Zero-point Vibrational Energy Research Articles

The Symmetric Exchange Reaction OH + H2O → H2O + OH: Convergent Quantum Mechanical Predictions.

The symmetric hydrogen exchange reaction OH + H2O → H2O + OH has been studied using the "gold standard" CCSD(T) method with the correlation-consistent basis sets up to aug-cc-pV5Z. The CCSDT and CCSDT(Q) methods were used for the final energic predictions. Two entrance complexes and two transition states on the H3O2 potential surface were located. The vibrational frequencies and the zero-point vibrational energies of these stationary points for the reaction are reported. The entrance complex H2O···HO is predicted to lie 3.7 kcal mol-1 below the separated reactants, whereas the second complex HOH···OH lies only 2.1 kcal mol-1 below the separated reactants. The classical barrier height for the title reaction is predicted to be 8.4 kcal mol-1, and the transition state between the two complexes is only slightly higher than the second complex. We estimate a reliability of ±0.2 kcal mol-1 for these predictions. The capabilities of different density functional theory methods is also tested for this reaction.

Investigating the ground-state rotamers of n-propylperoxy radical.

The n-propylperoxy radical has been described as a molecule of critical importance to studies of low temperature combustion. Ab initio methods were used to study this three-carbon alkylperoxy radical, normal propylperoxy. Reliable CCSD(T) (coupled-cluster theory, incorporating single, double, and perturbative triple)/ANO0 geometries were predicted for the molecule's five rotamers. For each rotamer, energetic predictions were made using basis sets as large as the cc-pV5Z in conjunction with coupled cluster levels of theory up to CCSDT(Q). Along with the extrapolations, corrections for relativistic effects, zero-point vibrational energies, and diagonal Born-Oppenheimer corrections were used to further refine energies. The results indicate that the lowest conformer is the gauche-gauche (GG) rotamer followed by the gauche-trans (0.12 kcal mol-1 above GG), trans-gauche (0.44 kcal mol-1), gauche'-gauche (0.47 kcal mol-1), and trans-trans (0.57 kcal mol-1). Fundamental vibrational frequencies were obtained using second-order vibrational perturbation theory. This is the first time anharmonic frequencies have been computed for this system. The most intense IR features include all but one of the C-H stretches. The O-O fundamental (1063 cm-1 for the GG structure) also has a significant IR intensity, 19.6 km mol-1. The anharmonicity effects on the potential energy surface were also used to compute vibrationally averaged rg,0K bond lengths, accounting for zero-point vibrations present within the molecule.

Communication: Understanding molecular representations in machine learning: The role of uniqueness and target similarity.

The predictive accuracy of Machine Learning (ML) models of molecular properties depends on the choice of the molecular representation. Inspired by the postulates of quantum mechanics, we introduce a hierarchy of representations which meet uniqueness and target similarity criteria. To systematically control target similarity, we simply rely on interatomic many body expansions, as implemented in universal force-fields, including Bonding, Angular (BA), and higher order terms. Addition of higher order contributions systematically increases similarity to the true potential energy and predictive accuracy of the resulting ML models. We report numerical evidence for the performance of BAML models trained on molecular properties pre-calculated at electron-correlated and density functional theory level of theory for thousands of small organic molecules. Properties studied include enthalpies and free energies of atomization, heat capacity, zero-point vibrational energies, dipole-moment, polarizability, HOMO/LUMO energies and gap, ionization potential, electron affinity, and electronic excitations. After training, BAML predicts energies or electronic properties of out-of-sample molecules with unprecedented accuracy and speed.

Computational thermochemistry: Automated generation of scale factors for vibrational frequencies calculated by electronic structure model chemistries

