Semiempirical Quantum-Chemical Methods with Orthogonalization and Dispersion Corrections

Accurate and Affordable Simulation of Molecular Infrared Spectra with AIQM Models

Infrared (IR) spectroscopy is a potent tool for identifying molecular structures and studying the chemical properties of compounds, and hence, various theoretical approaches have been developed to simulate and predict the IR spectra. However, the theoretical approaches based on quantum chemical calculations suffer from high computational cost (e.g., density functional theory, DFT) or insufficient accuracy (e.g., semiempirical methods orders of magnitude faster than DFT). Here, we introduce a new approach, based on the universal machine learning (ML) models of the AIQM series targeting CCSD(T)/CBS level, that can deliver molecular IR spectra with accuracy close to DFT (compared to the experiment) and the speed close to a semiempirical GFN2-xTB method. This approach is based on the harmonic oscillator approximation with the frequency scaling factors fitted to experimental data. While the benchmarks reported here are focused on harmonic IR spectra, our implementation supports anharmonic spectra simulations via molecular dynamics and VPT2. These implementations are available in MLatom as described in https://github.com/dralgroup/mlatom and can be performed online via a web browser.

Polarized molecular wires for efficient photo-generation of free electric charge carriers

In this study, five all-organic polarized molecular wires (PMWs) for photovoltaic applications are introduced and investigated by means of theoretical chemistry methods. Structurally based on polarized pyrrole and isoindole moieties, the proposed systems demonstrate efficient and ultrafast charge separation upon light absorption. The relevant PMW properties are evaluated using semi-empirical and ab initio quantum-chemical calculations, as well as nonadiabatic molecular dynamics simulations. For each system, the individual mechanism of charge carrier separation is identified and characterized, with all proposed wires exhibiting remarkable charge carrier separation efficiencies and rates. Furthermore, the designed PMW structures enable their straightforward incorporation into more extended molecular frameworks.

General strategy for boosting the performance of speed-tunable rotary molecular motors with visible light

Light-driven molecular rotary motors perform chirality-controlled unidirectional rotations fueled by light and heat. This unique function renders them appealing for the construction of dynamic molecular systems, actuating materials, and molecular machines. Achieving a combination of high photoefficiency, visible-light responsiveness, synthetic accessibility, and easy tuning of dynamic properties within a single scaffold is critical for these applications but remains a longstanding challenge. Herein, a series of highly photoefficient visible-light-responsive molecular motors (MMs), featuring various rotary speeds, was obtained by a convenient one-step formylation of their parent motors. This strategy greatly improves all aspects of the performance of MMs-red-shifted wavelengths of excitation, high photoisomerization quantum yields, and high photostationary state distributions of isomers-beyond the state-of-the-art light-responsive MM systems. The development of this late-stage functionalization strategy of MMs opens avenues for the construction of high-performance molecular machines and devices for applications in materials science and biological systems, representing a major advance in the synthetic toolbox of molecular machines.

Theoretical Insights into Ultrafast Separation of Photogenerated Charges in a Push-Pull Polarized Molecular Triad

Herein, we propose a purely-organic donor-acceptor (D-A) molecular triad, with a light-absorbing polarized molecular wire (PMW) used as a central linkage, as a proof of concept for the possible future applications of the D-PMW-A arrangement in molecular photovoltaics. This work builds upon our earlier study on the PMW unit itself, which proved to be highly promising for the ultrafast photogeneration of free charge carriers. Quantum-chemical calculations performed for the D-PMW-A triad at a semi-empirical level of theory reveal a large electric dipole moment of the system, and show strong charge-transfer (CT) character of its lowest-energy excited electronic states, including theS 1 ${S_1 }$ , which favours efficient dissociation of an exciton initially formed upon the absorption of light. The confirmation for this effect was found with nonadiabatic molecular dynamics simulations, revealing an ultrafast relaxation from higher, bright excited states toS 1 ${S_1 }$ , completed on a subpicosecond timescale. The architecture of the proposed molecular triad enables its electronic coupling to the surrounding environment through chemical bonds, or noncovalent stacking interactions, which might open way for synthesis of a new class of D-PMW-A efficient molecular organic photovoltaic materials.

Assessing Nonadiabatic Dynamics Methods in Long Timescales

Nonadiabatic dynamics simulations complement time-resolved experiments by revealing ultrafast excited-state mechanistic information in photochemical reactions. Understanding the relaxation mechanisms of photoexcited molecules finds application in energy, material, and medicinal research. However, with substantial computational costs, the nonadiabatic dynamics simulations have been restricted to ultrafast timescales, typically less than a few picoseconds, thus neglecting a wide range of photoactivated processes occurring in much longer timescales. Before developing new methodologies, we must ask: How well do the popular nonadiabatic dynamics methods perform in a long timescale simulation? In this study, we employ the multiconfiguration time-dependent Hartree (MCTDH) and its multilayer variants (ML-MCTDH), ab initio multiple spawning (AIMS), and fewest-switches surface hopping (FSSH) methodologies to simulate the excited-states dynamics of a weakly coupled multidimensional Spin-Boson model Hamiltonian designed for a long timescale decay behavior. Our study assures that despite having very different theoretical backgrounds, all the above methods deliver qualitatively similar results. While quantum dynamics would be very costly for long timescale simulations, the trajectory-based approaches are paving the way for future advancements.

