Nonstatistical Dynamics Research Articles

Nuclear Quantum Effects on the Nature of Hydroboration Selectivity: Experimental Effects of First-Collision Tunneling.

The understanding of selectivity in reactions exhibiting nonstatistical dynamics is impeded by the limitations of trajectory studies with regard to nuclear quantum effects, especially tunneling. We described here the use of ring-polymer molecular dynamics (RPMD) to account for an unusual regiochemical isotope effect on the regioselectivity of hydroborations of alkenes with BH3/BD3. RPMD is able to account for the experimental observation, while statistical approaches and classical trajectories fail. The combination of experiment and RPMD trajectories suggests that tunneling in the initial collision of reactants is the major source of the nonstatistical selectivity.

Prediction of Kinetic Product Ratios: Investigation of a Dynamically Controlled Case.

Of the various factors influencing kinetically controlled product ratios, the role of nonstatistical dynamics is arguably the least well understood. In this paper, reactions were chosen in which dynamics played a dominant role in product selection, by design. Specifically, the reactions studied were the ring openings of cyclopropylidene to allene and tetramethylcyclopropylidene to tetramethylallene (2,4-dimethylpenta-2,3-diene). Both reactions have intrinsic reaction coordinates that bifurcate symmetrically, leading to products that are enantiomeric once the atoms are uniquely labeled. The question addressed in the study was whether the outcomes─that is, which product well on the potential energy surface was selected─could be predicted from their initial conditions for individual trajectories in quasiclassical dynamics simulations. Hybrid potentials were developed based on cooperative interaction between molecular mechanics and artificial neural networks, trained against data from electronic structure calculations. These potentials allowed simulations of both gas-phase and condensed-phase reactions. The outcome was that, for both reactions, prediction of initial selection of product wells could be made with >95% success from initial conditions of the trajectories in the gas phase. However, when trajectories were run for longer, looking for "final" products for each trajectory, the predictability dropped off dramatically. In the gas-phase simulations, this drop off was caused by trajectories hopping between product wells on the potential energy surface. That behavior could be suppressed in condensed phases, but then new uncertainty was introduced because the intermolecular interactions between solute and bath, necessary to permit intermolecular energy transfer and cooling of the hot initial products, often led to perturbations of the initial directions of trajectories on the potential energy surface. It would consequently appear that a general ability to predict outcomes for reactions in which nonstatistical dynamics dominate remains a challenge even in the age of sophisticated machine-learning capabilities.

Non-statistical rational maps

We show that in the family of degree $$d\geqslant 2$$ rational maps of the Riemann sphere, the closure of strictly postcritically finite maps contains a (relatively) Baire generic subset of maps displaying maximal non-statistical behavior: for a map f in this generic subset, the set of accumulation points of the sequence of empirical measures of almost every point in the phase space, is equal to the largest possible one, that is the set of all f-invariant measures. We also introduce an abstract setting to study non-statistical dynamics and sufficient conditions for their existence in a general family of maps. These sufficient conditions are related to the notions of “statistical instability” and “statistical bifurcation” for which we give a general formalization in the first section. The proof of our result in the family of rational maps is based on a transversality argument which allows us to control the behavior of the orbits of critical points for maps close to strictly postcritically finite rational maps. Using this property and doing careful perturbations, we show that the closure of strictly postcritically finite maps satisfies the sufficient conditions introduced in the abstract setting.

Interpolating Moving Ridge Regression (IMRR): A machine learning algorithm to predict energy gradients for ab initio molecular dynamics simulations

Ab initio molecular dynamics (AIMD) simulations are a direct way to visualize chemical reactions and help elucidate non-statistical dynamics that does not follow the intrinsic reaction coordinate. However, due to the enormous amount of ab initio energy gradient calculations needed, it has been largely restrained to limited sampling and low level of theory (i.e., density functional theory with small basis sets). To overcome this issue, a number of machine learning (ML) methods have been developed to predict the energy gradient of the system of interest. In this manuscript, we outline the theoretical foundations of a novel ML method which trains from a varying set of atomic positions and their energy gradients, called “Interpolating Moving Ridge Regression” (IMRR), and directly predicts the energy gradient of a new set of atomic positions. Several key theoretical findings are presented regarding the inputs used to train IMRR and its predicted energy gradient. A hyperparameter used to guide IMRR is rigorously examined as well. IMRR is then applied to three bimolecular reactions studied with AIMD, including HBr+ + CO2, H2S + CH, and C4H2 + CH, to demonstrate its performance on different chemical systems of different sizes. This manuscript also compares the computational cost of the energy gradient calculation with IMRR vs. ab initio, and the results highlight IMRR as a viable option to greatly increase the efficiency of AIMD.

