Pub Date : 2026-03-23DOI: 10.1021/acs.jctc.6c00215
Qingpeng Wang, Ning Zhang, Wenjian Liu
The integration of quantum chemical methods with high-performance computing is indispensable for handling large systems with modest accuracy or even small systems but with high accuracy. Continuing with the unified implementation of nonrelativistic and relativistic wave function methods within the MetaWave platform (J. Phys. Chem. A2025, 129, 5170), we present here a unified MPI parallelization of the methods by abstracting every computational step of a method as a dynamically scheduled loop via ghost process, followed by a global reduction of local results from each node. The algorithmic abstraction enables the use of a single MPI template in various steps of different methods. Taking iCIPT2 [J. Chem. Theory Comput.2021, 17, 949] as a showcase, the parallel efficiencies achieve 94% and 89% on 16 nodes (1024 cores) for the perturbation and whole calculations, respectively. Further combined with an improved algorithm for the matrix-vector product in the matrix diagonalization and an orbital-configuration-based semistochastic estimator for the perturbation correction, this renders large active space calculations possible, so as to obtain benchmarks for the automerization of cyclobutadiene, ground-state energy of benzene, and potential energy profile of ozone. It is also shown that the error of iCIPT2 follows a power law with respect to the number of configuration state functions.
{"title":"Unified MPI Parallelization of Wave Function Methods: iCIPT2 as a Showcase.","authors":"Qingpeng Wang, Ning Zhang, Wenjian Liu","doi":"10.1021/acs.jctc.6c00215","DOIUrl":"https://doi.org/10.1021/acs.jctc.6c00215","url":null,"abstract":"<p><p>The integration of quantum chemical methods with high-performance computing is indispensable for handling large systems with modest accuracy or even small systems but with high accuracy. Continuing with the unified implementation of nonrelativistic and relativistic wave function methods within the MetaWave platform (<i>J. Phys. Chem. A</i> <b>2025</b>, <i>129</i>, 5170), we present here a unified MPI parallelization of the methods by abstracting every computational step of a method as a dynamically scheduled loop via ghost process, followed by a global reduction of local results from each node. The algorithmic abstraction enables the use of a single MPI template in various steps of different methods. Taking iCIPT2 [<i>J. Chem. Theory Comput.</i> <b>2021</b>, <i>17</i>, 949] as a showcase, the parallel efficiencies achieve 94% and 89% on 16 nodes (1024 cores) for the perturbation and whole calculations, respectively. Further combined with an improved algorithm for the matrix-vector product in the matrix diagonalization and an orbital-configuration-based semistochastic estimator for the perturbation correction, this renders large active space calculations possible, so as to obtain benchmarks for the automerization of cyclobutadiene, ground-state energy of benzene, and potential energy profile of ozone. It is also shown that the error of iCIPT2 follows a power law with respect to the number of configuration state functions.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":" ","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147502754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-23DOI: 10.1021/acs.jctc.5c01837
Gianluca Levi, Max Kroesbergen, Louis Thirion, Yorick L A Schmerwitz, Elvar Ö Jónsson, Pavlo Bilous, Philipp Hansmann, Hannes Jónsson
Rydberg excited states of molecules pose a challenge for electronic structure calculations because of their highly diffuse electron distribution. Even large and elaborate atomic basis sets tend to underrepresent the long-range tail, overly confining the Rydberg state. An approach is presented here where the molecular orbitals are variationally optimized for the excited state using a plane wave basis set in a Hartree-Fock calculation, followed by a configuration interaction calculation. The use of excited state optimized orbitals greatly enhances the convergence of the many-body calculation, as illustrated by a full configuration interaction calculation of the 2s Rydberg state of H2. A neural-network-based selective configuration interaction approach is then applied to calculations of 3s and 3p states of H2O and NH3. The obtained values of excitation energy are in close agreement with experimental measurements as well as previous many-body calculations where sufficiently diffuse atomic basis sets were used. Calculations using atomic basis sets lacking extra diffuse functions, such as aug-cc-pVTZ, give significantly higher estimates due to confinement of the Rydberg states.
