Reaction Barrier Heights Research Articles

A new meta-GGA exchange functional based on an improved constraint-based GGA

We report the performance of a non-empirical meta-GGA that comes from converting our simple VT{8,4} GGA. That GGA satisfies the large dimensionless reduced gradient limit, obeys the Lieb–Oxford bound, and reduces to the exact second-order gradient expansion approximation in the slowly varying limit. Validation studies of meta-VT{8,4} for several properties using well-known test sets shows a modest improvement with respect to revTPSS. Compared with the heavily parameterized M06-L, the heats of formation of meta-VT{8,4} are substantially better but reaction barrier heights are considerably worse. This suggests the opportunity for additional constraints and the need for better correlation functionals.

Infinite Basis Set Extrapolation for Double Hybrid Density Functional Theory 2: Effect of Adding Diffuse Basis Functions

AbstractWe applied the Infinite Basis (IB) set extrapolation and Double Hybrid Density Functional Theory (DHDF) to calculate the electron affinities, reaction barrier heights, proton affinities, non‐covalent interactions, atomization, ionization, and alkyl bond dissociation energies. We previously found that the mean unsigned error of the B2KPLYP‐IB calculation with the combination of cc‐pVTZ and cc‐pVQZ reach the chemical accuracy limit (∼2 kcal/mol) where the largest deviation occurred in the electron affinity calculations and the weak interactions between noble gases and nonpolar molecules. Here, we investigated the basis set effect using the B2KPLYP‐IB extrapolation scheme that involves (1) the addition of extra tight d basis functions to the second row elements (i.e. cc‐pV(L+d)Z), (2) the addition of extra s, p, and d diffuse basis functions, and (3) a comparison between Dunning's Correlation Consistent and Jensen's Polarization Consistent (pc‐L) basis sets. We found that the addition of extra s and p diffuse basis functions formed the minimal augmented basis sets proposed by Truhlar. This addition permitted the B2KPLYP‐IB to reach the chemical accuracy limit with the combination of the double ζ and triple ζ basis sets. Adding extra s, p diffuse functions to the pc‐L series permitted only a small improvement. This small improvement is due to the fact that the pc‐L basis sets already contain a large number of functions for the p block elements. Taken together, the results suggest that this minimal augmented basis sets is useful for due to its accuracy and affordable computational cost.

First-Principles Analysis of Dissociative Absorption of HF Molecule at SiC Surface Step Edge

It has been reported that SiC surface can be etched off in a concentrated aqueous solution of hydrogen fluoride with making contacts with Pt plate catalyst, named Catalyst-referred Etching (CARE) [1]. In this report, we present first-principles molecular-dynamic simulations on the initial stage of the etching process. Reaction barrier heights of dissociative absorption reactions of hydrogen fluoride molecule breaking into back-bonds at step edge of 3C-SiC(111) are analyzed.

Exploring hydrogen bond in the excited state leading toward intramolecular proton transfer: detailed analysis of the structure and charge density topology along the reaction path using QTAIM

Excited state intramolecular proton transfer (ESIPT) reaction along the O-H[Symbol: see text][Symbol: see text][Symbol: see text][Symbol: see text]O hydrogen bond of o-hydroxy benzaldehyde (OHBA), methyl salicylate (MS) and salicylic acid (SA) was investigated by ab-initio quantum chemical calculation and theory of atoms and molecules (QTAIM) for the first time. Variation in several geometric as well as QTAIM parameters along the reaction coordinate was monitored in the fully relaxed excited state potential energy curve (PEC) obtained from intrinsic reaction coordinate (IRC) analysis. Although, the excited state barrier height for the forward reaction (∆E (0) (#) ) reduces substantially in all the systems, MS and SA do not show any obvious asymmetry for proton transfer. For MS and SA, the crossover of the bond index as well as the lengths of the participating bonds at the saddle point is assigned due to this symmetry in accordance with bond energy - bond order (BEBO) model, which does not hold true in OHBA both in the ground and excited states. Bond ellipticity, covalent and metallic character were examined for different structures along the reaction path within the QTAIM framework. The QTAIM analysis was found to be able to uniquely distinguish between the ground and excited states of the OHBA molecule as well as both determining the effects on the bonding character of adding different substituent groups and differentiating between the ESIPT reactions in the SA and MS molecules.