We present a Python program, FREQ, for calculating the optimal scale factors for calculating harmonic vibrational frequencies, fundamental vibrational frequencies, and zero-point vibrational energies from electronic structure calculations. The program utilizes a previously published scale factor optimization model (Alecu et al., 2010) to efficiently obtain all three scale factors from a set of computed vibrational harmonic frequencies. In order to obtain the three scale factors, the user only needs to provide zero-point energies of 15 or 6 selected molecules. If the user has access to the Gaussian 09 or Gaussian 03 program, we provide the option for the user to run the program by entering the keywords for a certain method and basis set in the Gaussian 09 or Gaussian 03 program. Four other Python programs, input.py, input6, pbs.py, and pbs6.py, are also provided for generating Gaussian 09 or Gaussian 03 input and PBS files. The program can also be used with data from any other electronic structure package. A manual of how to use this program is included in the code package. Program summaryProgram title: FREQCatalogue identifier: AFBH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBH_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland at http://www.cpc.cs.qub.ac.uk or from Truhlar group software page at comp.chem.umn.edu/freq/Licensing provisions: GNU GPL v3No. of lines in distributed program, including test data, etc.: 3013No. of bytes in distributed program, including test data, etc.: 212537Distribution format: tar.gzProgramming language: PYTHON.Computer: Any computer with PYTHON compiler.Operating systems: Linux, Unix.Classifications: 16.3, 23.External routines: Gaussian 03 or Gaussian 09 (see “Restrictions”).Nature of problem:Optimization of property-specific scale factors for vibrational frequencies for a specific electronic model chemistry.Solution method:The method is based on minimizing the root-mean-square deviation between a set of zero-point energies derived from harmonic vibrational frequencies (either provided by the user or computed on the fly) and their experimentally determined counterparts.Restrictions:In order to compute the electronic model chemistry’s harmonic zero-point energies on the fly, the user must have access to the Gaussian 03 or Gaussian 09 program. If the electronic model chemistry’s zero-point energies are read in, no other program is required.Additional comments:After opening the FREQ.tar.gz file, the user will find a run.sh file which can be used to run all the programs to obtain the scaling factors for a user-chosen electronic structure model chemistry.Running time:Less than a second if the user provides the zero-point energies; if zero-point energies are to be computed, the running time depends on the electronic model chemistry used to compute them as well as the efficiency of the Gaussian 09 program, in our test we obtain the results within 10 min by using one node with eight processors for each Gaussian 09 input on Minnesota Supercomputing Institute’s Mesabi supercomputer.

Rate coefficients and kinetic isotope effects of the abstraction reaction of H atoms from methylsilane

ABSTRACTThermal rate constants for chemical reactions using improved canonical variational transition state theory (ICVT) with small-curvature tunnelling (SCT) contributions in a temperature range 180–2000 K are reported. The general procedure is used with high-quality ab initio computations and semi-classical reaction probabilities along the minimum energy path (MEP). The approach is based on a vibrational adiabatic reaction path and is applied to the multiple-channel hydrogen abstraction reaction H + SiH3CH3 → products and its isotopically substituted variants. All the degrees of freedom are optimised and harmonic vibrational frequencies and zero-point energies are calculated at the MP2 level with the cc-pVTZ basis set. Single-point energies are calculated at a higher level of theory; CCSD(T)-F12a/VTZ-F12. ICVT/SCT rate constants show that the quantum tunnelling contributions at low temperatures are relatively important and the H-abstraction channel from SiH3 group of SiH3CH3 is the major pathway. The total rate constants are given by the following expression: ktot(ICVT/SCT) = 2.29 10−18 T2.42 exp(−350.9/T) cm3 molec−1 s−1. These calculated rates are in agreement with the available experiments. The ICVT/SCT method is further exploited to predict primary and secondary kinetic isotope effects, respectively).

A direct potential fitting RKR method: Semiclassical vs. quantal comparisons

Quantal and semiclassical (SC) eigenvalues are compared for three diatomic molecular potential curves: the X state of CO, the X state of Rb2, and the A state of I2. The comparisons show higher levels of agreement than generally recognized, when the SC calculations incorporate a quantum defect correction to the vibrational quantum number, in keeping with the Kaiser modification. One particular aspect of this is better agreement between quantal and SC estimates of the zero-point vibrational energy, supporting the need for the Y00 correction in this context. The pursuit of a direct-potential-fitting (DPF) RKR method is motivated by the notion that some of the limitations of RKR potentials may be innate, from their generation by an exact inversion of approximate quantities: the vibrational energy Gυ and rotational constant Bυ from least-squares analysis of spectroscopic data. In contrast, the DPF RKR method resembles the quantal DPF methods now increasingly used to analyze diatomic spectral data, but with the eigenvalues obtained from SC phase integrals. Application of this method to the analysis of 9500 assigned lines in the I2A←X spectrum fails to alter the quantal-SC disparities found for the A-state RKR curve from a previous analysis. On the other hand, the SC method can be much faster than the quantal method in exploratory work with different potential functions, where it is convenient to use finite-difference methods to evaluate the partial derivatives required in nonlinear fitting.

