Analytical Gradients for Electron-Attached and Ionized States for the Algebraic-Diagrammatic Construction Scheme for the Electron Propagator up to Third Order

The derivation and implementation of analytical gradients for methods based on the non-Dyson algebraic diagrammatic construction for the electron propagator, IP-ADC and EA-ADC, up to the third order is presented. Using nuclear gradients, ground-state equilibrium structures for small open-shell systems are calculated. In addition, we investigated the performance of IP/EA-ADC methods for the calculation of adiabatic ionization potentials and electron affinities for medium-sized organic molecules.

Multi-GPU RI-HF Energies and Analytic Gradients─Toward High-Throughput Ab Initio Molecular Dynamics

This article presents an optimized algorithm and implementation for calculating resolution-of-the-identity Hartree-Fock (RI-HF) energies and analytic gradients using multiple graphics processing units (GPUs). The algorithm is especially designed for high throughput ab initio molecular dynamics simulations of small and medium size molecules (10-100 atoms). Key innovations of this work include the exploitation of multi-GPU parallelism and a workload balancing scheme that efficiently distributes computational tasks among GPUs. Our implementation also employs techniques for symmetry utilization, integral screening, and leveraging sparsity to optimize memory usage. Computational results show that the implementation achieves significant performance improvements, including over 3 × speedups in single GPU AIMD throughput compared to previous GPU-accelerated RI-HF and traditional HF methods. Furthermore, utilizing multiple GPUs can provide superlinear speedup when the additional aggregate GPU memory allows for the storage of decompressed three-center integrals.

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories

The accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH3) molecule and the nucleophilic substitution (SN2) reaction F- + CH3F → FCH3 + F-. We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Flat-Bottom Elastic Network Model for Generating Improved Plausible Reaction Paths

Rapid generation of a plausible reaction path connecting a given reactant and product in advance is crucial for the efficient computation of precise reaction paths or transition states. We propose a computationally efficient potential energy based on the molecular structure to generate such paths. This potential energy has a flat bottom consisting of structures without atomic collisions while preserving nonreactive chemical bonds, bond angles, and partial planar structures. By combining this potential energy with the direct MaxFlux method, a recently developed reaction-path/transition-state search method, we can find the shortest plausible path passing within the bottom. Numerical results show that this combination yields lower energy paths compared to the paths obtained by the well-known image-dependent pair potential. We also theoretically investigate the differences between these two potential energies. The proposed potential energy and path generation routine are implemented in our Python version of the direct MaxFlux method, available on GitHub.

Optimizing Conical Intersections without Explicit Use of Non-Adiabatic Couplings

We present two alternative methods for optimizing minimum energy conical intersection (MECI) molecular geometries without knowledge of the derivative coupling (DC). These methods are based on the utilization of Lagrange multipliers: (i) one method uses an approximate calculation of the DC, while the other (ii) do not require the DC. Both methods use the fact that information on the DC is contained in the Hessian of the squared energy difference. Tests done on a set of small molecular systems, in comparison with other methods, show the ability of the proposed methods to optimize MECIs. Finally, we apply the methods to the furimamide molecule, to optimize and characterize its S1/S2 MECI, and to optimizing the S0/S1 MECI of the silver trimer.

Development of a machine learning interatomic potential for exploring pressure-dependent kinetics of phase transitions in germanium

We introduce a data-driven potential aimed at the investigation of pressure-dependent phase transitions in bulk germanium, including the estimate of kinetic barriers. This is achieved by suitably building a database including several configurations along minimum energy paths, as computed using the solid-state nudged elastic band method. After training the model based on density functional theory (DFT)-computed energies, forces, and stresses, we provide validation and rigorously test the potential on unexplored paths. The resulting agreement with the DFT calculations is remarkable in a wide range of pressures. The potential is exploited in large-scale isothermal-isobaric simulations, displaying local nucleation in the R8 to β-Sn pressure-induced phase transformation, taken here as an illustrative example.

Chromatography Scrutiny, Molecular Docking, Clarifying the Selectivities and the Mechanism of [3 + 2] Cycloloaddition Reaction between Linallol and Chlorobenzene-Nitrile-oxide

Employing the Molecular Electron Density Theory, [3 + 2] cycloaddition processes between 4-chlorobenzenenitrileoxide and linalool, have been applied using the DFT/B3LYP/6-311(d,p) method, activation, reaction energies and the reactivity indices are calculated. In an investigation of conceptual DFT indices, LIL-1 will contribute to this reaction as a nucleophile, whilst NOX-2 will participate as an electrophile. This cyclization is regio, chemo and stereospecific, as demonstrated by the reaction and activation energies, in clear agreement with the experiment's results, in addition, ELF analysis revealed that the mechanism for this cycloaddition occurs in two steps. Furthermore, a docking study was conducted on the products studied, and the interaction with the protein protease COVID-19 (PDB ID: 6LU7), our results indicate that the presence of the -OH group increases the affinity of these products, moreover, adsorption study by chromatography was made on silica gel as support; our outcome reveals that the -OH group creates an intramolecular hydrogen bond in the product P2, while in the product P3 will create a hydrogen bond with the silica gel which makes the two products P2 and P3 are very easy to separate by chromatography, this result is in excellent agreement with the Rf retention value. The study might provide a fundamental for developing natural anti-viral compound in promoting human health.

SCINE-Software for chemical interaction networks

The software for chemical interaction networks (SCINE) project aims at pushing the frontier of quantum chemical calculations on molecular structures to a new level. While calculations on individual structures as well as on simple relations between them have become routine in chemistry, new developments have pushed the frontier in the field to high-throughput calculations. Chemical relations may be created by a search for specific molecular properties in a molecular design attempt, or they can be defined by a set of elementary reaction steps that form a chemical reaction network. The software modules of SCINE have been designed to facilitate such studies. The features of the modules are (i) general applicability of the applied methodologies ranging from electronic structure (no restriction to specific elements of the periodic table) to microkinetic modeling (with little restrictions on molecularity), full modularity so that SCINE modules can also be applied as stand-alone programs or be exchanged for external software packages that fulfill a similar purpose (to increase options for computational campaigns and to provide alternatives in case of tasks that are hard or impossible to accomplish with certain programs), (ii) high stability and autonomous operations so that control and steering by an operator are as easy as possible, and (iii) easy embedding into complex heterogeneous environments for molecular structures taken individually or in the context of a reaction network. A graphical user interface unites all modules and ensures interoperability. All components of the software have been made available as open source and free of charge.