{"title":"Orbital Optimization and Neural-Network-Assisted Configuration Interaction Calculations of Rydberg States.","authors":"Gianluca Levi, Max Kroesbergen, Louis Thirion, Yorick L A Schmerwitz, Elvar Ö Jónsson, Pavlo Bilous, Philipp Hansmann, Hannes Jónsson","doi":"10.1021/acs.jctc.5c01837","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c01837","url":null,"abstract":"<p><p>Rydberg excited states of molecules pose a challenge for electronic structure calculations because of their highly diffuse electron distribution. Even large and elaborate atomic basis sets tend to underrepresent the long-range tail, overly confining the Rydberg state. An approach is presented here where the molecular orbitals are variationally optimized for the excited state using a plane wave basis set in a Hartree-Fock calculation, followed by a configuration interaction calculation. The use of excited state optimized orbitals greatly enhances the convergence of the many-body calculation, as illustrated by a full configuration interaction calculation of the 2s Rydberg state of H<sub>2</sub>. A neural-network-based selective configuration interaction approach is then applied to calculations of 3s and 3p states of H<sub>2</sub>O and NH<sub>3</sub>. The obtained values of excitation energy are in close agreement with experimental measurements as well as previous many-body calculations where sufficiently diffuse atomic basis sets were used. Calculations using atomic basis sets lacking extra diffuse functions, such as aug-cc-pVTZ, give significantly higher estimates due to confinement of the Rydberg states.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":" ","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147502739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-23DOI: 10.1021/acs.jctc.5c01818
Alex Krotz, Antonio J Garzón-Ramírez, Ethan Byrd, Ken Miyazaki, Roel Tempelaar
QC Lab is an open-source Python package for quantum-classical (QC) dynamics simulations aimed to promote the development of QC algorithms, and their application to a wide variety of relevant model problems. It follows a modular design that facilitates cross-compatibility between algorithms and models. By decomposing algorithms and models into a series of tasks and ingredients that can be substituted and reused, it minimizes development efforts and code redundancy. In this Paper, we introduce the first stable version of QC Lab, and describe its design philosophy.
{"title":"QC Lab: A Python Package for Quantum-Classical Dynamics.","authors":"Alex Krotz, Antonio J Garzón-Ramírez, Ethan Byrd, Ken Miyazaki, Roel Tempelaar","doi":"10.1021/acs.jctc.5c01818","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c01818","url":null,"abstract":"<p><p>QC Lab is an open-source Python package for quantum-classical (QC) dynamics simulations aimed to promote the development of QC algorithms, and their application to a wide variety of relevant model problems. It follows a modular design that facilitates cross-compatibility between algorithms and models. By decomposing algorithms and models into a series of tasks and ingredients that can be substituted and reused, it minimizes development efforts and code redundancy. In this Paper, we introduce the first stable version of QC Lab, and describe its design philosophy.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":" ","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147502777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-23DOI: 10.1021/acs.jctc.6c00065
Melissa T Manetsch, David W Kastner, Yuriy Román-Leshkov, Heather J Kulik
We introduce pyEF, a software package for computing molecular electric fields, electrostatic interaction energies, and electrostatic potentials from quantum mechanical (QM) atom-centered multipole expansions with atom-wise decomposable contributions. We demonstrate the computational efficiency and accuracy of this QM-derived electric field evaluation tool through several tests. To assess the influence of the underlying QM method and charge partitioning scheme on these electrostatic quantities, we analyze over 250 configurations of an acetone solute molecule in five solvents of variable polarity. We find that electric field calculations are highly sensitive to the choice of charge partitioning method. Even among real-space charge schemes, acetone Stark tuning rates differ by up to a factor of 2. Benchmarking computed solvent dipole moments against experimental bulk values, we conclude that the CM5, ADCH, and Hirshfeld-I charge schemes most reliably capture solvent electrostatics and therefore provide a more faithful foundation for computing electric fields. When constructed from these real-space charges, electric fields are nearly insensitive to basis set size and monotonically increase in magnitude with higher Fock exchange. We also demonstrate efficient convergence of QM electrostatics when more distant molecules are represented solely by MM point charges, reducing computational overhead. Leveraging these findings, we demonstrate the use of pyEF to deduce environmental effects on a transition metal complex from a Ga4L612- nanocage and quantify the dominant role of organic linkers in orchestrating electrostatic preorganization.