Susceptibility formulation of density matrix perturbation theory

Density matrix perturbation theory based on recursive Fermi-operator expansions provides a computationally efficient framework for time-independent response calculations in quantum chemistry and materials science. From a perturbation in the Hamiltonian, we can calculate the first-order perturbation in the density matrix, which then gives us the linear response in the expectation values for some chosen set of observables. We present an alternative, dual formulation, where we instead calculate the static susceptibility of an observable, which then gives us the linear response in the expectation values for any number of different Hamiltonian perturbations. We show how the calculation of the susceptibility can be performed with the same expansion schemes used in recursive density matrix perturbation theory, including generalizations to fractional occupation numbers and self-consistent linear response calculations, i.e., similar to density functional perturbation theory. As with recursive density matrix perturbation theory, the dual susceptibility formulation is well suited for numerically thresholded sparse matrix algebra, which has linear scaling complexity for sufficiently large sparse systems. Similarly, the recursive computation of the susceptibility also seamlessly integrates with the computational framework of deep neural networks used in artificial intelligence (AI) applications. This integration enables the calculation of quantum response properties that can leverage cutting-edge AI-hardware, such as NVIDIA Tensor Cores or Google Tensor Processing Units. We demonstrate performance for recursive susceptibility calculations using NVIDIA Graphics Processing Units and Tensor Cores.

Accelerating Molecular Dynamics Simulations Using Socket-Based Interprocess Communication

Molecular dynamics (MD) simulations are essential for studying the time evolution of molecular systems. Still, their efficiency is often bottlenecked by file-based interprocess communication (IPC) between MD and electronic structure programs. We present a socket-based IPC implementation that dramatically accelerates MD simulations, reducing the computational time by >10-fold compared to those of traditional file-based methods. Our approach, applied to nonadiabatic molecular dynamics with the Newton-X program, eliminates disk read/write overhead, allowing for faster simulations over longer time scales. This method opens the door to more efficient high-throughput simulations, providing new opportunities for exploring complex molecular processes in real time.

Light-induced selectivity in an exemplary photodimerization reaction of varied azaanthracenes

Currently, there is intense interest in light-driven chemical reactions, including photocatalytic processes, photopolymerization and photodimerization. The need for regiocontrol in such reactions is obvious, especially in cases where many products can potentially be formed. Here, the photodimerization involving various azaanthracenes is presented for the first time. Specifically, 2-azaanthracene (A) and N-methyl-2-azaanthracene (M) are considered. Photoreactions of A, M and the A + M mixture under two irradiation wavelengths (365 and 420 nm) and in two solvents (methanol, dichloromethane) were carried out. In the case of A, four regiomers were obtained, in contrast to the available literature data, where only two products were reported. The relative ratio of these products is a function of the irradiation wavelength, the solvent used, and the irradiation time. In the case of M, we have identified two main products and a small amount of a third one, again contradicting the literature data. Irradiation of an equimolar A and M mixture at 365 nm led to a mixture of several products, where the yield of the AM dimers was about 40%. Importantly, the change of the irradiation wavelength to 420 nm significantly increased the AM yield (to about 80%). We demonstrated that only two AM dimers were formed (out of a possible four). The products were comprehensively characterized by NMR spectroscopy. We have determined the photophysical parameters of A and M and measured the quantum yield of photodimerization using UV-vis spectroscopy. The quantum-chemical calculations in the excited state allowed us to propose a plausible explanation for why only two AM dimers are formed upon irradiation. The presented results indicated that photodimerization among various molecules can have advantages and, in particular, does not need to give a complex mixture of multiple products. Importantly, it has been observed that the wavelength shift can significantly improve the photoreaction selectivity.

Constructing Accurate and Efficient General-Purpose Atomistic Machine Learning Model with Transferable Accuracy for Quantum Chemistry

Density functional theory (DFT) has been a cornerstone in computational science, providing powerful insights into structure-property relationships for molecules and materials through first-principles quantum-mechanical (QM) calculations. However, the advent of atomistic machine learning (ML) is reshaping the landscape by enabling large-scale dynamics simulations and high-throughput screening at DFT-equivalent accuracy with drastically reduced computational cost. Yet, the development of general-purpose atomistic ML models as surrogates for QM calculations faces several challenges, particularly in terms of model capacity, data efficiency, and transferability across chemically diverse systems. This work introduces a novel extension of the polarizable atom interaction neural network (namely, XPaiNN) to address these challenges. Two distinct training strategies have been employed, one direct-learning and the other Δ-ML on top of a semiempirical QM method. These methodologies have been implemented within the same framework, allowing for a detailed comparison of their results. The XPaiNN models, in particular the one using Δ-ML, not only demonstrate competitive performance on standard benchmarks, but also demonstrate the effectiveness against other ML models and QM methods on comprehensive downstream tasks, including noncovalent interactions, reaction energetics, barrier heights, geometry optimization and reaction thermodynamics, etc. This work represents a significant step forward in the pursuit of accurate and efficient atomistic ML models of general-purpose, capable of handling complex chemical systems with transferable accuracy.