Automatic Determination of the Non-Covalent Stable Conformations of the NO2-Pyrene Cluster in Full Dimensionality (81D) Using the vdW-TSSCDS Approach

We present the detailed topographical characterisation (stationary points and minimum energy paths connecting them) of the full dimensional (81D) intermolecular potential energy surface associated with the non-covalent interactions between the NO2 radical and the pyrene (C16H10) molecule. The whole procedure is (quasi) fully automated. We have used our recent algorithm vdW-TSSCDS as implemented on the freely-available AutoMekin software package. To this end, a series of inexpensive classical trajectories using forces from a low-level (semi-empirical) theory are used to sample the configuration space of the system in the search for candidates to first order saddle points. These guess structures are determined by means of a graph-theory based algorithm using the concept of adjacency matrix. Low-level optimizations are followed by re-optimizations at a final high-level of theory (DFT and CCSD(T)-F12 in our case.). The resulting set of stationary points and paths connecting them constitutes the so-called reaction network. In the case of NO2-pyrene, this network exhibits four major basins which can be characterized by their point-group symmetry. A central one, of global C2 symmetry, comprises the global minimum (as well as all other permutationally related conformers) together with the corresponding C2v saddle points connecting them. This central basin is connected to three others of lower C1 symmetry. The latter can be distinguished by the projection of the position of the NO2 nitrogen atom on the pyrene plane in combination with the relative orientation of the oxygen pair pointing either inwards, outwards, upwards or downwards.

Locating Transition States by Variational Reaction Path Optimization with an Energy-Derivative-Free Objective Function

Locating transition states is essential for understanding molecular reactions. We propose a double-ended transition state search method by revisiting a variational reaction path optimization method known as the MaxFlux method. Although its original purpose is to add temperature effects to reaction paths, we conversely let the temperature approach zero to obtain an asymptotically exact minimum energy path and its corresponding transition state in variational formalism with an energy-derivative-free objective function. Using several numerical techniques to directly optimize the objective function, the present method reliably finds transition states with low computational cost. In particular, only three force evaluations per iteration are sufficient. This is confirmed on a variety of molecular reactions where the nudged elastic band method often fails. The present method is implemented in Python using the Atomic Simulation Environment and is available on GitHub.

Simulating chemical reaction dynamics on quantum computer

The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl- + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices.

High-Performance Multi-GPU Analytic RI-MP2 Energy Gradients

This article presents a novel algorithm for the calculation of analytic energy gradients from second-order Møller-Plesset perturbation theory within the Resolution-of-the-Identity approximation (RI-MP2), which is designed to achieve high performance on clusters with multiple graphical processing units (GPUs). The algorithm uses GPUs for all major steps of the calculation, including integral generation, formation of all required intermediate tensors, solution of the Z-vector equation and gradient accumulation. The implementation in the EXtreme Scale Electronic Structure System (EXESS) software package includes a tailored, highly efficient, multistream scheduling system to hide CPU-GPU data transfer latencies and allows nodes with 8 A100 GPUs to operate at over 80% of theoretical peak floating-point performance. Comparative performance analysis shows a significant reduction in computational time relative to traditional multicore CPU-based methods, with our approach achieving up to a 95-fold speedup over the single-node performance of established software such as Q-Chem and ORCA. Additionally, we demonstrate that pairing our implementation with the molecular fragmentation framework in EXESS can drastically lower the computational scaling of RI-MP2 gradient calculations from quintic to subquadratic, enabling further substantial savings in runtime while retaining high numerical accuracy in the resulting gradients.

Mechanism of the Sharpless Epoxidation Reaction: A DFT Study

The Sharpless reaction is an enantioselective epoxidation of prochiral allylic alcohols that employs a Ti(IV) catalyst formed from titanium tetra(isopropoxide), Ti(O-i-Pr)4, diethyl tartrate (DET), and the oxidizing agent tert-butyl hydroperoxide. The M06-2X DFT functional with the 6-311+G(d,p) basis set has been employed to model the structures and energetics of the Sharpless epoxidation reaction. The monomeric tetracoordinate titanium(IV) diethyltartrate is thermodynamically strongly favored to dimerize, producing a pentacoordinate catalyst, [Ti(DET)(O-i-Pr)2]2, that is a more reactive chiral epoxidation catalyst. The rapid ligand exchange reactions needed to generate the "loaded" catalyst and to repeat the overall catalytic cycle have been examined and are found to have activation energies that are much lower than the epoxidation barriers. The transition structures and activation energies for the enantioselective epoxidation of allyl alcohol, trans-methyl-allyl alcohol and trans-tert-butyl-allyl alcohol with the "loaded" Sharpless catalyst, [Ti2(DET)2(O-i-Pr)2-(OAllyl)-(OOt-Bu)], are presented. The effect of the C═O···Ti interactions on the activation energies and the significance of the O-C-C═C dihedral angle on the enantioselectivity of the epoxidation reaction are discussed.

CREST-A program for the exploration of low-energy molecular chemical space

Conformer-rotamer sampling tool (CREST) is an open-source program for the efficient and automated exploration of molecular chemical space. Originally developed in Pracht et al. [Phys. Chem. Chem. Phys. 22, 7169 (2020)] as an automated driver for calculations at the extended tight-binding level (xTB), it offers a variety of molecular- and metadynamics simulations, geometry optimization, and molecular structure analysis capabilities. Implemented algorithms include automated procedures for conformational sampling, explicit solvation studies, the calculation of absolute molecular entropy, and the identification of molecular protonation and deprotonation sites. Calculations are set up to run concurrently, providing efficient single-node parallelization. CREST is designed to require minimal user input and comes with an implementation of the GFNn-xTB Hamiltonians and the GFN-FF force-field. Furthermore, interfaces to any quantum chemistry and force-field software can easily be created. In this article, we present recent developments in the CREST code and show a selection of applications for the most important features of the program. An important novelty is the refactored calculation backend, which provides significant speed-up for sampling of small or medium-sized drug molecules and allows for more sophisticated setups, for example, quantum mechanics/molecular mechanics and minimum energy crossing point calculations.