{"title":"pyEF: A Python Framework for QM and QM/MM Atom-Wise Electric Field Analysis.","authors":"Melissa T Manetsch, David W Kastner, Yuriy Román-Leshkov, Heather J Kulik","doi":"10.1021/acs.jctc.6c00065","DOIUrl":"https://doi.org/10.1021/acs.jctc.6c00065","url":null,"abstract":"<p><p>We introduce pyEF, a software package for computing molecular electric fields, electrostatic interaction energies, and electrostatic potentials from quantum mechanical (QM) atom-centered multipole expansions with atom-wise decomposable contributions. We demonstrate the computational efficiency and accuracy of this QM-derived electric field evaluation tool through several tests. To assess the influence of the underlying QM method and charge partitioning scheme on these electrostatic quantities, we analyze over 250 configurations of an acetone solute molecule in five solvents of variable polarity. We find that electric field calculations are highly sensitive to the choice of charge partitioning method. Even among real-space charge schemes, acetone Stark tuning rates differ by up to a factor of 2. Benchmarking computed solvent dipole moments against experimental bulk values, we conclude that the CM5, ADCH, and Hirshfeld-I charge schemes most reliably capture solvent electrostatics and therefore provide a more faithful foundation for computing electric fields. When constructed from these real-space charges, electric fields are nearly insensitive to basis set size and monotonically increase in magnitude with higher Fock exchange. We also demonstrate efficient convergence of QM electrostatics when more distant molecules are represented solely by MM point charges, reducing computational overhead. Leveraging these findings, we demonstrate the use of pyEF to deduce environmental effects on a transition metal complex from a Ga<sub>4</sub>L<sub>6</sub><sup>12-</sup> nanocage and quantify the dominant role of organic linkers in orchestrating electrostatic preorganization.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":" ","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147496925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-21DOI: 10.1021/acs.jctc.5c01949
Katharina Rüther,Ken Bunge,Lasse M Hilmer,Janine Hellmers,Carolin König
Conventional quantum chemical (QC) methods exhibit a steep computational scaling with respect to the number of atoms in the investigated system. Hence, working with larger systems like peptides or even proteins becomes computationally unfeasible with traditional QC methods. One way to overcome this challenge is through molecular fragmentation methods. Many different flavours of molecular fragmentation schemes based on different partitionings have been suggested in the literature, but have hardly been compared numerically. Our group has recently reported a common formalism for molecular fragmentation schemes, which enables a consistent benchmark of different approaches. Here, we assess the performance of the molecular fractionation with hydrogen caps (MFHC), the pair-pair approximation to the generalized many-body expansion (pp-GMBE), the molecules-in-molecules (MIM) approach, and the kernel energy method (KEM) within this general framework. Our benchmark includes single- and multilevel schemes as well as an electrostatic embedding of the fragments in point charges of the whole system. The energies and computational demand of a chosen set of proteins are evaluated with the different methods within the framework. This enables a rare numerical comparison between the different schemes. Of the compared methods, our implementation of pp-GMBE yields the best agreement with supermolecular QC reference calculations, while MFHC with additional pair couplings offers a good cost-accuracy ratio.