Photoisomerization pathways of trans-resveratrol

Resveratrol is well-known for promoting health benefits due to its antioxidant, anti-aging, anti-carcinogenic, and other beneficial activities. Understanding the photophysics of resveratrol is essential for determining its applicability to pharmaceutical innovations. In the present work, we used an explore-then-assess strategy to map the internal conversion pathways of trans-resveratrol. This strategy consists of exploring the multidimensional configurational space with nonadiabatic dynamics simulations based on a semiempirical multireference method, followed by a feasibility assessment of reduced-dimensionality pathways at a high ab initio theoretical level. The exploration step revealed that internal conversion to the ground state may occur near five distinct conical intersections. The assessment step showed that the main photoisomerization pathway involves a twisted-pyramidalized S1/S0 conical intersection, yielding either trans or cis isomers. However, a secondary path was identified, where cis-trans isomerization happens in the excited state and internal conversion occurs at a cyclic conical intersection, yielding a closed-ring resveratrol derivative. This derivative, which can be formed through this direct path or an indirect photoexcitation, may be connected to the production of oxygen-reactive species previously reported and have implications in photodynamic therapy.

MLatom Software Ecosystem for Surface Hopping Dynamics in Python with Quantum Mechanical and Machine Learning Methods

We present an open-source MLatom@XACS software ecosystem for on-the-fly surface hopping nonadiabatic dynamics based on the Landau-Zener-Belyaev-Lebedev algorithm. The dynamics can be performed via Python API with a wide range of quantum mechanical (QM) and machine learning (ML) methods, including ab initio QM (CASSCF and ADC(2)), semiempirical QM methods (e.g., AM1, PM3, OMx, and ODMx), and many types of ML potentials (e.g., KREG, ANI, and MACE). Combinations of QM and ML methods can also be used. While the user can build their own combinations, we provide AIQM1, which is based on Δ-learning and can be used out-of-the-box. We showcase how AIQM1 reproduces the isomerization quantum yield of trans-azobenzene at a low cost. We provide example scripts that, in dozens of lines, enable the user to obtain the final population plots by simply providing the initial geometry of a molecule. Thus, those scripts perform geometry optimization, normal mode calculations, initial condition sampling, parallel trajectories propagation, population analysis, and final result plotting. Given the capabilities of MLatom to be used for training different ML models, this ecosystem can be seamlessly integrated into the protocols building ML models for nonadiabatic dynamics. In the future, a deeper and more efficient integration of MLatom with Newton-X will enable a vast range of functionalities for surface hopping dynamics, such as fewest-switches surface hopping, to facilitate similar workflows via the Python API.

Accelerating reliable multiscale quantum refinement of protein-drug systems enabled by machine learning

Biomacromolecule structures are essential for drug development and biocatalysis. Quantum refinement (QR) methods, which employ reliable quantum mechanics (QM) methods in crystallographic refinement, showed promise in improving the structural quality or even correcting the structure of biomacromolecules. However, vast computational costs and complex quantum mechanics/molecular mechanics (QM/MM) setups limit QR applications. Here we incorporate robust machine learning potentials (MLPs) in multiscale ONIOM(QM:MM) schemes to describe the core parts (e.g., drugs/inhibitors), replacing the expensive QM method. Additionally, two levels of MLPs are combined for the first time to overcome MLP limitations. Our unique MLPs+ONIOM-based QR methods achieve QM-level accuracy with significantly higher efficiency. Furthermore, our refinements provide computational evidence for the existence of bonded and nonbonded forms of the Food and Drug Administration (FDA)-approved drug nirmatrelvir in one SARS-CoV-2 main protease structure. This study highlights that powerful MLPs accelerate QRs for reliable protein-drug complexes, promote broader QR applications and provide more atomistic insights into drug development.

New insights into the photocyclization reaction of a popular diarylethene switch: a nonadiabatic molecular dynamics study

Diarylethene (DAE) molecular switches have continued to attract the attention of researchers for over 20 years. Their remarkable photophysical properties endow them with countless applications in photonics and molecular technologies. However, despite extensive experimental and theoretical research, the mechanism of DAE photoswitching is not yet fully rationalized. In this work, we investigate the ring closure dynamics of a popular DAE switch, 1,2-bis(3-methyl-5-phenyl-2 thienyl)perfluorocyclopentene (PT), using nonadiabatic molecular dynamics (NAMD) simulations. Employing the fewest switches surface hopping protocol, along with the semi-empirical multireference ODM2/MRCI-SD method, we investigate possible reaction pathways for this photoprocess, as well as their timescales and resulting photoproducts. Furthermore, using a dynamic configuration-space sampling procedure, we elucidate the role of triplet states in the photocyclization of PT, supporting available experimental data for the closely related DMPT molecule, which indicate an ultrafast intersystem crossing (ISC) transition competing with the singlet-driven photoswitching reaction. Our findings not only corroborate experimental studies on DAE switches, but also provide new mechanistic insights into the potential use in the rational design of DAE switches tailored for specific technological applications.

Prediction Challenge: Simulating Rydberg photoexcited cyclobutanone with surface hopping dynamics based on different electronic structure methods

This research examines the nonadiabatic dynamics of cyclobutanone after excitation into the n → 3s Rydberg S2 state. It stems from our contribution to the Special Topic of the Journal of Chemical Physics to test the predictive capability of computational chemistry against unseen experimental data. Decoherence-corrected fewest-switches surface hopping was used to simulate nonadiabatic dynamics with full and approximated nonadiabatic couplings. Several simulation sets were computed with different electronic structure methods, including a multiconfigurational wavefunction [multiconfigurational self-consistent field (MCSCF)] specially built to describe dissociative channels, multireference semiempirical approach, time-dependent density functional theory, algebraic diagrammatic construction, and coupled cluster. MCSCF dynamics predicts a slow deactivation of the S2 state (10 ps), followed by an ultrafast population transfer from S1 to S0 (<100 fs). CO elimination (C3 channel) dominates over C2H4 formation (C2 channel). These findings radically differ from the other methods, which predicted S2 lifetimes 10-250 times shorter and C2 channel predominance. These results suggest that routine electronic structure methods may hold low predictive power for the outcome of nonadiabatic dynamics.

