Pub Date : 2026-03-18DOI: 10.1021/acs.jctc.6c00107
Javier Carmona-Espíndola,José L Gázquez
The constrained dipole moment density functional theory allows one to control the magnitude and the components of the molecular dipole moment. In this work, we present a methodology which can control the dipole, quadrupole, and octupole moments in a variational and nonempirical way. This development allows us to estimate the individual (dipole, quadrupole, and octupole) and the combined (dipole-quadrupole, dipole-octupole, quadrupole-octupole, and dipole-quadrupole-octupole) multipole contributions in the formation of the ground state of the complex, taking as reference the frozen state of the complex. These contributions allow us to introduce an approximation to the variational frozen state and the corresponding frozen contribution. To test the reliability of the theoretical development, we study four sets of noncovalent complexes from the literature with a total of 24 systems. The individual and the combined multipole contributions results reveal the nature of the interaction between fragments according to these multipole moments, and the rather fast convergence of the multipole expansion, which, according to the results obtained, indicates that by including just the dipole, quadrupole, and octupole moments, one can describe the frozen state reasonably well.
{"title":"Constrained Multipole Moment Density Functional Theory for the Frozen Contribution in Non-Covalent Complexes.","authors":"Javier Carmona-Espíndola,José L Gázquez","doi":"10.1021/acs.jctc.6c00107","DOIUrl":"https://doi.org/10.1021/acs.jctc.6c00107","url":null,"abstract":"The constrained dipole moment density functional theory allows one to control the magnitude and the components of the molecular dipole moment. In this work, we present a methodology which can control the dipole, quadrupole, and octupole moments in a variational and nonempirical way. This development allows us to estimate the individual (dipole, quadrupole, and octupole) and the combined (dipole-quadrupole, dipole-octupole, quadrupole-octupole, and dipole-quadrupole-octupole) multipole contributions in the formation of the ground state of the complex, taking as reference the frozen state of the complex. These contributions allow us to introduce an approximation to the variational frozen state and the corresponding frozen contribution. To test the reliability of the theoretical development, we study four sets of noncovalent complexes from the literature with a total of 24 systems. The individual and the combined multipole contributions results reveal the nature of the interaction between fragments according to these multipole moments, and the rather fast convergence of the multipole expansion, which, according to the results obtained, indicates that by including just the dipole, quadrupole, and octupole moments, one can describe the frozen state reasonably well.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"52 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147478790","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 : 2026-03-17DOI: 10.1021/acs.jctc.5c02114
Simon A Liedtke,Martin Trulsson,Petter Persson
A computational method to simulate bimolecular quenching reactions using coarse-grained reaction-diffusion dynamics is presented and applied to the quenching of molecular photosensitizers in solution. The simulations describe photoinduced reactions involving explicit excited states of light-harvesting species together with intrinsic deactivation, as well as collision quenching from separate quencher species. The simulation methodology is applied to time-resolved quenching of light-harvesting Fe(III) complexes in electron-donating solvents as a prototype system for reaction-diffusion dynamics of experimental interest over a wide range of quencher concentrations. The results show clear signatures for the transition from classical diffusion-limited Stern-Volmer dynamics to close-contact quencher-photosensitizer interactions at high quencher concentrations, and the simulations are used to elucidate physically realistic photosensitizer-quenching collision interaction parameters for photoinduced dynamics beyond the classical Stern-Volmer model. The simulation method provides the means to directly model and analyze system kinetics and dynamics beyond standard theoretical equations, opening up significant opportunities to simulate a broad range of reactions in solutions.
