"Transitivity": A Code for Computing Kinetic and Related Parameters in Chemical Transformations and Transport Phenomena.

The Transitivity function, defined in terms of the reciprocal of the apparent activation energy, measures the propensity for a reaction to proceed and can provide a tool for implementing phenomenological kinetic models. Applications to systems which deviate from the Arrhenius law at low temperature encouraged the development of a user-friendly graphical interface for estimating the kinetic and thermodynamic parameters of physical and chemical processes. Here, we document the Transitivity code, written in Python, a free open-source code compatible with Windows, Linux and macOS platforms. Procedures are made available to evaluate the phenomenology of the temperature dependence of rate constants for processes from the Arrhenius and Transitivity plots. Reaction rate constants can be calculated by the traditional Transition-State Theory using a set of one-dimensional tunneling corrections (Bell (1935), Bell (1958), Skodje and Truhlar and, in particular, the deformed ( d -TST) approach). To account for the solvent effect on reaction rate constant, implementation is given of the Kramers and of Collins-Kimball formulations. An input file generator is provided to run various molecular dynamics approaches in CPMD code. Examples are worked out and made available for testing. The novelty of this code is its general scope and particular exploit of d -formulations to cope with non-Arrhenius behavior at low temperatures, a topic which is the focus of recent intense investigations. We expect that this code serves as a quick and practical tool for data documentation from electronic structure calculations: It presents a very intuitive graphical interface which we believe to provide an excellent working tool for researchers and as courseware to teach statistical thermodynamics, thermochemistry, kinetics, and related areas.

Deformed transition-state theory: Deviation from Arrhenius behavior and application to bimolecular hydrogen transfer reaction rates in the tunneling regime.

A formulation is presented for the application of tools from quantum chemistry and transition-state theory to phenomenologically cover cases where reaction rates deviate from Arrhenius law at low temperatures. A parameter d is introduced to describe the deviation for the systems from reaching the thermodynamic limit and is identified as the linearizing coefficient in the dependence of the inverse activation energy with inverse temperature. Its physical meaning is given and when deviation can be ascribed to quantum mechanical tunneling its value is calculated explicitly. Here, a new derivation is given of the previously established relationship of the parameter d with features of the barrier in the potential energy surface. The proposed variant of transition state theory permits comparison with experiments and tests against alternative formulations. Prescriptions are provided and implemented to three hydrogen transfer reactions: CH4 + OH → CH3 + H2 O, CH3 Cl + OH → CH2 Cl + H2 O and H2 + CN → H + HCN, widely investigated both experimentally and theoretically. © 2016 Wiley Periodicals, Inc.

Stereodirectional Origin of anti-Arrhenius Kinetics for a Tetraatomic Hydrogen Exchange Reaction: Born-Oppenheimer Molecular Dynamics for OH + HBr.

Among four-atom processes, the reaction OH + HBr → H2O + Br is one of the most studied experimentally: its kinetics has manifested an unusual anti-Arrhenius behavior, namely, a marked decrease of the rate constant as the temperature increases, which has intrigued theoreticians for a long time. Recently, salient features of the potential energy surface have been characterized and most kinetic aspects can be considered as satisfactorily reproduced by classical trajectory simulations. Motivation of the work reported in this paper is the investigation of the stereodirectional dynamics of this reaction as the prominent reason for the peculiar kinetics: we started in a previous Letter ( J. Phys. Chem. Lett. 2015 , 6 , 1553 - 1558 ) a first-principles Born-Oppenheimer "canonical" molecular dynamics approach. Trajectories are step-by-step generated on a potential energy surface quantum mechanically calculated on-the-fly and are thermostatically equilibrated to correspond to a specific temperature. Here, refinements of the method permitted a major increase of the number of trajectories and the consideration of four temperatures -50, +200, +350, and +500 K, for which the sampling of initial conditions allowed us to characterize the stereodynamical effect. The role is documented of the adjustment of the reactants' mutual orientation to encounter the entrance into the "cone of acceptance" for reactivity. The aperture angle of this cone is dictated by a range of directions of approach compatible with the formation of the specific HOH angle of the product water molecule; and consistently the adjustment is progressively less effective the higher the kinetic energy. Qualitatively, this emerging picture corroborates experiments on this reaction, involving collisions of aligned and oriented molecular beams, and covering a range of energies higher than the thermal ones. The extraction of thermal rate constants from this molecular dynamics approach is discussed and the systematic sampling of the canonical ensemble is indicated as needed for quantitative comparison with the kinetic experiments.

Stereodynamical Origin of Anti-Arrhenius Kinetics: Negative Activation Energy and Roaming for a Four-Atom Reaction.