AI in computational chemistry through the lens of a decade-long journey

This article gives a perspective on the progress of AI tools in computational chemistry through the lens of the author's decade-long contributions put in the wider context of the trends in this rapidly expanding field. This progress over the last decade is tremendous: while a decade ago we had a glimpse of what was to come through many proof-of-concept studies, now we witness the emergence of many AI-based computational chemistry tools that are mature enough to make faster and more accurate simulations increasingly routine. Such simulations in turn allow us to validate and even revise experimental results, deepen our understanding of the physicochemical processes in nature, and design better materials, devices, and drugs. The rapid introduction of powerful AI tools gives rise to unique challenges and opportunities that are discussed in this article too.

MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows

Machine learning (ML) is increasingly becoming a common tool in computational chemistry. At the same time, the rapid development of ML methods requires a flexible software framework for designing custom workflows. MLatom 3 is a program package designed to leverage the power of ML to enhance typical computational chemistry simulations and to create complex workflows. This open-source package provides plenty of choice to the users who can run simulations with the command-line options, input files, or with scripts using MLatom as a Python package, both on their computers and on the online XACS cloud computing service at XACScloud.com. Computational chemists can calculate energies and thermochemical properties, optimize geometries, run molecular and quantum dynamics, and simulate (ro)vibrational, one-photon UV/vis absorption, and two-photon absorption spectra with ML, quantum mechanical, and combined models. The users can choose from an extensive library of methods containing pretrained ML models and quantum mechanical approximations such as AIQM1 approaching coupled-cluster accuracy. The developers can build their own models using various ML algorithms. The great flexibility of MLatom is largely due to the extensive use of the interfaces to many state-of-the-art software packages and libraries.

Synergy of semiempirical models and machine learning in computational chemistry

Catalyzed by enormous success in the industrial sector, many research programs have been exploring data-driven, machine learning approaches. Performance can be poor when the model is extrapolated to new regions of chemical space, e.g., new bonding types, new many-body interactions. Another important limitation is the spatial locality assumption in model architecture, and this limitation cannot be overcome with larger or more diverse datasets. The outlined challenges are primarily associated with the lack of electronic structure information in surrogate models such as interatomic potentials. Given the fast development of machine learning and computational chemistry methods, we expect some limitations of surrogate models to be addressed in the near future; nevertheless spatial locality assumption will likely remain a limiting factor for their transferability. Here, we suggest focusing on an equally important effort-design of physics-informed models that leverage the domain knowledge and employ machine learning only as a corrective tool. In the context of material science, we will focus on semi-empirical quantum mechanics, using machine learning to predict corrections to the reduced-order Hamiltonian model parameters. The resulting models are broadly applicable, retain the speed of semiempirical chemistry, and frequently achieve accuracy on par with much more expensive ab initio calculations. These early results indicate that future work, in which machine learning and quantum chemistry methods are developed jointly, may provide the best of all worlds for chemistry applications that demand both high accuracy and high numerical efficiency.

Energy-conserving molecular dynamics is not energy conserving

Molecular dynamics (MD) is a widely-used tool for simulating molecular and materials properties. It is common wisdom that molecular dynamics simulations should obey physical laws and, hence, lots of effort is put into ensuring that molecular dynamics simulations are energy conserving. The emergence of machine learning (ML) potentials for MD leads to a growing realization that monitoring conservation of energy during simulations is of low utility because the dynamics is often unphysically dissociative. Other ML methods for MD are not based on a potential and provide only forces or trajectories which are reasonable but not necessarily energy-conserving. Here we propose to clearly distinguish between the simulation-energy and true-energy conservation and highlight that the simulations should focus on decreasing the degree of true-energy non-conservation. We introduce very simple, new criteria for evaluating the quality of molecular dynamics by estimating the degree of true-energy non-conservation and we demonstrate their practical utility on an example of infrared spectra simulations. These criteria are more important and intuitive than simply evaluating the quality of the ML potential energies and forces as is commonly done and can be applied universally, e.g., even for trajectories with unknown or discontinuous potential energy. Such an approach introduces new standards for evaluating MD by focusing on the true-energy conservation and can help in developing more accurate methods for simulating molecular and materials properties.

Corrigendum: Coupled cluster theory on modern heterogeneous supercomputers

[This corrects the article DOI: 10.3389/fchem.2023.1154526.].

Coupled cluster theory on modern heterogeneous supercomputers

This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory-a linear-scaling, massively parallel framework-as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models.

