Transition State Optimization Research Articles

Analytical ab initio hessian from a deep learning potential for transition state optimization

Identifying transition states—saddle points on the potential energy surface connecting reactant and product minima—is central to predicting kinetic barriers and understanding chemical reaction mechanisms. In this work, we train a fully differentiable equivariant neural network potential, NewtonNet, on thousands of organic reactions and derive the analytical Hessians. By reducing the computational cost by several orders of magnitude relative to the density functional theory (DFT) ab initio source, we can afford to use the learned Hessians at every step for the saddle point optimizations. We show that the full machine learned (ML) Hessian robustly finds the transition states of 240 unseen organic reactions, even when the quality of the initial guess structures are degraded, while reducing the number of optimization steps to convergence by 2–3× compared to the quasi-Newton DFT and ML methods. All data generation, NewtonNet model, and ML transition state finding methods are available in an automated workflow.

With a little help from our (AI) friend: A general transition state sampling method for tropospheric hydrogen abstraction reactions

Due to their pivotal role in atmospheric processes, hydrogen abstraction reactions are vital in the study of tropospheric chemistry. In this work, we present an algorithm that generates a large number of chemically sound geometries for the optimization of transition states (TSs) of tropospheric bimolecular H abstraction reactions. The code, which was developed in the early stages with the help of artificial intelligence (AI), automatically detects the active H atoms of the molecule and can be used with the OH, Cl, and NO3 oxidants. Given the ubiquity of H transfer reactions in various fields, the algorithm was designed in general terms to facilitate easy adaptation to other oxidants, thus allowing for a broader range of applications. As a result of its use, a much greater number of TSs is predicted when compared with previous theoretical studies of six oxidation reactions. In addition to improving our understanding of the H-abstraction process, obtaining an increased number of TSs is also fundamentally important in calculating more accurate rate constants and atmospheric lifetimes for volatile organic compounds. The simplicity and significance of such a tool in the context of environmental chemistry should make it appealing to researchers of all backgrounds.

QMMM 2023: A program for combined quantum mechanical and molecular mechanical modeling and simulations

Combined quantum mechanical and molecular mechanical (QM/MM) methods play an important role in multiscale modeling and simulations. QMMM 2023 is a general-purpose program for single-point calculations, geometry optimizations, transition-state optimizations, and molecular dynamics (MD) at the QM/MM level. It calls a QM package and an MM package to perform the required single-level calculations and combines them into a QM/MM energy by a variety of schemes. QMMM 2023 supports GAMESS-US, Gaussian, and ORCA as QM packages and Tinker as the MM package. Four types of treatments are available for embedding the QM subsystem in the MM environment: mechanical embedding with gas-phase calculations of the QM region, electronic embedding that allows polarization of the QM region by the MM environment, polarizable embedding for mutual polarization of the QM and MM regions, and flexible embedding for both mutual polarization and partial charge transfer between the QM and MM regions. Boundaries between QM and MM regions that pass through covalent bonds can be treated by several methods, including the redistributed charge (RC) scheme, redistributed charge and dipole (RCD) scheme, balanced-RC scheme, balanced-RCD scheme, screened charge scheme that takes account of charge penetration effects, and smeared charge scheme that delocalizes the MM charges near the QM–MM boundary. Geometry optimization can be done using the optimizer implemented in QMMM 2023 or the Berny optimizer in Gaussian through external calls to Gaussian. Molecular dynamics simulations can be performed at the pure-MM level, pure-QM level, fixed-partitioning QM/MM level, and adaptive-partitioning QM/MM level. The adaptive-partitioning treatments permit on-the-fly relocation of the QM–MM boundary by dynamically reclassifying atoms or groups into the QM or MM subsystems. Program SummaryProgram Title: QMMM 2023.CPC Library link to program files:https://doi.org/10.17632/zmkc9db4zj.1.Licensing provisions: Apache-2.0 for the program and CC-BY-4.0 for the manual.Programming languages: Fortran90, Perl, and shell scripting.Nature of problem: Multiscale modeling and simulations by the combined quantum mechanical and molecular mechanical (QM/MM) method.Solution method: The program performs single-point calculations, geometry optimizations, transition state optimizations, and molecular dynamics (MD) by the QM/MM method by interfacing calls to binary executables in a QM package (GAMESS-US, Gaussian, or ORCA) and an MM package (TINKER) for the required calculations. QMMM 2023 supports various types of embedding schemes and multiple ways of treating a QM-MM boundary passing through a covalent bond.Additional comments including restrictions and unusual features: (1) QMMM 2023 supports polarizable-embedding and flexible-embedding schemes based on the electronegativity equalization principle and allowing charge transfer between the QM and MM regions. (2) For a QM-MM boundary passing through covalent bonds, all link-atom-based treatments preserve the charge of the MM region (and MM bond dipoles if desired) while effectively avoiding the over-polarization of the QM region. Further tuning is available to account for the charge penetration effects at the QM-MM boundary. (3) For dynamics simulations, Hamiltonian-based adaptive-partitioning algorithms allow on-the-fly reclassification of atoms or groups into the QM or MM regions without abrupt changes in the energy of the entire system or in the forces on all atoms.

