Accurate treatment of two-dimensional non-separable hindered internal rotors

The following article appeared in The Journal of Chemical Physics 138, 134112 (2013) and may be found at https://doi.org/10.1063/1.4798407This work presents an accurate way for calculating partition functions of strongly coupled hindered rotors in two dimensions. The two-dimensional torsional potential is generated from electronic structure calculations and fitted to Fourier series. The kinetic energy includes off-diagonal terms which are allowed to vary with the torsional angles, and these terms were also fitted to Fourier series. The resulting Hamiltonian leads to a coupled Schrödinger equation which was solved by the variational method. Therefore, the final two-dimensional non-separable (2D-NS) partition function incorporates coupling terms in both the kinetic and the potential energy. The methodology has been tested for propane, methyl formate, and a hydrogen abstraction transition state from propanone by the OH radical. How to incorporate the 2D-NS partition function in the total vibrational-rotational partition function is also discussedThis work was partially financed by Xunta de Galicia through Grant No. 2012/314 para a consolidación e a estruturación de unidades de investigación competitivas do Sistema Universitario de Galicia, 2012S

Correct Interpretation of How Tunneling Proceeds at Low Temperatures in the Proton Transfer Reactions Involving Thiotropolone: A Comment

This is the peer reviewed version of the following article: Fernández-Ramos, A. (2013). Correct Interpretation of How Tunneling Proceeds at Low Temperatures in the Proton Transfer Reactions Involving Thiotropolone: A Comment. Angewandte Chemie International Edition, 52(32), 8204-8205. doi: 10.1002/anie.201303206, which has been published in final form at https://doi.org/10.1002/anie.201303206. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsThe correct interpretation is provided of how tunneling proceeds at low temperatures in the proton transfer Reactions (1) and (3) involving thiotropolone and tropolone (see the Arrhenius plots). It is also shown that the variational transition‐state theory calculations carried out by Jose and Datta (Angew. Chem.­ 2012, 124, 9523; Angew. Chem. Int. Ed.­ 2012, 51, 9389), as well as their conclusions regarding these two processes are erroneousS

Positive solutions for some indefinite nonlinear eigenvalue elliptic problems with Robin boundary conditions

We consider a nonlinear eigenvalue problem with indefinite weight under Robin boundary condition. We prove the existence and multiplicity of positive solutions. To this end, we carry out a detailed study of some linear eigenvalues problems and we use mainly bifurcation and sub-supersolution methods.Ministerio de Economía y CompetitividadFondo Nacional de Desarrollo Científico y Tecnológico (Comisión Nacional de Investigación Científica y Tecnológica) (Chile

Accounting for conformational flexibility and torsional anharmonicity in the H + CH3CH2OH hydrogen abstraction reactions: A multi-path variational transition state theory study

This work reports a detailed theoretical study of the hydrogen abstraction reactions from ethanol by atomic hydrogen. The calculated thermal rate constants take into account torsional anharmonicity and conformational flexibility, in addition to the variational and tunneling effects. Specifically, the kinetics calculations were performed by using multi-path canonical variational transition state theory with least-action path tunneling corrections, to which we have added the two-dimensional non-separable method to take into account torsional anharmonicity. The multi-path thermal rate constant is expressed as a sum over conformational reaction channels. Each of these channels includes all the transition states that can be reached by internal rotations. The results show that, in the interval of temperatures between 250 and 2500 K, the account for multiple paths leads to higher thermal rate constants with respect to the single path approach, mainly at low and at high temperatures. In addition, torsional anharmonicity enhances the slope of the Arrhenius plot in this range of temperatures. Finally, we show that the incorporation of tunneling into the hydrogen abstraction reactions substantially changes the contribution of each of the transition states to the conformational reaction channelThe following article appeared in The Journal of Chemical Physics 140, 174303 (2014) and may be found at https://doi.org/10.1063/1.4873350S

A Combined Systematic-Stochastic Algorithm for the Conformational Search in Flexible Acyclic Molecules

We propose an algorithm that is a combination of systematic variation of the torsions and Monte Carlo (or stochastic) search. It starts with a trial geometry in internal coordinates and with a set of preconditioned torsional angles, i.e., torsional angles at which minima are expected according to the chemical knowledge. Firstly, the optimization of those preconditioned geometries is carried out at a low electronic structure level, generating an initial set of conformers. Secondly, random points in the torsional space are generated outside the “area of influence” of the previously optimized minima (i.e., outside a hypercube about each minima). These random points are used to build the trial structure, which is optimized by an electronic structure software. The optimized structure may correspond to a new conformer (which would be stored) or to an already existing one. Initial torsional angles (and also final ones if a new conformer is found) are stored to prevent visiting the same region of the torsional space twice. The stochastic search can be repeated as many times as desired. Finally, the low-level geometries are recovered and used as the starting point for the high-level optimizations. The algorithm has been employed in the calculation of multi-structural quasi harmonic and multi-structural torsional anharmonic partition functions for a series of alcohols ranging from n-propanol to n-heptanol. It was also tested for the amino acid L-serineFinancial support from the Consellería de Cultura, Educación e Ordenación Universitaria (Axuda para Consolidación e Estructuración de unidades de investigación competitivas do Sistema Universitario de Galicia, Xunta de Galicia ED431C 2017/17 & Centro singular de investigación de Galicia acreditación 2016-2019, ED431G/09) and the European Regional Development Fund (ERDF) is gratefully acknowledgedS