Shadow energy functionals and potentials in Born-Oppenheimer molecular dynamics

In Born-Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born-Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born-Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born-Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born-Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "zeroth-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Niklasson, Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree-Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

Benchmark of general-purpose machine learning-based quantum mechanical method AIQM1 on reaction barrier heights

Artificial intelligence-enhanced quantum mechanical method 1 (AIQM1) is a general-purpose method that was shown to achieve high accuracy for many applications with a speed close to its baseline semiempirical quantum mechanical (SQM) method ODM2*. Here, we evaluate the hitherto unknown performance of out-of-the-box AIQM1 without any refitting for reaction barrier heights on eight datasets, including a total of ∼24 thousand reactions. This evaluation shows that AIQM1's accuracy strongly depends on the type of transition state and ranges from excellent for rotation barriers to poor for, e.g., pericyclic reactions. AIQM1 clearly outperforms its baseline ODM2* method and, even more so, a popular universal potential, ANI-1ccx. Overall, however, AIQM1 accuracy largely remains similar to SQM methods (and B3LYP/6-31G* for most reaction types) suggesting that it is desirable to focus on improving AIQM1 performance for barrier heights in the future. We also show that the built-in uncertainty quantification helps in identifying confident predictions. The accuracy of confident AIQM1 predictions is approaching the level of popular density functional theory methods for most reaction types. Encouragingly, AIQM1 is rather robust for transition state optimizations, even for the type of reactions it struggles with the most. Single-point calculations with high-level methods on AIQM1-optimized geometries can be used to significantly improve barrier heights, which cannot be said for its baseline ODM2* method.

Graph-based quantum response theory and shadow Born-Oppenheimer molecular dynamics

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

Ultra-fast semi-empirical quantum chemistry for high-throughput computational campaigns with Sparrow

Semi-empirical quantum chemical approaches are known to compromise accuracy for the feasibility of calculations on huge molecules. However, the need for ultrafast calculations in interactive quantum mechanical studies, high-throughput virtual screening, and data-driven machine learning has shifted the emphasis toward calculation runtimes recently. This comes with new constraints for the software implementation as many fast calculations would suffer from a large overhead of the manual setup and other procedures that are comparatively fast when studying a single molecular structure, but which become prohibitively slow for high-throughput demands. In this work, we discuss the effect of various well-established semi-empirical approximations on calculation speed and relate this to data transfer rates from the raw-data source computer to the results of the visualization front end. For the former, we consider desktop computers, local high performance computing, and remote cloud services in order to elucidate the effect on interactive calculations, for web and cloud interfaces in local applications, and in world-wide interactive virtual sessions. The models discussed in this work have been implemented into our open-source software SCINE Sparrow.

Deep learning of dynamically responsive chemical Hamiltonians with semiempirical quantum mechanics

Machine learning is revolutionizing computational chemistry by greatly reducing the computational difficulty of many simulations performed by computational chemists while maintaining accuracies of 1 kcal/mol or better. A major challenge in this field is addressing the poor extensibility and transferability of conventional machine-learning (ML) models, which result in degraded accuracy when applying these models to large or new chemical systems. To build a more general and interpretable model, we incorporate a quantum chemistry framework into the deep neural network, resulting in an interpretable Hamiltonian-based model with markedly high training efficiency. We validate this method on multiple large biochemical molecules by predicting various properties with consistently high accuracies, indicating the model is both extensible and transferable.

Conventional machine-learning (ML) models in computational chemistry learn to directly predict molecular properties using quantum chemistry only for reference data. While these heuristic ML methods show quantum-level accuracy with speeds several orders of magnitude faster than traditional quantum chemistry methods, they suffer from poor extensibility and transferability; i.e., their accuracy degrades on large or new chemical systems. Incorporating quantum chemistry frameworks into the ML models directly solves this problem. Here we take the structure of semiempirical quantum mechanics (SEQM) methods to construct dynamically responsive Hamiltonians. SEQM methods use empirical parameters fitted to experimental properties to construct reduced-order Hamiltonians, facilitating much faster calculations than ab initio methods but with compromised accuracy. By replacing these static parameters with machine-learned dynamic values inferred from the local environment, we greatly improve the accuracy of the SEQM methods. Trained on molecular energies and atomic forces, these dynamically generated Hamiltonian parameters show a strong correlation with atomic hybridization and bonding. Trained with only about 60,000 small organic molecular conformers, the resulting model retains interpretability, extensibility, and transferability when testing on much larger chemical systems and predicting various molecular properties. Overall, this work demonstrates the virtues of incorporating physics-based descriptions with ML to develop models that are simultaneously accurate, transferable, and interpretable.

Providing theoretical insight into the role of symmetry in the photoisomerization mechanism of a non-symmetric dithienylethene photoswitch

Dithienylethene (DTE) molecular photoswitches have shown to be excellent candidates in the design of efficient optoelectronic devices, due to their high photoisomerization quantum yield (QY), for which symmetry is suggested to play a crucial role. Here, we present a theoretical study on the photochemistry of a non-symmetric dithienylethene photoswitch, with a special emphasis on the effect of asymmetric substitution on the photocyclization and photoreversion mechanisms. We used the Spin-Flip Time Dependent Density Functional Theory (SF-TDDFT) method to locate and characterize the main structures (conical intersections and minima) of the ground state and the first two excited states, S₁ and S₂, along the ring-opening/closure reaction coordinate of the photocyclization and photoreversion processes, and to identify the important coordinates governing the radiationless decay pathways. Our results suggest that while the main features that characterize the photoisomerization of symmetric DTEs are also present for the photoisomerization of the non-symmetric DTE, the lower energy barrier on S₁ along the cycloreversion reaction speaks in favor of a more efficient and therefore a higher cycloreversion QY for the non-symmetric DTEs, making them a better candidate for molecular optoelectronic devices than their symmetric counterparts.