Polyrate 2023: A computer program for the calculation of chemical reaction rates for polyatomics. New version announcement

Polyrate 2023: A computer program for the calculation of chemical reaction rates for polyatomics. New version announcement

Asymmetric catalysis by l-prolinamide based small molecules: synthesis, characterization and first principle studies on their enantioselectivity

This paper delineates the stepwise synthesis of l-prolinamide organocatalysts and their comparative NMR studies to investigate the effect of the position and electronic nature of groups attached to the aryl ring, on the chemical shifts of l-proline's protons, particularly H7 and amide protons (-CH7CONH). The catalytic activity of these catalysts has been explored and compared for Michael and oxa-Michael-Henry reactions. This catalytic system displayed excellent catalytic efficiency for both the reactions and provided the corresponding products in high yields. The enantioselectivity of the products was found to be affected by the structure of reactants. The mechanistic routes of these reaction have also been explored by performing density functional calculations that explained the (R,R)- and (S)-enantiomer preferences for the Michael addition and oxa-Michael Henry reactions, respectively, via transition state optimization studies.

Investigating the Thermodynamics and Kinetics of Catechin Pyrolysis for Environmentally Friendly Binders.

The thermodynamics and kinetics of the pyrolysis of (+)-catechin, a building block of the condensed tannins found in recipes for sustainable binders, are evaluated at the DLPNO-CCSD(T) level and compared to other methods from quantum chemistry. Using the climbing image nudged elastic band method coupled with transition state optimization, minimum energy paths and highest-energy transition states are identified for the first two pyrolysis steps, a catechol split-off with subsequent dehydrogenation. While the catechol split-off path was very smooth, the dehydrogenation featured an additional transition state in the form of an OH group rotation. The combined reaction was judged endothermic in the range of 0 to 1250 K and exergonic at 1000 K and above. It is shown that the catechol split-off is the rate-determining step of the pyrolysis of catechin, which is equivalent to kinetic inhibition at all investigated temperatures.

Efficient quantum analytic nuclear gradients with double factorization.

Efficient representations of the Hamiltonian, such as double factorization, drastically reduce the circuit depth or the number of repetitions in error corrected and noisy intermediate-scale quantum (NISQ) algorithms for chemistry. We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians, unlocking efficiency improvements in computing the nuclear gradient and related derivative properties. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically simulated examples with up to 327 quantum and 18 470 total atoms in QM/MM simulations with modest-sized quantum active spaces. We show this in the context of the variational quantum eigensolver in case studies, such as transition state optimization, ab initio molecular dynamics simulation, and energy minimization of large molecular systems.

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.

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.

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 extreme pressure polarizable continuum model framework. The effective potential energy surface is defined as 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 a 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 the optimized geometry of compressed methane and the transition states of the electrocyclic ring-closure of hexatriene and of H-transfer between two methyl radicals.

Expansive Quantum Mechanical Exploration of Chemical Reaction Paths.

