Quantum chemical methods and their applications to chemical reactions

This review is concerned with the impact of quantum chemistry on chemical reactions. Starting from the mid-sixties it focusses on those developments which have enabled us to predict essential features of simple chemical reactions. Thus model theories and computational methods are presented which provide the tools for these predictions. Then procedures to characterize potential surfaces and search methods for reaction paths are described. It is also attempted to relate these features to the terminology of the experimentalist. Finally a systematic survey of the main types of reaction (rearrangement, addition, elimination, substitution) is given.     

Quantum Dynamics of Oxyhydrogen Complex-Forming Reactions for the HO2 and HO3 Systems

Complex-forming reactions widely exist in gas-phase chemical reactions.Various complexforming bimolecular reactions have been investigated and interesting phenomena have been discovered.The complex-forming reactions usually have small or no barrier in the entrance channel, which leads to obvious differences in kinetic and dynamic characteristics compared with direct reactions.Theoretically, quantum state-resolved reaction dynamics can provide the most detailed microscopic dynamic mechanisms and is now feasible for a direct reaction with only one potential barrier.However, it is of great challenge to construct accurate potential energy surfaces and perform accurate quantum dynamics calculations for a complex polyatomic reaction involving deep potential wells and multi-channels.This paper reviews the most recent progress in two prototypical oxyhydrogen complex-forming reaction systems, HO₂ and HO₃, which are significant in combustion, atmospheric, and interstellar chemistry.We will present a brief survey of both computational and experimental work and emphasize on some unsolved problems existing in these systems.     

Computational models of chemical systems inspired by Braess’ paradox

Systems chemistry is a new discipline which investigates the interactions within a network of chemical reactions. We have studied several computational models of chemical systems inspired by mathematical paradoxes and have found that even simple systems may behave in a counterintuitive, non-linear manner depending upon various conditions. In the present study, we modeled a set of reactions inspired by one such paradox, Braess’ paradox, an interesting phenomenon whereby the introduction of additional capacity (e.g. pathways) in some simple network systems can lead to an unexpected reduction in the overall flow rate of “traffic” through the system. We devised several chemical systems that behaved in this counterintuitive manner; the overall rate of product formation was diminished when an additional pathway was introduced and, conversely, there was an enhancement of product formation when the same interconnecting pathway was removed. We found that, unlike a traffic model, the chemical model needed to include reversible pathways in order to mimic “congestion”—a condition necessary to produce Braess-like behavior. The model was investigated numerically, but a full analytical solution is also included. We propose that this intriguing situation may have interesting implications in chemistry, biochemistry and chemical engineering.     

Systematic procedure for reduction of kinetic mechanisms of complex chemical processes and its software implementation

Feasibility of multidimensional hydrodynamic modeling depends critically on the availability of accurate reduced kinetic mechanisms of physical and chemical processes taking place in the system. Such mechanisms should describe the processes under consideration within a specified error tolerance in the range of initial conditions of interest while keeping the number of species and reactions as small as possible. We have developed an advanced tool for reduction of detailed kinetic mechanisms with a minimal human effort. The tool includes 10 reduction and 2 analysis methods which are based on the results of zero-dimensional modeling. The methods can be combined and applied in sequence. The reduction tool has been implemented as a part the Chemical Workbench computational package and has been tested for a number of large kinetic mechanisms of gas-phase processes. Using this tool, we reduced the mechanism of tar gasification from 177 species and 879 reversible reactions to only 83 species and 278 reactions, while the mechanism of methane combustion initially involving 127 species and 1,206 reactions was reduced to 42 species and 173 reactions.     