Doubly hybrid density functional xDH-PBE0 from a parameter-free global hybrid model PBE0

Following the XYG3 model which uses orbitals and density from B3LYP, an empirical doubly hybrid (DH) functional is developed by using inputs from PBE0. This new functional, named xDH-PBE0, has been tested on a number of different molecular properties, including atomization energies, bond dissociation enthalpies, reaction barrier heights, and nonbonded interactions. From the results obtained, xDH-PBE0 not only displays a significant improvement with respect to the parent PBE0, but also shows a performance that is comparable to XYG3. Arguably, while PBE0 is a parameter-free global hybrid (GH) functional, the B3LYP GH functional contains eight fit parameters. From a more general point of view, the present work points out that reliable and general-purpose DHs can be obtained with a limited number of fit parameters.

Kinetics and Thermochemistry of 2,5-Dimethyltetrahydrofuran and Related Oxolanes: Next Next-Generation Biofuels

The enthalpies of formation, entropies, specific heats at constant pressure, enthalpy functions, and all carbon-hydrogen and carbon-methyl bond dissociation energies have been computed using high-level methods for the cyclic ethers (oxolanes) tetrahydrofuran, 2-methyltetrahydrofuran, and 2,5-dimethyltetrahydrofuran. Barrier heights for hydrogen-abstraction reactions by hydrogen atoms and the methyl radical are also computed and shown to correlate with reaction energy change. The results show a pleasing consistency and considerably expands the available data for these important compounds. Abstraction by ȮH is accompanied by formation of both pre- and postreaction weakly bound complexes. The resulting radicals formed after abstraction undergo ring-opening reactions leading to readily recognizable intermediates, while competitive H-elimination reactions result in formation of dihydrofurans. Formation enthalpies of all 2,3- and 2,5-dihydrofurans and associated radicals are also reported. It is probable that the compounds at the center of this study will be relatively clean-burning biofuels, although formation of intermediate aldehydes might be problematic.

Assessment of Theoretical Procedures for Calculating Barrier Heights for a Diverse Set of Water-Catalyzed Proton-Transfer Reactions

Accurate electronic barrier heights are obtained for a set of nine proton-transfer tautomerization reactions, which are either (i) uncatalyzed, (ii) catalyzed by one water molecule, or (iii) catalyzed by two water molecules. The barrier heights for reactions (i) and (ii) are obtained by means of the high-level ab initio W2.2 thermochemical protocol, while those for reaction (iii) are obtained using the W1 protocol. These three sets of benchmark barrier heights allow an assessment of the performance of more approximate theoretical procedures for the calculation of barrier heights of uncatalyzed and water-catalyzed reactions. We evaluate initially the performance of the composite G4 procedure and variants thereof (e.g., G4(MP2) and G4(MP2)-6X), as well as that of standard ab initio procedures (e.g., MP2, SCS-MP2, and MP4). We find that the performance of the G4(MP2)-type thermochemical procedures deteriorates with the number of water molecules involved in the catalysis. This behavior is linked to deficiencies in the MP2-based basis-set-correction term in the G4(MP2)-type procedures. This is remedied in the MP4-based G4 procedure, which shows good performance for both the uncatalyzed and the water-catalyzed reactions, with mean absolute deviations (MADs) from the benchmark values lying below the threshold of "chemical accuracy" (arbitrarily defined as 1 kcal mol(-1) ≈ 4.2 kJ mol(-1)). We also examine the performance of a large number of density functional theory (DFT) and double-hybrid DFT (DHDFT) procedures. We find that, with few exceptions (most notably PW6-B95 and B97-2), the performance of the DFT procedures that give good results for the uncatalyzed reactions deteriorates with the number of water molecules involved in the catalysis. The DHDFT procedures, on the other hand, show excellent performance for both the uncatalyzed and catalyzed reactions. Specifically, almost all of them afford MADs below the "chemical accuracy" threshold, with ROB2-PLYP and B2K-PLYP showing the best overall performance.