Quantum mechanical methods have been well-established for the elucidation of reaction paths of chemical processes and for the explicit dynamics of molecular systems. While they are usually deployed in routine manual calculations on reactions for which some insights are already available (typically from experiment), new algorithms and continuously increasing capabilities of modern computer hardware allow for exploratory open-ended computational campaigns that are unbiased and therefore enable unexpected discoveries. Highly efficient and even automated procedures facilitate systematic approaches toward the exploration of uncharted territory in molecular transformations and dynamics. In this work, we elaborate on such explorative approaches that range from reaction network explorations with (stationary) quantum chemical methods to explorative molecular dynamics and migrant wave packet dynamics. The focus is on recent developments that cover the following strategies. (i) Pruning search options for elementary reaction steps by heuristic rules based on the first-principles of quantum mechanics: Rules are required for reducing the combinatorial explosion of potentially reactive atom pairings, and rooting them in concepts derived from the electronic wave function makes them applicable to any molecular system. (ii) Enforcing reactive events by external biases: Inducing a reaction requires constraints that steer and direct elementary-step searches, which can be formulated in terms of forces, velocities, or supplementary potentials. (iii) Manual steering facilitated by interactive quantum mechanics: As ultrafast quantum chemical methods allow for real-time manual interactions with molecular systems, human-intuition-guided paths can be easily explored with suitable human-machine interfaces. (iv) New approaches for transition-state optimization with continuous curve representations can provide stable schemes to be driven in an automated way by allowing for an efficient tuning of the curve's parameters (instead of a manipulation of a collection of structures along the path), and (v) reactive molecular dynamics and direct wave packet propagation exploit the equations of motion of an underlying mechanical theory (usually, classical Newtonian mechanics or Schrödinger quantum mechanics). Explorative approaches are likely to replace the current state of the art in computational chemistry, because they reduce the human effort to be invested in reaction path elucidations, they are less prone to errors and bias-free, and they cover more extensive regions of the relevant configuration space. As a result, computational investigations that rely on these techniques are more likely to deliver surprising discoveries.

Nazarov Cyclizations Catalyzed by BINOL Phosphoric Acid Derivatives: Quantum Chemistry Struggles To Predict the Enantioselectivity.

Quantum chemical calculations have successfully predicted the stereoselectivities of many BINOL phosphoric acid catalyzed reactions over the past 10-15 years. Herein we report a contrasting example: a reaction for which standard quantum chemistry techniques have proven unexpectedly ineffective at explaining the stereoselectivity. The Nazarov cyclizations of a divinyl ketone catalyzed by a BINOL phosphoric acid or H8-BINOL dithiophosphoric acid were studied with a conventional contemporary quantum chemical approach, consisting of transition state optimizations with B3LYP-D3(BJ) and single-point calculations with several functionals in implicit solvent. Unexpectedly, different functionals gave widely different predictions of the level of enantioselectivity and were unable even to agree on which enantiomer of the product would predominate. Molecular dynamics simulations with the OPLS-AA force field provided evidence that the transition state geometries optimized with DFT in the gas phase or in implicit solvent are not good representations of the true transition states of these reactions in solution. One possible reason for this, which may also explain the failure of quantum chemical techniques to reliably predict the enantioselectivity, is the fact that the transition states contain ion pairs which are not highly organized and do not contain any strongly directional noncovalent interactions between the substrate and the catalyst.

Theoretical investigations on mechanisms and kinetics of methylketene with H reaction in the atmosphere

AbstractDetailed oxidation course of H‐initiated degradation of CH3CHCO has been researched taking advantage of quantum chemical methods. Geometrical optimizations of reactants, intermediates, transition states, and products were operated at the B3LYP/6‐31++G(d,p) level. Single‐point energy computations were implemented at the CCSD(T)/cc‐pVTZ//B3LYP/6‐311++G(d,p) level. The results state clearly that the H association was more energetically beneficial than the abstraction of H, and the dominant pathway is generation of P1 (CH3CH2 + CO). Rate constants of H association reactions are computed by making use of Rice–Ramsperger–Kassel–Marcus (RRKM) program at 200–3000 K. Specifically, the total rate constant of H association reactions is 6.47 × 10−13 cm3 molecule−1 s−1 at 298 K, which is consistent with the experimental results (6.58 × 10−13 cm3 molecule−1 s−1). This research offers a thorough comprehending of the reaction mechanism involved in H‐initiated atmospheric degradation of CH3CHCO and might act as a relevant supplemental reference criteria for experimental research.