{"title":"Comprehensive Comparison of Molecular Fragmentation Schemes for Proteins.","authors":"Katharina Rüther,Ken Bunge,Lasse M Hilmer,Janine Hellmers,Carolin König","doi":"10.1021/acs.jctc.5c01949","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c01949","url":null,"abstract":"Conventional quantum chemical (QC) methods exhibit a steep computational scaling with respect to the number of atoms in the investigated system. Hence, working with larger systems like peptides or even proteins becomes computationally unfeasible with traditional QC methods. One way to overcome this challenge is through molecular fragmentation methods. Many different flavours of molecular fragmentation schemes based on different partitionings have been suggested in the literature, but have hardly been compared numerically. Our group has recently reported a common formalism for molecular fragmentation schemes, which enables a consistent benchmark of different approaches. Here, we assess the performance of the molecular fractionation with hydrogen caps (MFHC), the pair-pair approximation to the generalized many-body expansion (pp-GMBE), the molecules-in-molecules (MIM) approach, and the kernel energy method (KEM) within this general framework. Our benchmark includes single- and multilevel schemes as well as an electrostatic embedding of the fragments in point charges of the whole system. The energies and computational demand of a chosen set of proteins are evaluated with the different methods within the framework. This enables a rare numerical comparison between the different schemes. Of the compared methods, our implementation of pp-GMBE yields the best agreement with supermolecular QC reference calculations, while MFHC with additional pair couplings offers a good cost-accuracy ratio.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"17 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147492953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-20DOI: 10.1021/acs.jctc.5c01988
Anthony O Lara, Justin J Talbot, Zhe Wang, Martin Head-Gordon
Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-ζ (QZ) size are required to adequately converge Kohn-Sham density functional theory (DFT) calculations toward the complete basis set limit. However, incrementing the cardinal number by one nearly doubles the AO basis dimension, and the computational cost scales as the cube of the AO dimension, so this is very computationally demanding. In this work, we develop and test a threshold-based natural atomic orbital (NAO) scheme in which ϵ-NAOs are obtained as eigenfunctions of atomic blocks of the density matrix in a one-center orthogonalized representation. This enables compression of the AO basis that is optimal for a given threshold, 10-ϵ, by discarding NAOs with occupation numbers below that threshold. Extensive pilot test calculations using the Hartree-Fock functional and taking the converged density matrix as input suggest that a threshold of 10-5 can yield a compression factor (ratio of AO to compressed ϵ-NAO dimension) between 2.5 and 4.5 for the QZ pc-3 basis. The errors in relative energies are typically less than 0.1 kcal/mol when the compressed basis is used instead of the uncompressed basis. Between 10 and 100 times smaller errors (i.e., usually less than 0.01 kcal/mol) can be obtained with a threshold 10-7, while the compression factor is typically between 2 and 2.5.
{"title":"An Algorithm for Atom-Centered Lossy Compression of the Atomic Orbital Basis in Density Functional Theory Calculations.","authors":"Anthony O Lara, Justin J Talbot, Zhe Wang, Martin Head-Gordon","doi":"10.1021/acs.jctc.5c01988","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c01988","url":null,"abstract":"<p><p>Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-ζ (QZ) size are required to adequately converge Kohn-Sham density functional theory (DFT) calculations toward the complete basis set limit. However, incrementing the cardinal number by one nearly doubles the AO basis dimension, and the computational cost scales as the cube of the AO dimension, so this is very computationally demanding. In this work, we develop and test a threshold-based natural atomic orbital (NAO) scheme in which ϵ-NAOs are obtained as eigenfunctions of atomic blocks of the density matrix in a one-center orthogonalized representation. This enables compression of the AO basis that is optimal for a given threshold, 10<sup>-ϵ</sup>, by discarding NAOs with occupation numbers below that threshold. Extensive pilot test calculations using the Hartree-Fock functional and taking the converged density matrix as input suggest that a threshold of 10<sup>-5</sup> can yield a compression factor (ratio of AO to compressed ϵ-NAO dimension) between 2.5 and 4.5 for the QZ pc-3 basis. The errors in relative energies are typically less than 0.1 kcal/mol when the compressed basis is used instead of the uncompressed basis. Between 10 and 100 times smaller errors (i.e., usually less than 0.01 kcal/mol) can be obtained with a threshold 10<sup>-7</sup>, while the compression factor is typically between 2 and 2.5.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":" ","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147490284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-20DOI: 10.1021/acs.jctc.5c02151