Exploration of biochemical reactivity with a QM/MM growing string method

In this work, we have implemented the single-ended growing string method using a hybrid internal/Cartesian coordinate scheme within our in-house QM/MM package, QoMMMa, representing the first implementation of the growing string method in the QM/MM framework. The goal of the implementation was to facilitate generation of QM/MM reaction pathways with minimal user input, and also to improve the quality of the pathways generated as compared to the widely used adiabatic mapping approach. We have validated the algorithm against a reaction which has been studied extensively in previous computational investigations - the Claisen rearrangement catalysed by chorismate mutase. The nature of the transition state and the height of the barrier was predicted well using our algorithm, where more than 88% of the pathways generated were deemed to be of production quality. Directly compared to using adiabatic mapping, we found that while our QM/MM single-ended growing string method is slightly less efficient, it readily produces reaction pathways with fewer discontinuites and thus minimises the need for involved remapping of unsatisfactory energy profiles.

Self-Assembly of a Novel Pentapeptide into Hydrogelated Dendritic Architecture: Synthesis, Properties, Molecular Docking and Prospective Applications

Currently, ultrashort oligopeptides consisting of fewer than eight amino acids represent a cutting-edge frontier in materials science, particularly in the realm of hydrogel formation. By employing solid-phase synthesis with the Fmoc/tBu approach, a novel pentapeptide, FEYNF-NH2, was designed, inspired by a previously studied sequence chosen from hen egg-white lysozyme (FESNF-NH2). Qualitative peptide analysis was based on reverse-phase high performance liquid chromatography (RP-HPLC), while further purification was accomplished using solid-phase extraction (SPE). Exact molecular ion confirmation was achieved by matrix-assisted laser desorption-ionization mass spectrometry (MALDI-ToF MS) using two different matrices (HCCA and DHB). Additionally, the molecular ion of interest was subjected to tandem mass spectrometry (MS/MS) employing collision-induced dissociation (CID) to confirm the synthesized peptide structure. A combination of research techniques, including Fourier-transform infrared spectroscopy (FTIR), fluorescence analysis, transmission electron microscopy, polarized light microscopy, and Congo red staining assay, were carefully employed to glean valuable insights into the self-assembly phenomena and gelation process of the modified FEYNF-NH2 peptide. Furthermore, molecular docking simulations were conducted to deepen our understanding of the mechanisms underlying the pentapeptide's supramolecular assembly formation and intermolecular interactions. Our study provides potential insights into amyloid research and proposes a novel peptide for advancements in materials science. In this regard, in silico studies were performed to explore the FEYNF peptide's ability to form polyplexes.

Diffusion-based generative AI for exploring transition states from 2D molecular graphs

The exploration of transition state (TS) geometries is crucial for elucidating chemical reaction mechanisms and modeling their kinetics. Recently, machine learning (ML) models have shown remarkable performance for prediction of TS geometries. However, they require 3D conformations of reactants and products often with their appropriate orientations as input, which demands substantial efforts and computational cost. Here, we propose a generative approach based on the stochastic diffusion method, namely TSDiff, for prediction of TS geometries just from 2D molecular graphs. TSDiff outperforms the existing ML models with 3D geometries in terms of both accuracy and efficiency. Moreover, it enables to sample various TS conformations, because it learns the distribution of TS geometries for diverse reactions in training. Thus, TSDiff finds more favorable reaction pathways with lower barrier heights than those in the reference database. These results demonstrate that TSDiff shows promising potential for an efficient and reliable TS exploration.

MolOpt: Autonomous Molecular Geometry Optimization Using Multiagent Reinforcement Learning

Most optimization problems require the user to select an algorithm and, to some extent, also tune it for better performance. Although intuition and knowledge about the problem can speed up these selection and fine-tuning processes, users often use trial-and-error methodologies, which can be time-consuming and inefficient. With all of that in mind and much more, the concept of "learned optimizers", "learning to learn", and "meta-learning" has been gathering attention in recent years. In this article, we propose MolOpt that uses multiagent reinforcement learning (MARL) for autonomous molecular geometry optimization (MGO). Typically MGO algorithms are hand-designed, but MolOpt uses MARL to learn a learned optimizer (policy) that can perform MGO without the need for other hand-designed optimizers. We cast MGO as a MARL problem, where each agent corresponds to a single atom in the molecule. MolOpt performs MGO by minimizing the forces on each atom of the molecule. Our experiments demonstrate the generalizing ability of MolOpt for the MGO of propane, pentane, heptane, hexane, and octane when trained on ethane, butane, and isobutane. In terms of performance, MolOpt outperforms the MDMin optimizer and demonstrates performance similar to that of the FIRE optimizer. However, it does not surpass the BFGS optimizer. The results demonstrate that MolOpt has the potential to introduce innovative advancements in MGO by providing a novel approach using reinforcement learning (RL), which may open up new research directions for MGO. Overall, this work serves as a proof-of-concept for the potential of MARL in MGO.

Integrating Chemical Information into Reinforcement Learning for Enhanced Molecular Geometry Optimization

Geometry optimization is a crucial step in computational chemistry, and the efficiency of optimization algorithms plays a pivotal role in reducing computational costs. In this study, we introduce a novel reinforcement-learning-based optimizer that surpasses traditional methods in terms of efficiency. What sets our model apart is its ability to incorporate chemical information into the optimization process. By exploring different state representations that integrate gradients, displacements, primitive type labels, and additional chemical information from the SchNet model, our reinforcement learning optimizer achieves exceptional results. It demonstrates an average reduction of about 50% or more in optimization steps compared to the conventional optimization algorithms that we examined when dealing with challenging initial geometries. Moreover, the reinforcement learning optimizer exhibits promising transferability across various levels of theory, emphasizing its versatility and potential for enhancing molecular geometry optimization. This research highlights the significance of leveraging reinforcement learning algorithms to harness chemical knowledge, paving the way for future advancements in computational chemistry.