Organic crystal polymorphism: a benchmark for dispersion corrected mean field electronic structure methods

We analyze the energy landscape of the sixth crystal structure prediction blind test targets with various first principles and semi-empirical quantum chemical methodologies. A new benchmark set of 59 crystal structures (termed POLY59) for testing quantum chemical methods based on the blind test target crystals is presented. We focus on different means to include London dispersion interactions within the density functional theory (DFT) framework. We show the impact of pairwise dispersion corrections like the semi-empirical D2 scheme, the Tkatchenko–Scheffler (TS) method, and the density-dependent dispersion correction dDsC. Recent methodological progress includes higher-order contributions in both the many-body and multipole expansions. We use the D3 correction with Axilrod–Teller–Muto type three-body contribution, the TS based many-body dispersion (MBD), and the nonlocal van der Waals density functional (vdW-DF2). The density functionals with D3 and MBD correction provide an energy ranking of the blind test polymorphs in excellent agreement with the experimentally found structures. As a computationally less demanding method, we test our recently presented minimal basis Hartree–Fock method (HF-3c) and a density functional tight-binding Hamiltonian (DFTB). Considering the speed-up of three to four orders of magnitudes, the energy ranking provided by the low-cost methods is very reasonable. We compare the computed geometries with the corresponding X-ray data where TPSS-D3 performs best. The importance of zero-point vibrational energy and thermal effects on crystal densities is highlighted.

Theoretical study of the neutral decomposition of SF6 in the presence of H2O and O2 in discharges in power equipment

In the presence of H2O and O2, the dissociation products of SF6 will decompose to form several main stable byproducts (i.e. SOF2, SOF4 and SO2F2) in an electrical discharge. These byproducts are chemically active and have been shown experimentally to be associated with discharge faults. However, the relationships between the discharges and types of decomposition components are still not clear, mainly due to the fact that the complex chemical processes during SF6 discharges are not fully understood. In order to comprehensively investigate the decomposition of SF6, an approach combining density functional theory (DFT) and transition state theory (TST) was used to study the pathways of SF6 decomposition in mixtures with H2O and O2 that involve electrically-neutral species. The complex chemical reactions were analyzed, and the corresponding rate constants were predicted. The structural optimizations, vibrational frequency calculations and zero-point energy calculations of the species involved in each chemical reaction considered were carried out using the DFT-B3LYP method. Single-point energies were calculated using the CCSD(T) method. Based on the energy information obtained, the rate constants were predicted by TST, over a large temperature range, from 300 to 12 000 K.

Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks of Electronically Excited States.

The semiempirical orthogonalization-corrected OMx methods have recently been shown to perform well in extensive ground-state benchmarks. They can also be applied to the computation of electronically excited states when combined with a suitable multireference configuration interaction (MRCI) treatment. We report on a comprehensive evaluation of the performance of the OMx/MRCI methods for electronically excited states. The present benchmarks cover vertical excitation energies, excited-state equilibrium geometries (including an analysis of significant changes between ground- and excited-state geometries), minimum-energy conical intersections, ground- and excited-state zero-point vibrational energies, and 0-0 transition energies for a total of 520 molecular structures and 412 excited states. For comparison, we evaluate the TDDFT/B3LYP method for all benchmark sets, and the CC2, MRCISD, and CASPT2 methods for some of them. We find that the current OMx/MRCI methods perform reasonably well for many of the excited-state properties. However, in comparison to the first-principles methods, there are also a number of shortcomings that should be addressed in future developments.

Organic crystal polymorphism: a benchmark for dispersion-corrected mean-field electronic structure methods.