Internal conversion of the anionic GFP chromophore: in and out of the I-twisted S1/S0 conical intersection seam.

The functional diversity of the green fluorescent protein (GFP) family is intimately connected to the interplay between competing photo-induced transformations of the chromophore motif, anionic p-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI−). Its ability to undergo Z/E-isomerization is of particular importance for super-resolution microscopy and emerging opportunities in optogenetics. Yet, key dynamical features of the underlying internal conversion process in the native HBDI− chromophore remain largely elusive. We investigate the intrinsic excited-state behavior of isolated HBDI− to resolve competing decay pathways and map out the factors governing efficiency and the stereochemical outcome of photoisomerization. Based on non-adiabatic dynamics simulations, we demonstrate that non-selective progress along the two bridge-torsional (i.e., phenolate, P, or imidazolinone, I) pathways accounts for the three decay constants reported experimentally, leading to competing ultrafast relaxation primarily along the I-twisted pathway and S1 trapping along the P-torsion. The majority of the population (∼70%) is transferred to S0 in the vicinity of two approximately enantiomeric minima on the I-twisted intersection seam (MECI-Is). Despite their sloped, reactant-biased topographies (suggesting low photoproduct yields), we find that decay through these intersections leads to products with a surprisingly high quantum yield of ∼30%. This demonstrates that E-isomer generation results at least in part from direct isomerization on the excited state. A photoisomerization committor analysis reveals a difference in intrinsic photoreactivity of the two MECI-Is and that the observed photoisomerization is the combined result of two effects: early, non-statistical dynamics around the less reactive intersection followed by later, near-statistical behavior around the more reactive MECI-I. Our work offers new insight into internal conversion of HBDI− that both establishes the intrinsic properties of the chromophore and enlightens principles for the design of chromophore derivatives and protein variants with improved photoswitching properties.

Ab Initio Direct Dynamics.

The reactivity and dynamics of molecular systems can be explored computationally by classical trajectory calculations. The traditional approach involves fitting a functional form of a potential energy surface (PES) to the energies from a large number of electronic structure calculations and then integrating numerous trajectories on this fitted PES to model the molecular dynamics. The ever-decreasing cost of computing and continuing advances in computational chemistry software have made it possible to use electronic structure calculations directly in molecular dynamics simulations without first having to construct a fitted PES. In this "on-the-fly" approach, every time the energy and its derivatives are needed for the integration of the equations of motion, they are obtained directly from quantum chemical calculations. This approach started to become practical in the mid-1990s as a result of increased availability of inexpensive computer resources and improved computational chemistry software. The application of direct dynamics calculations has grown rapidly over the last 25 years and would require a lengthy review article. The present Account is limited to some of our contributions to methods development and various applications. To improve the efficiency of direct dynamics calculations, we developed a Hessian-based predictor-corrector algorithm for integrating classical trajectories. Hessian updating made this even more efficient. This approach was also used to improve algorithms for following the steepest descent reaction paths. For larger molecular systems, we developed an extended Lagrangian approach in which the electronic structure is propagated along with the molecular structure. Strong field chemistry is a rapidly growing area, and to improve the accuracy of molecular dynamics in intense laser fields, we included the time-varying electric field in a novel predictor-corrector trajectory integration algorithm. Since intense laser fields can excite and ionize molecules, we extended our studies to include electron dynamics. Specifically, we developed code for time-dependent configuration interaction electron dynamics to simulate strong field ionization by intense laser pulses. Our initial application of ab initio direct dynamics in 1994 was to CH2O → H2 + CO; the calculated vibrational distributions in the products were in very good agreement with experiment. In the intervening years, we have used direct dynamics to explore energy partitioning in various dissociation reactions, unimolecular dissociations yielding three fragments, reactions with branching after the transition state, nonstatistical dynamics of chemically activated molecules, dynamics of molecular fragmentation by intense infrared laser pulses, selective activation of specific dissociation channels by aligned intense infrared laser fields, angular dependence of strong field ionization, and simulation of sequential double ionization.

