The C(3P) + NO(X2Π) → O(3P) + CN(X2Σ+), N(2D)/N(4S) + CO(X1Σ+) reaction: Rates, branching ratios, and final states from 15 K to 20 000 K

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

High-Energy Reaction Dynamics of N3

The atom-exchange and atomization dissociation dynamics for the N(4S) + N2(1Σg+) reaction are studied using a reproducing kernel Hilbert space (RKHS)-based, global potential energy surface (PES) at the MRCI-F12/aug-cc-pVTZ-F12 level of theory (MRCI, multireference configuration interaction). For the atom exchange reaction (NANB + NC → NANC + NB), computed thermal rates and their temperature dependence from quasi-classical trajectory (QCT) simulations agree to within error bars with the available experiments. Companion QCT simulations using a recently published CASPT2-based PES confirm these findings. For the atomization reaction, leading to three N(4S) atoms, the computed rates from the RKHS-PES overestimate the experimentally reported rates by 1 order of magnitude, whereas those from the permutationally invariant polynomial (PIP)-PES agree favorably, and the T dependence of both computations is consistent with the experiment. These differences can be traced back to the different methods and basis sets used. The lifetime of the metastable N3 molecule is estimated to be ∼200 fs depending on the initial state of the reactants. Finally, neural-network-based exhaustive state-to-distribution models are presented using both PESs for the atom exchange reaction. These models will be instrumental for a broader exploration of the reaction dynamics of air.

High-accuracy DMBE potential energy surface for CNO(A''4) and the rate coefficients for the C + NO reaction in the A'2, A''2, and A''4 states

An accurate potential energy surface (PES) for the lowest lying A''4 state of the CNO system is presented based on explicitly correlated multi-reference configuration interaction calculations with quadruple zeta basis set (MRCI-F12/cc-pVQZ-F12). The ab initio energies are fitted using the double many-body expansion method, thus incorporating long-range energy terms that can accurately describe the electrostatic and dispersion interactions with physically motivated decaying functions. Together with the previously fitted lowest A'2 and A''2 states using the same theoretical framework, this constitutes a new set of PESs that are suitable to predict rate coefficients for all atom-diatom reactions of the CNO system. We use this set of PESs to calculate thermal rate coefficients for the C(P3) + NO(Π2) reaction and compare the temperature dependence and product branching ratios with experimental results. The comparison between theory and experiment is shown to be improved over previous theoretical studies. We highlight the importance of the long-range interactions for low-temperature rate coefficients.

Ar+ ArH+ Reactive Collisions of Astrophysical Interest: The Case of 36 Ar

The reactive collision between 36 Ar and the 36 ArH+ species has been investigated by means of quantum mechanical (QM), quasiclassical trajectories (QCT) and statistical quantum mechanical (SQM) approaches. Reaction probabilities, cross sections as a function of the energy and rate constants in terms of the temperature have been obtained. Cumulative distributions as a function of the collision time and the inspection of selected QCT corresponding to specific dynamical mechanisms have been analysed. Predictions by means of the SQM method are in good agreement with the QM results, thus supporting the complex-forming nature of the process.

Electronic Free Energy Surface of the Nitrogen Dimer Using First-Principles Finite Temperature Electronic Structure Methods

We use full configuration interaction and density matrix quantum Monte Carlo methods to calculate the electronic free energy surface of the nitrogen dimer within the free-energy Born-Oppenheimer approximation. As the temperature is raised from T = 0, we find a temperature regime in which the internal energy causes bond strengthening. At these temperatures, adding in the entropy contributions is required to cause the bond to gradually weaken with increasing temperature. We predict a thermally driven dissociation for the nitrogen dimer between 22,000 to 63,200 K depending on symmetries and basis set. Inclusion of more spatial and spin symmetries reduces the temperature required. The origin of these observations is explored using the structure of the density matrix at various temperatures and bond lengths.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Quantum and quasi-classical dynamics of the C(3P) + O2(3Σ-g) → CO(1Σ+) + O(1D) reaction on its electronic ground state

The dynamics of the C(³P) + O₂(³Σ⁻_g) → CO(¹Σ⁺) + O(¹D) reaction on its electronic ground state is investigated by using time-dependent wave packet propagation (TDWP) and quasi-classical trajectory (QCT) simulations. For the moderate collision energies considered (E_c = 0.001 to 0.4 eV, corresponding to a range from 10 K to 4600 K) the total reaction probabilities from the two different treatments of the nuclear dynamics agree very favourably. The undulations present in P(E) from the quantum mechanical treatment can be related to stabilization of the intermediate CO₂ complex with lifetimes on the 0.05 ps time scale. This is also confirmed from direct analysis of the TDWP simulations and QCT trajectories. Product diatom vibrational and rotational level resolved state-to-state reaction probabilities from TDWP and QCT simulations agree well except for the highest product vibrational states (v′ ≥ 15) and for the lowest product rotational states (j′ ≤ 10). Opening of the product vibrational level CO(v′ = 17) requires ∼0.2 eV from QCT and TDWP simulations with O₂(j = 0) and decreases to 0.04 eV if all initial rotational states are included in the QCT analysis, compared with E_c > 0.04 eV obtained from experiments. It is thus concluded that QCT simulations are suitable for investigating and realistically describe the C(³P) + O₂(³Σ⁻_g) → CO(¹Σ⁺) + O(¹D) reaction down to low collision energies when compared with results from a quantum mechanical treatment using TDWPs.