The OH + HBr → H2O + Br reaction, prototypical of halogen-atom liberating processes relevant to mechanisms for atmospheric ozone destruction, attracted frequent attention of experimental chemical kinetics: the nature of the unusual reactivity drop from low to high temperatures eluded a variety of theoretical efforts, ranking this one among the most studied four-atom reactions. Here, inspired by oriented molecular-beams experiments, we develop a first-principles stereodynamical approach. Thermalized sets of trajectories, evolving on a multidimensional potential energy surface quantum mechanically generated on-the-fly, provide a map of most visited regions at each temperature. Visualizations of rearrangements of bonds along trajectories and of the role of specific angles of reactants' mutual approach elucidate the mechanistic change from the low kinetic energy regime (where incident reactants reorient to find the propitious alignment leading to reaction) to high temperature (where speed hinders adjustment of directionality and roaming delays reactivity).

An alternative interpretation of the ultracold methylhydroxycarbene rearrangement mechanism: cooperative effects.

Recent studies have reported surprising results related to the rearrangement of carbenes under ultracold conditions, making use of sophisticated models of quantum tunnelling to explain the observed phenomena. Here, we demonstrate that a methylhydroxycarbene (H3C-C-OH) rearrangement is possible by making changes in molecularity (i.e., through cooperative effects), owing to intermolecular hydrogen bond/H-transfer. The model used for accomplishing these changes in molecularity suggests the occurrence of two chemical species during the rearrangement and preferential formation of acetaldehyde. We propose an alternative interpretation for the methylhydroxycarbene rearrangement, as well as for a bimolecular isomerization mechanism for acetaldehyde formation with an activation barrier, Ea, of +0.25 kcal mol(-1), relative to 1a' (−8.06 kcal mol(-1) relative to 1a); this barrier is lower than that required by H-tunnelling as proposed by Schreiner et al. We also note that the mechanism for obtaining vinyl alcohol leads to the simultaneous formation of acetaldehyde through an Ea of +13.53 kcal mol(-1), relative to 1a (+0.93 kcal mol(-1) relative to 1b), again confirming the predominant presence of acetaldehyde.

Alternative approach to calculate two-center overlap matrix through deformed exponential function.

In this work, we propose an alternative approach to evaluate two-center overlap integrals. It is computationally more efficient than the standard procedure and is based on the deformed exponential function. In the new procedure, the CPU time to calculate each element of the overlap matrix (Sµ,ν) is constant and independent of the number of Gaussian primitives (NG), whereas in the usual procedure this time increases, formally, with NG2. To evaluate the accuracy of the proposed methodology, we computed different molecular properties such as dipole moments, hardness values, atomic charges, multicenter bond indices, group indices, and some thermodynamic properties. In this work, all calculations were performed using a minimal STO-6G basis set and WTBS and the double-ζ Pople split-valence 6-31G basis set on the Hartree­Fock (HF) and post-HF approximations. The integrals were parametrized for the atoms of the first two rows of the periodic table. All calculations were performed in the general ab initio quantum chemistry package GAMESS, where the integrals were implemented.

Fully relativistic rovibrational energies and spectroscopic constants of the lowest X:(1)0(+)g, A':(1)2( u ), A:(1)1 ( u ), B':(1)0(-)u and B:(1)0(+)u states of molecular chlorine.

The main goal of this paper is to present the rovibrational energies and spectroscopic constants of the Cl(2) molecular system in the relativistic states [Formula: see text], A':(1)2( u ), A:(1)1( u ), [Formula: see text] and [Formula: see text]. More precisely, we have evaluated the Cl(2) ω ( e ), ω ( e ) x ( e ), ω ( e ) y ( e ), α ( e ), γ ( e ) and B ( e ) rovibrational spectroscopic constants using two different procedures. The first was obtained by combining the rovibrational energies, calculated through solving Schrödinger's nuclear equation and the diatomic rovibrational energy equation. The second was obtained by using the Dunham method. The calculated properties are in good agreement with available experimental data.

Performance and parameterization of the algorithm Simplified Generalized Simulated Annealing

The main goal of this study is to find the most effective set of parameters for the Simplified Generalized Simulated Annealing algorithm, SGSA, when applied to distinct cost function as well as to find a possible correlation between the values of these parameters sets and some topological characteristics of the hypersurface of the respective cost function. The SGSA algorithm is an extended and simplified derivative of the GSA algorithm, a Markovian stochastic process based on Tsallis statistics that has been used in many classes of problems, in particular, in biological molecular systems optimization. In all but one of the studied cost functions, the global minimum was found in 100 percent of the 50 runs. For these functions the best visiting parameter, qV, belongs to the interval [1.2, 1.7]. Also, the temperature decaying parameter, qT, should be increased when better precision is required. Moreover, the similarity in the locus of optimal parameter sets observed in some functions indicates that possibly one could extract topological information about the cost functions from these sets.