Density functional theory studies on the Diels–Alder reaction of [3]dendralene with C60: an attractive approach for functionalization of fullerene

The Diels–Alder reaction between C60 and [3]dendralene has been carried out using density functional theory based Becke’s three-parameter hybrid exchange functional and Lee–Yang–Parr correlation functional (B3LYP) method with 6−31G* basis set. The importance of dispersion corrections has been assessed by performing calculation at dispersion corrected B2PLYP-D/6–31G* level. The results reveal that the fullerene can be functionalized using [3]dendralenes. Several new types of adducts viz. mono (1), bis (1–1′ and 1–2), tris (1–1′–2 and 1–2–1′), tetrakis (1–1′–2–2′), pentakis (1–1′–2–2′–3), and hexakis (1–1′–2–2′–3–3′) can be formed by the stepwise addition of [3]dendralene due to its multifarious reactive sites. Furthermore, it is observed that the 1–2 additions are thermodynamically and kinetically more feasible than the 1–1′ ones. The geometrical distortion energy (Edis) exhibits a linear relationship with the corresponding reaction barrier heights. The HOMO and LUMO energies of various reactants elicit that DA reaction is driven by normal electron demand. It is interesting to note from the energy decomposition analysis that although the steric effects dominate the addition reaction, the dispersion interaction plays a significant role in the stabilization of transition states. It is evident from the density of state and HOMO–LUMO gap (Egap) that the functionalization of C60 by [3]dendralene marginally alters the conductivity.

Non-empirical improvement of PBE and its hybrid PBE0 for general description of molecular properties

Imposition of the constraint that, for the hydrogen atom, the exchange energy cancels the Coulomb repulsion energy yields a non-empirical re-parameterization of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) exchange-correlation energy functional, and of the related PBE hybrid (PBE0). The re-parameterization, which leads to an increase of the gradient contribution to the exchange energy with respect to the original PBE functional, is tested through the calculation of heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies, for some well known test sets designed to validate energy functionals. The results for the re-parameterized PBE GGA, called PBEmol, give substantial improvement over the original PBE in the prediction of the heats of formation, while retaining the quality of the original PBE functional for description of all the other properties considered. The results for the hybrids indicate that, although the PBE0 functional provides a rather good description of these properties, the predictions of the re-parameterized functional, called PBEmolβ0, are, except in the case of the ionization potentials, modestly better. Also, the results for PBEmolβ0 are comparable to those of B3LYP. In particular, the mean absolute error for the bond distance test set is 17% lower than the corresponding error for B3LYP. The re-parameterization for the pure GGA (PBEmol) differs from that for the hybrid (PBEmolβ0), illustrating that improvement at the GGA level of complexity does not necessarily provide the best GGA for use in a hybrid.

Hybrid Quantum Mechanical and Molecular Mechanics Study of the SN2 Reaction of CCl4 + OH– in Aqueous Solution: The Potential of Mean Force, Reaction Energetics, and Rate Constants