We analyze the energy landscape of the sixth crystal structure prediction blind test targets with various first principles and semi-empirical quantum chemical methodologies. A new benchmark set of 59 crystal structures (termed POLY59) for testing quantum chemical methods based on the blind test target crystals is presented. We focus on different means to include London dispersion interactions within the density functional theory (DFT) framework. We show the impact of pairwise dispersion corrections like the semi-empirical D2 scheme, the Tkatchenko-Scheffler (TS) method, and the density-dependent dispersion correction dDsC. Recent methodological progress includes higher-order contributions in both the many-body and multipole expansions. We use the D3 correction with Axilrod-Teller-Muto type three-body contribution, the TS based many-body dispersion (MBD), and the nonlocal van der Waals density functional (vdW-DF2). The density functionals with D3 and MBD correction provide an energy ranking of the blind test polymorphs in excellent agreement with the experimentally found structures. As a computationally less demanding method, we test our recently presented minimal basis Hartree-Fock method (HF-3c) and a density functional tight-binding Hamiltonian (DFTB). Considering the speed-up of three to four orders of magnitudes, the energy ranking provided by the low-cost methods is very reasonable. We compare the computed geometries with the corresponding X-ray data where TPSS-D3 performs best. The importance of zero-point vibrational energy and thermal effects on crystal densities is highlighted.

Frequency Scale Factors for Some Double-Hybrid Density Functional Theory Procedures: Accurate Thermochemical Components for High-Level Composite Protocols

In the present study, we have obtained geometries and frequency scale factors for a number of double-hybrid density functional theory (DH-DFT) procedures. We have evaluated their performance for obtaining thermochemical quantities [zero-point vibrational energies (ZPVE) and thermal corrections for 298 K enthalpies (ΔH298) and 298 K entropies (S298)] to be used within high-level composite protocols (using the W2X procedure as a probe). We find that, in comparison with the previously prescribed protocol for optimization and frequency calculations (B3-LYP/cc-pVTZ+d), the use of contemporary DH-DFT methods such as DuT-D3 and DSD-type procedures leads to a slight overall improved performance compared with B3-LYP. A major strength of this approach, however, lies in the better robustness of the DH-DFT methods in that the largest deviations are notably smaller than those for B3-LYP. In general, the specific choices of the DH-DFT procedure and the associated basis set do not drastically change the performance. Nonetheless, we find that the DSD-PBE-P86/aug'-cc-pVTZ+d combination has a very slight edge over the others that we have examined, and we recommend its general use for geometry optimization and vibrational frequency calculations, in particular within high-level composite methods such as the higher-level members of the WnX series of protocols. The scale factors determined for DSD-PBE-P86/aug'-cc-pVTZ+d are 0.9830 (ZPVE), 0.9876 (ΔH298), and 0.9923 (S298).

Vibrational zero point energy of organophosphorus(V) compounds

The calculation of vibrational zero-point energies (ZPEs) of organophosphorus(V) compounds is reported. The contributions of P O and PS bonds have been determined and incorporated in our empirical formula to estimate vibrational zero point energies of the investigated compounds. The calculated ZPEs for more than 80 organophosphorus compounds (V) containing these bonds correlate well with the reported available values. In addition, the comparison of these results with those obtained by quantum chemistry methods (HF/6-31G*, B3LYP/6-31G*) and by a similar empirical approach, indicates the reliability of our empirical model.

THE H2 + CO H2CO REACTION: RATE CONSTANTS AND RELEVANCE TO HOT AND DENSE ASTROPHYSICAL MEDIA

ABSTRACT A theoretical thermochemical and kinetic investigation of the thermal H2 + CO ↔ H2CO reaction was performed for a temperature range from 200 to 4000 K. Geometries and vibrational frequencies of reactants, product, and transition state (TS) were obtained at CCSD/cc-pVxZ (x = T and Q) levels and scaling factors were employed to consider anharmonicity effects on vibrational frequencies, zero-point energies, and thermal corrections provided by these methodologies. Enthalpies Gibbs energies, and rate constants for this reaction were determined by including a complete basis set extrapolation correction for the electronic properties calculated at CCSD(T)/cc-pVyZ (y = Q and 5) levels. Our study indicates that enthalpy changes for this reaction are highly dependent on temperature. Moreover, forward and reverse (high-pressure limit) rate constants were obtained from variational TS theory with quantum tunneling corrections. Thus, modified Arrhenius’ equations were fitted by means of the best forward and reverse rate constant values, which provide very reliable estimates for these quantities within the temperature range between 700 and 4000 K. To our knowledge, this is the first kinetic study done for the forward H2 + CO H2CO process in a wide temperature range. Finally, these results can be used to explain the formaldehyde abundance in hot and dense interstellar media, possibly providing data about the physical conditions associated with H2CO masers close to massive star-forming regions.

