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The infrared (IR) spectra of fentanyl, carfentanil and remifentanil, and protonated salts, are computed using quantum chemistry methods. New experimental FTIR spectra are also reported and compared to the calculations. The accuracy of two density functional theory methods, B3LYP and M06-2X, are tested against higher level theories (MP2) and the experimental data. Gas phase IR spectra are calculated for both the neutral and protonated molecules in order to compare with the experimental data measured for various salts of fentanyl and its analogues. Key vibrational modes are selected and studied in detail using a vibrational mode locality calculation. The main contributing atomic movements in these vibrational modes are identified., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Crown Copyright © 2022. Published by Elsevier B.V. All rights reserved.)

It is very difficult to perform experiments on the physical parameters for the thermal decomposition of chemical nerve agents such as VX and computations, therefore, are useful. The reaction dynamics of the gas-phase pericyclic hydrogen transfer of the nerve agent VX is studied computationally. The geometries of the stationary structures are calculated at M06-2X/jul-cc-pVTZ level of theory. Single point energy calculations are carried out at the CBS/QB3 level to correct the energy barriers. Canonical reaction rate constants are calculated as a function of temperature. The one-dimensional semiclassical transition state theory is used to analyse the quantum tunneling effects. A reduced-dimensional hindered rotor model is proposed, tested, and applied to calculate the vibrational partition functions. It is found that the ester (O-side) and thioester (S-side) side chains of VX undergo pericyclic H-transfer reactions that result in decomposition of the molecule. The S-side reaction is favoured both kinetically and thermodynamically and dominates the pyrolysis over the temperature range from 600 K to 1000 K. It is predicted that VX completely decomposes in 2 s at temperatures above 750 K.

This Feature Article describes some recent developments and applications of the Semiclassical Transition-State Theory (SCTST) for treating quantum tunneling in chemical reactions. A reduced dimensional form of the SCTST is discussed and is shown to be particularly efficient, as the required number of electronic structure calculations is reduced to an absolute minimum. We also describe how an alternative formulation of SCTST developed by Hernandez and Miller [ Chem. Phys. Lett. 1993 , 214 , 129 ], the SCTST-θ, has advantages in allowing for straightforward applications of the SCTST for any form of the potential expansion at the transition state. We also illustrate the power of SCTST in applications to more complex systems. We show how polyatomic modes such as internal rotations and torsions can be treated efficiently in SCTST calculations. We also describe some applications of the method to hydrogen atom tunneling in unimolecular reactions including the degradation of chemical nerve agents and the decay of the atmospherically important Criegee intermediates.

In order to further understand and support approaches for the degradation and destruction of toxic chemicals, the thermal decomposition of the nerve agent VX through possible pericyclic hydrogen transfer reactions is investigated using simulant molecules. A total of four simulant molecules are studied. Three of them have only one possible H-transfer site, while the other has two. They are chosen to bring physical insights into individual steps of the pericyclic reaction mechanism as well as the possible existence of competing mechanisms. The unimolecular reaction rate constants at the high-pressure limit are calculated. Geometries of stationary structures on the potential energy surfaces are calculated with the MP2 method as well as the B3LYP and M06-2X functionals and 6-311++G(d,p), jul-cc-pVTZ, and aug-cc-pVTZ basis sets. The barrier heights are corrected using energy values obtained at the CBS/QB3 level of theory. The contribution of the quantum tunneling effect to the reaction rate constants is included using one-dimensional semiclassical transition state theory. Adiabatic barrier heights, reaction rate constants, and branching ratio of the competing mechanisms are reported.

This Spiers Memorial Lecture discusses quantum effects that can be calculated and observed in the chemical reactions of small molecules. This includes quantum reactive scattering resonances, vibrational and rotational state effects, and quantum tunnelling in chemical reactions. Both experimental and theoretical advances are reviewed. Of particular emphasis is a description of the development of reduced dimensional theories which can highlight chemical reactions that are likely to be of interest for more accurate quantum reactive scattering studies and new experiments. Furthermore, the reduced dimensional models allow for the development and testing of computationally inexpensive procedures that enable calculations to be performed on quantum effects in reactions of larger polyatomic molecules.