The bimolecular nucleophilic substitution reaction of CCl(4) and OH(-) in aqueous solution was investigated on the basis of a combined quantum mechanical and molecular mechanics method. A multilayered representation approach is employed to achieve high accuracy results at the CCSD(T) level of theory. The potential of mean force calculations at the DFT level and CCSD(T) level of theory yield reaction barrier heights of 22.7 and 27.9 kcal/mol, respectively. Both the solvation effects and the solvent-induced polarization effect have significant contributions to the reaction energetics, for example, the solvation effect raises the saddle point by 10.6 kcal/mol. The calculated rate constant coefficient is 8.6 × 10(-28) cm(3) molecule(-1) s(-1) at the standard state condition, which is about 17 orders magnitude smaller than that in the gas phase. Among the four chloromethanes (CH(3)Cl, CH(2)Cl(2), CHCl(3), and CCl(4)), CCl(4) has the lowest free energy activation barrier for the reaction with OH(-) in aqueous solution, confirming the trend that substitution of Cl by H in chloromethanes diminishes the reactivity.

Structure–Correlation Principles Connecting Ground State Properties and Reaction Barrier Heights for the Cope Rearrangement of Semibullvalenes

A direct relationship exists between the properties of substituted semibullvalenes and their Cope rearrangement activation barrier. This unique correlation not only enables the determination of kinetic data from ground state information, but also provides a rationalization for the extent to which ground state properties are altered with respect to their "normal" values (i.e., that of their localized Lewis structure). Examination of electron density distribution, geometrical parameters, and J-coupling constant differences between canonical and Lewis structures deliver quantitative evidence for the structure-correlation principle.

Accurate thermochemistry from a parameterized coupled-cluster singles and doubles model and a local pair natural orbital based implementation for applications to larger systems

We have recently introduced a parameterized coupled-cluster singles and doubles model (pCCSD(α, β)) that consists of a bivariate parameterization of the CCSD equations and is inspired by the coupled electron pair approximations. In our previous work, it was demonstrated that the pCCSD(-1, 1) method is an improvement over CCSD for the calculation of geometries, harmonic frequencies, and potential energy surfaces for single bond-breaking. In this paper, we find suitable pCCSD parameters for applications in reaction thermochemistry and thermochemical kinetics. The motivation is to develop an accurate and economical methodology that, when coupled with a robust local correlation framework based on localized pair natural orbitals, is suitable for large-scale thermochemical applications for sizeable molecular systems. It is demonstrated that the original pCCSD(-1, 1) method and several other pCCSD methods are a significant improvement upon the standard CCSD approach and that these methods often approach the accuracy of CCSD(T) for the calculation of reaction energies and barrier heights. We also show that a local version of the pCCSD methodology, implemented within the local pair natural orbital (LPNO) based CCSD code in ORCA, is sufficiently accurate for wide-scale chemical applications. The LPNO based methodology allows us for routine applications to intermediate sized (20-100 atoms) molecular systems and is a significantly more accurate alternative to MP2 and density functional theory for the prediction of reaction energies and barrier heights.

Long-range correlation energies from frequency-dependent weighted exchange-hole dipole polarisabilities

Long-range correlation energies are calculated using an approximation of the single-particle density-density response function of the system that leads to an expression requiring only occupied orbitals and eigenvalues. Dipole-dipole polarisabilities and isotropic leading-order dispersion coefficients obtained from this approximation are shown to be in a reasonable agreement with corresponding values from the experiment or dipole oscillator strength distributions. The localised polarisabilities were used to calculate a long-range correlation correction to a hybrid-generalised gradient approximation functional using a proper damping function at short ranges. It was found that the hybrid density-functional theory+dispersion method obtained in this way has a comparable accuracy than high-level ab initio wave function methods at a much lower computational cost. This has been analysed for a number of systems from the GMTKN30 database including subsets for noncovalently bound complexes, relative energies for sugar conformers and reaction energies and barrier heights of pericyclic reactions of some medium sized organic molecules.