Secondary kinetic deuterium isotope effects. The CC cleavage of labeled tetramethylethylenediamine radical cations—Who gets to keep the electron?

The simple cleavage of the C–C bond in tetramethylethylenediamine molecular ions yields two fragments that are identical but for the positions of the charge and radical; nonetheless, the reactions of deuterium labeled analogs are accompanied by substantial secondary kinetic isotope effects. The underlying transition state zero-point vibrational energy differences depend particularly on the properties of the incipient radicals rather than on those of the charge-retaining products. The α-secondary effects arise primarily from vibrations related to deformation of the product –CH2N– and –CD2N– groups when the reactant is labeled at the central C–C bond, whereas CH/CD stretching vibrations are the origin of the γ-secondary effects observed for reactants with labeled methyl groups. These zero-point energy differences are mainly due to hyperconjugative interactions (Bohlmann shifts) and do not reflect bonding changes in the transition state; the secondary isotope effects on the dissociation of protonated amine dimers have a similar origin.

Trajectory Calculations for Bergman Cyclization Predict H/D Kinetic Isotope Effects Due to Nonstatistical Dynamics in the Product

An unusual H/D kinetic isotope effect (KIE) is described, in which isotopic selectivity arises primarily from nonstatistical dynamics in the product. In DFT-based quasiclassical trajectories of Bergman cyclization of (Z)-3-hexen-1,5-diyne (1) at 470 K, the new CC bond retains its energy, and 28% of nascent p-benzyne recrosses back to the enediyne on a vibrational time scale. The competing process of intramolecular vibrational redistribution (IVR) in p-benzyne is too slow to prevent this. Deuteration increases the rate of IVR, which decreases the fraction of recrossing and increases the yield of statistical (trapable) p-benzyne, 2. Trapable yields for three isotopomers of 2 range from 72% to 86%. The resulting KIEs for Bergman cyclization differ substantially from KIEs predicted by transition state theory, which suggests that IVR in this reaction can be studied by conventional KIEs. Leakage of vibrational zero point energy (ZPE) into the reaction coordinate was probed by trajectories in which initial ZPE in the CH/CD stretching modes was reduced by 25%. This did not change the predicted KIEs.

Spectroscopic [FT-IR and FT-Raman] and molecular modeling (MM) study of benzene sulfonamide molecule using quantum chemical calculations

The spectroscopic and molecular modeling (MM) study includes, FT-IR, FT-Raman and 13C NMR and 1H NMR spectra of the Benzene sulfonamide were recorded for the analysis. The observed experimental and theoretical frequencies (IR and Raman) were assigned according to their distinctive region. The present study of this title molecule have been carried out by hybrid computational calculations of HF and DFT (B3LYP) methods with 6-311+G(d,p) and 6-311++G(d,p) basis sets and the corresponding results are tabulated. The structural modifications of the compound due to the substitutions of NH2 and SO2 were investigated. The minimum energy conformers of the compound were studied using conformational analysis. The alternations of the vibrational pattern of the base structure related to the substitutions were analyzed. The thermodynamic parameters (such as zero-point vibrational energy, thermal energy, specific heat capacity, rotational constants, entropy, and dipole moment) of Benzene sulfonamide have been calculated. The donor acceptor interactions of the compound and the corresponding UV transitions are found out using NBO analysis. The NMR spectra were simulated by using the gauge independent atomic orbital (GIAO) method with B3LYP methods and the 6-311++G(d,p) basis set and their spectra were simulated and the chemical shifts related to TMS were compared. A quantum computational study on the electronic and optical properties absorption wavelengths, excitation energy, dipole moment and frontier molecular orbital energies, were performed by HF and DFT methods. The energy gap of the present compound was calculated related to HOMO and LUMO energies which confirm the occurring of charge transformation between the base and ligand group. Besides frontier molecular orbitals (FMO), molecular electrostatic potential (MEP) was performed. The thermodynamic properties (heat capacity, entropy, and enthalpy) of the title compound at different temperatures were calculated in gas phase and solvents (DMSO and methanol).