A critical analysis of electrospray techniques for the determination of accelerated rates and mechanisms of chemical reactions in droplets

Electrospray and Electrosonic Spray Ionization Mass Spectrometry (ESI-MS and ESSI-MS) have been widely used to report evidence that many chemical reactions in micro- and nano-droplets are dramatically accelerated by factors of ∼10² to 10⁶ relative to macroscale bulk solutions. Despite electrospray''s relative simplicity to both generate and detect reaction products in charged droplets using mass spectrometry, substantial complexity exists in how the electrospray process itself impacts the interpretation of the mechanism of these observed accelerated rates. ESI and ESSI are both coupled multi-phase processes, in which analytes in small charged droplets are transferred and detected as gas-phase ions with a mass spectrometer. As such, quantitative examination is needed to evaluate the impact of multiple experimental factors on the magnitude and mechanisms of reaction acceleration. These include: (1) evaporative concentration of reactants as a function of droplet size and initial concentration, (2) competition from gas-phase chemistry and reactions on experimental surfaces, (3) differences in ionization efficiency and ion transmission and (4) droplet charge. We examine (1–4) using numerical models, new ESI/ESSI-MS experimental data, and prior literature to assess the limitations of these approaches and the experimental best practices required to robustly interpret acceleration factors in micro- and nano-droplets produced by ESI and ESSI.

The application of Electrospray and Electrosonic Spray Ionization Mass Spectrometry (ESI-MS and ESSI-MS) to study accelerated reaction kinetics in droplets is examined using numerical models, new experimental data, and prior literature.     

Spatial distributions and interstellar reaction processes

Methyl formate presents a challenge for the conventional chemical mechanisms assumed to guide interstellar organic chemistry. Previous studies of potential formation pathways for methyl formate in interstellar clouds ruled out gas-phase chemistry as a major production route, and more recent chemical kinetics models indicate that it may form efficiently from radical-radical chemistry on ice surfaces. Yet, recent chemical imaging studies of methyl formate and molecules potentially related to its formation suggest that it may form through previously unexplored gas-phase chemistry. Motivated by these findings, two new gas-phase ion-molecule formation routes are proposed and characterized using electronic structure theory with conformational specificity. The proposed reactions, acid-catalyzed Fisher esterification and methyl cation transfer, both produce the less stable trans-conformational isomer of protonated methyl formate in relatively high abundance under the kinetically controlled conditions relevant to interstellar chemistry. Gas-phase neutral methyl formate can be produced from its protonated counterpart through either a dissociative electron recombination reaction or a proton transfer reaction to a molecule with larger proton affinity. Retention (or partial retention) of the conformation in these neutralization reactions would yield trans-methyl formate in an abundance that exceeds predictions under thermodynamic equilibrium at typical interstellar temperatures of ≤100 K. For this reason, this conformer may prove to be an excellent probe of gas-phase chemistry in interstellar clouds. Motivated by new theoretical predictions, the rotational spectrum of trans-methyl formate has been measured for the first time in the laboratory, and seven lines have now been detected in the interstellar medium using the publicly available PRIMOS survey from the NRAO Green Bank Telescope.     

A computational study of the intramolecular deprotonation of a carbon acid in aqueous solution

Proton transfer reactions are the rate-limiting steps in many biological and synthetic chemical processes, often requiring complex cofactors or catalysts to overcome the generally unfavourable thermodynamic process of carbanion intermediate formation. It has been suggested that quantum tunnelling processes enhance the kinetics of some of these reactions, which when coupled to protein motions may be an important consideration for enzyme catalysis. To obtain a better fundamental and quantitative understanding of these proton transfer mechanisms, a computational analysis of the intramolecular proton transfer from a carbon acid in the small molecule, 4-nitropentanoic acid, in aqueous solution is presented. Potential-energy surfaces from gas-phase, implicit and QM/MM (quantum mechanical/molecular mechanical) explicit solvation quantum chemistry models are compared, and the potential of mean force, for the full reaction coordinate, using umbrella-sampling molecular dynamics is analysed. Semi-classical multidimensional tunnelling corrections are also used to estimate the quantum tunnelling contributions and to understand the origin of the primary deuterium kinetic isotope effects (KIEs). The computational results are found to be in excellent agreement with the KIEs and the energetics obtained experimentally.     