The dynamics of the C(³P) + O₂(³Σ⁻_g) → CO(¹Σ⁺) + O(¹D) reaction on its electronic ground state is investigated by using time-dependent wave packet propagation (TDWP) and quasi-classical trajectory (QCT) simulations.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Photodissociation dynamics of N3+

The photodissociation dynamics of [Formula: see text] excited from its (linear) 3[Formula: see text]/(bent) 3A″ ground to the first excited singlet and triplet states is investigated. Three-dimensional potential energy surfaces for the 1A′, 1A″, and 3A′ electronic states, correlating with the 1Δg and 3Πu states in linear geometry, for [Formula: see text] are constructed using high-level electronic structure calculations and represented as reproducing kernels. The reference ab initio energies are calculated at the MRCI+Q/aug-cc-pVTZ level of theory. For following the photodissociation dynamics in the excited states, rotational and vibrational distributions P( v′) and P( j′) for the N2 product are determined from vertically excited ground state distributions. Due to the different shapes of the ground state 3A″ potential energy surface and the excited states, appreciable angular momentum j′ ∼ 60 is generated in diatomic fragments. The lifetimes in the excited states extend to at least 50 ps. Notably, results from sampling initial conditions from a thermal ensemble and from the Wigner distribution of the ground state wavefunction are comparable.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.

Genesis of Polyatomic Molecules in Dark Clouds: CO2 Formation on Cold Amorphous Solid Water

Understanding the formation of molecules under conditions relevant to interstellar chemistry is fundamental to characterize the chemical evolution of the universe. Using reactive molecular dynamics simulations with model-based or high-quality potential energy surfaces provides a means to specifically and quantitatively probe individual reaction channels at a molecular level. The formation of CO₂ from collision of CO(¹Σ) and O(¹D) is characterized on amorphous solid water (ASW) under conditions typical in cold molecular clouds. Recombination takes place on the subnanosecond time scale and internal energy redistribution leads to stabilization of the product with CO₂ remaining adsorbed on the ASW on extended time scales. Using a high-level, reproducing kernel-based potential energy surface for CO₂, formation into and stabilization of CO₂ and COO are observed.

Atom-Diatom Reactive Scattering Collisions in Protonated Rare Gas Systems

The study of the dynamics of atom-diatom reactions involving two rare gas (Rg) atoms and protons is of crucial importance given the astrophysical relevance of these processes. In a series of previous studies, we have been investigating a number of such Rg(1)+ Rg(2)H+→ Rg(2)+ Rg(1)H+ reactions by means of different numerical approaches. These investigations comprised the construction of accurate potential energy surfaces by means of ab initio calculations. In this work, we review the state-of-art of the study of these protonated Rg systems making special emphasis on the most relevant features regarding the dynamical mechanisms which govern these reactive collisions. The aim of this work therefore is to provide an as complete as possible description of the existing information regarding these processes.

Quantum and Classical Dynamics of the N(2D) + N2 Reaction on Its Ground Doublet State N3(12A″) Potential Energy Surface

The initial state-selected dynamics of the N(²D) + N₂(X¹∑) → N₂(X¹∑) + N(²D) exchange reaction on its electronic ground doublet state N₃(1²A″) potential energy surface (PES) has been studied here by time-dependent quantum mechanics (TDQM) and quasi-classical trajectory (QCT) methods. Dynamical attributes such as total reaction probabilities, state-selected integral cross sections, and initial state-selected rate constants have been calculated. The presence of metastable quasi-bound complexes in the collision process is confirmed by substantial oscillatory structures in the reaction probability curves. Also, rotational excitations of reagent N₂ on the reactivity have been examined by calculating the probabilities for the two-body rotational angular momentum up to j = 10. We conclude that the reagent rotational excitation increases the reactivity. The TDQM results are compared with QCT results.