DFT computations on the hydrogen bonding interactions between methacrylic acid-trimethylolpropane trimethacrylate copolymers and letrozole as drug delivery systems

The hydrogen bonding interactions between letrozole (Let) anticancer drug and three copolymers of methacrylic acid-trimethylolpropane trimethacrylate (M1–M3 as molecular imprinted polymers) were studied using density functional theory (DFT) at both B3LYP and B3PW91 levels. The binding energies were corrected for the basis set superposition error (BSSE) and zero-point vibrational energies (ZPVE) so that the most negative [Formula: see text] were measured for compounds 7 and 8 formed between M1 copolymer and endocyclic N1 and N2 atoms of drug, respectively. Also, among complexes 13–15 in which two copolymers were contributed in the formation of O–H[Formula: see text]N bonds with the drug, compound 13 (containing two M1 copolymers) showed the highest [Formula: see text] value. The interactions of all copolymers with drug were exergonic (spontaneous interaction) and exothermic. The QTAIM data supported the covalent character of the C–N, C–H, N–N, C–O, O–H and O–H[Formula: see text]N bonds, the intermediate nature of C[Formula: see text]N and C[Formula: see text]O bonds while the electrostatic character of C–H[Formula: see text]O, HC[Formula: see text]HC and CH[Formula: see text]N interactions. According to the [Formula: see text], [Formula: see text] and [Formula: see text] values, it was suggested that t complexes 7 and 8 (among two particles systems) as well as complex 13 (among three particles systems) can be the most promising drug delivery systems.

The equilibrium geometries of heptatriynylidene, cyclohepta-1,2,3,4-tetraen-6-yne, and heptahexaenylidene

The equilibrium geometries of heptatriynylidene (1), cyclohepta-1,2,3,4-tetraen-6-yne (2), and heptahexaenylidene (3) have been theoretically investigated at various level of theories. The methods employed are Møller–Plesset perturbation level of theory until second-order, coupled-cluster singles and doubles (CCSD), and CCSD with perturbative triple excitations [CCSD(T)]. Correlation consistent polarized valence double and triple zeta (cc-pVXZ; X=D and T) basis sets are used in all calculations, which are compatible with the frozen-core approximation entreated in this study. The relative energies of the ground triplet electronic state (X∼3Σg-) of 1 – the most stable isomer of C7H2 – to the ground singlet electronic states of 2 (X∼1A1) and 3 (X∼1A1) have also been estimated at different levels. With zero-point vibrational energy corrections, 2 and 3 are found to lie ∼12.27 and ∼20.62kcalmol−1, respectively, above 1 at the highest level of theory (CCSD(T)/cc-pVTZ). While 1 and 3 are observed in the laboratory, 2 is a hypothetical molecule hitherto. Since the optimal geometry of 2 suggests the presence of biradical character, the singlet–triplet (X∼1A1–3B1) energy gap for isomer 2 was also calculated at various levels. The ab initio data presented here may be useful for the laboratory detection of 2 and astronomical detection of2and3.

Pathways for the OH + Br2 → HOBr + Br and HOBr + Br → HBr + BrO Reactions.