New computational tools for chemical kinetics: the Cathedral Package

The advent of recent technological developments in software engineering has enabled the exploration of reaction mechanisms inside intricate reaction networks, thereby propelling the beginning of a new era in ab initio kinetics. While it is feasible to consider a substantial number of reactions, determining their rate constants with precision remains an arduous task, even for gas-phase processes. The difficulties are attributed not only to the inherent limitations in the calculation methodology but also to the manual labor and extensive chemical dynamics required, rendering these calculations inaccessible to the general public. As such, there is a pressing need for the development of automated codes and user-friendly interfaces to address this limitation. The present work focuses on the introduction of the Cathedral package, a unified computational code comprising the Q2DTor, TorsiFlex, and Pilgrim programs. This package serves to bridge the gap between theoretical studies in chemical kinetics and non-specialist users, making it more accessible and user-friendlyThe authors thank “Centro de Supercomputación de Galicia” (CESGA) for the use of their computational facilities. This work was partially supported by the Consellería de Cultura, Educación e Ordenación Universitaria (Centro singular de investigación de Galicia acreditación 2019-2022, ED431G 2019/03 and Grupo de referencia competitiva ED431C 2021/40) and the European Regional Development Fund (ERDF), and the Ministerio de Ciencia e Innovación through Grant PID2019-107307RB-I00. D.F.-C. thanks Xunta de Galicia for fnancial support through a postdoctoral grantS

Tunneling and Conformational Flexibility Play Critical Roles in the Isomerization Mechanism of Vitamin D

The thermal isomerization reaction converting previtamin D to vitamin D is an intramolecular [1,7]-sigmatropic hydrogen shift with antarafacial stereochemistry. We have studied the dynamics of this reaction by means of the variational transition-state theory with multidimensional corrections for tunneling in both gas-phase and n-hexane environments. Two issues that may have important effects on the dynamics were analyzed in depth, i.e., the conformations of previtamin D and the quantum effects associated with the hydrogen-transfer reaction. Of the large number of conformers of previtamin D that were located, there are 16 that have the right disposition to react. The transition-state structures associated with these reaction paths are very close in energy, so all of them should be taken into account for an accurate calculation of both the thermal rate constants and the kinetic isotope effects. This issue is particularly important because the contribution of each of the reaction paths to the total thermal rate constant is quite sensitive to the environment. The dynamics results confirm that tunneling plays an important role and that model systems that were considered previously to study the hydrogen shift reaction cannot mimic the complexity introduced by the flexibility of the rings of previtamin D. Finally, the characterization of the conformers of both previtamin D and vitamin D allowed the calculation of the thermal equilibrium constants of the isomerization processS

Calculation of the two-dimensional non-separable partition function for two molecular systems

This is a post-peer-review, pre-copyedit version of an article published in Journal of Molecular Modeling. The final authenticated version is available online at: https://doi.org/10.1007/s00894-014-2190-zWe present the application of an accurate quantum treatment, called two-dimensional non-separable (2D-NS), to the calculation of internal rotation partition functions of molecules with two rotors. This methodology involves full coupling in the kinetic and potential energies; the later is written as a Fourier series type potential. The resulting Hamiltonian is introduced in the Schrödinger equation and solved by the variational method. The method was applied to the 2-propenol and to the 3-fluoro-2-propenol molecular systems. The former molecule presents weak coupling between the torsion, whereas the later is an example of strong coupling. The comparison of 2D-NS with one-dimensional accurate models that involve separation of the two torsions, indicate that a separable model is inadequate to study systems in the strong coupling regime. The results indicate that for the case of strong coupling the multi-conformer harmonic approximation gives better results than a separable anharmonic modelS

The rainbow instanton method: A new approach to tunneling splitting in polyatomics

The following article appeared in The Journal of Chemical Physics 137, 224105 (2012) and may be found at https://doi.org/10.1063/1.4769198A new instanton approach is reported to tunneling at zero-temperature in multidimensional (MD) systems in which a “light particle” is transferred between two equivalent “heavy” sites. The method is based on two concepts. The first is that an adequate MD potential energy surface can be generated from input of the stationary configurations only, by choosing as a basis the normal modes of the transition state. It takes the form of a double-minimum potential along the mode with imaginary frequency and coupling terms to the remaining (harmonic) oscillators. Standard integrating out of the oscillators gives rise to an effective 1D instanton problem for the adiabatic potential, but requires evaluation of a nonlocal term in the Euclidean action, governed by exponential (memory) kernels. The second concept is that this nonlocal action can be treated as a “perturbation,” for which a new approximate instanton solution is derived, termed the “rainbow” solution. Key to the approach is avoidance of approximations to the exponential kernels, which is made possible by a remarkable conversion property of the rainbow solution. This leads to a new approximation scheme for direct evaluation of the Euclidean action, which avoids the time-consuming search of the exact instanton trajectory. This “rainbow approximation” can handle coupling to modes that cover a wide range of frequencies and bridge the gap between the adiabatic and sudden approximations. It suffers far fewer restrictions than these conventional approximations and is proving particularly effective for systems with strong coupling, such as proton transfer in hydrogen bonds. Comparison with the known exact instanton action in two-dimensional models and application to zero-level tunneling splittings in two isotopomers of malonaldehyde are presented to show the accuracy and efficiency of the approachS

Ab initio investigation of the H2O2 + F elementary reaction

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