Visualization of the Dynamics Effect: Projection of on-the-Fly Trajectories to the Subspace Spanned by the Static Reaction Path Network

Theoretical Insights into Ultrafast-Decaying and Long-Lived States of ortho-Nitrophenol upon Photoexcitation in the Gas Phase

Nitrophenols in the atmosphere are chromophore pollutants that absorb sunlight. Among them, ortho-nitrophenol (o-NP) stands out due to its strong intramolecular hydrogen bond which facilitates excited-state intramolecular proton transfer (ESIPT) and influences its photoisomerization and dissociation. Time-resolved experiments have captured both ultrafast-decaying and long-lived signals. Here, we employ non-adiabatic molecular dynamics simulations and the reaction space projector method to elucidate the photoinduced reactions of o-NP. Our simulations show that photoexcited o-NP in the S1(ππ*) state undergoes ultrafast ESIPT followed by rapid decay through one of two non-adiabatic pathways: ultrafast internal conversion to the S0 state and intersystem crossing (ISC) to the triplet states. Furthermore, trajectories undergoing ISC remain trapped in triplet states, with reverse ISC to the singlet states rarely observed. These trajectories are clearly linked to the long-lived excited-state signal, providing more conclusive computational evidence of the origin.

ULaMDyn: enhancing excited-state dynamics analysis through streamlined unsupervised learning

The analysis of nonadiabatic molecular dynamics (NAMD) data presents significant challenges due to its high dimensionality and complexity. To address these issues, we introduce ULaMDyn, a Python-based, open-source package designed to automate the unsupervised analysis of large datasets generated by NAMD simulations. ULaMDyn integrates seamlessly with the Newton-X platform and employs advanced dimensionality reduction and clustering techniques to uncover hidden patterns in molecular trajectories, enabling a more intuitive understanding of excited-state processes. Using the photochemical dynamics of fulvene as a test case, we demonstrate how ULaMDyn efficiently identifies critical molecular geometries and critical nonadiabatic transitions. The package offers a streamlined, scalable solution for interpreting large NAMD datasets. It is poised to facilitate advances in the study of excited-state dynamics across a wide range of molecular systems.

Acceleration of Reaction Space Projector Analysis Using Combinatorial Optimization: Application to Organic Chemical Reactions

In recent years, automated reaction path search methods have established the concept of a reaction route network. The Reaction Space Projector (ReSPer) visualizes the potential energy hypersurface into a lower-dimensional subspace using principal coordinates. The main time-consuming process in ReSPer is calculating the structural distance matrix, making it impractical for complex organic reaction route networks. We implemented the Alternate Optimization (AO) algorithm, one of the combinatorial optimizations, in ReSPer to reduce computational costs. Evaluations using gold clusters and the Au5 several reaction route networks showed that ReSPer-AO accurately computes distances with lower computational costs. Applying ReSPer-AO to the C5H8O reaction route network clarified dynamic conformation changes in its potential energy landscape. The ReSPer-AO method enables analysis of chemical reactions and dynamic conformations in a low-dimensional reaction space that accurately represents hydrocarbon reaction route networks.

Unsupervised Machine Learning in the Analysis of Nonadiabatic Molecular Dynamics Simulation

The all-atomic full-dimensional-level simulations of nonadiabatic molecular dynamics (NAMD) in large realistic systems has received high research interest in recent years. However, such NAMD simulations normally generate an enormous amount of time-dependent high-dimensional data, leading to a significant challenge in result analyses. Based on unsupervised machine learning (ML) methods, considerable efforts were devoted to developing novel and easy-to-use analysis tools for the identification of photoinduced reaction channels and the comprehensive understanding of complicated molecular motions in NAMD simulations. Here, we tried to survey recent advances in this field, particularly to focus on how to use unsupervised ML methods to analyze the trajectory-based NAMD simulation results. Our purpose is to offer a comprehensive discussion on several essential components of this analysis protocol, including the selection of ML methods, the construction of molecular descriptors, the establishment of analytical frameworks, their advantages and limitations, and persistent challenges.