The OH radical reaction with Br2 and the subsequent reaction HOBr + Br are of exceptional importance to atmospheric chemistry and environmental chemistry. The entrance complex, transition state, and exit complex for both reactions have been determined using the coupled-cluster method with single, double, and perturbative triple excitations CCSD(T) with correlation consistent basis sets up to size cc-pV5Z and cc-pV5Z-PP. Coupled cluster effects with full triples (CCSDT) and full quadruples (CCSDTQ) are explicitly investigated. Scalar relativistic effects, spin-orbit coupling, and zero-point vibrational energy corrections are evaluated. The results from the all-electron basis sets are compared with those from the effective core potential (ECP) pseudopotential (PP) basis sets. The results are consistent. The OH + Br2 reaction is predicted to be exothermic 4.1 ± 0.5 kcal/mol, compared to experiment, 3.9 ± 0.2 kcal/mol. The entrance complex HO···BrBr is bound by 2.2 ± 0.2 kcal/mol. The transition state lies similarly well below the reactants OH + Br2. The exit complex HOBr···Br is bound by 2.7 ± 0.6 kcal/mol relative to separated HOBr + Br. The endothermicity of the reaction HOBr + Br → HBr + BrO is 9.6 ± 0.7 kcal/mol, compared with experiment 8.7 ± 0.3 kcal/mol. For the more important reverse (exothermic) HBr + BrO reaction, the entrance complex BrO···HBr is bound by 1.8 ± 0.6 kcal/mol. The barrier for the HBr + BrO reaction is 6.8 ± 0.9 kcal/mol. The exit complex (Br···HOBr) for the HBr + BrO reaction is bound by 1.9 ± 0.2 kcal/mol with respect to the products HOBr + Br.

Impact of OH Radical-Initiated H2CO3 Degradation in the Earth's Atmosphere via Proton-Coupled Electron Transfer Mechanism.

The decomposition of isolated carbonic acid (H2CO3) molecule into CO2 and H2O (H2CO3 → CO2 + H2O) is prevented by a large activation barrier (>35 kcal/mol). Nevertheless, it is surprising that the detection of the H2CO3 molecule has not been possible yet, and the hunt for the free H2CO3 molecule has become challenging not only in the Earth's atmosphere but also on Mars. In view of this fact, we report here the high levels of quantum chemistry calculations investigating both the energetics and kinetics of the OH radical-initiated H2CO3 degradation reaction to interpret the loss of the H2CO3 molecule in the Earth's atmosphere. It is seen from our study that proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) are the two mechanisms by which the OH radical initiates the degradation of the H2CO3 molecule. Moreover, the PCET mechanism is potentially the important one, as the effective barrier, defined as the difference between the zero point vibrational energy (ZPE) corrected energy of the transition state and the total energy of the isolated starting reactants in terms of bimolecular encounters, for the PCET mechanism at the CCSD(T)/6-311++G(3df,3pd) level of theory is ∼3 to 4 kcal/mol lower than the effective barrier height associated with the HAT mechanism. The CCSD(T)/6-311++G(3df,3pd) level predicted effective barrier heights for the degradations of the two most stable conformers of H2CO3 molecule via the PCET mechanism are only ∼2.7 and 4.3 kcal/mol. A comparative reaction rate analysis at the CCSD(T)/6-311++G(3df,3pd) level of theory has also been carried out to explore the potential impact of the OH radical-initiated H2CO3 degradation relative to that from water (H2O), formic acid (FA), acetic acid (AA) and sulfuric acid (SA) assisted H2CO3 → CO2 + H2O decomposition reactions in both the Earth's troposphere and stratosphere. The comparison of the reaction rates reveals that, although the atmospheric concentration of the OH radical is substantially lower than the concentrations of the H2O, FA, AA in the Earth's atmosphere, nevertheless, the OH radical-initiated H2CO3 degradation reaction has significant impact, especially toward the loss of the H2CO3 molecule in the Earth's atmosphere. In clean environments, which exist in greater numbers in comparison to the polluted environments of the Earth's atmosphere, the impact of the OH radical-initiated H2CO3 degradation reaction is seen to be comparable to that from a competing pathway which utilizes hydrogen bonded molecules such as H2O, FA or AA to catalyze the H2CO3 decomposition. Similarly, in the polluted environments, and especially in the Earth's troposphere, although the reactions rates for the OH radical-initiated H2CO3 degradation and FA-assisted H2CO3 decomposition are comparable within a factor of ∼15, nevertheless, the AA-assisted H2CO3 decomposition reaction is appeared to be the dominant channel. This follows only because of slightly greater catalytic efficiency of the AA over FA upon the H2CO3 → CO2 + H2O decomposition reaction. In contrary, although the catalytic efficiencies of SA, FA, and AA upon the H2CO3 decomposition reaction are similar to each other and the concentrations of both the SA and OH radical in the Earth's atmosphere are more-or-less equal to each other, but nevertheless, the SA-assisted H2CO3 decomposition reaction cannot compete with the OH radical-initiated H2CO3 degradation reaction.