Chelate effect and thermodynamics of metal complex formation in solution: a quantum chemical study

The accuracy of quantum chemical predictions of structures and thermodynamic data for metal complexes depends both on the quantum chemical methods and the chemical models used. A thermodynamic analogue of the Eigen-Wilkins mechanism for ligand substitution reactions (Model A) turns out to be sufficiently simple to catch the essential chemistry of complex formation reactions and allows quantum chemical calculations at the ab initio level of thermodynamic quantities both in gas phase and solution; the latter by using the conductor-like polarizable continuum (CPCM) model. Model A describes the complex formation as a two-step reaction: 1. [M(H2O)x](aq) + L(aq) <==>[M(H2O)x], L(aq); 2. [M(H2O)x], L(aq) <==>[M(H2O)(x-1)L],(H2O)(aq). The first step, the formation of an outer-sphere complex is described using the Fuoss equation and the second, the intramolecular exchange between an entering ligand from the second and water in the first coordination shell, using quantum chemical methods. The thermodynamic quantities for this model were compared to those for the reaction: [M(H2O)x](aq) + L(aq) <==>[M(H2O)(x-1)L](aq) + (H2O)(aq) (Model B), as calculated for each reactant and product separately. The models were tested using complex formation between Zn(2+) and ammonia, methylamine, and ethylenediamine, and complex formation and chelate ring closure reactions in binary and ternary UO(2)(2+)-oxalate systems. The results show that the Gibbs energy of reaction for Model A are not strongly dependent on the number of water ligands and the structure of the second coordination sphere; it provides a much more precise estimate of the thermodynamics of complex formation reactions in solution than that obtained from Model B. The agreement between the experimental and calculated data for the formation of Zn(NH(3))(2+)(aq) and Zn(NH(3))(2)(2+)(aq) is better than 8 kJ/mol for the former, as compared to 30 kJ/mol or larger, for the latter. The Gibbs energy of reaction obtained for the UO(2)(2+) oxalate systems using model B differs between 80 and 130 kJ/mol from the experimental results, whereas the agreement with Model A is better. The errors in the quantum chemical estimates of the entropy and enthalpy of reaction are somewhat larger than those for the Gibbs energy, but still in fair agreement with experiments; adding water molecules in the second coordination sphere improves the agreement significantly. Reasons for the different performance of the two models are discussed. The quantum chemical data were used to discuss the microscopic basis of experimental enthalpy and entropy data, to determine the enthalpy and entropy contributions in chelate ring closure reactions and to discuss the origin of the so-called "chelate effect". Contrary to many earlier suggestions, this is not even in the gas phase, a result of changes in translation entropy contributions. There is no simple explanation of the high stability of chelate complexes; it is a result of both enthalpy and entropy contributions that vary from one system to the other.     

Integration of chemical stiff ODEs using exponential propagation method

In this paper, we study the numerical long time integration of large stiff systems of differential equations arising from chemical reactions by exponential propagation methods. These methods, which typically converge faster, use matrix-vector products with the exponential or other related function of the Jacobian that can be effectively approximated by Krylov sabspace methods. We equip these methods to an automatic stepsize control technique and apply the method of order 4 for numerical integration of some famous stiff chemical problems such as Belousov-Zhabotinskii reaction, the Chapman atmosphere, Hydrogen chemistry, chemical Akzo-Nobel problem and air pollution problem.     

量子化学模型方法在机械力化学中的应用

机械力化学作为一种无需溶剂的绿色化学技术得到广泛关注。然而,机械力化学反应机制需要从原子和分子尺度上深入理解力诱导的化学反应。在过去的20年中,量子化学模型方法在机械力化学机理研究中得到广泛应用,高精度量化计算可得到外力下变形分子的几何结构、能量、过渡态等诸多性质。本文介绍了目前机械力化学领域的主流量子化学模型的基本原理,同时也关注了这些模型方法在软件上的具体实现,并借助典型的案例阐述了量子化学模型在解释机械力化学机理中的作用与价值。     

Atoms and bonds in molecules and chemical explanations

The concepts of atoms and bonds in molecules which appeared in chemistry during the nineteenth century are unavoidable to explain the structure and the reactivity of the matter at a chemical level of understanding. Although they can be criticized from a strict reductionist point of view, because neither atoms nor bonds are observable in the sense of quantum mechanics, the topological and statistical interpretative approaches of quantum chemistry (quantum theory of atoms in molecules, electron localization function and maximum probability domain) provide consistent definitions which accommodate chemistry and quantum mechanics.     