Energy transfer, pre-reactive complex formation and recombination reactions during the collision of peroxy radicals

In this paper we study collisions between polyatomic radicals - an important process in fields ranging from biology to combustion. Energy transfer, formation of intermediate complexes and recombination reactions are treated, with applications to peroxy radicals in atmospheric chemistry. Multi-reference perturbation theory, supplemented by coupled-cluster calculations, describes the potential energy surfaces with high accuracy, including the interaction of singlet and triplet spin states during radical recombination. Our multi-reference molecular dynamics (MD) trajectories on methyl peroxy radicals confirm the reaction mechanism postulated in earlier studies. Specifically, they show that if suitable pre-reactive complexes are formed, they will rapidly lead to the formation and subsequent decomposition of tetroxide intermediates. However, generating multi-reference MD trajectories is exceedingly computationally demanding, and we cannot adequately sample the whole conformational space. To answer this challenge, we promote the use of a novel simplified semi-empirical MD methodology. It assumes the collision is governed by two states, a singlet (S₀) and a triplet (T₁) state. The method predicts differences between collisions on S₀ and T₁ surfaces, and qualitatively includes not only pre-reactive complex formation, but also recombination processes such as tetroxide formation. Finally, classical MD simulations using force-fields for non-reactive collisions are employed to generate thousands of collision trajectories, to verify that the semi-empirical method is sampling collisions adequately, and to carry out preliminary investigations of larger systems. For systems with low activation energies, the experimental rate coefficient is surprisingly well reproduced by simply multiplying the gas-kinetic collision rate by the simulated probability for long-lived complex formation.

Toward Chemical Accuracy in Predicting Enthalpies of Formation with General-Purpose Data-Driven Methods

Enthalpies of formation and reaction are important thermodynamic properties that have a crucial impact on the outcome of chemical transformations. Here we implement the calculation of enthalpies of formation with a general-purpose ANI-1ccx neural network atomistic potential. We demonstrate on a wide range of benchmark sets that both ANI-1ccx and our other general-purpose data-driven method AIQM1 approach the coveted chemical accuracy of 1 kcal/mol with the speed of semiempirical quantum mechanical methods (AIQM1) or faster (ANI-1ccx). It is remarkably achieved without specifically training the machine learning parts of ANI-1ccx or AIQM1 on formation enthalpies. Importantly, we show that these data-driven methods provide statistical means for uncertainty quantification of their predictions, which we use to detect and eliminate outliers and revise reference experimental data. Uncertainty quantification may also help in the systematic improvement of such data-driven methods.

The PM6-FGC Method: Improved Corrections for Amines and Amides

Recently, we reported a new approach to develop pairwise analytical corrections to improve the description of noncovalent interactions, by approximate methods of electronic structures, such as semiempirical quantum mechanical (SQM) methods. In particular, and as a proof of concept, we used the PM6 Hamiltonian and we named the method PM6-FGC, where the FGC acronym, corresponding to Functional Group Corrections, emphasizes the idea that the corrections work for specific functional groups rather than for individual atom pairs. The analytical corrections were derived from fits to B3LYP-D3/def2-TZVP (reference). PM6 interaction energy differences, evaluated for a reduced set of small bimolecular complexes, were chosen as representatives of saturated hydrocarbons, carboxylic, amine and, tentatively, amide functional groups. For the validation, the method was applied to several complexes of well-known databases, as well as to complexes of diglycine and dialanine, assuming the transferability of amine group corrections to amide groups. The PM6-FGC method showed great potential but revealed significant inaccuracies for the description of some interactions involving the –NH₂ group in amines and amides, caused by the inadequate selection of the model compound used to represent these functional groups (an NH₃ molecule). In this work, methylamine and acetamide are used as representatives of amine and amide groups, respectively. This new selection leads to significant improvements in the calculation of noncovalent interactions in the validation set.

Absorption Properties of Large Complex Molecular Systems: The DFTB/Fluctuating Charge Approach

We report on the first formulation of a novel polarizable QM/MM approach, where the density functional tight binding (DFTB) is coupled to the fluctuating charge (FQ) force field. The resulting method (DFTB/FQ) is then extended to the linear response within the TD-DFTB framework and challenged to study absorption spectra of large condensed-phase systems.

An open-source framework for fast-yet-accurate calculation of quantum mechanical features

We present the open-source framework kallisto that enables the efficient and robust calculation of quantum mechanical features for atoms and molecules. For a benchmark set of 49 experimental molecular polarizabilities,...

Artificial intelligence-enhanced quantum chemical method with broad applicability

High-level quantum mechanical (QM) calculations are indispensable for accurate explanation of natural phenomena on the atomistic level. Their staggering computational cost, however, poses great limitations, which luckily can be lifted to a great extent by exploiting advances in artificial intelligence (AI). Here we introduce the general-purpose, highly transferable artificial intelligence-quantum mechanical method 1 (AIQM1). It approaches the accuracy of the gold-standard coupled cluster QM method with high computational speed of the approximate low-level semiempirical QM methods for the neutral, closed-shell species in the ground state. AIQM1 can provide accurate ground-state energies for diverse organic compounds as well as geometries for even challenging systems such as large conjugated compounds (fullerene C60) close to experiment. This opens an opportunity to investigate chemical compounds with previously unattainable speed and accuracy as we demonstrate by determining geometries of polyyne molecules-the task difficult for both experiment and theory. Noteworthy, our method's accuracy is also good for ions and excited-state properties, although the neural network part of AIQM1 was never fitted to these properties.