Molecular Hessian matrices from a machine learning random forest regression algorithm

In this article, we present a machine learning model to obtain fast and accurate estimates of the molecular Hessian matrix. In this model, based on a random forest, the second derivatives of the energy with respect to redundant internal coordinates are learned individually. The internal coordinates together with their specific representation guarantee rotational and translational invariance. The model is trained on a subset of the QM7 dataset but is shown to be applicable to larger molecules picked from the QM9 dataset. From the predicted Hessian, it is also possible to obtain reasonable estimates of the vibrational frequencies, normal modes, and zero point energies of the molecules.

Cartesian constraints in QM/MM optimizations

With the rise of quantum mechanical/molecular mechanical (QM/MM) methods, the interest in the calculation of molecular assemblies has increased considerably. The structures and dynamics of such assemblies are usually governed to a large extend by intermolecular interactions. As a result, the corresponding potential energy surfaces are topological rich and possess many shallow minima. Therefore, local structure optimizations of QM/MM molecular assemblies can be challenging, in particular if optimization constraints are imposed. To overcome this problem, structure optimization in normal coordinate space is advocated. To do so, the external degrees of freedom of a molecule are separated from the internal ones by a projector matrix in the space of the Cartesian coordinates. Here we extend this approach to Cartesian constraints. To this end, we devise an algorithm that adds the Cartesian constraints directly to the projector matrix and in this way eliminates them from the reduced coordinate space in which the molecule is optimized. To analyze the performance and stability of the constrained optimization algorithm in normal coordinate space, we present constrained minimizations of small molecular systems and amino acids in gas phase as well as water employing QM/MM constrained optimizations. All calculations are performed in the framework of auxiliary density functional theory as implemented in the program deMon2k.

Geometry Optimization: A Comparison of Different Open-Source Geometry Optimizers

Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and energy calculations. The findings demonstrate how the choice of the coordinate system influences the optimization process to reach an equilibrium structure. With fewer steps, internal coordinates outperform Cartesian coordinates, while the choice of the initial Hessian and Hessian update method in quasi-Newton approaches made by different optimization algorithms also contributes to the rate of convergence. Furthermore, an available open-source machine learning method based on Gaussian process regression (GPR) was evaluated for energy minimizations over surrogate potential energy surfaces with both Cartesian and internal coordinates with internal coordinates outperforming Cartesian. Overall, geomeTRIC and DL-FIND with their default optimization method as well as with the GPR-based model using Hartree-Fock theory with the 6-31G** basis set needed a comparable number of geometry optimization steps to the approach of Baker using a unit matrix as the initial Hessian to reach the optimized geometry. On the other hand, the Berny and Sella offerings in ASE outperformed the other algorithms. Based on this, we recommend using the file-based approaches, ASE/Berny and ASE/Sella, for large-scale optimization efforts, while if using a single executable is preferable, we now distribute QUICK integrated with DL-FIND.

Structural Determination and Hierarchical Evolution of Transition Metal Clusters Based on an Improved Self-Adaptive Differential Evolution with Neighborhood Search Algorithm

Determining the optimal structures and clarifying the corresponding hierarchical evolution of transition metal clusters are of fundamental importance for their applications. The global optimization of clusters containing a large number of atoms, however, is a vastly challenging task encountered in many fields of physics and chemistry. In this work, a high-efficiency self-adaptive differential evolution with neighborhood search (SaNSDE) algorithm, which introduced an optimized cross-operation and an improved Basin Hopping module, was employed to search the lowest-energy structures of CoN, PtN, and FeN (N = 3-200) clusters. The performance of the SaNSDE algorithm was first evaluated by comparing our results with the parallel results collected in the Cambridge Cluster Database (CCD). Subsequently, different analytical methods were introduced to investigate the structural and energetic properties of these clusters systematically, and special attention was paid to elucidating the structural evolution with cluster size by exploring their overall shape, atomic arrangement, structural similarity, and growth pattern. By comparison with those results listed in the CCD, 13 lower-energy structures of FeN clusters were discovered. Moreover, our results reveal that the clusters of three metals had different magic numbers with superior stable structures, most of which possessed high symmetry. The structural evolution of Co, Pt, and Fe clusters could be, respectively, considered as predominantly closed-shell icosahedral, Marks decahedral, and disordered icosahedral-ring growth. Further, the formation of shell structures was discovered, and the clusters with hcp-, fcc-, and bcc-like configurations were ascertained. Nevertheless, the growth of the clusters was not simply atom-to-atom piling up on a given cluster despite gradual saturation of the coordination number toward its bulk limit. Our work identifies the general growth trends for such a wide region of cluster sizes, which would be unbearably expensive in first-principles calculations, and advances the development of global optimization algorithms for the structural prediction of clusters.

Fantastical excited state optimized structures and where to find them

The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima and saddle points. Always implicit in using this machinery is the fact that an excited state PES only exists within the realm of the Born-Oppenheimer approximation, where the nuclear and electronic degrees of freedom separate. This work demonstrates through ab initio calculations and simple nonadiabatic dynamics that some excited state minimum structures are fantastical: they appear to exist as stable configurations only as a consequence of the PES construct, rather than being physically observable. Each fantastical structure exhibits an unphysically high predicted harmonic frequency and associated force constant. This fact can serve as a valuable diagnostic of when an optimized excited state structure is non-observable. The origin of this phenomenon can be attributed to the coupling between different electronic states. As PESs approach one another, the upper surface can form a minimum that is very close to a near-touching point. The force constant, evaluated at this minimum, relates to the strength of the electronic coupling rather than to any characteristic excited state vibration. Nonadiabatic dynamics results using a Landau-Zener model illustrate that fantastical excited state structures have extremely short lifetimes on the order of a few femtoseconds. Their appearance in a calculation signals the presence of a nearby conical intersection through which the system will rapidly cross to a lower surface.

Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Fragment-based models for dissociation of strong acids in water: Electrostatic embedding minimizes the dependence on the fragmentation schemes

Fragmentation methods such as MIM (Molecules-in-Molecules) provide a route to accurately model large systems and have been successful in predicting their structures, energies, and spectroscopic properties. However, their use is often limited to systems at equilibrium due to the inherent complications in the choice of fragments in systems away from equilibrium. Furthermore, the presence of charges resulting from any heterolytic bond breaking may increase the fragmentation error. We have previously suggested EE-MIM (Electrostatically Embedded Molecules-In-Molecules) as a method to mitigate the errors resulting from the missing long-range interactions in molecular clusters in equilibrium. Here, we show that the same method can be applied to improve the performance of MIM to solve the longstanding problem of dependency of the fragmentation energy error on the choice of the fragmentation scheme. We chose four widely used acid dissociation reactions (HCl, HClO4, HNO3, and H2SO4) as test cases due to their importance in chemical processes and complex reaction potential energy surfaces. Electrostatic embedding improves the performance at both one and two-layer MIM as shown by lower EE-MIM1 and EE-MIM2 errors. The EE-MIM errors are also demonstrated to be less dependent on the choice of the fragmentation scheme by analyzing the variation in fragmentation energy at the points with more than one possible fragmentation scheme (points where the fragmentation scheme changes). EE-MIM2 with M06-2X as the low-level resulted in a variation of less than 1 kcal/mol for all the cases and 1 kJ/mol for all but three cases, rendering our method fragmentation scheme-independent for acid dissociation processes.

Combining [MoVIO3] and [M0(CO)3] (M = Mo, Cr) Fragments within the Same Complex: Synthesis and Reactivity of the Single Oxo-Bridged Heterobimetallics Supported by Xanthene-Based Heterodinucleating Ligands

A functional model of Mo-Cu carbon monoxide dehydrogenase (CODH) enzyme requires the presence of an oxidant (metal-oxo) and a metal-bound carbonyl in close proximity. In this work, we report the synthesis, characterization, and reactivity of a heterobimetallic complex combining Mo(VI) trioxo with Mo(0) tricarbonyl. The formation of the heterobimetallic complex is facilitated by the xanthene-bridged heterodinucleating ligand containing a hard catecholate chelate and a soft iminopyridine chelate. A catechol-coordinated square-pyramidal [MoVIO3] fragment interacts directly with the iminopyridine-bound [Mo0(CO)3] fragment via a single (oxo) bridge, with the overall disposition being related to the proposed first step in the CODH mechanism, where square-pyramidal [MoVIO2S] interacts with the [Cu-CO] via a single sulfido bridge. Our attempt to obtain a sulfido-bridged analogue (using [MoO3S]2- precursor) led to a mixture of products possibly containing different (oxo and sulfido) bridges. Despite a direct interaction between Mo(VI) and Mo(0) segments, no internal redox is observed, with the high lying occupied MOs being mostly d-π orbitals at Mo0(CO)3 and the low lying unoccupied MOs being d-π orbitals at MoVIO3. Due to the overall rigid structure, the heterobimetallic complex was found to be stable up to 100 °C in DMF-d7 (based on 1H NMR). The decomposition of the complex above this temperature does not produce CO2 (based on gas chromatography), dissociating stable Mo(CO)3(DMF)3 instead (based on IR). We also synthesized and studied the reactivity of the Mo(VI)/Cr(0) analogue. While this complex demonstrated more facile decomposition, no CO2 production was observed. Density functional theory calculations suggest that the formation of [CO2]2- and its subsequent reductive elimination is endergonic in the present system, likely due to the stability of fac-Mo0(CO)3 and the relative nucleophilic character of the carbonyl carbon engendered by back donation from Mo(0). The calculations also indicate that the replacement of one oxo by sulfido (both terminal and bridging), replacement of catechol with dithiolene, and replacement of Mo(0) with Cr(0) does not affect significantly the energetics of the process, likely requiring the use a less stable and less π-basic CO anchor.

Smooth Things Come in Threes: A Diabatic Surrogate Model for Conical Intersection Optimization

The optimization of conical intersection structures is complicated by the nondifferentiability of the adiabatic potential energy surfaces. In this work, we build a pseudodiabatic surrogate model, based on Gaussian process regression, formed by three smooth and differentiable surfaces that can adequately reproduce the adiabatic surfaces. Using this model with the restricted variance optimization method results in a notable decrease of the overall computational effort required to obtain minimum energy crossing points.

Absorption wavelength (TD-DFT) and adsorption of metal chalcogen clusters with methyl nicotinate: Structural, electronic, IRI, SERS, pharmacological and antiviral studies (HIV and omicron)

The DFT B3LYP-LAND2DZ technique is used to examine interactions of Methyl nicotinate with copper selenide and zinc selenide clusters. The existence of reactive sites is determined using ESP maps and Fukui data. The energy variations between HOMO and LUMO are utilised to calculate various energy parameters. The Atoms in Molecules and ELF (Electron Localisation Function) maps are employed to investigate the topology of the molecule. The Interaction Region Indicator is used to determine the existence of non-covalent zones in the molecule. The UV-Vis spectrum using the TD-DFT method and DOS graphs are used to obtain the theoretical determination of electronic transition and properties. Structural analysis of the compound is obtained using theoretical IR spectra. To explore the adsorption of copper selenide and zinc selenide clusters on the Methyl nicotinate, the adsorption energy and theoretical SERS spectra are employed. Furthermore, pharmacological investigations are carried out to confirm the drug's non-toxicity. The compound's antiviral efficacy against HIV and Omicron is demonstrated via protein-ligand docking.

Dehydration of a crystal hydrate at subglacial temperatures

Water is one of the most important substances on our planet1. It is ubiquitous in its solid, liquid and vaporous states and all known biological systems depend on its unique chemical and physical properties. Moreover, many materials exist as water adducts, chief among which are crystal hydrates (a specific class of inclusion compound), which usually retain water indefinitely at subambient temperatures2. We describe a porous organic crystal that readily and reversibly adsorbs water into 1-nm-wide channels at more than 55% relative humidity. The water uptake/release is chromogenic, thus providing a convenient visual indication of the hydration state of the crystal over a wide temperature range. The complementary techniques of X-ray diffraction, optical microscopy, differential scanning calorimetry and molecular simulations were used to establish that the nanoconfined water is in a state of flux above -70 °C, thus allowing low-temperature dehydration to occur. We were able to determine the kinetics of dehydration over a wide temperature range, including well below 0 °C which, owing to the presence of atmospheric moisture, is usually challenging to accomplish. This discovery unlocks opportunities for designing materials that capture/release water over a range of temperatures that extend well below the freezing point of bulk water.