Ali Eltareb,Gustavo E Lopez,Nicolas Giovambattista
We apply the potential energy landscape (PEL) formalism for quantum liquids, together with path-integral (PI) computer simulations, to derive the equation of state (EOS) for both equilibrium and supercooled water over a wide range of temperatures and pressures. The PEL-EOS for water, which includes nuclear quantum effects (NQE), is in very good agreement with the PI computer simulations, particularly in the proximity of water's liquid-liquid critical point (LLCP). Relative to the classical case, including NQE shifts the overall phase diagram of water toward lower temperatures and slightly lower pressures. In particular, the LLCP temperature and pressure are shifted by ΔTc ≈ 18 K and ΔPc ≈ 49 MPa, with a minor change in the LLCP density, Δρc ≈ 0.002 g/cm3. These values of (ΔPc, ΔTc, Δρc) represent, approximately, a maximum shift for the location of the LLCP for H2O due to isotope substitution (H2O → D2O → T2O). Additionally, NQE also affect the shape of the density and LL spinodal lines in the P-T plane. The PEL of (q-TIP4P/F) water is Gaussian, allowing for the evaluation of the configurational entropy SIS(T, V) and Kauzmann temperature, TK(V). NQE reduce the TK(V) of water by 5-20 K depending on the density, consistent with the observed increase in water diffusion coefficient D at low temperatures upon the inclusion of quantum fluctuations. Notably, the Adam-Gibbs relationship, which relates D and SIS, holds remarkably well at all densities studied. From the perspective of the PEL formalism, NQE primarily modify the curvature of water's PEL basins while the corresponding IS remain unchanged, isomorphic to the IS of classical water. The PEL-based approach employed in this work is versatile and physically intuitive, suitable for calculating the free energy and EOS of quantum liquids beyond water.
{"title":"Nuclear Quantum Effects on the Equation of State of Water: Insights from the Potential Energy Landscape Formalism.","authors":"Ali Eltareb,Gustavo E Lopez,Nicolas Giovambattista","doi":"10.1021/acs.jctc.5c02151","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c02151","url":null,"abstract":"We apply the potential energy landscape (PEL) formalism for quantum liquids, together with path-integral (PI) computer simulations, to derive the equation of state (EOS) for both equilibrium and supercooled water over a wide range of temperatures and pressures. The PEL-EOS for water, which includes nuclear quantum effects (NQE), is in very good agreement with the PI computer simulations, particularly in the proximity of water's liquid-liquid critical point (LLCP). Relative to the classical case, including NQE shifts the overall phase diagram of water toward lower temperatures and slightly lower pressures. In particular, the LLCP temperature and pressure are shifted by ΔTc ≈ 18 K and ΔPc ≈ 49 MPa, with a minor change in the LLCP density, Δρc ≈ 0.002 g/cm3. These values of (ΔPc, ΔTc, Δρc) represent, approximately, a maximum shift for the location of the LLCP for H2O due to isotope substitution (H2O → D2O → T2O). Additionally, NQE also affect the shape of the density and LL spinodal lines in the P-T plane. The PEL of (q-TIP4P/F) water is Gaussian, allowing for the evaluation of the configurational entropy SIS(T, V) and Kauzmann temperature, TK(V). NQE reduce the TK(V) of water by 5-20 K depending on the density, consistent with the observed increase in water diffusion coefficient D at low temperatures upon the inclusion of quantum fluctuations. Notably, the Adam-Gibbs relationship, which relates D and SIS, holds remarkably well at all densities studied. From the perspective of the PEL formalism, NQE primarily modify the curvature of water's PEL basins while the corresponding IS remain unchanged, isomorphic to the IS of classical water. The PEL-based approach employed in this work is versatile and physically intuitive, suitable for calculating the free energy and EOS of quantum liquids beyond water.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"12 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147483410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-19DOI: 10.1021/acs.jctc.5c02167
Shiyue Yang,Jing Huang
Polarizable force fields based on induced dipoles are widely implemented in molecular dynamics simulations of biological systems to explicitly capture electric induction effects. The iterative computation of induced dipoles suffers from convergence issue in large systems. We describe the implementation of an E(3)-equivariant neural network for predicting induced dipoles in polar solvent systems to avoid the numerical iterations. The neural network is combined with a physics-informed loss function to enable the use of artificially perturbed training data sets. The architecture is validated on water systems, benchmarked across varying densities, system sizes and ice polymorphs, and further integrated into molecular dynamics simulations. We demonstrate that perturbation-based data augmentation substantially enhances model transferability across diverse chemical environments, while physics-informed loss alone offers limited gains in generalization.