New Approach for Correcting Noncovalent Interactions in Semiempirical Quantum Mechanical Methods: The Importance of Multiple-Orientation Sampling

A new approach is presented to improve the performance of semiempirical quantum mechanical (SQM) methods in the description of noncovalent interactions. To show the strategy, the PM6 Hamiltonian was selected, although, in general, the procedure can be applied to other semiempirical Hamiltonians and to different methodologies. A set of small molecules were selected as representative of various functional groups, and intermolecular potential energy curves (IPECs) were evaluated for the most relevant orientations of interacting molecular pairs. Then, analytical corrections to PM6 were derived from fits to B3LYP-D3/def2-TZVP reference–PM6 interaction energy differences. IPECs provided by the B3LYP-D3/def2-TZVP combination of the electronic structure method and basis set were chosen as the reference because they are in excellent agreement with CCSD(T)/aug-cc-pVTZ curves for the studied systems. The resulting method, called PM6-FGC (from functional group corrections), significantly improves the performance of PM6 and shows the importance of including a sufficient number of orientations of the interacting molecules in the reference data set in order to obtain well-balanced descriptions.

The Middle Science: Traversing Scale In Complex Many-Body Systems

A roadmap is developed that integrates simulation methodology and data science methods to target new theories that traverse the multiple length- and time-scale features of many-body phenomena.

Photo-cycloreversion mechanism in diarylethenes revisited: A multireference quantum-chemical study at the ODM2/MRCI level

Photoswitchable diarylethenes (DAEs), over years of intense fundamental and applied research, have been established among the most commonly chosen molecular photoswitches, often employed as controlling units in molecular devices and smart materials. At the same time, providing reliable explanation for their photophysical behavior, especially the mechanism of the photo-cycloreversion transformation, turned out to be a highly challenging task. Herein, we investigate this mechanism in detail by means of multireference semi-empirical quantum chemistry calculations, allowing, for the first time, for a balanced treatment of the static and dynamic correlation effects, both playing a crucial role in DAE photochemistry. In the course of our study, we find the second singlet excited state of double electronic-excitation character to be the key to understanding the nature of the photo-cycloreversion transformation in DAE molecular photoswitches.

Quantum Chemistry Calculations for Metabolomics

A primary goal of metabolomics studies is to fully characterize the small-molecule composition of complex biological and environmental samples. However, despite advances in analytical technologies over the past two decades, the majority of small molecules in complex samples are not readily identifiable due to the immense structural and chemical diversity present within the metabolome. Current gold-standard identification methods rely on reference libraries built using authentic chemical materials ("standards"), which are not available for most molecules. Computational quantum chemistry methods, which can be used to calculate chemical properties that are then measured by analytical platforms, offer an alternative route for building reference libraries, i.e., in silico libraries for "standards-free" identification. In this review, we cover the major roadblocks currently facing metabolomics and discuss applications where quantum chemistry calculations offer a solution. Several successful examples for nuclear magnetic resonance spectroscopy, ion mobility spectrometry, infrared spectroscopy, and mass spectrometry methods are reviewed. Finally, we consider current best practices, sources of error, and provide an outlook for quantum chemistry calculations in metabolomics studies. We expect this review will inspire researchers in the field of small-molecule identification to accelerate adoption of in silico methods for generation of reference libraries and to add quantum chemistry calculations as another tool at their disposal to characterize complex samples.

Glucuronidation of Methylated Quercetin Derivatives: Chemical and Biochemical Approaches

Botanical supplements derived from grapes are functional in animal model systems for the amelioration of neurological conditions, including cognitive impairment. Rats fed with grape extracts accumulate 3'-O-methyl-quercetin-3-O-β-d-glucuronide (3) in their brains, suggesting 3 as a potential therapeutic agent. To develop methods for the synthesis of 3 and the related 4'-O-methyl-quercetin-7-O-β-d-glucuronide (4), 3-O-methyl-quercetin-3'-O-β-d-glucuronide (5), and 4'-O-methyl-quercetin-3'-O-β-d-glucuronide (6), which are not found in the brain, we have evaluated both enzymatic semisynthesis and full chemical synthetic approaches. Biocatalysis by mammalian UDP-glucuronosyltransferases generated multiple glucuronidated products from 4'-O-methylquercetin, and is not cost-effective. Chemical synthetic methods, on the other hand, provided good results; 3, 5, and 6 were obtained in six steps at 12, 18, and 30% overall yield, respectively, while 4 was synthesized in five steps at 34% overall yield. A mechanistic study on the unexpected regioselectivity observed in the quercetin glucuronide synthetic steps is also presented.

Mechanistic Understanding From Molecular Dynamics Simulation in Pharmaceutical Research 1: Drug Delivery

In this review, we outline the growing role that molecular dynamics simulation is able to play as a design tool in drug delivery. We cover both the pharmaceutical and computational backgrounds, in a pedagogical fashion, as this review is designed to be equally accessible to pharmaceutical researchers interested in what this new computational tool is capable of and experts in molecular modeling who wish to pursue pharmaceutical applications as a context for their research. The field has become too broad for us to concisely describe all work that has been carried out; many comprehensive reviews on subtopics of this area are cited. We discuss the insight molecular dynamics modeling has provided in dissolution and solubility, however, the majority of the discussion is focused on nanomedicine: the development of nanoscale drug delivery vehicles. Here we focus on three areas where molecular dynamics modeling has had a particularly strong impact: (1) behavior in the bloodstream and protective polymer corona, (2) Drug loading and controlled release, and (3) Nanoparticle interaction with both model and biological membranes. We conclude with some thoughts on the role that molecular dynamics simulation can grow to play in the development of new drug delivery systems.

