On the Statistical Regime, Coherence versus Incoherence and Ergodicity of Quantum Vibrational Trajectories in Soft Condensed Molecular Systems

A theoretical-computational procedure, recently proposed for modelling Vibrational Energy Relaxation (VER) processes of a molecule (Quantum Center, QC) embedded in a complex atomic-molecular system, is extended and applied for analyzing in detail the features of the QC density matrix (DM) temporal evolution. The results, obtained using aqueous azide ion as a case study, show the total lack of coherence in the DM, when the system is prepared to be initially in a pure vibrational eigenstate. This finding is fully in line with the statistical interpretation of the process typically adopted also in the experimental studies where the relaxation processes are all described within the typical schemes of chemical kinetics. Consistently, when the initial vibrational state corresponds to an eigenstate mixture, although initially coherent, the DM relaxes to a fully incoherent condition with a mean lifetime related to the one of the diagonal elements relaxation. These specific DM features turn out to be essentially governed by the thermal equilibrium condition of the atomic-molecular classical coordinates which drive the ensemble of the quantum-trajectories toward the observed statistical regime. Finally, from the analysis of a single long timescale quantum vibrational trajectory it also clearly emerges its ergodic behaviour.

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.

Effect of solvent motions on the dynamics of the Diels-Alder reaction

How solvent motions affect the dynamics of chemical reactions in which the solute undergoes a substantial shape change is a fundamental but elusive issue. This work utilizes reactive simulation and Grote-Hynes theory to explore the effect of solvent motions on the dynamics of the Diels-Alder reaction (in the reverse direction, this reaction involves very substantial solute expansion) in aprotic solvents. The results reveal that the solvent environment is not sufficiently constraining to influence transition state passage dynamics, with the calculated transmission coefficients being close to unity. Even when solvent motions are suppressed or artificially slowed down, the solvent only affects the reaction dynamics in the transition state region to a very small extent. The only notable effect of solvent occurs far from the transition state region and corresponds to caging of the reactants within the reactant well.

Molecules, the Ultimate Nanomotor: Linking Chemical Reaction Intermediates to their Molecular Diffusivity

The intellectual community focused on nanomotors has recently become interested in extending these concepts to individual molecules. Here, we study a chemical reaction according to whose mechanism some intermediate species should speed up while others slow down in predictable ways, if the nanomotor hypothesis of boosted diffusion holds. Accordingly, we scrutinize the absolute diffusion coefficient (D) during intermediate steps of the catalytic cycle for the CuAAC reaction (copper-catalyzed azide-alkyne cycloaddition click reaction), using proton pulsed field-gradient nuclear magnetic resonance to discriminate between the diffusion of various reaction intermediates. We observe time-dependent diffusion that is enhanced for some intermediate molecular species and depressed for those whose size increases owing to complex formation. These findings point to the failure of the conventional Stokes-Einstein equation to fully explain diffusivity during chemical reaction. Without attempting a firm explanation, this paper highlights aspects of the physics of chemical reactions that are imperfectly understood and presents systematic data that can be used to assess hypotheses.

Study of the Photoluminescence Characteristics of 4,4'-((1E,1'E)-Quinoxaline-2,3-diylbis(ethene-2,1-diyl))bis(N,N-dimethylaniline)

A comparative investigation on the photophysical properties of a quinoxaline derivative 4,4'-((1E,1'E)-quinoxaline-2,3-diylbis(ethene-2,1-diyl))bis(N,N-dimethylaniline) (QDMA2) was performed by employing many spectroscopies. Based on the pump-dump/push-probe measurement, it is found that a solvent-stabilized charge-transfer state can participate in the relaxation of excited QDMA2 with increasing solvent polarity. Meanwhile, the aggregated QDMA2 molecules were engineered into the organic light-emitting diode test, which showed a correlated color temperature value of 1875 K. With the help of a diamond anvil cell, the pressure-dependent photoluminescence of aggregated QDMA2 shows that the intermolecular interaction can affect the color and intensity of photoluminescence through adjusting the band gap and irradiative channel of the aggregated molecules. These results are important for understanding the structure-property relationships and the rational design of functional materials for optoelectronic applications.