Prediction of transition state structures of gas-phase chemical reactions via machine learning

The elucidation of transition state (TS) structures is essential for understanding the mechanisms of chemical reactions and exploring reaction networks. Despite significant advances in computational approaches, TS searching remains a challenging problem owing to the difficulty of constructing an initial structure and heavy computational costs. In this paper, a machine learning (ML) model for predicting the TS structures of general organic reactions is proposed. The proposed model derives the interatomic distances of a TS structure from atomic pair features reflecting reactant, product, and linearly interpolated structures. The model exhibits excellent accuracy, particularly for atomic pairs in which bond formation or breakage occurs. The predicted TS structures yield a high success ratio (93.8%) for quantum chemical saddle point optimizations, and 88.8% of the optimization results have energy errors of less than 0.1 kcal mol-1. Additionally, as a proof of concept, the exploration of multiple reaction paths of an organic reaction is demonstrated based on ML inferences. I envision that the proposed approach will aid in the construction of initial geometries for TS optimization and reaction path exploration.

Kylin 1.0: An ab-initio density matrix renormalization group quantum chemistry program

The accurate evaluation of electron correlations is highly necessary for the proper descriptions of the electronic structures in strongly correlated molecules, ranging from bond-dissociating molecules, polyradicals, to large conjugated molecules and transition metal complexes. For this purpose, in this paper, a new ab-initio quantum chemistry program Kylin 1.0 for electron correlation calculations at various quantum many-body levels, including configuration interaction (CI), perturbation theory (PT), and density matrix renormalization group (DMRG), is presented. Furthermore, fundamental quantum chemistry methods such as Hartree-Fock self-consistent field (HF-SCF) and the complete active space SCF (CASSCF) are also implemented. The Kylin 1.0 program possesses the following features: (1) a matrix product operator (MPO) formulation-based efficient DMRG implementation for describing static electron correlation within a large active space composed of more than 100 orbitals, supporting both U 1 n × U 1 S z $$ \mathrm{U}{(1)}_{\mathrm{n}}\times \mathrm{U}{(1)}_{{\mathrm{S}}_{\mathrm{z}}} $$ and U 1 n × SU 2 S $$ \mathrm{U}{(1)}_{\mathrm{n}}\times \mathrm{SU}{(2)}_{\mathrm{S}} $$ symmetries; (2) an efficient second-order DMRG-self-consistent field (SCF) implementation; (3) an externally contracted multi-reference CI (MRCI) and Epstein-Nesbet PT with DMRG reference wave functions for including the remaining dynamic electron correlation outside the large active spaces. In this paper, we introduce the capabilities and numerical benchmark examples of the Kylin 1.0 program.

Automated handling of complex chemical structures in Z-matrix coordinates-The chemcoord library

In this work, we present a fully automated method for the construction of chemically meaningful sets of hierarchical nonredundant internal coordinates (ICs; also commonly denoted as Z-matrices) from the Cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to linear arrangements of atoms, to consistently guarantee a well-defined transformation to Cartesian coordinates, even after structural changes. The representations thus obtained are particularly well suited for pathway construction in double-ended methods for transition state search and optimizations with nonlinear constraints. Analytical gradients for the transformation between the coordinate systems were derived for analytical geometry optimizations purely in Z-matrix coordinates. The geometry optimization was coupled with a Symbolic Algebra package to support arbitrary nonlinear constraints in Z-matrix coordinates, while retaining analytical energy gradient conversion. The difference to the commonly used nonhierarchical IC transformations is discussed. Sample applications are provided for a number of common chemical reactions and illustrative examples.

Density functional theory investigation of mechanisms of degradation reactions of sulfonated PEEK membranes with OH radicals in fuel cells: Addition-elimination reactions and acid catalyzed water elimination

Sulfonated polyether (ether) ketone, or sulfonated PEEK (sPEEK) membranes are one possible candidate for proton-transfer membranes in hydrogen fuel cells. Reaction with hydroxy radicals is expected to be a significant source of degradation of these membranes during fuel cell operation. In this work, the reactivity of the sPEEK polymer molecule with OH radicals is studied by M062X hybrid density functional calculations of the energetics of several reaction paths in a water environment as modeled by polarized continuum model (PCM) calculations. Reactants, products, encounter minima and transition states are optimized for a reaction pathway in which OH addition is followed by acid-catalyzed water elimination which cationizes the polymer, degradation is expected to follow this reaction as the unstable cation then undergoes bond-breaking or other reactions. Two pathways for this acid-catalyzed cationization, one in which a water molecule plays the role of an additional co-catalyst, are reported. Further calculations explore reaction pathways in which addition of OH to the polymer is followed by bond breaking reactions which would break the polymer chain or the bond between the polymer and sulfonyl groups. Examination of the free energy barriers to all these reactions, relative to reactants, suggest that these direct bond-breaking reactions may compete somewhat with acid-catalyzed water elimination following OH addition.

Density functional theory investigation of mechanisms of degradation reactions of sulfonated PEEK membranes with OH radicals in fuel cells: addition-elimination reactions and acid catalyzed water elimination

Sulfonated polyether (ether) ketone or sulfonated PEEK (sPEEK) membranes are one possible candidate for proton-transfer membranes in hydrogen fuel cells. Reaction with hydroxy radicals is expected to be a significant source of degradation of these membranes during fuel cell operation. In this work, the reactivity of the sPEEK polymer molecule with OH radicals is studied by M062X hybrid density functional calculations of the energetics of several reaction paths in a water environment as modeled by polarized continuum model calculations. Reactants, products, encounter minima and transition states are optimized for a reaction pathway in which OH addition is followed by acid-catalyzed water elimination which cationizes the polymer, degradation is expected to follow this reaction as the unstable cation then undergoes bond-breaking or other reactions. Two pathways for this acid-catalyzed cationization, one in which a water molecule plays the role of an additional co-catalyst, are reported. Further calculations explore reaction pathways in which addition of OH to the polymer is followed by bond breaking reactions which would break the polymer chain or the bond between the polymer and sulfonyl groups. Examination of the free energy barriers to all these reactions, relative to reactants, suggests that these direct bond-breaking reactions may compete somewhat with acid-catalyzed water elimination following OH addition.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00214-023-02981-2.

