworks. The new methods show broad applicability with accurate results and an adjustable and affordable computational cost.
Abstract We present an automated path-integral generator for resonance Raman (RR) calculations supporting Herzberg–Teller effects and Duschinsky rotation, and able to treat any type of vibrational transition, including overtones, combination bands, as well as hot bands. The method constructs the required tensor invariants directly from low-rank intermediates, avoiding both transition-specific manual derivations and the explicit construction of high-order correlation functions. The generated expressions are canonicalized symbolically and evaluated through optimized contraction paths. Compared to formulations based on explicit high-rank correlation tensors, this substantially lowers the asymptotic cost for several higher-order transition classes while providing a unified workflow for automatic expression generation. We validate the approach for multiple transition families, examine the influence of finite-temperature effects through hot-band contributions, and show how it can be straightforwardly extended to resonance Raman optical activity (RROA).
Abstract Position-dependent diffusivities are central parameters in reduced stochastic descriptions of molecular transport in heterogeneous environments, but their reliable estimation from molecular dynamics simulations remains challenging. We present a residence-time approach (RTA) that extracts local diffusivities from first-exit statistics measured in biased simulations after compensation of the mean free-energy gradient. We apply the method to oxygen diffusion across a hexadecane/water slab, water permeation across a POPC lipid bilayer, and transport of water and volatile organic compounds through a model skin-barrier membrane. In the slab system, RTA diffusivities agree with independently determined bulk reference values. In the membrane systems, propagator predictions based on RTA-derived diffusivities reproduce unbiased molecular dynamics propagators over substantial lag-time ranges, while also revealing that, in some cases, no single lag-time-independent diffusivity profile captures the dynamics across all time scales. These results support residence-time statistics as a practical route for determining effective position-dependent diffusivities from biased molecular simulations.
We report the state-averaged spin-orbit driven similarity renormalization group second-order perturbation theory (SA-SO-DSRG-PT2) for efficient computations of spin-orbit coupling (SOC) effects in multireference systems. This approach adopts a set of multiconfigurational reference states obtained with a spin-free relativistic Hamiltonian and introduces SOC during the perturbative treatment of dynamical correlation. Specifically, the zeroth-order Hamiltonian is defined from the spin-free Hamiltonian, while the remaining spin-free contributions and the spin-dependent Hamiltonian enter as first-order perturbations in the DSRG transformation. This formulation generates an SOC-containing SA-DSRG-PT2 effective Hamiltonian while largely preserving the computational cost of the conventional spin-free theory. Two spin-dependent Hamiltonians are examined: the first-order Douglas-Kroll-Hess spin-orbit Hamiltonian with mean-field approximated two-electron contributions and the spin-dependent part of the one-electron X2C Hamiltonian with the screened-nuclear spin-orbit approximation. Benchmarks on main-group atoms and diatomic molecules, transition-metal elements, trivalent lanthanide cations, and actinide dioxide cations show consistent accuracy across the periodic table for both spin-dependent Hamiltonians. Applications to Co(II) single-ion magnets, including systems described with up to 1790 basis functions, further highlight the promise of SA-SO-DSRG-PT2 for efficient SOC calculations in large open-shell molecules.
X-ray absorption spectroscopy (XAS) is widely used as an element-specific probe of local electronic and geometric structures, yet its accurate simulation for correlated systems remains challenging because it requires the simultaneous treatment of large active spaces and dynamic electron correlation. In this work, we present a matrix-product-state-based multireference configuration interaction (MPS-MRCI) approach for XAS simulations in such systems. The method is assessed across closed-shell, strongly correlated, and open-shell systems. For pyrazine, systematic calculations reveal the influence of active space size and dynamic correlation on the C and N K-edge spectra. Applications to pentacene, ozone, and the allyl radical further evaluate the performance of MPS-MRCI for a large π-conjugated system, a strongly correlated biradicaloid, and an open-shell system, respectively. The calculated spectra generally reproduce the major experimental features, with natural transition orbital analysis providing insight into the corresponding core excitations through visualization of hole-particle pairs. This work establishes MPS-MRCI as a viable approach for core-level spectroscopy of correlated systems, enabling the treatment of large active spaces and the recovery of dynamic correlation.