Blue LED-Mediated N-H Insertion of Indoles into Aryldiazoesters at Room Temperature in Batch and Flow: Reaction Kinetics, Density Functional Theory, and Mechanistic Study.

Mild blue light-mediated N-H insertion of indole and its derivatives into aryldiazoesters has been reported in a batch and flow strategy to afford the corresponding N-alkylated product in moderate-to-excellent yield. Detailed high-performance liquid chromatography-based reaction kinetics measurements, control experiments, and kinetic isotope effect reveal that 3-substituted indoles with electron-withdrawing groups such as -CN and -CHO facilitated the product formation, whereas the electron-donating group retarded the process. The neutral indole performed in between them. Furthermore, Hammett plot and density functional theory-based transition-state optimization studies showed substantial correlation of the electronic nature of the substituents at the C3 position of indoles with the rate of the N-H insertion reaction. The strategy was utilized to synthesize a key intermediate for the natural product (-)-psychotrimine.

New pathways of stability for NHCs derived from azole, di-azole, n-tetrazole, and ab-tetrazole, by DFT.

We have investigated the pathways of stability for NHCs derived from azole, di-azole, n-tetrazole, and ab-tetrazole (1a, 2a, 3a, and 4a, respectively), at the M06/6-311++G** level of theory. Optimization and vibrational frequency calculations of ground states (GS) and transition states (TS) are performed to identify Gibbs free energies and nature of stationary points, respectively. Two possible pathways of stability for 1a-4a are compared and contrasted which entail dimerization through hydrogen bonding (HB) and covalent bonding (CB). The CB pathway comprises head to head (HH) and head to tail (HT) dimerizations. Plausible reaction profiles are illustrated for 1a-4a along with the mechanism of each dimerization. Structures 1a-3a show one possibility for HB while 4a represents two possibilities. Structures 1a and 4a display two HH dimers while 2a and 3a show one. Structures 1a-4a undergo HT dimerizations to yield three possible dimers which include trans, cis, and [2+3] isomers. Interestingly, for all 1a-4a, HB dimerization turns out as the most favorable stability pathway for showing no barrier of reaction. Structures 4b and 4c indicate the highest stability with respect to their initial 4a compared to remaining HB dimers 1b-3b. In addition, the 1,2-H shift appears as a possible rearrangement for 1a-4a to yield their corresponding tautomers (1i, 2h, 3h, and 4k, respectively). The reaction profile of this rearrangement indicates that 1a-4a favor HB dimerization pathway more than 1,2-H shift, in terms of kinetic and thermodynamic. Graphical Abstract.

Pysisyphus: Exploring potential energy surfaces in ground and excited states

AbstractPredicting the energetics of chemical transformations requires localizing stationary points on a potential energy surface. While educts and products of a chemical reaction may be known, transition state optimization is challenging as good guesses may be unavailable. Extending stationary point searches to the excited state leads to additional difficulties as several states may be close in energy, requiring efficient state tracking. Here, we report the implementation of pysisyphus, an external optimizer, that allows localization of stationary points not only in the ground state but also for excited state by providing several state‐tracking algorithms. pysisyphus offers all necessary tools for calculating reaction paths, starting from the optimization of the reactants, running chain‐of‐states methods such as the nudged elastic band or the growing string method with subsequent transition state optimization, and a concluding intrinsic reaction coordinate calculation.

Unraveling the Mechanism of Tricyclic Bis-spiroketal Formation from Diyne Diol by DFT Study

The mechanism of addition of nucleophiles to the π-acid complexed alkynes has been studied successfully by the assessment of energy of intermediates and activation parameters. To elucidate the origin of stereoselectivity and predict the reaction pathways, the geometry optimizations of reactants, products, intermediates and transition states, were calculated by using density functional theory (DFT) at the B3LYP/6-31+G(d) method. The reaction mechanism of hydration of alkynes in the catalyzed synthesis of bis-spiroketal by DFT calculations is explored. The pyranyl enol ether was formed regioselectively by the first ring closure. Further, bis-enol ether was formed by second 6-exodig addition. Then, dehydration, followed by dehydrative ring closure finally gave bis-spiroketal product. It is concluded that one of the most feasible reaction pathways comprises pyranyl enol ether and bis-enol ether formation as intermediates. The final cyclization step of product formation is endothermic. In terms of stereochemistry, the trans-product is found to be energetically more stable than cisproduct and hence supports the electivity of the reaction.