Towards chemically accurate simulation of molecule–surface reactions

This perspective addresses four challenges facing theorists whose aim is to make quantitatively accurate predictions for reactions of molecules on metal surfaces, and suggests ways of meeting these challenges, focusing on dissociative chemisorption reactions of H(2), N(2), and CH(4). Addressing these challenges is ultimately of practical importance to a more accurate description of overall heterogeneously catalysed reactions, which play a role in the production of more than 90% of man-made chemicals. One challenge is to describe the interaction of a molecule with a metal surface with chemical accuracy, i.e., with errors in reaction barrier heights less than 1 kcal mol(-1). In this framework, the potential of a new implementation of specific reaction parameter density functional theory (SRP-DFT) will be discussed, with emphasis on applications to reaction of H(2) with metal surfaces. Two additional challenges are to come up with improved descriptions of the effects of phonons and electron-hole pairs on reaction of molecules like N(2) on metal surfaces. Phonons can be tackled using sudden approximations in quantum dynamics, and through Ab Initio Molecular Dynamics (AIMD) calculations using classical dynamics. To additionally achieve an accurate description of the effect of electron-hole pair excitation on dissociative chemisorption within a classical dynamics framework, it may be possible to combine AIMD with electronic friction. The fourth challenge we will consider is how to achieve an accurate quantum mechanical description of the dissociative chemisorption of a polyatomic molecule, like methane, on a metal surface. A method of potential interest is the Multi-Configuration Time-Dependent Hartree (MCTDH) method.

Increasing the applicability of DFT I: Non-variational correlation corrections from Hartree–Fock DFT for predicting transition states

Hartree–Fock DFT (HF-DFT) uses the self-interaction error free HF density and DFT functional. Using HF-DFT for molecular structure determination requires a non-variational analytical gradient scheme. This has been developed and applied for the calculation of transition state geometries and barrier heights for chemical reactions. The barrier heights obtained show average absolute errors (AAE) of 2–3kcal/mol while ΛCCSD(T) show an AAE of 1.1–1.4kcal/mol. Standard variational DFT with the same functional has AAE’s of 6.3–8.3kcal/mol while the HF errors are about 12kcal/mol.

M11-L: A Local Density Functional That Provides Improved Accuracy for Electronic Structure Calculations in Chemistry and Physics

Local approximations to the exchange-correlation functional are of special interest because of their cost advantages and their useful accuracy for efficient calculations on systems (such as many transition metal catalysts) with significant multiconfigurational wave function character. We present a meta-GGA exchange-correlation functional, called M11-L, that employs dual-range local exchange to provide broad accuracy for both single-configurational and multiconfigurational molecules and for solid-state lattice constants. Also notable is the high accuracy (for a local functional) for chemical reaction barrier heights. The mean unsigned error on a broad chemistry database of 338 energetic data is lower than that for any other known functional, even hybrid functionals and range-separated hybrid functionals. This success shows that the dependence of the exchange energy density on interelectronic distance is quite different at short-range and long-range, and it establishes a new standard for the limit of what can be achieved with a local exchange-correlation functional.

A fast doubly hybrid density functional method close to chemical accuracy using a local opposite spin ansatz.

We develop and validate the XYGJ-OS functional, based on the adiabatic connection formalism and Görling-Levy perturbation theory to second order and using the opposite-spin (OS) ansatz combined with locality of electron correlation. XYGJ-OS with local implementation scales as N(3) with an overall accuracy of 1.28 kcal/mol for thermochemistry, bond dissociation energies, reaction barrier heights, and nonbonded interactions, comparable to that of 1.06 kcal/mol for the accurate coupled-cluster based G3 method (scales as N(7)) and much better than many popular density functional theory methods: B3LYP (4.98), PBE0 (4.36), and PBE (12.10).

Spline Implementation of Generalized Gradient Approximations to the Exchange-Correlation Functional and Study of the Sensitivity of Density Functional Accuracy to Localized Domains of the Reduced Density Gradient.