{"title":"Reaction-Diffusion Dynamics Simulations of Bimolecular Quenching in Solution.","authors":"Simon A Liedtke,Martin Trulsson,Petter Persson","doi":"10.1021/acs.jctc.5c02114","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c02114","url":null,"abstract":"A computational method to simulate bimolecular quenching reactions using coarse-grained reaction-diffusion dynamics is presented and applied to the quenching of molecular photosensitizers in solution. The simulations describe photoinduced reactions involving explicit excited states of light-harvesting species together with intrinsic deactivation, as well as collision quenching from separate quencher species. The simulation methodology is applied to time-resolved quenching of light-harvesting Fe(III) complexes in electron-donating solvents as a prototype system for reaction-diffusion dynamics of experimental interest over a wide range of quencher concentrations. The results show clear signatures for the transition from classical diffusion-limited Stern-Volmer dynamics to close-contact quencher-photosensitizer interactions at high quencher concentrations, and the simulations are used to elucidate physically realistic photosensitizer-quenching collision interaction parameters for photoinduced dynamics beyond the classical Stern-Volmer model. The simulation method provides the means to directly model and analyze system kinetics and dynamics beyond standard theoretical equations, opening up significant opportunities to simulate a broad range of reactions in solutions.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"11 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147471639","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 : 2026-03-17DOI: 10.1021/acs.jctc.5c01970
Pavel Savchenko,Sayak Adhikari,Efrat Hadad,Eran Rabani,Roi Baer
Stochastic formulations of electronic-structure theory often reduce computational cost by replacing exact contractions with statistical estimates obtained from random samples, a procedure that inherently introduces random fluctuations and systematic bias. The fluctuations decay as M-1/2 with the number of samples M, whereas the bias generated in nonlinear or self-consistent settings decays as M-1 and can remain significant for moderate M. To control this bias we employ the jackknife-2 estimator, which reduces its leading term to O(M-2) with only modest extra cost. We examine bias formation and removal in three settings: (i) stochastic treatments of the Markovian master equation using bundled dissipators, (ii) stochastic Kohn-Sham density functional theory for warm dense hydrogen, and (iii) stochastic evaluation of the Hubbard-model partition function. The first two settings have been presented in earlier works; accordingly, we review them only briefly and focus primarily on the issue of bias control. The Hubbard-model application is entirely new. For this case, we present two approaches: a direct estimator, which has large variance but no bias, and a "midway transition probability" (ΣMTP) estimator, which has smaller variance but introduces bias. Applying the jackknife-2 procedure to the ΣMTP estimator controls this bias and yields a substantially lower total error than the direct estimator. Across all cases, jackknife bias removal markedly improves the accuracy and reliability of stochastic electronic-structure calculations without increasing the computational cost.
{"title":"Bias and Its Control in Stochastic Approaches to Electronic-Structure Theory.","authors":"Pavel Savchenko,Sayak Adhikari,Efrat Hadad,Eran Rabani,Roi Baer","doi":"10.1021/acs.jctc.5c01970","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c01970","url":null,"abstract":"Stochastic formulations of electronic-structure theory often reduce computational cost by replacing exact contractions with statistical estimates obtained from random samples, a procedure that inherently introduces random fluctuations and systematic bias. The fluctuations decay as M-1/2 with the number of samples M, whereas the bias generated in nonlinear or self-consistent settings decays as M-1 and can remain significant for moderate M. To control this bias we employ the jackknife-2 estimator, which reduces its leading term to O(M-2) with only modest extra cost. We examine bias formation and removal in three settings: (i) stochastic treatments of the Markovian master equation using bundled dissipators, (ii) stochastic Kohn-Sham density functional theory for warm dense hydrogen, and (iii) stochastic evaluation of the Hubbard-model partition function. The first two settings have been presented in earlier works; accordingly, we review them only briefly and focus primarily on the issue of bias control. The Hubbard-model application is entirely new. For this case, we present two approaches: a direct estimator, which has large variance but no bias, and a \"midway transition probability\" (ΣMTP) estimator, which has smaller variance but introduces bias. Applying the jackknife-2 procedure to the ΣMTP estimator controls this bias and yields a substantially lower total error than the direct estimator. Across all cases, jackknife bias removal markedly improves the accuracy and reliability of stochastic electronic-structure calculations without increasing the computational cost.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"50 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147471595","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 : 2026-03-17DOI: 10.1021/acs.jctc.5c01812
Shun Li,Zhifan Wang,Zhihua Luo,Fan Wang
In nonrelativistic and scalar-relativistic electronic structure calculations, molecular orbitals (MOs) are usually chosen as real functions and multideterminant wave functions are required to describe multireference (MR) states. However, certain specific MR states in atoms, linear molecules, and nonlinear molecules possessing real two-dimensional irreducible representations can be represented by a single determinant when complex MOs are employed. For atoms and linear molecules, MOs that are eigenfunctions of the angular momentum operator are used, and the resulting single-determinants states are labeled by the angular momentum quantum numbers. Within density functional theory (DFT), an angular-momentum symmetry-broken method, analogous to the spin-symmetry broken method, is also developed for selected MR states in atoms and linear molecules. The performance of MP2, CCSD, CCSD(T), and DFT using complex MOs is assessed for low-spin states of some p- and d-block atoms, diatomic and nonlinear molecules, and for high-spin states of selected transition-metal diatomic molecules. CCSD(T) with complex MOs generally yields highly accurate results when applicable, while DFT provides reasonable accuracy with appropriately chosen exchange-correlation functionals.