SQM/COSMO Scoring Function: Reliable Quantum-Mechanical Tool for Sampling and Ranking in Structure-Based Drug Design

Quantum mechanical (QM) methods have been gaining importance in structure-based drug design where a reliable description of protein-ligand interactions is of utmost significance. However, strategies i. e. QM/MM, fragmentation or semiempirical (SQM) methods had to be pursued to overcome the unfavorable scaling of QM methods. Various SQM-based approaches have significantly contributed to the accuracy of docking and improvement of lead compounds. Parametrizations of SQM and implicit solvent methods in our laboratory have been instrumental to obtain a reliable SQM-based scoring function. The experience gained in its application for activity ranking of ligands binding to tens of protein targets resulted in setting up a faster SQM/COSMO scoring approach, which outperforms standard scoring methods in native pose identification for two dozen protein targets with ten thousand poses. Recently, SQM/COSMO was effectively applied in a proof-of-concept study of enrichment in virtual screening. Due to its superior performance, feasibility and chemical generality, we propose the SQM/COSMO approach as an efficient tool in structure-based drug design.

Fast Evaluation of Two-Center Integrals over Gaussian Charge Distributions and Gaussian Orbitals with General Interaction Kernels

We present efficient algorithms for computing two-center integrals and integral derivatives, with general interaction kernels K(r₁₂), over Gaussian charge distributions of general angular momenta l. While formulated in terms of traditional ab initio integration techniques, full derivations and required secondary information, as well as a reference implementation, are provided to make the content accessible to other fields. Concretely, the presented algorithms are based on an adaption of the McMurchie-Davidson Recurrence Relation (MDRR) combined with analytical properties of the solid harmonic transformation; this obviates all intermediate recurrences except the adapted MDRR itself, and allows it to be applied to fully contracted auxiliary kernel integrals. The technique is particularly well-suited for semiempirical molecular orbital methods, where it can serve as a more general and efficient replacement of Slater-Koster tables, and for first-principles quantum chemistry methods employing density fitting. But the formalism's high efficiency and ability of handling general interaction kernels K(r₁₂) and multipolar Gaussian charge distributions may also be of interest for modeling electrostatic interactions and short-range exchange and charge penetration effects in classical force fields and model potentials. With the presented technique, a 4894 × 4894 univ-JKFIT Coulomb matrix J_AB = (A|1/r₁₂|B) (183 MiB) can be computed in 50 ms on a Q2'2018 notebook CPU, without any screening or approximations.

Quantum Chemistry in the Age of Machine Learning

As the quantum chemistry (QC) community embraces machine learning (ML), the number of new methods and applications based on the combination of QC and ML is surging. In this Perspective, a view of the current state of affairs in this new and exciting research field is offered, challenges of using machine learning in quantum chemistry applications are described, and potential future developments are outlined. Specifically, examples of how machine learning is used to improve the accuracy and accelerate quantum chemical research are shown. Generalization and classification of existing techniques are provided to ease the navigation in the sea of literature and to guide researchers entering the field. The emphasis of this Perspective is on supervised machine learning.

User-Friendly Quantum Mechanics: Applications for Drug Discovery

Quantum mechanics (QM) methods provide a fine description of receptor-ligand interactions and of chemical reactions. Their use in drug design and drug discovery is increasing, especially for complex systems including metal ions in the binding sites, for the design of highly selective inhibitors, for the optimization of bi-specific compounds, to understand enzymatic reactions, and for the study of covalent ligands and prodrugs. They are also used for generating molecular descriptors for predictive QSAR/QSPR models and for the parameterization of force fields. Thanks to the continuous increase of computational power offered by GPUs and to the development of sophisticated algorithms, QM methods are becoming part of the standard tools used in computer-aided drug design (CADD). We present the most used QM methods and software packages, and we discuss recent representative applications in drug design and drug discovery.

Revisiting the Potential Energy Surface of the Stacked Cytosine Dimer: FNO-CCSD(T) Interaction Energies, SAPT Decompositions, and Benchmarking

Nucleobase stacking interactions are crucial for the stability of nucleic acids. This study investigates base stacking energies of the cytosine homodimer in different configurations, including intermolecular separation plots, detailed twist dependence, and displaced structures. Highly accurate ab initio quantum chemical single point energies using an energy function based on MP2 complete basis set extrapolation ([6 → 7]ZaPa-NR) and a CCSD(T)/cc-pVTZ-F12 high-level correction are presented as new reference data, providing the most accurate stacking energies of nucleobase dimers currently available. Accurate SAPT2+(3)δMP2 energy decomposition is used to obtain detailed insights into the nature of base stacking interactions at varying vertical distances and twist values. The ab initio symmetry adapted perturbation theory (SAPT) energy decomposition suggests that the base stacking originates from an intricate interplay between dispersion attraction, short-range exchange-repulsion, and Coulomb interaction. The interpretation of the SAPT data is a complex issue as key energy terms vary substantially in the region of optimal (low energy) base stacking geometries. Thus, attempts to highlight one leading stabilizing SAPT base stacking term may be misleading and the outcome strongly depends on the used geometries within the range of geometries sampled in nucleic acids upon thermal fluctuations. Modern dispersion-corrected density functional theory (among them DSD-BLYP-D3, ωB97M-V, and ωB97M-D3BJ) is benchmarked and often reaches up to spectroscopic accuracy (below 1 kJ/mol). The classical AMBER force field is benchmarked with multiple different sets of point-charges (e.g. HF, DFT, and MP2-based) and is found to produce reasonable agreement with the benchmark data.