We present a natural cubic spline implementation of the exchange enhancement factor as a function of the reduced density gradient, and we demonstrate its performance by replicating the results of common GGA functionals. We also investigate the effect on the accuracy of various calculated properties of changing the shape of the exchange enhancement factor and an analogous factor for correlation. The properties considered are main group atomization energies, ionization potentials, electron affinities, proton affinities, alkyl bond dissociation energies, difficult hydrocarbon cases, barrier heights for chemical reactions, noncovalent interactions, atomic energies, metal bond energies, and main group bond lengths.

Formic Acid Catalyzed Hydrolysis of SO3 in the Gas Phase: A Barrierless Mechanism for Sulfuric Acid Production of Potential Atmospheric Importance

Computational studies at the B3LYP/6-311++G(3df,3pd) and MP2/6-311++G(3df,3pd) levels are performed to explore the changes in reaction barrier height for the gas phase hydrolysis of SO(3) to form H(2)SO(4) in the presence of a single formic acid (FA) molecule. For comparison, we have also performed calculations for the reference reaction involving water assisted hydrolysis of SO(3) at the same level. Our results show that the FA assisted hydrolysis of SO(3) to form H(2)SO(4) is effectively a barrierless process. The barrier heights for the isomerization of the SO(3)···H(2)O···FA prereactive collision complex, which is the rate limiting step in the FA assisted hydrolysis, are found to be respectively 0.59 and 0.08 kcal/mol at the B3LYP/6-311++G(3df,3pd) and MP2/6-311++G(3df,3pd) levels. This is substantially lower than the ~7 kcal/mol barrier for the corresponding step in the hydrolysis of SO(3) by two water molecules--which is currently the accepted mechanism for atmospheric sulfuric acid production. Simple kinetic analysis of the relative rates suggests that the reduction in barrier height facilitated by FA, combined with the greater stability of the prereactive SO(3)···H(2)O···FA collision complex compared to SO(3)···H(2)O···H(2)O and the rather plentiful atmospheric abundance of FA, makes the formic acid mediated hydrolysis reaction a potentially important pathway for atmospheric sulfuric acid production.

The ν2 bending vibrational structure of the $\tilde{X}$X̃ 2Σ+ state of MgNC

We have generated MgNC in supersonic free jet expansions and observed the laser induced fluorescence (LIF) of the Ã(2)Π-X̃(2)Σ(+) transition. We measured the LIF dispersed spectra from the single vibronic levels of the Ã(2)Π electronic state of MgNC, following excitation of each ν(2) bending vibronic band observed, i.e., the κ series of the (0,v(2)('),0)-(0,0,0), v(2)(') = 0, 1, 2, 4, and 6 vibronic bands. In the vibrational structure in the dispersed fluorescence spectra measured, the long progression of the ν(2) bending mode in the X̃(2)Σ(+) state is identified, e.g., up to v(2)('')=14 in the (0,6,0)-(0,v(2)(''),0) spectrum. This enables us to derive the potential curve of the ν(2) bending mode in the X̃(2)Σ(+) state. We used two kinds of models to obtain the potential curve; (I) the customary formula expressed in the polynomial series of the (v(2)('')+(d(2)/2)) term and (II) the internal rotation model. The potential curve derived from model (I) indicates the convergence of the bending vibrational levels at about 800 cm(-1) from the vibrationless level of MgNC, which may correspond to the barrier height of the isomerization reaction, MgNC ⇌ MgCN, in the X̃(2)Σ(+) state. Model (II) gives a simple picture for the isomerization reaction pathway with a barrier height of about 630 cm(-1) from the vibrationless level of the more stable species, MgNC. This shows that the v(2)('')=8 bending vibrational level of MgNC is already contaminated by the v(2)('')=2 bending vibrational level of the isomer, MgCN, and implies that the isomerization reaction begins at the v(2) ('')=8 level. The bending potential surface and the isomerization reaction pathway, MgNC ⇌ MgCN, in the X̃(2)Σ(+) state are discussed by comparing the potential derived in this study with the surface obtained by quantum chemical calculation.