{"title":"Single-Reference Methods Based on Complex Orbital in Electronic Structure Calculations for High-Symmetry Systems.","authors":"Shun Li,Zhifan Wang,Zhihua Luo,Fan Wang","doi":"10.1021/acs.jctc.5c01812","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c01812","url":null,"abstract":"In nonrelativistic and scalar-relativistic electronic structure calculations, molecular orbitals (MOs) are usually chosen as real functions and multideterminant wave functions are required to describe multireference (MR) states. However, certain specific MR states in atoms, linear molecules, and nonlinear molecules possessing real two-dimensional irreducible representations can be represented by a single determinant when complex MOs are employed. For atoms and linear molecules, MOs that are eigenfunctions of the angular momentum operator are used, and the resulting single-determinants states are labeled by the angular momentum quantum numbers. Within density functional theory (DFT), an angular-momentum symmetry-broken method, analogous to the spin-symmetry broken method, is also developed for selected MR states in atoms and linear molecules. The performance of MP2, CCSD, CCSD(T), and DFT using complex MOs is assessed for low-spin states of some p- and d-block atoms, diatomic and nonlinear molecules, and for high-spin states of selected transition-metal diatomic molecules. CCSD(T) with complex MOs generally yields highly accurate results when applicable, while DFT provides reasonable accuracy with appropriately chosen exchange-correlation functionals.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"97 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147471638","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}
Automated reaction path network exploration and product identification through kinetic analysis are essential for mimicking real reaction vessels. A common practice involves using inexpensive semiempirical methods for initial exploration, followed by energy refinement using more accurate density functional theory (DFT) methods. However, semiempirical methods often yield less accurate reaction kinetics, making them unsuitable for efficient exploration and reliable product prediction. Here, we demonstrate the advantages of iterative training of a delta-learning neural network potential (ΔNNP) for automated reaction path exploration. Using ethylene polymerization catalyzed by the [ZrCp2CH3]+ catalyst as a model system, we achieve DFT-level accuracy by learning the energy difference between DFT and semiempirical methods. Training the ΔNNP on reaction path networks involving one and two ethylene molecules with the catalyst successfully captures all key elementary steps─initiation, propagation, and termination─which can then be extended to study the polymerization of up to six ethylene molecules. Furthermore, a minimally trained ethylene polymerization model provides a robust foundation for propylene polymerization. We also explore the influence of a cocatalyst on the polymerization elementary step network through additional iterative training. Beyond polymerization, this framework can incorporate other ZrCp2-mediated chemistry, such as metallacycle formation, with minimal additional training─yielding several new metallacycle structures. Overall, this iterative training framework is particularly effective for reactions involving repeated analogous elementary steps, such as polymer growth. The approach enables the model to handle increasingly complex reactions, representing an important step toward realistic mimicking of reaction vessels.