Vibrationally Hot and Cold Triplets. Sensitizer-Dependent Dynamics and Localized Vibrational Promotion of a Di-π-methane Rearrangement.

Large intramolecular 13C kinetic isotope effects (KIEs) for the di-π-methane rearrangement of benzobarrelene fit with statistical expectations from heavy-atom tunneling when a low-energy sensitizer is employed, but much lower KIEs are observed with higher-energy sensitizers. These results in combination with trajectory studies suggest that the excess vibrational energy available from triplet energy transfer leads to hot and nonstatistical dynamics in the rearrangement.

Nonstatistical Reaction Dynamics.

Nonstatistical dynamics is important for many chemical reactions. The Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular kinetics assumes a reactant molecule maintains a statistical microcanonical ensemble of vibrational states during its dissociation so that its unimolecular dynamics are time independent. Such dynamics results when the reactant's atomic motion is chaotic or irregular. Intrinsic non-RRKM dynamics occurs when part of the reactant's phase space consists of quasiperiodic/regular motion and a bottleneck exists, so that the unimolecular rate constant is time dependent. Nonrandom excitation of a molecule may result in short-time apparent non-RRKM dynamics. For rotational activation, the 2J + 1 K levels for a particular J may be highly mixed, making K an active degree of freedom, or K may be a good quantum number and an adiabatic degree of freedom. Nonstatistical dynamics is often important for bimolecular reactions and their intermediates and for product-energy partitioning of bimolecular and unimolecular reactions. Post-transition state dynamics is often highly complex and nonstatistical.

Direct Dynamics Simulations of the Unimolecular Decomposition of the Randomly Excited 1CH2O2 Criegee Intermediate. Comparison with 3CH2 + 3O2 Reaction Dynamics.

The 3CH2 + 3O2 reaction has a quite complex ground state singlet potential energy surface (PES). There are multiple minima and transition states before forming the 10 possible reaction products. A previous direct chemical dynamics simulation at the UM06/6-311++G(d,p) level of theory ( J. Phys. Chem. A 2019, 123, 4360-4369) found that reaction on this PES is predominantly direct without trapping in the potential minima. The first minima 3CH2 + 3O2 encounters is that for the 1CH2O2 Criegee intermediate and statistical theory assumes the reactive system is trapped in this intermediate with a lifetime given by Rice-Ramsperger-Kassel-Marcus (RRKM) theory. In the work presented here, a direct dynamics simulation is performed with the above UM06 theory, with the trajectories initialized in the 1CH2O2 intermediate with a random distribution of vibrational energy as assumed by RRKM theory. There are substantial differences between the dynamics for 1CH2O2 dissociation and 3CH2 + 3O2 reaction. For the former there are four product channels, while for the latter there are seven in agreement with experiment. Product energy partitioning for the two simulations are in overall good agreement for the CO2 + H2 and CO + H2O product channels, but in significant disagreement for the HCO + OH product channel. Though 1CH2O2 is excited randomly in accord with RRKM theory, its dissociation probability is biexponential and not exponential as assumed by RRKM. In addition, the 1CH2O2 dissociation dynamics follow non-intrinsic reaction coordinate (non-IRC) pathways. An important finding is that the nonstatistical dynamics for the 3CH2 + 3O2 reaction give results in agreement with experiment.

Acoustical genesis of uniqueness of tanpura-drone signal—Probing with non-statistical fluctuation pattern