Machine Learning for Chemical Reactions

Machine learning (ML) techniques applied to chemical reactions have a long history. The present contribution discusses applications ranging from small molecule reaction dynamics to computational platforms for reaction planning. ML-based techniques can be particularly relevant for problems involving both computation and experiments. For one, Bayesian inference is a powerful approach to develop models consistent with knowledge from experiments. Second, ML-based methods can also be used to handle problems that are formally intractable using conventional approaches, such as exhaustive characterization of state-to-state information in reactive collisions. Finally, the explicit simulation of reactive networks as they occur in combustion has become possible using machine-learned neural network potentials. This review provides an overview of the questions that can and have been addressed using machine learning techniques, and an outlook discusses challenges in this diverse and stimulating field. It is concluded that ML applied to chemistry problems as practiced and conceived today has the potential to transform the way with which the field approaches problems involving chemical reactions, in both research and academic teaching.

The C(3P) + O2(3Σg-) → CO2 ↔ CO(1Σ+) + O(1D)/O(3P) reaction: thermal and vibrational relaxation rates from 15 K to 20 000 K

Thermal rates for the C(3P) + O2(3Σg-) ↔ CO(1Σ+)+ O(1D)/O(3P) reaction are investigated over a wide temperature range based on quasi classical trajectory (QCT) simulations on 3-dimensional, reactive potential energy surfaces (PESs) for the 1A', (2)1A', 1A'', 3A' and 3A'' states. These five states are the energetically low-lying states of CO2 and their PESs are computed at the MRCISD+Q/aug-cc-pVTZ level of theory using a state-average CASSCF reference wave function. Analysis of the different electronic states for the CO2 → CO + O dissociation channel rationalizes the topography of this region of the PESs. The forward rates from QCT simulations match measurements between 15 K and 295 K whereas the equilibrium constant determined from the forward and reverse rates is consistent with that derived from statistical mechanics at high temperature. Vibrational relaxation, O + CO(ν = 1,2) → O + CO(ν = 0), is found to involve both, non-reactive and reactive processes. The contact time required for vibrational relaxation to take place is τ ≥ 150 fs for non-reacting and τ ≥ 330 fs for reacting (oxygen atom exchange) trajectories and the two processes are shown to probe different parts of the global potential energy surface. In agreement with experiments, low collision energy reactions for the C(3P) + O2(3Σg-, ν = 0) → CO(1Σ+) + O(1D) lead to CO(1Σ+, ν' = 17) with an onset at Ec ∼ 0.15 eV, dominated by the 1A' surface with contributions from the 3A' surface. Finally, the barrier for the COA(1Σ+) + OB(3P) → COB(1Σ+) + OA(3P) atom exchange reaction on the 3A' PES yields a barrier of ∼7 kcal mol-1 (0.300 eV), consistent with an experimentally reported value of 6.9 kcal mol-1 (0.299 eV).

Quantum and quasiclassical dynamical simulations for the Ar2H+ on a new global analytical potential energy surface

A new analytical potential energy surface (PES) has been constructed for the Ar₂H⁺ system from a dataset consisting of a large number of ab initio energies computed using the coupled-cluster singles, doubles and perturbative triples method and aug-cc-pVQZ basis set. The long-range interaction is added to the diatomic potentials using a standard long range expansion form to better describe the asymptotic regions. The vibrational states for the most stable structures of the Ar₂H⁺ system have been calculated, and few low lying states are assigned to quantum numbers. Reactive scattering studies have been performed for the Ar + Ar'H⁺ → Ar' + ArH⁺ proton exchange reaction on the newly generated PES. Reaction probability, cross sections, and rate constants are calculated for the Ar + Ar'H⁺(v = 0, j = 0) collisions within 0.01 eV-0.6 eV of relative translational energy using exact quantum dynamical simulations as well as quasiclassical trajectory (QCT) calculations. The effect of vibrational excitation of the reactants is also explored for the reaction. State averaged rate constants are calculated for the proton exchange reaction at different temperatures using the QCT method. The mechanistic pathways for the reaction are understood by analyzing the quasiclassical trajectories.

Accurate DMBE potential-energy surface for CNO(2A″) and rate coefficients in C(3P)+NO collisions

A realistic double many-body expansion potential energy surface (PES) is developed for the ²A″ state of the carbon-nitrogen-oxygen (CNO) system based on MRCI-F12/cc-pVQZ-F12 ab initio energies. The new PES reproduces the fitted points with chemical accuracy (root mean square deviation up to 0.043 eV) and explicitly incorporates long range energy terms that can accurately describe the electrostatic and dispersion interactions. Thermal rate coefficients were computed for the C(³P) + NO(²Π) reaction for temperatures ranging from 15 K to 10 000 K, and the values are compared to previously reported results. The differences are rationalized, and the major importance of long range forces in predicting the rate coefficients for barrierless reactions is emphasized.

