An Efficient Computational Approach for the Calculation of the Vibrational Density of States

A time averaged semiclassical approach to IR spectroscopy

We propose a new semiclassical approach to the calculation of molecular IR spectra. The method employs the time averaging technique of Kaledin and Miller upon symmetrization of the quantum dipole-dipole autocorrelation function. Spectra at high and low temperatures are investigated. In the first case, we are able to point out the possible presence of hot bands in the molecular absorption line shape. In the second case, we are able to reproduce accurate IR spectra as demonstrated by a calculation of the IR spectrum of the water molecule, which is within 4% of the exact intensity. Our time averaged IR spectra can be directly compared to time averaged semiclassical power spectra as shown in an application to the CO2 molecule, which points out the differences between IR and power spectra and demonstrates that our new approach can identify active IR transitions correctly. Overall, the method features excellent accuracy in calculating absorption intensities and provides estimates for the frequencies of vibrations in agreement with the corresponding power spectra. In perspective, this work opens up the possibility to interface the new method with the semiclassical techniques developed for power spectra, such as the divide-and-conquer one, to get accurate IR spectra of complex and high-dimensional molecular systems.

Coupled Cluster Semiclassical Estimates of Experimental Reaction Rates: The Interconversion of Glycine Conformer VIp to Ip

We apply the full-dimensional Semiclassical Transition State Theory (SCTST) to estimate the rate constant of glycine molecule interconversion between the VIp and Ip conformers. We have reached an electronic structure accuracy up to the explicitly correlated Coupled Cluster method (CCSD(T)-F12b/cc-pVDZ-F12) thanks to our parallel implementation. The reaction has been experimentally investigated in the literature and is known to proceed by quantum mechanical tunneling. The SCTST rates improve over other theoretical methods, and our results align with the experimental measurements, thus confirming the accuracy of the fully coupled anharmonic semiclassical tunneling treatment, providing that the level of electronic structure theory gives a reliable estimate of the reaction barrier height and shape. The comparison with experimental half-life times supports the validity of SCTST for glycine VIp-Ip conformer conversion in the cryogenic temperature range, where this theory is usually not considered applicable due to the onset of the deep tunneling regime.

Defining the temperature of an isolated molecule

The microcanonical temperature of an isolated molecule is derived in terms of Boltzmann and Gibbs volume entropies within the quantum harmonic vibrational and equivalent degenerated model approximations. The effects of the entropy functional choice and various approximations are examined. The difference between Boltzmann and Gibbs volume temperatures is negligible for molecules bigger than ten atoms. However, it is significant for smaller systems, opening a way to probe them experimentally. A simple, analytical expression of the temperature as a function of the vibrational energy is provided, allowing predictions with a ±3% margin of error compared to the exact harmonic estimate. The microcanonical temperature is discussed and exemplified with polycyclic aromatic hydrocarbon molecules and other molecules of astrophysical interest.

Heavy Atom Tunneling in Organic Reactions at Coupled Cluster Potential Accuracy with a Parallel Implementation of Anharmonic Constant Calculations and Semiclassical Transition State Theory

We describe and test on some organic reactions a parallel implementation strategy to compute anharmonic constants, which are employed in semiclassical transition state theory reaction rate calculations. Our software can interface with any quantum chemistry code capable of a single point energy estimate, and it is suitable for both minimum and transition state geometry calculations. After testing the accuracy and comparing the efficiency of our implementation against other software, we use it to estimate the semiclassical transition state theory (SCTST) rate constant of three reactions of increasing dimensionality, known as examples of heavy atom tunneling. We show how our method is improved in efficiency with respect to other existing implementations. In conclusion, our approach allows SCTST rates and heavy atom tunneling at a high level of electronic structure theory (up to CCSD(T)) to be evaluated. This work shows how crucial the possibility to perform high level ab initio rate evaluations can be.

Ab Initio Calculation of Surface Thermochemistry for Popular Solid Transition Metal-Based Species

This work reports the thermochemistry calculations for solid-phase periodic models of ten popular transition metal-based species. These model structures were refined to stable geometry by geometric optimization along with calculating the thermodynamic properties including enthalpy, entropy, heat capacity at constant pressure, and Gibbs free energy by DMol3 package via first-principles ab initio calculations. The temperature-dependent thermochemistry values were converted to a NASA seven-polynomial format. The behavior of different thermodynamic parameters based on temperature was investigated and their comparative analysis was done. A higher number of atoms tends to show higher thermodynamic values. Moreover, these thermodynamic values agree reasonably well with previously reported experimental and computational values. Metal copper shows higher thermodynamic values as compared to its oxide. The thermodynamic properties of lanthanum-based oxides have been newly calculated through the ab initio method. Amorphous structures reveal higher thermodynamic values compared to their crystalline counterparts. A comparison between different transition metal-based species gives a better understanding of the different crystalline structures and their surface sites. These calculated thermodynamic data and polynomials can be used for a variety of thermodynamic calculations and kinetic modeling.