Benchmark ab initio characterization of the complex potential energy surfaces of the HOO- + CH3Y [Y = F, Cl, Br, I] reactions

The α-effect is a well-known phenomenon in organic chemistry, and is related to the enhanced reactivity of nucleophiles involving one or more lone-pair electrons adjacent to the nucleophilic center. The gas-phase bimolecular nucleophilic substitution (SN2) reactions of α-nucleophile HOO- with methyl halides have been thoroughly investigated experimentally and theoretically; however, these investigations have mainly focused on identifying and characterizing the α-effect of HOO-. Here, we perform the first comprehensive high-level ab initio mapping for the HOO- + CH3Y [Y = F, Cl, Br and I] reactions utilizing the modern explicitly-correlated CCSD(T)-F12b method with the aug-cc-pVnZ [n = 2-4] basis sets. The present ab initio characterization considers five distinct product channels of SN2: (CH3OOH + Y-), proton abstraction (CH2Y- + H2O2), peroxide ion substitution (CH3OO- + HY), SN2-induced elimination (CH2O + HY + HO-) and SN2-induced rearrangement (CH2(OH)O- + HY). Moreover, besides the traditional back-side attack Walden inversion, the pathways of front-side attack, double inversion and halogen-bond complex formation have also been explored for SN2. With regard to the Walden inversion of HOO- + CH3Cl, the previously unaddressed discrepancies concerning the geometry of the corresponding transition state are clarified. For the HOO- + CH3F reaction, the recently identified SN2-induced elimination is found to be more exothermic than the SN2 channel, submerged by ∼36 kcal mol-1. The accuracy of our high-level ab initio calculations performed in the present study is validated by the fact that our new benchmark 0 K reaction enthalpies show excellent agreement with the experimental data in nearly all cases.

Non-IRC Mechanism of Bimolecular Reactions with Submerged Barriers: A Case Study of Si+ + H2O Reaction

Chemical reactions with submerged barriers may feature interesting dynamic behaviors that are distinct from those with substantial barriers or those entirely dominated by capture. The Si+ + H2O reaction is a prototypical example, involving even two submerged saddle points along the reaction path: one for the direct dissociation of H (H-dissociation SP) and another for H migration from the O-side to the Si-side (H-migration SP). We investigated the intricacies of this process by employing quasi-classical trajectory calculations on an accurate, full-dimensional ab initio potential energy surface. Through careful trajectory analysis, an interesting nonintrinsic reaction coordinate mechanism was found to play an important role in producing SiOH+ and H. This new pathway is featured as that the H atoms do not form HSiOH+ complexes along the minimum-energy path but directly dissociate into the products after passing through the H-migration SP. Furthermore, based on artificially scaled potential energy surfaces (PESs), the impact of barrier height on the reaction is also explored. This work provides new insights into the dynamics of the Si+ + H2O reaction and enriches our understanding of reactions with submerged barriers.

Quasi-classical trajectory study of the OH- + CH3I reaction: theory meets experiment

Regarding OH^- + CH₃I, several studies have focused on the dynamics of the reaction. Here, high-level quasi-classical trajectory simulations are carried out at four different collision energies on our recently developed potential energy surface. In all, more than half a million trajectories are performed, and for the first time, the detailed quasi-classical trajectory results are compared with the reanalysed crossed-beam ion imaging experiments. Concerning the previously reported direct dynamics study of OH^- + CH₃I, a better agreement can be obtained between the revised experiment and our novel theoretical results. Furthermore, in the present work, the benchmark geometries, frequencies and relative energies of the stationary points are also determined for the OH^- + CH₃I proton-abstraction channel along with the earlier characterized S_N2 channel.