{"title":"Induced Dipole Calculation with E(3)-Equivariant Neural Networks and Multipole Field Perturbation.","authors":"Shiyue Yang,Jing Huang","doi":"10.1021/acs.jctc.5c02167","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c02167","url":null,"abstract":"Polarizable force fields based on induced dipoles are widely implemented in molecular dynamics simulations of biological systems to explicitly capture electric induction effects. The iterative computation of induced dipoles suffers from convergence issue in large systems. We describe the implementation of an E(3)-equivariant neural network for predicting induced dipoles in polar solvent systems to avoid the numerical iterations. The neural network is combined with a physics-informed loss function to enable the use of artificially perturbed training data sets. The architecture is validated on water systems, benchmarked across varying densities, system sizes and ice polymorphs, and further integrated into molecular dynamics simulations. We demonstrate that perturbation-based data augmentation substantially enhances model transferability across diverse chemical environments, while physics-informed loss alone offers limited gains in generalization.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"52 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147483420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-19DOI: 10.1021/acs.jctc.6c00044
Cem Oran,Riccarda Caputo,Pierre Villars,Adem Tekin
Crystal structure prediction (CSP) is central to materials discovery, yet its efficiency and interpretability remain limited by the vast configurational space and reliance on costly local optimizations. Although template-based and machine-learning (ML) approaches have improved exploration, many approaches still require large data sets, complex similarity metrics, or opaque generative pipelines. In this work, we introduce PNcsp+, an enhanced and chemically interpretable CSP framework that uses the Mendeleev Periodic Number (PN) as a transparent descriptor of elemental similarity. PNcsp+ expands the original implementation through a larger prototype library, an improved data management strategy, and ML-assisted prototype scoring by combining cutting-edge neural network models such as MACE, M3GNet, and ALIGNN-FF. Despite its simplicity, PNcsp+ reaches state-of-the-art performance. In evaluations on the CSPBench data set─a curated set of 180 benchmark crystal structures for assessing CSP methods─our approach surpasses alternative methods by achieving 86.1% space group accuracy and 85.0% structure matching accuracy within the Top-5 predictions, all without structure relaxations. Moreover, our case study on several hybrid systems, including ammonium and methylammonium cations, demonstrated that molecular components emerge autonomously in the predicted lattices, guided solely by PN-derived similarity relationships. Overall, PNcsp+ shows that fundamental periodic trends, combined with targeted ML-based evaluation, offer an efficient, scalable, and interpretable CSP framework, enabling accelerated discovery across both inorganic and hybrid chemical spaces.
{"title":"PNcsp+: A Periodic Number-Based Crystal Structure Prediction Method Enhanced by Machine Learning.","authors":"Cem Oran,Riccarda Caputo,Pierre Villars,Adem Tekin","doi":"10.1021/acs.jctc.6c00044","DOIUrl":"https://doi.org/10.1021/acs.jctc.6c00044","url":null,"abstract":"Crystal structure prediction (CSP) is central to materials discovery, yet its efficiency and interpretability remain limited by the vast configurational space and reliance on costly local optimizations. Although template-based and machine-learning (ML) approaches have improved exploration, many approaches still require large data sets, complex similarity metrics, or opaque generative pipelines. In this work, we introduce PNcsp+, an enhanced and chemically interpretable CSP framework that uses the Mendeleev Periodic Number (PN) as a transparent descriptor of elemental similarity. PNcsp+ expands the original implementation through a larger prototype library, an improved data management strategy, and ML-assisted prototype scoring by combining cutting-edge neural network models such as MACE, M3GNet, and ALIGNN-FF. Despite its simplicity, PNcsp+ reaches state-of-the-art performance. In evaluations on the CSPBench data set─a curated set of 180 benchmark crystal structures for assessing CSP methods─our approach surpasses alternative methods by achieving 86.1% space group accuracy and 85.0% structure matching accuracy within the Top-5 predictions, all without structure relaxations. Moreover, our case study on several hybrid systems, including ammonium and methylammonium cations, demonstrated that molecular components emerge autonomously in the predicted lattices, guided solely by PN-derived similarity relationships. Overall, PNcsp+ shows that fundamental periodic trends, combined with targeted ML-based evaluation, offer an efficient, scalable, and interpretable CSP framework, enabling accelerated discovery across both inorganic and hybrid chemical spaces.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"97 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147483416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-19DOI: 10.1021/acs.jctc.6c00045