Vibrational Energy Relaxation of Deuterium Fluoride in d-Dichloromethane: Insights from Different Potentials

Vibrationally excited deuterium fluoride (DF) formed by fluorine atom reaction with a solvent was found (Science, 2015, 347, 530) to relax rapidly (less than 10 ps) in acetonitrile-d₃ (CD₃CN) and dichloromethane-d₂ (CD₂Cl₂). However, insights into how CD₂Cl₂ facilitates this energy relaxation have so far been lacking, given the weak interaction between DF and a single CD₂Cl₂. In this work, we report the results of reactive simulations with a two-state reactive empirical valence bond (EVB) potential to study the energy deposited into nascent DF after transition-state passage and of nonequilibrium molecular dynamics simulations using multiple different potential energy functions to model the relaxation dynamics. For these second simulations, we used the standard Merck molecular force field (MMFF) potential, an MMFF-based covalent-ionic empirical valence bond (EVB) potential (EVB^CI), a newly developed potential [referred to as MMFF(rDF)] which extends upon the MMFF potential by making the DF/CD₂Cl₂ interaction depend on the value of the D-F bond stretching coordinate and by taking the anisotropic charge distribution of the solvent molecules into account, the polarizable atomic multipole optimized energetics for biomolecular applications (AMOEBA) potential, and the quantum mechanics/molecular mechanics (QM/MM) potential. The relaxation is revealed to be highly sensitive to the potential used. Neither standard MMFF nor EVB^CI reproduces the experimentally observed rapid relaxation dynamics, and they also fail to provide a good description of the interaction potential between DF and CD₂Cl₂ as calculated using CCSD(T)-F12. This is attributed to the use of a point-charge model for the solute and to failing to model the anisotropic electrostatic properties of CD₂Cl₂. The MMFF(rDF), AMOEBA, and QM/MM potentials all reproduce the CCSD(T)-F12 two-body DF---CD₂Cl₂ interaction potential rather well but only with the QM/MM approach is fast vibrational relaxation obtained (lifetimes of ∼288, ∼186, and ∼8 ps, respectively), which we attribute to differences in the solute-solvent local structure. With QM/MM, a unique "many-body" interaction pattern in which DF is in close contact with two solvent Cl atoms and more than three solvent D atoms is found, but this structure is not seen with other potentials. The QM/MM dynamics also display enhanced solute-solvent interactions with vibrationally excited DF that induce a DF band redshift and hence a resonant overlap with solvent C-D modes, which facilitate the intermolecular energy transfer. Our work also suggests that potentials used to model energy relaxation need to capture the fine structure of solute-solvent interactions and not just the two-body part.

Stereodynamical control of product branching in multi-channel barrierless hydrogen abstraction of CH3OH by F

Comprehensive dynamical simulations of a prototypical multi-channel reaction on a globally accurate potential energy surface show that the non-statistical product branching is dictated by unique stereodynamics in the entrance channels.

Hydrogen abstraction from methanol (CH₃OH) by F atoms presents an ideal proving ground to investigate dynamics of multi-channel reactions, because two types of hydrogen can be abstracted from the methanol molecule leading to the HF + CH₃O and HF + CH₂OH products. Using the quasi-classical trajectory approach on a globally accurate potential energy surface based on high-level ab initio calculations, this work reports a comprehensive dynamical investigation of this multi-channel reaction, yielding measurable attributes including integral and differential cross sections, as well as branching ratios. It is shown that while complex-forming and direct mechanisms coexist at low collision energies, these barrierless reaction channels are dominated at high energies by the direct mechanism, in which the reaction is only possible for trajectories entering into the respective dynamical cones of acceptance. Perhaps more importantly, the non-statistical product branching is found to be dictated by unique stereodynamics in the entrance channels.

Interactive molecular dynamics in virtual reality from quantum chemistry to drug binding: An open-source multi-person framework