{"title":"Toward Reaction Vessel Mimicry: Machine Learning-Assisted Automated Exploration of Alkene Polymerization and Its Transferability.","authors":"Sagar Ghorai,Ruben Staub,Yu Harabuchi,Takashi Nakano,Alexandre Varnek,Satoshi Maeda","doi":"10.1021/acs.jctc.5c02120","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c02120","url":null,"abstract":"Automated reaction path network exploration and product identification through kinetic analysis are essential for mimicking real reaction vessels. A common practice involves using inexpensive semiempirical methods for initial exploration, followed by energy refinement using more accurate density functional theory (DFT) methods. However, semiempirical methods often yield less accurate reaction kinetics, making them unsuitable for efficient exploration and reliable product prediction. Here, we demonstrate the advantages of iterative training of a delta-learning neural network potential (ΔNNP) for automated reaction path exploration. Using ethylene polymerization catalyzed by the [ZrCp2CH3]+ catalyst as a model system, we achieve DFT-level accuracy by learning the energy difference between DFT and semiempirical methods. Training the ΔNNP on reaction path networks involving one and two ethylene molecules with the catalyst successfully captures all key elementary steps─initiation, propagation, and termination─which can then be extended to study the polymerization of up to six ethylene molecules. Furthermore, a minimally trained ethylene polymerization model provides a robust foundation for propylene polymerization. We also explore the influence of a cocatalyst on the polymerization elementary step network through additional iterative training. Beyond polymerization, this framework can incorporate other ZrCp2-mediated chemistry, such as metallacycle formation, with minimal additional training─yielding several new metallacycle structures. Overall, this iterative training framework is particularly effective for reactions involving repeated analogous elementary steps, such as polymer growth. The approach enables the model to handle increasingly complex reactions, representing an important step toward realistic mimicking of reaction vessels.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"54 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147461669","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 : 2026-03-16DOI: 10.1021/acs.jctc.5c02055
Francesco Calcagno,Luca Serfilippi,Giorgio Franceschelli,Marco Garavelli,Mirco Musolesi,Ivan Rivalta
The inverse design (ID) of molecules remains one of the greatest challenges in chemistry. Machine learning and artificial intelligence (AI) methods are increasingly employed to generate candidate molecules with tailored properties but mostly rely on pretraining over large data sets, which introduces bias. Here, we present a data-free generative AI model called PROTEUS that integrates reinforcement learning with on-the-fly quantum mechanical calculations to enable the de novo design of molecules from first-principles. The AI tool uses a custom syntax and hierarchical learning architecture to navigate the chemical space without prior knowledge, optimizing the desired chemical property. We demonstrate the efficiency of our software by solving complex molecular design tasks related to the maximization of isomerization energy gaps for styrene derivatives. By solving ID problems for which the exact solutions are known, PROTEUS proved to be robust and flexible enough to perform a broad exploration of different chemical spaces while successfully exploiting chemical rewards. This framework opens new avenues for quantum chemistry-driven unbiased molecular design, offering a flexible and scalable strategy to address design challenges in chemistry.
{"title":"Quantum Chemistry-Driven Molecular Inverse Design of Stable Isomers with Data-Free Reinforcement Learning","authors":"Francesco Calcagno,Luca Serfilippi,Giorgio Franceschelli,Marco Garavelli,Mirco Musolesi,Ivan Rivalta","doi":"10.1021/acs.jctc.5c02055","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c02055","url":null,"abstract":"The inverse design (ID) of molecules remains one of the greatest challenges in chemistry. Machine learning and artificial intelligence (AI) methods are increasingly employed to generate candidate molecules with tailored properties but mostly rely on pretraining over large data sets, which introduces bias. Here, we present a data-free generative AI model called PROTEUS that integrates reinforcement learning with on-the-fly quantum mechanical calculations to enable the de novo design of molecules from first-principles. The AI tool uses a custom syntax and hierarchical learning architecture to navigate the chemical space without prior knowledge, optimizing the desired chemical property. We demonstrate the efficiency of our software by solving complex molecular design tasks related to the maximization of isomerization energy gaps for styrene derivatives. By solving ID problems for which the exact solutions are known, PROTEUS proved to be robust and flexible enough to perform a broad exploration of different chemical spaces while successfully exploiting chemical rewards. This framework opens new avenues for quantum chemistry-driven unbiased molecular design, offering a flexible and scalable strategy to address design challenges in chemistry.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"3 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147462240","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 : 2026-03-16DOI: 10.1021/acs.jctc.5c02153
Zhengzheng Dang,Lei Cheng,Zhichen Tang,Zeyu Zhang,Yu Tian,Jixin Wu,Yide Chang,Chi Chen,Yanming Wang
Chemical reaction dynamics, critical to advancing technologies in energy, environment, and materials, can in principle be captured via reactive molecular dynamics (RMD). Time-series machine learning algorithms enable prediction of species evolution information hidden in these simulations, but long-horizon autoregressive accuracy often degrades due to error accumulation, and generating sufficiently large and diverse RMD data sets across operating conditions is computationally expensive. Here, we propose DEAL-TCN (deep-ensemble active learning with temporal convolutional networks), an active-learning framework that effectively disentangles the high-dimensional complexity of reaction dynamics spanning species, time, and operating conditions. It adopts the query-by-committee strategy to select informative conditions and leverages one-dimensional temporal convolutions to capture interspecies and long timescale couplings, enabling efficient modeling and long-term prediction of species evolution. In a prototypical case study of Mo–O–S precursors, DEAL-TCN robustly identifies and accurately predicts the concentration evolution of all involved chemical species across orthogonally designed test sets spanning a broad parameter range (1100–1500 K, 2–6 atm, and a feed ratio of 1/25–1/15). Given only the first 50 ps of each trajectory as input, the model attains a mean prediction error of 4.8% at the picosecond level while maintaining a mean error of 18.2% over the subsequent 0.45 ns, representing improvements of ∼29% and 24% over baseline LSTM and Transformer architectures, respectively. Meanwhile, DEAL-TCN outperforms random sampling in 98.8% of active-learning iterations with the same labeling budget. These results underscore DEAL-TCN’s potential as a scalable and generalizable approach for mechanistic discovery, reaction design, and optimization.