The unimolecular decay of Criegee intermediates is the major producer of OH radicals in the atmosphere. Here, Semi-Classical Transition State Theory (SCTST) in full and reduced dimensions is used to determine thermal rate constants for their unimolecular decay, as well as their decay catalysed by a single water molecule. These reactions shed light on the applicability of SCTST for catalysed hydrogen transfer reactions.

The rate constants of the two branches of H-abstractions from CH 3 OH by the H-atom and the corresponding reactions in the reverse direction are calculated using the one-dimensional semiclassical transition state theory (1D SCTST). In this method, only the reaction mode vibration of the transition state (TS) is treated anharmonically, while the remaining internal degrees of freedom are treated as they would have been in a standard TS theory calculation. A total of eight ab initio single-point energy calculations are performed in addition to the computational cost of a standard TS theory calculation. This allows a second-order Richardson extrapolation method to be employed to improve the numerical estimation of the third- and fourth-order derivatives, which in turn are used in the calculation of the anharmonic constant. Hindered-rotor (HR) vibrations are identified in the equilibrium states of CH 3 OH and CH 2 OH, and the TSs of the reactions. The partition function of the HRs are calculated using both a simple harmonic oscillator model and a more sophisticated one-dimensional torsional eigenvalue summation (1D TES) method. The 1D TES method can be easily adapted in 1D SCTST computation. The resulting 1D SCTST with 1D TES rate constants show good agreement to previous theoretical and experimental works. The effects of the HR on rate constants for different reactions are also investigated.This article is part of the theme issue 'Modern theoretical chemistry'., (© 2018 The Author(s).)

This review surveys quantum scattering calculations on chemical reactions of polyatomic molecules in the gas phase published in the last ten years. These calculations are useful because they provide highly accurate information on the dynamics of chemical reactions which can be compared in detail with experimental results. They also serve as quantum mechanical benchmarks for testing approximate theories which can more readily be applied to more complicated reactions. This review includes theories for calculating quantities such as rate constants which have many important scientific applications.

Theoretical and experimental results are presented for the pyrolytic decomposition of the nerve agent sarin (GB) in the gas phase. High-level quantum chemistry calculations are performed together with a semiclassical transition-state theory for describing quantum mechanical tunneling. The experimental and theoretical results for the temperature dependence of the survival times show very good agreement, as does the calculated and measured activation energy for thermal decomposition. The combined results suggest that the thermal decomposition of GB, for temperature ranging from 350 to 500 °C, goes through a pericyclic reaction mechanism with a transition state consisting of a six-membered ring structure.

Semiclassical Transition State Theory (SCTST), a method for calculating rate constants of chemical reactions, offers gains in computational efficiency relative to more accurate quantum scattering methods. In full-dimensional (FD) SCTST, reaction probabilities are calculated from third and fourth potential derivatives along all vibrational degrees of freedom. However, the computational cost of FD SCTST scales unfavorably with system size, which prohibits its application to larger systems. In this study, the accuracy and efficiency of 1-D SCTST, in which only third and fourth derivatives along the reaction mode are used, are investigated in comparison to those of FD SCTST. Potential derivatives are obtained from numerical ab initio Hessian matrix calculations at the MP2/cc-pVTZ level of theory, and Richardson extrapolation is applied to improve the accuracy of these derivatives. Reaction barriers are calculated at the CCSD(T)/cc-pVTZ level. Results from FD SCTST agree with results from previous theoretical and experimental studies when Richardson extrapolation is applied. Results from our implementation of 1-D SCTST, which uses only 4 single-point MP2/cc-pVTZ energy calculations in addition to those for conventional TST, agree with FD results to within a factor of 5 at 250 K. This degree of agreement and the efficiency of the 1-D method suggest its potential as a means of approximating rate constants for systems too large for existing quantum scattering methods.

We investigate which terms in Reduced-Dimensionality Semiclassical Transition State Theory (RD SCTST) contribute most significantly in rate constant calculations of hydrogen extraction and exchange reactions of hydrocarbons. We also investigate the importance of deep tunneling corrections to the theory. In addition, we introduce a novel formulation of the theory in Jacobi coordinates. For the reactions of H atoms with methane, ethane, and cyclopropane, we find that a one-dimensional (1-D) version of the theory without deep tunneling corrections compares well with 2-D SCTST results and accurate quantum scattering results. For the "heavy-light-heavy" H atom exchange reaction between CH3 and CH4, deep tunneling corrections are needed to yield 1-D results that compare well with 2-D results. The finding that accurate rate constants can be obtained from derivatives of the potential along only one dimension further validates RD SCTST as a computationally efficient yet accurate rate constant theory.