Tanpura-drone is one of the most commonly used string instrument used as accompaniment with vocal of other musical forms of Indian Classical Music genre. It is an exceptional and intriguing one owing to its capability of the generation of rich pattern of fine overtones. The acoustic analysis of tanpura signal had been initiated by C.V. Raman. Raman observed that the virtual overtones are heard while one is playing tanpura, which as per the conventional acoustic principles should never be generated. After that different models of its vibration pattern had been proposed to understand the theory based on the essential features of the tanpura’s string-bridge interaction, for empirical simulation of the tanpura signal and also for various synthesis-oriented analysis. But various challenges arise while defining accurate algorithms for real-time sound synthesis, due to the inherent non-statistical dynamics of tanpura signal. In this work we have converted tanpura signal into a two-dimensional space. Along one dimension of the space there is time-displacement pattern. Along the other dimension the signal changes its pattern along its progression to generate musicality. Then, we propose a novel and robust methodology in the line of the works done for analyzing the pattern of non-statistical fluctuation of fluctuations inherent in the two-dimensional space of the tanpura signal along its progression with time. We have done similar analysis for the signals of other two commonly used string instruments used in Indian Classical Music – sitar and sarod, and compared the results with that of tanpura signal. When compared, it was strikingly revealed that the pattern of fluctuation of fluctuations inherent in tanpura sound is altogether different from that of the rest of the two types of string instrument. Further, we confirm computationally that the nature of the non-statistical fluctuation of the tanpura signal is consistently different from that of other string instruments like sitar and sarod signal.

Nonstatistical Dissociation Dynamics of Nitrobenzene and ortho-Nitrophenol

Nonstatistical Dissociation Dynamics of Nitrobenzene and ortho-Nitrophenol

Fragmentation of a dioxolanyl radical via nonstatistical reaction dynamics: characterization of the vinyloxy radical by ns time-resolved laser flash photolysis.

The photochemistry of two Barton esters, one derived from a dioxolane carboxylic acid and the other from pivalic acid, was investigated by product analysis and nanosecond laser flash photolysis (LFP). As expected, photolysis of the pivalate ester resulted in formation of the pyridine-2-thiyl and the t-butyl radical. Photolysis of the Barton ester of 2,2-dimethyl-1,3-dioxolane-4-carboxylic acid, on the other hand, revealed a complex multi-step fragmentation. In addition to the pyridine-2-thiyl and dioxolanyl radical, we gained evidence for the formation of the vinyloxy radical, CH2[double bond, length as m-dash]CHO˙. The latter was identified in the LFP by its π-complexes with benzene and diphenylether, its rapid quenching by electron-rich arenes and tri-n-butyl tin hydride, and its oxidative power in presence of trifluoroacetic acid as demonstrated by the oxidation of ferrocene to ferrocenium. Formation of CH2[double bond, length as m-dash]CHO˙ can be rationalized via fragmentation of the dioxolanyl radical. As the calculated barriers are too high for the reaction sequence to occur on the LFP time scale, we investigated the fragmentation of the photoexcited Barton ester via Born-Oppenheimer molecular dynamics simulations. In one trajectory, we could observe all reaction steps including ring opening of the dioxolanyl radical, suggesting that the excess energy gained in the ester cleavage and decarboxylation may lead to fragmentation of the hot dioxolanyl radical.

Perspective: chemical dynamics simulations of non-statistical reaction dynamics.

Non-statistical chemical dynamics are exemplified by disagreements with the transition state (TS), RRKM and phase space theories of chemical kinetics and dynamics. The intrinsic reaction coordinate (IRC) is often used for the former two theories, and non-statistical dynamics arising from non-IRC dynamics are often important. In this perspective, non-statistical dynamics are discussed for chemical reactions, with results primarily obtained from chemical dynamics simulations and to a lesser extent from experiment. The non-statistical dynamical properties discussed are: post-TS dynamics, including potential energy surface bifurcations, product energy partitioning in unimolecular dissociation and avoiding exit-channel potential energy minima; non-RRKM unimolecular decomposition; non-IRC dynamics; direct mechanisms for bimolecular reactions with pre- and/or post-reaction potential energy minima; non-TS theory barrier recrossings; and roaming dynamics.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'.

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'.

Phase-space methods for the spin dynamics in condensed matter systems.

Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin-[Formula: see text] fermions (typically, electrons) including the Zeeman effect and the spin-orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. A simple closure relation is proposed to obtain a closed set of hydrodynamic equations.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'.

A velocity-map imaging study of methyl non-resonant multiphoton ionization from the photodissociation of CH3I in the A-band.