E-Z Isomerization in Guanidine: Second-order Saddle Dynamics, Non-statisticality, and Time-frequency Analysis

Our recent work on the E-Z isomerization reaction of guanidine using ab initio chemical dynamics simulations [Rashmi et al., Regul. Chaotic Dyn. 2021, 26, 119] emphasized the role of second-order saddle (SOS) in the isomerization reaction; however, we could not unequivocally establish the non-statistical nature of the dynamics followed in the reaction. In the present study, we performed thousands of on-the-fly trajectories using forces computed at the MNDO level to investigate the influence of second-order saddle in the E-Z isomerization reaction of guanidine and the role of intramolecular vibrational energy redistribution (IVR) on the reaction dynamics. The simulations reveal that while majority of the trajectories follow the traditional transition state pathways, 15 % of the trajectories follow the SOS path. The dynamics was found to be highly non-statistical with the survival probabilities of the reactants showing large deviations from those obtained within the RRKM assumptions. In addition, a detailed analysis of the dynamics using time-dependent frequencies and the frequency ratio spaces reveal the existence of multiple resonance junctions that indicate the existence of regular dynamics and long-lived quasi-periodic trajectories in the phase space associated with non-RRKM behavior.

Multi-state Energy Landscape for Photoreaction of Stilbene and Dimethyl-stilbene

We have recently developed the reaction space projector (ReSPer) method, which constructs a reduced-dimensionality reaction space uniquely determined from reference reaction paths for a polyatomic molecular system and projects classical trajectories into the same reaction space. In this paper, we extend ReSPer to the analysis of photoreaction dynamics and relaxation processes of stilbene and present the concept of a "multi-state energy landscape," incorporating the ground- and excited-state reaction subspaces. The multi-state energy landscape successfully explains the previously established photoreaction processes of cis-stilbene, such as the cis-trans photoisomerization and photocyclization. In addition, we discuss the difference in the excited-state reaction dynamics between stilbene and 1,1'-dimethyl stilbene based on a common reaction subspace determined from the framework part of reference structures with different number of atoms. This approach allows us to target any molecule with a common framework, greatly expanding the applicability of the ReSPer analysis. The multi-state energy landscape provides fruitful insight into photochemical reactions, exploring the excited- and ground-state potential energy surfaces, as well as comprehensive reaction processes with nonradiative transitions between adiabatic states, within the stage of a reduced-dimensionality reaction space.

The principal component analysis of the ring deformation in the nonadiabatic surface hopping dynamics

The analysis of the leading active molecular motions in the on-the-fly trajectory surface hopping simulation provides the essential information to understand the geometric evolution in nonadiabatic dynamics. When the ring deformation is involved, the identification of the key active coordinates becomes challenging. A "hierarchical" protocol based on the dimensionality reduction and clustering approaches is proposed for the automatic analysis of the ring deformation in the nonadiabatic molecular dynamics. The representative system keto isocytosine is taken as the prototype to illustrate this protocol. The results indicate that the current hierarchical analysis protocol is a powerful way to clearly clarify both the major and minor active molecular motions of the ring distortion in nonadiabatic dynamics.

Unconventional SN2 retention pathways induced by complex formation: High-level dynamics investigation of the NH2 - + CH3I polyatomic reaction

Investigations on the dynamics of chemical reactions have been a hot topic for experimental and theoretical studies over the last few decades. Here, we carry out the first high-level dynamical characterization for the polyatom-polyatom reaction between NH₂ ^- and CH₃I. A global analytical potential energy surface is developed to describe the possible pathways with the quasi-classical trajectory method at several collision energies. In addition to S_N2 and proton abstraction, a significant iodine abstraction is identified, leading to the CH₃ + [NH₂⋯I]^- products. For S_N2, our computations reveal an indirect character as well, promoting the formation of [CH₃⋯NH₂] complexes. Two novel dominant S_N2 retention pathways are uncovered induced by the rotation of the CH₃ fragment in these latter [CH₃⋯NH₂] complexes. Moreover, these uncommon routes turn out to be the most dominant retention paths for the NH₂ ^- + CH₃I S_N2 reaction.