Complex reaction processes in combustion unraveled by neural network-based molecular dynamics simulation

Combustion is a complex chemical system which involves thousands of chemical reactions and generates hundreds of molecular species and radicals during the process. In this work, a neural network-based molecular dynamics (MD) simulation is carried out to simulate the benchmark combustion of methane. During MD simulation, detailed reaction processes leading to the creation of specific molecular species including various intermediate radicals and the products are intimately revealed and characterized. Overall, a total of 798 different chemical reactions were recorded and some new chemical reaction pathways were discovered. We believe that the present work heralds the dawn of a new era in which neural network-based reactive MD simulation can be practically applied to simulating important complex reaction systems at ab initio level, which provides atomic-level understanding of chemical reaction processes as well as discovery of new reaction pathways at an unprecedented level of detail beyond what laboratory experiments could accomplish.

Gaining insights into combustion processes is challenging due to the complex reactions involved. The present work proposes a neural network potential model trained to ab initio data that enables to simulate the combustion of methane by predicting reactants, products and reaction intermediates.

The N(4S) + O2(X3Σ−g) ↔ O(3P) + NO(X2Π) reaction: thermal and vibrational relaxation rates for the 2A′, 4A′ and 2A′′ states

Cross sections, rates, equilibrium constants and vibrational relaxation times for the N(⁴S) + O₂(X³Σ−g) ↔ O(³P) + NO(X²Π) reaction from simulations on new, RKHS-based surfaces for the three lowest electronic states.

Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N2O and dynamics for the N + NO ↔ O + N2 and N2 + O → 2N + O reactions

Reproducing kernel-based potential energy surface based on MRCI+Q/aug-cc-pVTZ energies for the triplet states of N₂O and quasiclassical dynamical study for the reaction, dissociation and vibrational relaxation.

Thermal activation of methane by MgO+: temperature dependent kinetics, reactive molecular dynamics simulations and statistical modeling

The kinetics methane activation (MgO⁺ + CH₄) was studied experimentally and computationally by running and analyzing reactive atomistic simulations.

Long-range versus short-range effects in cold molecular ion-neutral collisions

The investigation of cold interactions between ions and neutrals has recently emerged as a new scientific frontier at the interface of physics and chemistry. Here, we report a study of charge-transfer (CT) collisions of Rb atoms with N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}^{+}$$\end{document}2+ and O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}^{+}$$\end{document}2+ ions in the mK regime using a dynamic ion-neutral hybrid trapping experiment. We observe markedly different CT kinetics and dynamics for the different systems and reaction channels studied. While the kinetics in some channels are consistent with classical capture theory, others show distinct non-universal dynamics. The experimental results are interpreted with the help of classical-capture, quasiclassical-trajectory and quantum-scattering calculations using ab-initio potentials for the highly excited molecular states involved. The theoretical analysis reveals an intricate interplay between short- and long-range effects in the different reaction channels which ultimately determines the CT dynamics and rates. Our results illustrate salient mechanisms that determine the efficiency of cold molecular CT reactions.

Studies on reactions between cold molecular ions and neutral atoms provide insights into intermolecular interactions. Here the authors explore the kinetics and dynamics of charge-transfer collisions between the cold N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}^{+}$$\end{document}2+ and O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}^{+}$$\end{document}2+ ions and neutral Rb atoms and discuss the role of long- and short-range effects.

Quasiclassical Study of the C(3P) + NO(X2Π) and O(3P) + CN(X2Σ+) Collisional Processes on an Accurate DMBE Potential Energy Surface

The predicted rate constants for C + NO and O + CN collisions in three potential energy surfaces (PESs) for the ²A' state of the CNO molecule are compared using quasiclassical trajectories. Different temperature dependencies are obtained for the C + NO reaction, which are explained in terms of the long-range properties of the PESs. Recommended values and mechanistic details are also reported. For O + CN collisions, a better agreement between the theoretical results is found, except for temperatures below 100 K.

O2 formation in cold environments

The diffusional dynamics of atomic oxygen in and on amorphous solid water (ASW) to form molecular oxygen is characterized. Reactive molecular dynamics simulations to study bond breaking and bond formation show that vibrational relaxation of the highly excited diatomic occurs on the 10 ns to 100 ns time scale. The relaxation process is highly nonexponential and can be characterized by a stretched exponential decay reminiscent of the dynamics of glasses. The stretched exponents range from β = 0.15 for relaxation on the surface to β = 0.21 for the dynamics in bulk. It is also found that coupling of the O2 relaxation to the internal water modes occurs which speeds up the vibrational relaxation by a factor of 4. Extrapolation of the stretched exponential decay to 1 μs yields a final vibrational quantum number v = 2 for O2(X3Σ-g), consistent with experimental results from photolysis of SO2 on ASW at 193 nm which find v ≤ 3. Desorption energies of water from the surface range from 1.5 to 2.0 kcal mol-1 compared with 1.8 kcal mol-1 found from experiment, depending on whether the water molecules are flexible or not.