Chemical reaction dynamics and, particularly, photodissociation in the gas phase are generally studied using pump-probe schemes where a first laser pulse induces the process under study and a second one detects the produced fragments. Providing an efficient detection of ro-vibrationally state-selected photofragments, the resonance enhanced multiphoton ionization (REMPI) technique is, without question, the most popular approach used for the probe step, while non-resonant multiphoton ionization (NRMPI) detection of the products is scarce. The main goal of this work is to test the sensitivity of the NRMPI technique to fragment vibrational distributions arising from molecular photodissociation processes. We revisit the well-known process of methyl iodide photodissociation in the A-band at around 280 nm, using the velocity-map imaging technique in conjunction with NRMPI of the methyl fragment. The detection wavelength, carefully selected to avoid any REMPI transition, was scanned between 325 and 335 nm seeking correlations between the different observables-the product vibrational, translational and angular distributions-and the excitation wavelength of the probe laser pulse. The experimental results have been discussed on the base of quantum dynamics calculations of photofragment vibrational populations carried out on available ab initio potential-energy surfaces using a four-dimensional model.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'.

A new (multi-reference configuration interaction) potential energy surface for H2CO and preliminary studies of roaming.

We report a new global potential energy surface (PES) for H2CO, based on precise fitting of roughly 67 000 MRCI/cc-pVTZ energies. This PES describes the global minimum, the cis- and trans-HCOH isomers, and barriers relevant to isomerization, formation of the molecular (H2+CO) and radical (H+HCO) products, and the loose so-called roaming transition-state saddle point. The key features of the PES are reviewed and compared with a previous PES, denoted by PES04, based on five local fits that are 'stitched' together by switching functions (Zhang et al. 2004 J. Phys. Chem. A108, 8980-8986 (doi:10.1021/jp048339l)). Preliminary quasi-classical trajectory calculations are performed at the total energy of 36 233 cm-1 (103 kcal mol-1), relative to the H2CO global minimum, using the new PES, with a particular focus on roaming dynamics. When compared with the results from PES04, the new PES findings show similar rotational distributions, somewhat more roaming and substantially higher H2 vibrational excitation.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'.

Insights into the deactivation of 5-bromouracil after ultraviolet excitation.

5-Bromouracil is a nucleobase analogue that can replace thymine in DNA strands and acts as a strong radiosensitizer, with potential applications in molecular biology and cancer therapy. Here, the deactivation of 5-bromouracil after ultraviolet irradiation is investigated in the singlet and triplet manifold by accurate quantum chemistry calculations and non-adiabatic dynamics simulations. It is found that, after irradiation to the bright ππ* state, three main relaxation pathways are, in principle, possible: relaxation back to the ground state, intersystem crossing (ISC) and C-Br photodissociation. Based on accurate MS-CASPT2 optimizations, we propose that ground-state relaxation should be the predominant deactivation pathway in the gas phase. We then employ different electronic structure methods to assess their suitability to carry out excited-state dynamics simulations. MRCIS (multi-reference configuration interaction including single excitations) was used in surface hopping simulations to compute the ultrafast ISC dynamics, which mostly involves the 1nOπ* and 3ππ* 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'.

Dissociation of polycyclic aromatic hydrocarbons: molecular dynamics studies.

We present dynamical studies of the dissociation of polycyclic aromatic hydrocarbon (PAH) radical cations in their ground electronic states with significant internal energy. Molecular dynamics simulations are performed, the electronic structure being described on-the-fly at the self-consistent-charge density functional-based tight binding (SCC-DFTB) level of theory. The SCC-DFTB approach is first benchmarked against DFT results. Extensive simulations are achieved for naphthalene [Formula: see text], pyrene [Formula: see text] and coronene [Formula: see text] at several energies. Such studies enable one to derive significant trends on branching ratios, kinetics, structures and hints on the formation mechanism of the ejected neutral fragments. In particular, dependence of branching ratios on PAH size and energy were retrieved. The losses of H and C2H2 (recognized as the ethyne molecule) were identified as major dissociation channels. The H/C2H2 ratio was found to increase with PAH size and to decrease with energy. For [Formula: see text], which is the most interesting PAH from the astrophysical point of view, the loss of H was found as the quasi-only channel for an internal energy of 30 eV. Overall, in line with experimental trends, decreasing the internal energy or increasing the PAH size will favour the hydrogen loss channels with respect to carbonaceous fragments.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’.