Role of quantum chemical calculations in molecular biophysics with a historical perspective

We discuss how the basic principles of quantum chemistry and quantum mechanics can be and have been applied to a variety of problems in molecular biophysics. First, the historical development of quantum concepts in biophysics is discussed. Next, we describe a series of interesting applications of quantum chemical methods for studying biologically active molecules, molecular structures, and some of the important processes which play a role in living organisms. We discuss the application of quantum chemistry to such processes as energy storage and transformation, and the transmission of genetic information. Quantum chemical approaches are essential to comprehend and understand the molecular nature of these processes. To conclude our work, we present a short discussion of the perspectives of quantum chemical methods in modern biophysics, the field of experimental and theoretical chiral vibrational and electronic spectroscopy.     

Parity conservation and polarization of differential cross sections in complex-forming chemical reactions

For complex-forming chemical reactions, such as atom-diatom insertion reactions, quantum scattering and quantum statistical calculations usually predict sharp forward/backward peaks in the Differential Cross Sections (DCS). Conversely, the corresponding classical calculations are unable to reproduce these peaks. We show here that the basic reason for such an intriguing failure is that parity conservation is ignored in classical mechanics. A by-product of the analysis is a simple parity-restoring approximation that might significantly increase the ability of classical mechanics to describe DCSs over the whole angular range for the title processes.     

A theoretical study on the cyclopropane adsorption onto the copper surfaces by density functional theory and quantum chemical molecular dynamics methods

We report a theoretical study on the cyclopropane adsorption onto Cu(1 1 1) surfaces by density functional theory (DFT) and quantum chemical molecular dynamics methods. The equilibrium geometry of the physisorbed species was obtained using both periodic and cluster models by DFT methods that employ Cambridge serial total energy package (CASTEP), DMol ab initio quantum chemistry software of Accelrys’ materials studio (DMol), and Amsterdam density functional (ADF) program. It was found that the adsorbate molecule was tilted towards the metal surface with one C---C bond (upwards) parallel to the surface and that the physisorption occurred via a third carbon atom pointing (downwards) towards the surface. The electronic distribution and geometrical structure of physisorbed cyclopropane were slightly deviated from its gas phase molecule. The calculated vibrational frequencies and adsorption energies are close to experimental data, confirming the reliability of our DFT results. The adsorption process was simulated using our novel tight-binding quantum chemical molecular dynamics program, ‘Colors’. The calculation results indicated that both the adsorption and desorption processes of cyclopropane took place molecularly. The electron transfer and structural properties of equilibrium position obtained by ‘Colors’ are consistent with those by the first principles DFT methods.     

Effect of Si-H bond on the gas-phase chemistry of trimethylsilane in the hot wire chemical vapor deposition process

The effect of the Si-H bond on the gas-phase reaction chemistry of trimethylsilane in the hot-wire chemical vapor deposition (HWCVD) process has been studied by examining its decomposition on a hot tungsten filament and the secondary gas-phase reactions in a reactor using a soft laser ionization source coupled with mass spectrometry. Trimethylsilane decomposes on the hot filament via Si-H and Si-CH(3) bond cleavages. A short-chain mechanism is found to dominate in the secondary reactions in the reactor. It has been shown that the hydrogen abstractions of both Si-H and C-H occur simultaneously, with the abstraction of Si-H being favored. Tetramethylsilane and hexamethyldisilane are the two major products formed from the radical recombination reactions in the termination steps. Three methyl-substituted disilacyclobutane molecules, i.e., 1,3-dimethyl-1,3-disilacyclobutane, 1,1,3-trimethyl-1,3-disilacyclobutane, and 1,1,3,3-tetramethyl-1,3-disilacyclobutane are also produced in reactor from the cycloaddition reactions of methyl-substituted silene species. Compared to tetramethylsilane and hexamethyldisilane, a common feature with trimethylsilane is that the short-chain mechanism still dominates. However, a more active involvement of the reactive silene intermediates has been found with trimethylsilane.     