As molecular scientists have made progress in their ability to engineer nanoscale molecular structure, we face new challenges in our ability to engineer molecular dynamics (MD) and flexibility. Dynamics at the molecular scale differs from the familiar mechanics of everyday objects because it involves a complicated, highly correlated, and three-dimensional many-body dynamical choreography which is often nonintuitive even for highly trained researchers. We recently described how interactive molecular dynamics in virtual reality (iMD-VR) can help to meet this challenge, enabling researchers to manipulate real-time MD simulations of flexible structures in 3D. In this article, we outline various efforts to extend immersive technologies to the molecular sciences, and we introduce "Narupa," a flexible, open-source, multiperson iMD-VR software framework which enables groups of researchers to simultaneously cohabit real-time simulation environments to interactively visualize and manipulate the dynamics of molecular structures with atomic-level precision. We outline several application domains where iMD-VR is facilitating research, communication, and creative approaches within the molecular sciences, including training machines to learn potential energy functions, biomolecular conformational sampling, protein-ligand binding, reaction discovery using "on-the-fly" quantum chemistry, and transport dynamics in materials. We touch on iMD-VR's various cognitive and perceptual affordances and outline how these provide research insight for molecular systems. By synergistically combining human spatial reasoning and design insight with computational automation, technologies such as iMD-VR have the potential to improve our ability to understand, engineer, and communicate microscopic dynamical behavior, offering the potential to usher in a new paradigm for engineering molecules and nano-architectures.

Anharmonic Molecular Mechanics: Ab Initio Based Morse Parametrizations for the Popular MM3 Force Field

Methodologies for creating reactive potential energy surfaces from molecular mechanics force-fields are becoming increasingly popular. To date, molecular mechanics force-fields in biochemistry and small molecule organic chemistry tend to use harmonic expressions to treat bonding stretches, which is a poor approximation in reactive and nonequilibirum molecular dynamics simulations since bonds are often displaced significantly from their equilibrium positions. For such applications there is need for a better treatment of anharmonicity. In this contribution, Morse bonding potentials have been extensively parametrized for the atom types in the MM3 force field of Allinger and co-workers using high level CCSD(T)(F12*) energies. To our knowledge this is among the first instances of a comprehensive parametrization of Morse potentials in a popular organic chemistry force field. In the context of molecular dynamics simulations, these data will: (1) facilitate the fitting of reactive potential energy surfaces using empirical valence bond approaches and (2) enable more accurate treatments of energy transfer.

EVB and polarizable MM study of energy relaxation in fluorine–acetonitrile reactions

Many-body effects can impact on rates of energy transfer from a ‘hot’ DF solute to acetonitrile solvent.

Taking the plunge: chemical reaction dynamics in liquids

The dynamics of chemical reactions in liquid solutions are now amenable to direct study using ultrafast laser spectroscopy techniques and advances in computer simulation methods. The surrounding solvent affects the chemical reaction dynamics in numerous ways, which include: (i) formation of complexes between reactants and solvent molecules; (ii) modifications to transition state energies and structures relative to the reactants and products; (iii) coupling between the motions of the reacting molecules and the solvent modes, and exchange of energy; (iv) solvent caging of reactants and products; and (v) structural changes to the solvation shells in response to the changing chemical identity of the solutes, on timescales which may be slower than the reactive events. This article reviews progress in the study of bimolecular chemical reaction dynamics in solution, concentrating on reactions which occur on ground electronic states. It illustrates this progress with reference to recent experimental and computational studies, and considers how the various ways in which a solvent affects the chemical reaction dynamics can be unravelled. Implications are considered for research in fields such as mechanistic synthetic chemistry.

Acceleration of a ground-state reaction by selective femtosecond-infrared-laser-pulse excitation

Infrared (IR) excitation of vibrations that participate in the reaction coordinate of an otherwise thermally driven chemical reaction are believed to lead to its acceleration. Attempts at the practical realization of this concept have been hampered so far by competing processes leading to sample heating. Here we demonstrate, using femtosecond IR-pump IR-probe experiments, the acceleration of urethane and polyurethane formation due to vibrational excitation of the reactants for 1:1 mixtures of phenylisocyanate and cyclohexanol, and toluene-2,4-diisocyanate and 2,2,2-trichloroethane-1,1-diol, respectively. We measured reaction rate changes upon selective vibrational excitation with negligible heating of the sample and observed an increase of the reaction rate up to 24%. The observation is rationalized using reactant and transition-state structures obtained from quantum chemical calculations. We subsequently used IR-driven reaction acceleration to write a polyurethane square on sample windows using a femtosecond IR pulse.

Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces

In this Introduction, we show the basic problems of non-statistical and non-equilibrium phenomena related to the papers collected in this themed issue. Over the past few years, significant advances in both computing power and development of theories have allowed the study of larger systems, increasing the time length of simulations and improving the quality of potential energy surfaces. In particular, the possibility of using quantum chemistry to calculate energies and forces 'on the fly' has paved the way to directly study chemical reactions. This has provided a valuable tool to explore molecular mechanisms at given temperatures and energies and to see whether these reactive trajectories follow statistical laws and/or minimum energy pathways. This themed issue collects different aspects of the problem and gives an overview of recent works and developments in different contexts, from the gas phase to the condensed phase to excited states.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Reaction and relaxation at surface hotspots: using molecular dynamics and the energy-grained master equation to describe diamond etching

The extent to which vibrational energy transfer dynamics can impact reaction outcomes beyond the gas phase remains an active research question. Molecular dynamics (MD) simulations are the method of choice for investigating such questions; however, they can be extremely expensive, and therefore it is worth developing cheaper models that are capable of furnishing reasonable results. This paper has two primary aims. First, we investigate the competition between energy relaxation and reaction at 'hotspots' that form on the surface of diamond during the chemical vapour deposition process. To explore this, we developed an efficient reactive potential energy surface by fitting an empirical valence bond model to higher-level ab initio electronic structure theory. We then ran 160 000 NVE trajectories on a large slab of diamond, and the results are in reasonable agreement with experiment: they suggest that energy dissipation from surface hotspots is complete within a few hundred femtoseconds, but that a small fraction of CH₃ does in fact undergo dissociation prior to the onset of thermal equilibrium. Second, we developed and tested a general procedure to formulate and solve the energy-grained master equation (EGME) for surface chemistry problems. The procedure we outline splits the diamond slab into system and bath components, and then evaluates microcanonical transition-state theory rate coefficients in the configuration space of the system atoms. Energy transfer from the system to the bath is estimated using linear response theory from a single long MD trajectory, and used to parametrize an energy transfer function which can be input into the EGME. Despite the number of approximations involved, the surface EGME results are in reasonable agreement with the NVE MD simulations, but considerably cheaper. The results are encouraging, because they offer a computationally tractable strategy for investigating non-equilibrium reaction dynamics at surfaces for a broader range of systems.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Reaction Mechanism of Covalent Modification of Phosphatidylethanolamine Lipids by Reactive Aldehydes 4-Hydroxy-2-nonenal and 4-Oxo-2-nonenal

4-Hydroxy-2-nonenal (HNE) and 4-oxo-2-nonenal (ONE) are biologically important reactive aldehydes formed during oxidative stress in phospholipid bilayers. They are highly reactive species due to presence of several reaction centers and can react with amino acids in peptides and proteins, as well as phosphoethanolamine (PE) lipids, thus modifying their biological activity. The aim of this work is to study in a molecular detail the reactivity of HNE and ONE toward PE lipids in a simplified system containing only lipids and reactive aldehydes in dichloromethane as an inert solvent. We use a combination of quantum chemical calculations, ¹H NMR measurements, FT-IR spectroscopy, and mass spectrometry experiments and show that for both reactive aldehydes two types of chemical reactions are possible: formation of Michael adducts and Schiff bases. In the case of HNE, an initially formed Michael adduct can also undergo an additional cyclization step to a hemiacetal derivative, whereas no cyclization occurs in the case of ONE and a Michael adduct is identified. A Schiff base product initially formed when HNE is added to PE lipid can also further cyclize to a pyrrole derivative in contrast to ONE, where only a Schiff base product is isolated. The suggested reaction mechanism by quantum-chemical calculations is in a qualitative agreement with experimental yields of isolated products and is also additionally investigated by ¹H NMR measurements, FT-IR spectroscopy, and mass spectrometry experiments.

Adaptive free energy sampling in multidimensional collective variable space using boxed molecular dynamics