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.

Uncovering an oxide ion substitution for the OH- + CH3F reaction

Theoretical investigations on chemical reactions allow us to understand the dynamics of the possible pathways and identify new unexpected routes. Here, we develop a global analytical potential energy surface (PES) for the OH⁻ + CH₃F reaction in order to perform high-level dynamics simulations. Besides bimolecular nucleophilic substitution (S_N2) and proton abstraction, our quasi-classical trajectory computations reveal a novel oxide ion substitution leading to the HF + CH₃O⁻ products. This exothermic reaction pathway occurs via the CH₃OH⋯F⁻ deep potential well of the S_N2 product channel as a result of a proton abstraction from the hydroxyl group by the fluoride ion. The present detailed dynamics study of the OH⁻ + CH₃F reaction focusing on the surprising oxide ion substitution demonstrates how incomplete our knowledge is of fundamental chemical reactions.

Reaction dynamics simulations on a high-level ab initio analytical potential energy surface reveal a novel oxide ion substitution channel for the OH⁻ + CH₃F reaction.

Visualization of reaction route map and dynamical trajectory in reduced dimension

In the quantum chemical approach, chemical reaction mechanisms are investigated based on a potential energy surface (PES). Automated reaction path search methods enable us to construct a global reaction route map containing multiple reaction paths corresponding to a series of elementary reaction processes. The on-the-fly molecular dynamics (MD) method provides a classical trajectory exploring the full-dimensional PES based on electronic structure calculations. We have developed two reaction analysis methods, the on-the-fly trajectory mapping method and the reaction space projector (ReSPer) method, by introducing a structural similarity to a pair of geometric structures and revealed dynamic aspects affecting chemical reaction mechanisms. In this review, we will present the details of these analysis methods and discuss the dynamics effects of reaction path curvature and reaction path bifurcation with applications to the CH₃OH + OH^- collision reaction and the Au₅ cluster branching and isomerization reactions.

Analysis of bath motion in MM-SQC dynamics via dimensionality reduction approach: Principal component analysis

The system-plus-bath model is an important tool to understand the nonadiabatic dynamics of large molecular systems. Understanding the collective motion of a large number of bath modes is essential for revealing their key roles in the overall dynamics. Here, we applied principal component analysis (PCA) to investigate the bath motion in the basis of a large dataset generated from the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian nonadiabatic dynamics for the excited-state energy transfer in the Frenkel-exciton model. The PCA method clearly elucidated that two types of bath modes, which either display strong vibronic coupling or have frequencies close to that of the electronic transition, are important to the nonadiabatic dynamics. These observations were fully consistent with the physical insights. The conclusions were based on the PCA of the trajectory data and did not involve significant pre-defined physical knowledge. The results show that the PCA approach, which is one of the simplest unsupervised machine learning dimensionality reduction methods, is a powerful one for analyzing complicated nonadiabatic dynamics in the condensed phase with many degrees of freedom.

Dynamics of a gas-phase SNAr reaction: non-concerted mechanism despite the Meisenheimer complex being a transition state

The commonly accepted mechanism of the nucleophilic aromatic substitution (SNAr) reaction has been found to be governed by the nature of the Meisenheimer structure on the potential energy surface. A stable Meisenheimer intermediate favors a stepwise mechanism, while a Meisenheimer transition state favors a concerted mechanism. Here, we show by using a detailed potential energy map (using the DFT and DLPNO-CCSD(T)/CBS methods) and ab initio classical trajectory simulations that the F- + C6H5NO2 SNAr reaction involves a Meisenheimer transition state and follows a stepwise mechanism in contrast to the expected concerted pathway. The stepwise mechanism observed in the trajectory simulations takes place by the formation of various ion-dipole and σ-complexes. While the majority of the trajectories follow the multi-step mechanism and avoid the minimum energy path, a considerable fraction exhibit a roaming atom mechanism where the F atom hovers around the phenyl ring before the formation of the products.