The intertwined physics of active chemical reactions and phase separation

Phase separation is the thermodynamic process that explains how droplets form in multicomponent fluids. These droplets can provide controlled compartments to localize chemical reactions, and reactions can also affect the droplets' dynamics. This review focuses on the tight interplay between phase separation and chemical reactions, which originates from thermodynamic constraints. In particular, simple mass action kinetics cannot describe chemical reactions since phase separation requires non-ideal fluids. Instead, thermodynamics implies that passive chemical reactions reduce the complexity of phase diagrams and provide only limited control over the system's behavior. However, driven chemical reactions, which use external energy input to create spatial fluxes, can circumvent thermodynamic constraints. Such active systems can suppress typical droplet coarsening, control droplet size, and localize droplets. This review provides an extensible framework for describing active chemical reactions in phase separating systems, which forms a basis for improving control in technical applications and understanding self-organized structures in biological cells.     

The use of digital simulation to improve the cyclic voltammetric determination of rate constants for homogeneous chemical reactions following charge transfers

Cyclic voltammetry (CV) is a very useful electrochemical tool used to study reaction systems that include chemical steps that are coupled to electron transfers. This type of system generally involves the chemical reaction of an electrochemically generated free radical. Published methods exist that are used to determine the kinetics of electrochemically initiated chemical reactions from the measurements of the peak current ratio (i_pa/i_pc) of a cyclic voltammogram. The published method requires working curves to relate a kinetic parameter to the peak current ratio.In the presented work, a digital simulation package was used to obtain improved working curves for specific working conditions. The curves were compared with the published results for the first- and second-order chemical reactions following the charge transfer step mechanisms.According to the presented results, the previously published working curve is reliable for a mechanism with a first-order chemical reaction; however, a change in the switching potential requires a recalculation of the curve. In the case of mechanisms with a second-order step (dimerisation and disproportionation), several different views exist on how the second-order chemical term should be expressed so that different values of the constant are obtained. Parameters such as electrode type, electrode area, electroactive species concentration, switching potential, scan rate and method for peak current ratio calculation modify the working curves and must always be specified.We propose a standardised method to obtain the most reliable kinetic constant values.The results of this work will permit researchers who handle simulation software to construct their own working curves. Additionally, those who do not have the simulation software could use the working curves described here.The revelations of the presented experiments may be useful to a broad chemistry audience because this study presents a simple and low-cost procedure for the study of free radicals that otherwise should be studied with more sophisticated and expensive techniques, such as ESR or pulse radiolysis.     

Toward practical quantum embedding simulation of realistic chemical systems on near-term quantum computers

Quantum computing has recently exhibited great potential in predicting chemical properties for various applications in drug discovery, material design, and catalyst optimization. Progress has been made in simulating small molecules, such as LiH and hydrogen chains of up to 12 qubits, by using quantum algorithms such as variational quantum eigensolver (VQE). Yet, originating from the limitations of the size and the fidelity of near-term quantum hardware, the accurate simulation of large realistic molecules remains a challenge. Here, integrating an adaptive energy sorting strategy and a classical computational method—the density matrix embedding theory, which respectively reduces the circuit depth and the problem size, we present a means to circumvent the limitations and demonstrate the potential of near-term quantum computers toward solving real chemical problems. We numerically test the method for the hydrogenation reaction of C₆H₈ and the equilibrium geometry of the C₁₈ molecule, using basis sets up to cc-pVDZ (at most 144 qubits). The simulation results show accuracies comparable to those of advanced quantum chemistry methods such as coupled-cluster or even full configuration interaction, while the number of qubits required is reduced by an order of magnitude (from 144 qubits to 16 qubits for the C₁₈ molecule) compared to conventional VQE. Our work implies the possibility of solving industrial chemical problems on near-term quantum devices.

Quantum embedding simulation greatly enhanced the capability of near-term quantum computers on realistic chemical systems and reach accuracy comparable to advanced quantum chemistry methods.