Quantum Algorithm for Numerical Energy Gradient Calculations at the Full Configuration Interaction Level of Theory

A Bayesian phase difference estimation (BPDE) algorithm allows us to compute the energy gap of two electronic states of a given Hamiltonian directly by utilizing the quantum superposition of their wave functions. Here we report an extension of the BPDE algorithm to the direct calculation of the energy difference of two molecular geometries. We apply the BPDE algorithm for the calculation of numerical energy gradients based on the two-point finite-difference method, enabling us to execute geometry optimization of one-dimensional molecules at the full-CI level on a quantum computer. Results of numerical quantum circuit simulations of the geometry optimization of the H2 molecule with the STO-3G and 6-31G basis sets, the LiH and BeH2 molecules at the full-CI/STO-3G level, and the N2 molecule at the CASCI(6e,6o)/6-311G* level are given.

Fast Screening of Minimum Energy Crossing Points with Semiempirical Tight-Binding Methods

The investigation of photochemical processes is a highly active field in computational chemistry. One research direction is the automated exploration and identification of minimum energy conical intersection (MECI) geometries. However, due to the immense technical effort required to calculate nonadiabatic potential energy landscapes, the routine application of such computational protocols is severely limited. In this study, we will discuss the prospect of combining adiabatic potential energy surfaces from semiempirical quantum mechanical calculations with specialized confinement potential and metadynamics simulations to identify S₀/T₁ minimum energy crossing point (MECP) geometries. It is shown that MECPs calculated at the GFN2-xTB level can provide suitable approximations to high-level S₀/S₁ab initio conical intersection geometries at a fraction of the computational cost. Reference MECIs of benzene are studied to illustrate the basic concept. An example application of the presented protocol is demonstrated for a set of photoswitch molecules.

Aziridination Reactivity of a Manganese(II) Complex with a Bulky Chelating Bis(Alkoxide) Ligand

Treatment of Mn(N(SiMe₃)₂)₂(THF)₂ with bulky chelating bis(alkoxide) ligand [1,1′:4′,1′′-terphenyl]-2,2′′-diylbis(diphenylmethanol) (H₂[O-terphenyl-O]^Ph) formed a seesaw manganese(II) complex Mn[O-terphenyl-O]^Ph(THF)₂, characterized by structural, spectroscopic, magnetic, and analytical methods. The reactivity of Mn[O-terphenyl-O]^Ph(THF)₂ with various nitrene precursors was investigated. No reaction was observed between Mn[O-terphenyl-O]^Ph(THF)₂ and aryl azides. In contrast, the treatment of Mn[O-terphenyl-O]^Ph(THF)₂ with iminoiodinane PhINTs (Ts = p-toluenesulfonyl) was consistent with the formation of a metal-nitrene complex. In the presence of styrene, the reaction led to the formation of aziridine. Combining varying ratios of styrene and PhINTs in different solvents with 10 mol% of Mn[O-terphenyl-O]^Ph(THF)₂ at room temperature produced 2-phenylaziridine in up to a 79% yield. Exploration of the reactivity of Mn[O-terphenyl-O]^Ph(THF)₂ with various olefins revealed (1) moderate aziridination yields for p-substituted styrenes, irrespective of the electronic nature of the substituent; (2) moderate yield for 1,1′-disubstituted α-methylstyrene; (3) no aziridination for aliphatic α-olefins; (4) complex product mixtures for the β-substituted styrenes. DFT calculations suggest that iminoiodinane is oxidatively added upon binding to Mn, and the resulting formal imido intermediate has a high-spin Mn(III) center antiferromagnetically coupled to an imidyl radical. This imidyl radical reacts with styrene to form a sextet intermediate that readily reductively eliminates the formation of a sextet Mn(II) aziridine complex.

A comparison of hydrogen abstraction reaction between allyl-type monomers with thioxanthone-based photoinitiators without amine synergists

The photodriven radical-mediated [3 + 2] cyclization reaction was found to yield polymers efficiently without being hindered by degradative chain transfer. The first reaction is a hydrogen abstraction process in which one hydrogen atom migrates from the α-methylene group of an allyl monomer to the triplet state (or fragments) of the photoinitiator, thus yielding primary allyl radicals as primary radicals and then begins chain propagation via a 3 + 2 cyclization reaction. Allyl ether monomers were found to be significantly higher than other allyl monomers even with the absence of amine-like synergists. In order to clarify the procedure of the hydrogen abstraction mechanism, we used four allyl-type monomers as hydrogen donors and three thioxanthone photoinitiators as hydrogen acceptors by the quantum chemistry method in terms of geometry and energy. The results were interpreted with transition-state theory and the interaction/deformation model. Then, the tunneling factors of hydrogen abstraction reactions were also investigated by Eckart’s correction. The results show allyl ether systems are more reactive than other allyl systems, and it would provide us with new insights into these hydrogen abstractions.

Studying and exploring potential energy surfaces of compressed molecules: a fresh theory from the eXtreme Pressure Polarizable Continuum Model

We present a new theory for studying and exploring the potential energy surface of compressed molecular systems as described within the XP-PCM framework. The effective potential energy surface is defined by the sum of the electronic energy of the compressed system and the pressure-volume work that is necessary in order to create the compression cavity at the given condition of pressure. We show that the resulting total energy Gt is related to the electronic energy by a Legendre transform, in which the pressure and volume of the compression cavity are the conjugate variables. We present an analytical expression for the evaluation of the gradient of the total energy ∇Gt to be used for the geometry optimization of equilibrium geometries and transition states of compressed molecular systems. We also show that, as a result of the Legendre transform property, the potential energy surface can be studied explicitly as function of the pressure, leading to an explicit connection with the well-known Hammond postulate. As a proof of concept, we present the application of the theory to studying and determining of the optimized geometry of compressed methane and the transition state of electrocyclic ring-closure of hexatriene and of H-transfer between two methyl radicals.