{"title":"Uncertainty-Driven Deep-Ensemble Temporal Convolutional Networks for Predicting Chemical Reaction Dynamics","authors":"Zhengzheng Dang,Lei Cheng,Zhichen Tang,Zeyu Zhang,Yu Tian,Jixin Wu,Yide Chang,Chi Chen,Yanming Wang","doi":"10.1021/acs.jctc.5c02153","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c02153","url":null,"abstract":"Chemical reaction dynamics, critical to advancing technologies in energy, environment, and materials, can in principle be captured via reactive molecular dynamics (RMD). Time-series machine learning algorithms enable prediction of species evolution information hidden in these simulations, but long-horizon autoregressive accuracy often degrades due to error accumulation, and generating sufficiently large and diverse RMD data sets across operating conditions is computationally expensive. Here, we propose DEAL-TCN (deep-ensemble active learning with temporal convolutional networks), an active-learning framework that effectively disentangles the high-dimensional complexity of reaction dynamics spanning species, time, and operating conditions. It adopts the query-by-committee strategy to select informative conditions and leverages one-dimensional temporal convolutions to capture interspecies and long timescale couplings, enabling efficient modeling and long-term prediction of species evolution. In a prototypical case study of Mo–O–S precursors, DEAL-TCN robustly identifies and accurately predicts the concentration evolution of all involved chemical species across orthogonally designed test sets spanning a broad parameter range (1100–1500 K, 2–6 atm, and a feed ratio of 1/25–1/15). Given only the first 50 ps of each trajectory as input, the model attains a mean prediction error of 4.8% at the picosecond level while maintaining a mean error of 18.2% over the subsequent 0.45 ns, representing improvements of ∼29% and 24% over baseline LSTM and Transformer architectures, respectively. Meanwhile, DEAL-TCN outperforms random sampling in 98.8% of active-learning iterations with the same labeling budget. These results underscore DEAL-TCN’s potential as a scalable and generalizable approach for mechanistic discovery, reaction design, and optimization.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"60 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147462239","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 : 2026-03-16DOI: 10.1021/acs.jctc.5c01974
Yorick L. A. Schmerwitz,Elli Selenius,Gianluca Levi
Variational optimization of orbitals in time-independent density functional calculations of excited electronic states presents a significant challenge, as excited states typically correspond to saddle points on the electronic energy landscape. The optimization can be particularly difficult if the excitation involves significant rearrangement of the electron density, as for charge-transfer excitations. A simple strategy for variational orbital optimization of excited states is presented. The approach involves minimizing the energy while freezing the orbitals directly involved in the excitation, followed by a fully unconstrained saddle-point optimization. Both steps of this freeze-and-release strategy are carried out using direct optimization algorithms with the same computational scaling as ground-state calculations. The performance of the method is extensively assessed in calculations of intramolecular and intermolecular charge-transfer excited states of organic molecules and molecular dimers using a generalized gradient approximation functional. It is found that the freeze-and-release direct optimization approach can avoid variational collapse to spurious, charge-delocalized solutions for cases where conventional algorithms based on the maximum overlap method fail. For intermolecular charge transfer, the orbital-optimized calculations are found to provide the correct dependency of the energy on the donor–acceptor separation without requiring long-range exact exchange, something common time-dependent density functional theory approaches fail to achieve.