The past decade has seen the development of a new class of rare event methods in which molecular configuration space is divided into a set of boundaries/interfaces, and then short trajectories are run between boundaries. For all these methods, an important concern is how to generate boundaries. In this paper, we outline an algorithm for adaptively generating boundaries along a free energy surface in multi-dimensional collective variable (CV) space, building on the boxed molecular dynamics (BXD) rare event algorithm. BXD is a simple technique for accelerating the simulation of rare events and free energy sampling which has proven useful for calculating kinetics and free energy profiles in reactive and non-reactive molecular dynamics (MD) simulations across a range of systems, in both NVT and NVE ensembles. Two key developments outlined in this paper make it possible to automate BXD, and to adaptively map free energy and kinetics in complex systems. First, we have generalized BXD to multidimensional CV space. Using strategies from rigid-body dynamics, we have derived a simple and general velocity-reflection procedure that conserves energy for arbitrary collective variable definitions in multiple dimensions, and show that it is straightforward to apply BXD to sampling in multidimensional CV space so long as the Cartesian gradients ∇CV are available. Second, we have modified BXD to undertake on-the-fly statistical analysis during a trajectory, harnessing the information content latent in the dynamics to automatically determine boundary locations. Such automation not only makes BXD considerably easier to use; it also guarantees optimal boundaries, speeding up convergence. We have tested the multidimensional adaptive BXD procedure by calculating the potential of mean force for a chemical reaction recently investigated using both experimental and computational approaches – i.e., F + CD₃CN → DF + D₂CN in both the gas phase and a strongly coupled explicit CD₃CN solvent. The results obtained using multidimensional adaptive BXD agree well with previously published experimental and computational results, providing good evidence for its reliability.

Computational Study of Competition between Direct Abstraction and Addition-Elimination in the Reaction of Cl Atoms with Propene

Quasi-classical trajectory calculations on a newly constructed and full-dimensionality potential energy surface (PES) examine the dynamics of the reaction of Cl atoms with propene. The PES is an empirical valence bond (EVB) fit to high-level ab initio energies and incorporates deep potential energy wells for the 1-chloropropyl and 2-chloropropyl radicals, a direct H atom abstraction route to HCl + allyl radical (CH2CHCH2(•)) products (Δ(r)H(298K)(⊖) = −63.1 kJ mol(-1)), and a pathway connecting these regions. In total, 94 000 successful reactive trajectories were used to compute distributions of angular scattering and HCl vibrational and rotational level populations. These measures of the reaction dynamics agree satisfactorily with available experimental data. The dominant reaction pathway is direct abstraction of a hydrogen atom from the methyl group of propene occurring in under 500 fs. Less than 10% of trajectories follow an addition–elimination route via the two isomeric chloropropyl radicals. Large amplitude motions of the Cl about the propene molecular framework couple the addition intermediates to the direct abstraction pathway. The EVB method provides a good description of the complicated PES for the Cl + propene reaction despite fitting to a limited number of ab initio points, with the further advantage that dynamics specific to certain mechanisms can be studied in isolation by switching off coupling terms in the EVB matrix connecting different regions of the PES.

Vibrational Excitation of Both Products of the Reaction of CN Radicals with Acetone in Solution

Transient electronic and vibrational absorption spectroscopy unravel the mechanisms and dynamics of bimolecular reactions of CN radicals with acetone in deuterated chloroform solutions. The CN radicals are produced by ultrafast ultraviolet photolysis of dissolved ICN. Two reactive forms of CN radicals are distinguished by their electronic absorption bands: "free" (uncomplexed) CN radicals, and "solvated" CN radicals that are complexed with solvent molecules. The lifetimes of the free CN radicals are limited to a few picoseconds following their photolytic production because of geminate recombination to ICN and INC, complexation with CDCl3 molecules, and reaction with acetone. The acetone reaction occurs with a rate coefficient of (8.0 ± 0.5) × 10(10) M(-1) s(-1) and transient vibrational spectra in the C═N and C═O stretching regions reveal that both the nascent HCN and 2-oxopropyl (CH3C(O)CH2) radical products are vibrationally excited. The rate coefficient for the reaction of solvated CN with acetone is 40 times slower than for free CN, with a rate coefficient of (2.0 ± 0.9) × 10(9) M(-1) s(-1) obtained from the rise in the HCN product v1(C═N stretch) IR absorption band. Evidence is also presented for CN complexes with acetone that are more strongly bound than the CN-CDCl3 complexes because of CN interactions with the carbonyl group. The rates of reactions of these more strongly associated radicals are slower still.

Reactive force fields made simple

Combining QMDFF with EVB allows to generate reactive force fields of useful quality for widely varying reactions with minimal effort.

Solvent response to fluorine-atom reaction dynamics in liquid acetonitrile

Solvent restructuring and vibrational cooling follow exothermic fluorine-atom reactions in acetonitrile.