Automated input structure generation for single-ended reaction path optimizations

The exploration of a reaction network requires highly automated workflows to avoid error-prone and time-consuming manual steps. In this respect, a major bottleneck is the search for transition-state (TS) structures, which frequently fails and, therefore, makes (manual) revision necessary. In this work, we present a technique for obtaining suitable input structures for automated TS searches based on single-ended reaction path optimization algorithms, which makes subsequent TS searches via this method significantly more robust. First, possible input structures are generated based on the spatial alignment of the reactants. The appropriate orientation of reacting groups is achieved via stepwise rotations along selected torsional degrees of freedom. Second, a ranking of the obtained structures is performed according to selected geometric criteria. The main goals are to properly align the reactive atoms, to avoid hindrance within the reaction channel and to resolve steric clashes between the reactants. The developed procedure has been carefully tested on a variety of examples and provides suitable input structures for TS searches within seconds. The method is in daily use in an industrial setting.

Elastic Image Pair Method for Finding Transition States on Potential Energy Surfaces Using Only First Derivatives

Herein, an elastic image pair (EIP) method is proposed to search transition states between two potential-energy minima using only first derivatives. In this method, two images are generated, and the spring forces are added to the images to control the distance between the two images. Transition states are reached when the force and the distance of the image pair are both converged. A set of test molecules is optimized using the EIP method, which shows its efficiency in transition state searching compared to other methods. This new method is more stable and reliable in finding transition states with much less computations.

Efficient implementation of molecular CCSD gradients with Cholesky-decomposed electron repulsion integrals

We present an efficient implementation of ground and excited state coupled cluster singles and doubles (CCSD) gradients based on Cholesky-decomposed electron repulsion integrals. Cholesky decomposition and density fitting are both inner projection methods, and, thus, similar implementation schemes can be applied for both methods. One well-known advantage of inner projection methods, which we exploit in our implementation, is that one can avoid storing large V3 O and V4 arrays by instead considering three-index intermediates. Furthermore, our implementation does not require the formation and storage of Cholesky vector derivatives. The new implementation is shown to perform well, with less than 10% of the time spent calculating the gradients in geometry optimizations. Furthermore, the computational time per optimization cycle is significantly lower compared to other implementations based on an inner projection method. We showcase the capabilities of the implementation by optimizing the geometry of the retinal molecule (C20H28O) at the CCSD/aug-cc-pVDZ level of theory.

Exploring Potential Energy Surfaces Using Reinforcement Machine Learning

Reinforcement machine learning is implemented to survey a series of model potential energy surfaces and ultimately identify the global minima point. Through sophisticated reward function design, the introduction of an optimizing target, and incorporating physically motivated actions, the reinforcement learning agent is capable of demonstrating advanced decision making. These improved actions allow the agent to successfully converge to an optimal solution more rapidly when compared to an agent trained without the aforementioned modifications. This study showcases the conceptual feasibility of using reinforcement machine learning to solve difficult environments, namely, potential energy surfaces, with multiple, seemingly, correct solutions in the form of local minima regions. Through these results, we hope to encourage extending reinforcement learning to more complicated optimization problems and using these novel techniques to efficiently solve traditionally challenging problems in chemistry.

Quantum Chemical Calculations to Trace Back Reaction Paths for the Prediction of Reactants

The long-due development of a computational method for the ab initio prediction of chemical reactants that provide a target compound has been hampered by the combinatorial explosion that occurs when reactions consist of multiple elementary reaction processes. To address this challenge, we have developed a quantum chemical calculation method that can enumerate the reactant candidates from a given target compound by combining an exhaustive automated reaction path search method with a kinetics method for narrowing down the possibilities. Two conventional name reactions were then assessed by tracing back the reaction paths using this new method to determine whether the known reactants could be identified. Our method is expected to be a powerful tool for the prediction of reactants and the discovery of new reactions.

An Improved Self-Adaptive Differential Evolution with the Neighborhood Search Algorithm for Global Optimization of Bimetallic Clusters

Global optimization of multicomponent cluster structures is considerably time-consuming due to the existence of a vast number of isomers. In this work, we proposed an improved self-adaptive differential evolution with the neighborhood search (SaNSDE) algorithm and applied it to the global optimization of bimetallic cluster structures. The cross operation was optimized, and an improved basin hopping module was introduced to enhance the searching efficiency of SaNSDE optimization. Taking (PtNi)_N (N = 38 or 55) bimetallic clusters as examples, their structures were predicted by using this algorithm. The traditional SaNSDE algorithm was carried out for comparison with the improved SaNSDE algorithm. For all the optimized clusters, the excess energy and the second difference of the energy were calculated to examine their relative stabilities. Meanwhile, the bond order parameters were adopted to quantitatively characterize the cluster structures. The results reveal that the improved SaNSDE algorithm possessed significantly higher searching capability and faster convergence speed than the traditional SaNSDE algorithm. Furthermore, the lowest-energy configurations of (PtNi)₃₈ clusters could be classified as the truncated octahedral and disordered structures. In contrast, all the optimal (PtNi)₅₅ clusters were approximately icosahedral. Our work fully demonstrates the high efficiency of the improved algorithm and advances the development of global optimization algorithms and the structural prediction of multicomponent clusters.

Reaction Space Projector (ReSPer) for Visualizing Dynamic Reaction Routes Based on Reduced-Dimension Space

To analyze chemical reaction dynamics based on a reaction path network, we have developed the "Reaction Space Projector" (ReSPer) method with the aid of the dimensionality reduction method. This program has two functions: the construction of a reduced-dimensionality reaction space from a molecular structure dataset, and the projection of dynamic trajectories into the low-dimensional reaction space. In this paper, we apply ReSPer to isomerization and bifurcation reactions of the Au₅ cluster and succeed in analyzing dynamic reaction routes involved in multiple elementary reaction processes, constructing complicated networks (called "closed islands") of nuclear permutation-inversion (NPI) isomerization reactions, and elucidating dynamic behaviors in bifurcation reactions with reference to bundles of trajectories. Interestingly, in the second application, we find a correspondence between the contribution ratios in the ability to visualize and the symmetry of the morphology of closed islands. In addition, the third application suggests the existence of boundaries that determine the selectivity in bifurcation reactions, which was discussed in the phase space. The ReSPer program is a versatile and robust tool to clarify dynamic reaction mechanisms based on the reduced-dimensionality reaction space without prior knowledge of target reactions.