Quantum mechanical methods for calculating rate constants are often intractable for reactions involving many atoms. Semiclassical transition state theory (SCTST) offers computational advantages over these methods but nonetheless scales exponentially with the number of degrees of freedom (DOFs) of the system. Here we present a method with more favorable scaling, reduced-dimensionality SCTST (RD SCTST), that treats only a subset of DOFs of the system explicitly. We apply it to three H abstraction and exchange reactions for which two-dimensional potential energy surfaces (PESs) have previously been constructed and evaluated using RD quantum scattering calculations. We differentiated these PESs to calculate harmonic frequencies and anharmonic constants, which were then used to calculate cumulative reaction probabilities and rate constants by RD SCTST. This method yielded rate constants in good agreement with quantum scattering results. Notably, it performed well for a heavy-light-heavy reaction, even though it does not explicitly account for corner-cutting effects. Recent extensions to SCTST that improve its treatment of deep tunneling were also evaluated within the reduced-dimensionality framework. The success of RD SCTST in this study suggests its potential applicability to larger systems.

The dynamics of the abstraction reaction of H atoms with the cyclopropane molecule is studied using quantum mechanical scattering theory. The quantum scattering calculations are performed in hyperspherical coordinates with a two-dimensional (2D) potential energy surface. The ab initio energy calculations are carried out with CCSD(T)-F12a/cc-pVTZ-F12 level of theory with the geometry and frequency calculations at the MP2/cc-pVTZ level. The contribution to the potential energy surface from the spectator modes is included as the projected zero-point energy correction to the ab initio energy. The 2D surface is fitted with a 29-parameter double Morse potential. An R-matrix propagation scheme is carried out to solve the close-coupled equations. The adiabatic energy barrier and reaction enthalpy are compared with high level computational calculations as well as experimental data. The calculated reaction rate constants shows very good agreement when compared with the experimental data, especially at lower temperature highlighting the importance of quantum tunnelling. The reaction probabilities are also presented and discussed. The special features of performing quantum dynamics calculation on the chemical reaction of a cyclic molecule are discussed.

Recently, the authors developed a new method to construct a two-dimensional potential energy surface (PES) for use in reduced-dimensionality quantum scattering calculations in chemical reactions. In this approach the minimum energy path of a reaction was utilized and the rest of the surface was fitted by a Morse function. Here we test this method on the H + HCF3 ↔ H2 + CF3 reaction. The geometry optimizations and frequency calculations are done at the MP2/cc-pVTZ level of theory, while the energies are calculated at the CCSD(T)/aug-cc-pVTZ level. An adiabatic energy barrier of 59.61 kJ mol(-1) for the forward direction is suggested by our calculations, and the reaction is endothermic by 10.55 kJ mol(-1) in the same direction. When compared to classical transition state theory, quantum scattering calculations suggest that a tunnelling effect can be observed in both forward and backward reactions. For the forward direction, the quantum tunnelling is important at temperatures typically lower than 300 K. It has a greater contribution to the backward reaction, and is over a wider temperature range from 200 K to 1000 K. We also conducted an analysis of the kinetic isotope effects on the backward reaction by replacing H2 with D2. These results also clearly demonstrate the significance of quantum tunnelling in the reaction.

Recently, von Horsten et al. suggested an efficient method to construct two dimensional potential energy surfaces (PESs) for use in quantum scattering simulations, in which they utilised the minimum energy path (MEP) and assumed harmonic behaviour of the PES near the MEP. In the same paper, the authors applied this method to various H-abstraction reactions from C1-C3 alkane molecules. In this work we demonstrate an alternative PES construction method, and apply it to the more challenging H-abstraction from n-C(4)H(10) reactions. The geometry optimizations and frequency calculations are done at the MP2/cc-pVTZ level of theory, while the energies are calculated with the CCSD(T) method with the same basis set. The calculations give adiabatic energy barrier heights of 45.9 kJ mol(-1) and 34.4 kJ mol(-1) for the primary and secondary hydrogens in n-C(4)H(10). When compared to purely classical transition state theory, quantum scattering calculations show that quantum tunnelling and zero-point effects have large contributions at low temperatures, typically below 500 K. The branching ratio study suggests that the abstraction of secondary hydrogen in n-C(4)H(10) dominates the overall reaction rate at low temperatures. The rate constants for the two abstraction channels become more comparable as the temperature increases.