Alexandre Huguet,Ilaria Ciofini,Frédéric Labat
Electrostatic embedding schemes represent an affordable and accurate alternative to more costly approaches to model the excited-state properties of crystalline materials. They are commonly based on point-charge (PC) formalisms, which may lead to numerical instabilities and unphysical electron density (de)localization. In this work, we introduce and validate a Gaussian charge-based (GC) electrostatic embedding scheme for solid-state excited-state calculations based on analytical Ewald lattice summations. The implementation is first validated by systematically comparing electrostatic potentials obtained using PC and GC formalisms at the atomic sites of a broad and representative data set of 530 crystalline structures, covering all space-group types and crystallographic settings. Excellent agreement between PC and GC electrostatic potentials is obtained when the Gaussian width parameter is appropriately chosen. In particular, from the overlap of two GC distributions, we propose a criterion based on the minimal interatomic distance to define an upper bound of the Gaussian width parameter, which still maintains reasonable agreement with the PC-based Ewald potentials for embedded excited-state calculations. The GC embedding scheme is then applied to the modeling of excited-state properties of crystalline imidazole using embedded monomer and hydrogen-bonded dimer models in vacuum, dielectric media, and crystalline environments. The results demonstrate that, although both PC and GC embeddings yield excitation energies in very good agreement with GW-BSE and optimally tuned range-separated hybrid calculations, GC avoids the excessive electron density contraction observed with PC. Overall, the proposed GC-based electrostatic embedding scheme therefore offers a robust and physically sound alternative to PC models for excited-state calculations in solids and constitutes a promising framework for both future methodological developments and practical applications in embedded excited-state calculations.
{"title":"Gaussian Charge-Based Electrostatic Embedding Scheme for Solid-State Excited-State Modeling.","authors":"Alexandre Huguet,Ilaria Ciofini,Frédéric Labat","doi":"10.1021/acs.jctc.6c00045","DOIUrl":"https://doi.org/10.1021/acs.jctc.6c00045","url":null,"abstract":"Electrostatic embedding schemes represent an affordable and accurate alternative to more costly approaches to model the excited-state properties of crystalline materials. They are commonly based on point-charge (PC) formalisms, which may lead to numerical instabilities and unphysical electron density (de)localization. In this work, we introduce and validate a Gaussian charge-based (GC) electrostatic embedding scheme for solid-state excited-state calculations based on analytical Ewald lattice summations. The implementation is first validated by systematically comparing electrostatic potentials obtained using PC and GC formalisms at the atomic sites of a broad and representative data set of 530 crystalline structures, covering all space-group types and crystallographic settings. Excellent agreement between PC and GC electrostatic potentials is obtained when the Gaussian width parameter is appropriately chosen. In particular, from the overlap of two GC distributions, we propose a criterion based on the minimal interatomic distance to define an upper bound of the Gaussian width parameter, which still maintains reasonable agreement with the PC-based Ewald potentials for embedded excited-state calculations. The GC embedding scheme is then applied to the modeling of excited-state properties of crystalline imidazole using embedded monomer and hydrogen-bonded dimer models in vacuum, dielectric media, and crystalline environments. The results demonstrate that, although both PC and GC embeddings yield excitation energies in very good agreement with GW-BSE and optimally tuned range-separated hybrid calculations, GC avoids the excessive electron density contraction observed with PC. Overall, the proposed GC-based electrostatic embedding scheme therefore offers a robust and physically sound alternative to PC models for excited-state calculations in solids and constitutes a promising framework for both future methodological developments and practical applications in embedded excited-state calculations.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"85 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147483414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}