{"title":"Freeze-and-Release Direct Optimization Method for Variational Calculations of Excited Electronic States","authors":"Yorick L. A. Schmerwitz,Elli Selenius,Gianluca Levi","doi":"10.1021/acs.jctc.5c01974","DOIUrl":"https://doi.org/10.1021/acs.jctc.5c01974","url":null,"abstract":"Variational optimization of orbitals in time-independent density functional calculations of excited electronic states presents a significant challenge, as excited states typically correspond to saddle points on the electronic energy landscape. The optimization can be particularly difficult if the excitation involves significant rearrangement of the electron density, as for charge-transfer excitations. A simple strategy for variational orbital optimization of excited states is presented. The approach involves minimizing the energy while freezing the orbitals directly involved in the excitation, followed by a fully unconstrained saddle-point optimization. Both steps of this freeze-and-release strategy are carried out using direct optimization algorithms with the same computational scaling as ground-state calculations. The performance of the method is extensively assessed in calculations of intramolecular and intermolecular charge-transfer excited states of organic molecules and molecular dimers using a generalized gradient approximation functional. It is found that the freeze-and-release direct optimization approach can avoid variational collapse to spurious, charge-delocalized solutions for cases where conventional algorithms based on the maximum overlap method fail. For intermolecular charge transfer, the orbital-optimized calculations are found to provide the correct dependency of the energy on the donor–acceptor separation without requiring long-range exact exchange, something common time-dependent density functional theory approaches fail to achieve.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"91 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147462291","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 : 2026-03-16DOI: 10.1021/acs.jctc.6c00051
Konstantin Stracke,Jack D. Evans
Enhanced sampling methods in molecular dynamics simulations often struggle to handle interdependent modes in complex systems. This leads to nonergodic simulations characterized by hysteresis, dependence on initial configurations, and the need for intricate collective variables. We introduce bias-deletion metadynamics, a technique that conditionally deletes biases to enable repeated exploration of transition pathways and systematic refinement of the sampled configurational space. The underlying free-energy surface is accurately recovered by rescaling the resulting probability distribution by the number of repetitions. We benchmark bias-deletion metadynamics on alanine dipeptide, demonstrating its ability to handle recurrent rotational motion where conventional metadynamics can fail. We further show its power by resolving the distinct phases of CAU-13 using only a volume bias, a known challenge for other methods. Finally, by applying this approach to a series of isoreticular metal–organic frameworks (MIL-53(Al), NU-2002, MIL-cub, and NU-2000), we uncover the intricate coupling between linker rotation and framework volume, revealing how linker dimensionality dictates volume-specific rotational preferences.
{"title":"Bias-Deletion Metadynamics Revealing Volume–Rotation Coupling Mechanisms in Metal–Organic Frameworks","authors":"Konstantin Stracke,Jack D. Evans","doi":"10.1021/acs.jctc.6c00051","DOIUrl":"https://doi.org/10.1021/acs.jctc.6c00051","url":null,"abstract":"Enhanced sampling methods in molecular dynamics simulations often struggle to handle interdependent modes in complex systems. This leads to nonergodic simulations characterized by hysteresis, dependence on initial configurations, and the need for intricate collective variables. We introduce bias-deletion metadynamics, a technique that conditionally deletes biases to enable repeated exploration of transition pathways and systematic refinement of the sampled configurational space. The underlying free-energy surface is accurately recovered by rescaling the resulting probability distribution by the number of repetitions. We benchmark bias-deletion metadynamics on alanine dipeptide, demonstrating its ability to handle recurrent rotational motion where conventional metadynamics can fail. We further show its power by resolving the distinct phases of CAU-13 using only a volume bias, a known challenge for other methods. Finally, by applying this approach to a series of isoreticular metal–organic frameworks (MIL-53(Al), NU-2002, MIL-cub, and NU-2000), we uncover the intricate coupling between linker rotation and framework volume, revealing how linker dimensionality dictates volume-specific rotational preferences.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"40 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147462297","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 : 2026-03-15DOI: 10.1021/acs.jctc.6c00068
Julien Luzzatto,Feliks Nüske,Nicolas G Hadjiconstantinou,Danny Perez
Many physical and biological systems evolve through metastable dynamics characterized by long intervals during which the trajectory remains confined to a small region of the configuration space punctuated by rare but rapid transitions between such regions. Accurately quantifying both the local relaxation and the first-escape behavior from each metastable set is central to many applications including enabling the simulation of long-time dynamics. In this work, we extend well-established data-driven methods for estimating Koopman operators to the setting of quasi-stationary distributions (QSDs) by enforcing absorbing boundary conditions on metastable states. We show that this absorbing Koopman formulation reliably recovers the spectral properties governing relaxation and escape using only short-trajectory data. Finally, we show how these spectral estimates naturally couple with a general parallel-in-time simulation scheme, enabling rigorous and substantial extensions of the time scales accessible to direct simulation of complex metastable systems.
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