We performed a quasiclassical trajectory dynamics study on a model analytical 21-dimensional (7 active atoms) potential energy surface (PES) to examine in detail the mechanism of the hydrogen absorption in a simple (NaAlH(4))(2)Ti model system. The reaction involves a capture of H(2) by the Ti centre and formation of the (η(2)-H(2))Ti(NaAlH(3))(2) coordination complex containing the side-on bonded dihydrogen ligand. The calculated rate constant corresponds to a very fast capture of H(2) by the Ti coordination sphere without a demonstrable barrier. This implies that this step is not the rate-determining step in the complex multi-step process of the NaAlH(4) recovery. The model analytical PES captures the essence of this reaction well and the corresponding energy contours compare favourably to those based on the all-atom hybrid density functional theory calculations.

We present an efficient approach to the determination of two-dimensional potential energy surfaces for use in quantum reactive scattering simulations. Our method involves first determining the minimum energy path (MEP) for the reaction by means of an ab initio intrinsic reaction coordinate calculation. This one-dimensional potential is then corrected to take into account the zero point energies of the spectator modes. These are determined from Hessians in curvilinear coordinates after projecting out the modes to be explicitly treated in quantum scattering calculations. The final (1+1)-dimensional potential is constructed by harmonic expansion about each point along the MEP before transforming the whole surface to hyperspherical coordinates for use in the two-dimensional scattering simulations. This new method is applied to H-atom abstraction from methane, ethane and propane. For the latter, both reactive channels (producing i-C(3)H(7) or n-C(3)H(7)) are investigated. For all reactions, electronic structure calculations are performed using an efficient, explicitly correlated, coupled cluster methodology (CCSD(T)-F12). Calculated thermal rate constants are compared to experimental and previous theoretical results., (© 2011 American Institute of Physics)

A reduced dimensionality quantum scattering method is extended to the study of spin-orbit nonadiabatic transitions in the CH(3) + HCl ⇌ CH(4) + Cl((2)P(J)) reaction. Three two-dimensional potential energy surfaces are developed by fitting a 29 parameter double-Morse function to CCSD(T)/IB//MP2/cc-pV(T+d)Z-dk ab initio data; interaction between surfaces is described by geometry-dependent spin-orbit coupling functions fit to MCSCF/cc-pV(T+d)Z-dk ab initio data. Spectator modes are treated adiabatically via inclusion of curvilinear projected frequencies. The total scattering wave function is expanded in a vibronic basis set and close-coupled equations are solved via R-matrix propagation. Ground state thermal rate constants for forward and reverse reactions agree well with experiment. Multi-surface reaction probabilities, integral cross sections, and initial-state selected branching ratios all highlight the importance of vibrational energy in mediating nonadiabatic transition. Electronically excited state dynamics are seen to play a small but significant role as consistent with experimental conclusions., (© 2011 American Institute of Physics)

We present quantum dynamical investigations into the F + CHD(3) reaction. In our reduced dimensionality study we treat the two most important degrees of freedom, which describe the bond making and bond breaking explicitly, while treating the remaining spectator modes adiabatically. Cumulative as well as final state resolved reaction probabilities and cross sections are calculated for the two isotopic channels F + CHD(3) → FH + CD(3) and F + CHD(3) → FD + CHD(2). Our theoretical results are compared to the experimental findings of Liu and co-workers [Zhou et al., Mol. Phys., 2010, 108, 957]. Potential resonance states in the low collision energy regime are analyzed in detail employing Smith's lifetime matrix and bound state calculations.