Modeling Gas-Phase Unimolecular Dissociation for Bond Dissociation Energies: Comparison of Statistical Rate Models within RRKM Theory

The Rice-Ramsperger-Kassel-Marcus (RRKM) theory provides a simple yet powerful rate theory for calculating microcanonical rate constants. In particular, it has found widespread use in combination with gas-phase kinetic experiments of unimolecular dissociations to extract experimental bond dissociation energies (BDEs). We have previously found several discrepancies between the computed BDE values and the respective experimental ones, obtained with our empirical rate model, named L-CID. To investigate the reliability of our rate model, we conducted a theoretical analysis and comparison of the performance of conventional rate models and L-CID within the RRKM framework. Using the previously published microcanonical rate data as well as reaction cross-section data, we show that the BDE values obtained with the L-CID model agree with the ones from the other rate models within the expected uncertainty bounds. Based on this agreement, we discuss the possible rationalization of the good performance of the L-CID model.

Nuclear Quantum Effects from the Analysis of Smoothed Trajectories: Pilot Study for Water

Nuclear quantum effects have significant contributions to thermodynamic quantities and structural properties; furthermore, very expensive methods are necessary for their accurate computation. In most calculations, these effects, for instance, zero-point energies, are simply neglected or only taken into account within the quantum harmonic oscillator approximation. Herein, we present a new method, Generalized Smoothed Trajectory Analysis, to determine nuclear quantum effects from molecular dynamics simulations. The broad applicability is demonstrated with the examples of a harmonic oscillator and different states of water. Ab initio molecular dynamics simulations have been performed for ideal gas up to the temperature of 5000 K. Classical molecular dynamics have been carried out for hexagonal ice, liquid water, and vapor at atmospheric pressure. With respect to the experimental heat capacity, our method outperforms previous calculations in the literature in a wide temperature range at lower computational cost than other alternatives. Dynamic and structural nuclear quantum effects of water are also discussed.

Calculations on the unimolecular decomposition of the nerve agent VX

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.

Improved semiclassical dynamics through adiabatic switching trajectory sampling

We introduce an improved semiclassical dynamics approach to quantum vibrational spectroscopy. In this method, a harmonic-based phase space sampling is preliminarily driven toward non-harmonic quantization by slowly switching on the actual potential. The new coordinates and momenta serve as initial conditions for the semiclassical dynamics calculation, leading to a substantial decrease in the number of chaotic trajectories to deal with. Applications are presented for model and molecular systems of increasing dimensionality characterized by moderate or high chaoticity. They include a bidimensional Henon-Heiles potential, water, formaldehyde, and methane. The method improves accuracy and precision of semiclassical results and it can be easily interfaced with all pre-existing semiclassical theories.

Parallel Implementation of Semiclassical Transition State Theory

This paper presents the parsctst code, an efficient parallel implementation of the semiclassical transition state theory (SCTST) for reaction rate constant calculations. Parsctst is developed starting from a previously presented approach for the computation of the vibrational density of states of fully coupled anharmonic molecules ( Nguyen et al. Chem. Phys. Lett. 2010 , 499 , 915 ). The parallel implementation makes it practical to tackle reactions involving more than 100 fully coupled anharmonic vibrational degrees of freedom and also includes multidimensional tunneling effects. After describing the pseudocode and demonstrating its computational efficiency, we apply the new code for estimating the rate constant of the proton transfer isomerization reaction of the 2,4,6-tri- tert-butylphenyl to 3,5-di- tert-butylneophyl. Comparison with both theoretical and experimental results is presented. Parsctst code is user-friendly and provides a significant computational time saving compared to serial calculations. We believe that parsctst can boost the application of SCTST as an alternative to the basic transition state theory for accurate kinetics modeling not only in combustion or atmospheric chemistry, but also in organic synthesis, where bigger reactive systems are encountered.

Application of one-dimensional semiclassical transition state theory to the CH3OH + H ⇌ CH2OH/CH3O + H2 reactions

The rate constants of the two branches of H-abstractions from CH₃OH 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 CH₃OH and CH₂OH, 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'.

Kinetic and mechanistic study on gas phase reactions of ozone with a series ofcis-3-hexenyl esters

Reaction kinetics of O₃with fourcis-3-hexenyl esters were studied using experimental methods in a flow tube reactor as well as using theoretical methods.

Catalysis and tunnelling in the unimolecular decay of Criegee intermediates

Semi-classical Transition State theory can be applied to catalysed atmospheric reactions, but reaction mode anharmonicity must be treated carefully.

State-of-the-Art Thermochemical and Kinetic Computations for Astrochemical Complex Organic Molecules: Formamide Formation in Cold Interstellar Clouds as a Case Study

We describe an integrated computational strategy aimed at providing reliable thermochemical and kinetic information on the formation processes of astrochemical complex organic molecules. The approach involves state-of-the-art quantum-mechanical computations, second-order vibrational perturbation theory, and kinetic models based on capture and transition state theory together with the master equation approach. Notably, tunneling, quantum reflection, and leading anharmonic contributions are accounted for in our model. Formamide has been selected as a case study in view of its interest as a precursor in the abiotic amino acid synthesis. After validation of the level of theory chosen for describing the potential energy surface, we have investigated several pathways of the OH + CH2NH and NH2 + H2CO reaction channels. Our results show that both reaction channels are essentially barrierless (in the sense that all relevant transition states lie below or only marginally above the reactants) and once tunneling is taken into the proper account indicate that the reaction can occur under the low temperature conditions of interstellar environments.