Theoretical Calculation of Reaction Rates and Combustion Kinetic Modeling Study of Triethyl Phosphate (TEP).

Triethyl phosphate (TEP) is an organophosphorus compound used as a simulant for highly toxic nerve agents such as sarin GB. A high temperature decomposition pathway during TEP pyrolysis has been proposed previously and takes place via seven concerted elimination reactions. A computational study to investigate the kinetics of these seven reactions was carried out at the CBS-QB3 level of theory. The transition state optimization was done at the B3LYP/6-311G(2d,d,p) theory level, and CanTherm was used to derive the Arrhenius coefficients. The pre-exponential factors of the rate constant of these reactions were found to be up to 50 times lower than the estimated values from the literature. In addition, kinetics of reaction of the trioxidophosphorus radical (PO3) with H2 (H2 + PO3 → HOPO2 + H), which is one of the important reactions in predicting CO formation during TEP decomposition, was also investigated computationally at the same theory level. The new kinetic parameters derived from the computational study were used with the TEP kinetic model proposed recently by our group. In addition, an alternative decomposition pathway for TEP decomposition via H-abstraction, radical decomposition, and recombination reactions was added. The proposed mechanism was validated with the literature's experimental data, that is, intermediate CO time-history data from pyrolysis and oxidation experiments and ignition delay times. Fairly good agreement with experiments was obtained for pyrolysis and oxidation CO yield within 1200-1700 K. The model was able to predict the ignition times of the rich TEP mixture (φ = 2) within 25% of the experimental results, while the discrepancies for stoichiometric and rich mixtures were larger. Discussions on results of sensitivity and reaction pathway analysis are presented to identify the important phosphorus reactions and to understand the effect of addition of the alternative TEP decomposition pathway.

Accuracy of auxiliary density functional theory hybrid calculations for activation and reaction enthalpies of pericyclic reactions

Auxiliary density functional theory (ADFT) hybrid calculations are based on the variational fitting of the Coulomb and Fock potential and, therefore, are free of four-center electron repulsion integrals. So far, ADFT hybrid calculations have been validated successfully for standard enthalpies of formation. In this work the accuracy of ADFT hybrid calculations for the description of pericyclic reactions was quantitatively validated at the B3LYP/6-31G*/GEN-A2* level of theory. Our comparison with conventional Kohn-Sham density functional theory (DFT) results shows that the DFT and ADFT activation and reaction enthalpies are practically indistinguishable. A systematic study of various functionals (PBE, B3LYP, PBE0, CAMB3LYP, CAMPBE0 and HSE06) and basis sets (6-31G*, DZVP-GGA and aug-cc-pVXZ; X = D, T and Q) revealed that the ADFT HSE06/aug-cc-pVTZ/GEN-A2* level of theory yields best balanced accuracy for the activation and reaction enthalpies of the studied pericyclic reactions. With the successfully validate ADFT composite approach consisting of PBE/DZVP-GGA/GEN-A2* structure and transition state optimizations and single-point HSE06/aug-cc-pVTZ/GEN-A2* energy calculations, an accurate, reliable and efficient computational approach for the study of pericyclic reactions in systems at the nanometer scale is proposed.

Efficient Transition State Optimization of Periodic Structures through Automated Relaxed Potential Energy Surface Scans.

This work explores how constrained linear combinations of bond lengths can be used to optimize transition states in periodic structures. Scanning of constrained coordinates is a standard approach for molecular codes with localized basis functions, where a full set of internal coordinates is used for optimization. Common plane wave-codes for periodic boundary conditions almost exlusively rely on Cartesian coordinates. An implementation of constrained linear combinations of bond lengths with Cartesian coordinates is described. Along with an optimization of the value of the constrained coordinate toward the transition states, this allows transition optimization within a single calculation. The approach is suitable for transition states that can be well described in terms of broken and formed bonds. In particular, the implementation is shown to be effective and efficient in the optimization of transition states in zeolite-catalyzed reactions, which have high relevance in industrial processes.