On the basis of density functional theory and coupled-cluster CCSD(T) calculations we propose a mechanism of the dehydrogenation of transition metal doped sodium alanate. Insertion of two early 3d-transition metals, scandium and titanium, both of which are promising catalysts for reversible hydrogen storage in light metal hydrides, is compared. The mechanism is deduced from studies on the decomposition of a model system consisting of one transition metal atom and two NaAlH(4) units. Subsequently, the significance of such minimal cluster model systems to the real materials is tested by embedding the systems into the surface of the NaAlH(4) crystal. It is found that the dehydrogenation proceeds via breaking of the bridge H-Al bond and consequent formation of intermediate coordination compounds in which the H(2) molecule is side-on (eta(2)-) bonded to the transition metal centre. The total barrier to the H(2) release is thus dependent upon both the strength of the Al-H bond to be broken and the depth of the coordinative potential. The analogous mechanism applies for the recognized three successive dehydrogenation steps. The gas-phase model structures embedded into the surface of the NaAlH(4) crystal exhibit an unambiguous kinetic stability and their general geometric features remain largely unchanged.

A method for projecting chemical reaction surface coordinates from a Hessian in curvilinear internal coordinates has recently been developed. Here we introduce a modification to this approach which allows for analytical evaluation of the necessary coordinate derivatives, thus reducing the number of ab initio calculations required. We apply this method to the determination of spectator mode frequencies and zero-point energies for the series of hydrogen abstraction reactions X + CH(4) --> XH + CH(3), X = muonium (mu), H, D, CH(3). Comparison of these frequencies with those obtained using rectilinear coordinates allows us to examine how the mass of X affects the coordinate sensitivity of the spectator modes. We carry out two-dimensional quantum reactive scattering calculations for these reactions to highlight instances where the choice of coordinates may have a significant impact on the evaluated thermal rate constants.

The symmetric title reaction CH(3) + CH(4) --> CH(4) + CH(3) is studied using quantum scattering theory. Quantum dynamics calculations are performed in hyperspherical coordinates with a two-dimensional effective potential energy surface consisting of an analytical 18-parameter double Morse function fit to ab initio data at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level of theory. Spectator modes are treated adiabatically by inclusion of projected zero-point energy corrections in the effective potential. The close-coupled equations are solved via R-matrix propagation. Energy and J-shifted thermal rate constants are compared to experimental data and highlight the importance of quantum tunneling. Oscillating reactivity and metastable bound state resonances are observed in the cumulative and state-to-state reaction probabilities. State-to-state differential and initial state-selected integral cross sections are presented and discussed. Primary and secondary kinetic isotope effects for two symmetric deuterated variants of the title reaction are also presented.

We consider the general problem of vibrational analysis at nonglobally optimized points on a reduced dimensional reaction surface. We discuss the importance of the use of curvilinear internal coordinates to describe molecular motion and derive a curvilinear projection operator to remove the contribution of nonzero gradients from the Hessian matrix. Our projection scheme is tested in the context of a two-dimensional quantum scattering calculation for the reaction H + CH(4) --> H(2) + CH(3) and its reverse H(2) + CH(3) --> H + CH(4). Using zero-point energies calculated via rectilinear and curvilinear projections we construct two two-dimensional, adiabatically corrected, ab initio reaction surfaces for this system. It is shown that the use of curvilinear coordinates removes unphysical imaginary frequencies observed with rectilinear projection and leads to significantly improved thermal rate constants for both the forward and reverse reactions.

This perspective discusses progress in the theory of bimolecular reaction dynamics in the gas phase. The examples selected show that definitive quantum dynamical computations are providing insights into the detailed mechanisms of chemical reactions.

We present a new application for the Torsional Path Integral Monte Carlo (TPIMC) method in which the TPI partition functions are introduced into the calculation of Transition State Theory (TST) rate constants. In this way, an explicit treatment of torsional anharmonicity is included in the TST calculations and the magnitude of these effects can be assessed. The new method is tested on the C(2)H(6) + H hydrogen abstraction reaction and concerted hydrogen transfer in the carbonic acid dimer, for which we have developed torsional potential energy surfaces. For the C(2)H(6) + H reaction the rate constants are halved at room temperature on including a treatment of torsional anharmonicity, while the effects are found to be much smaller for the hydrogen transfer reaction in the carbonic acid dimer.