Reaction Barrier Heights Research Articles

MN15-L: A New Local Exchange-Correlation Functional for Kohn-Sham Density Functional Theory with Broad Accuracy for Atoms, Molecules, and Solids.

Kohn-Sham density functional theory is widely used for applications of electronic structure theory in chemistry, materials science, and condensed-matter physics, but the accuracy depends on the quality of the exchange-correlation functional. Here, we present a new local exchange-correlation functional called MN15-L that predicts accurate results for a broad range of molecular and solid-state properties including main-group bond energies, transition metal bond energies, reaction barrier heights, noncovalent interactions, atomic excitation energies, ionization potentials, electron affinities, total atomic energies, hydrocarbon thermochemistry, and lattice constants of solids. The MN15-L functional has the same mathematical form as a previous meta-nonseparable gradient approximation exchange-correlation functional, MN12-L, but it is improved because we optimized it against a larger database, designated 2015A, and included smoothness restraints; the optimization has a much better representation of transition metals. The mean unsigned error on 422 chemical energies is 2.32 kcal/mol, which is the best among all tested functionals, with or without nonlocal exchange. The MN15-L functional also provides good results for test sets that are outside the training set. A key issue is that the functional is local (no nonlocal exchange or nonlocal correlation), which makes it relatively economical for treating large and complex systems and solids. Another key advantage is that medium-range correlation energy is built in so that one does not need to add damped dispersion by molecular mechanics in order to predict accurate noncovalent binding energies. We believe that the MN15-L functional should be useful for a wide variety of applications in chemistry, physics, materials science, and molecular biology.

Comparative studies for different proximity potentials applied to sub-barrier fusion reactions

Coulomb barrier heights calculated by using 14 different versions of proximity potentials are studied and applied for experimental data of fusion in terms of a recently proposed energy scaling approach. The results show that the descriptions of proximity potentials 77 and 88 for the barrier heights seem to be closest to the values required by the systematics. On the basis of proximity potential 77, the parameterized formulas of the barrier height and radius are obtained. These formulas can calculate the barrier positions and barrier heights reasonably well within the error, respectively. Thus it provides a simple and direct way to calculate the barrier positions and barrier heights for heavy-ion fusion reactions.

DFTB/PCM Applied to Ground and Excited State Potential Energy Surfaces.

Accounting for solvent effects in quantum chemical calculations is vital for the accurate description of potential energy surfaces in solution. In this study, we derive a formulation of the analytical first-order geometrical derivative of ground- and excited-state energies within the time-dependent density-functional tight-binding (TD-DFTB) method with the polarizable continuum model (PCM), TD-DFTB/PCM. The performance of this is then evaluated for a series of halogen-exchange SN2 reactions. DFTB/PCM reproduces DFT results well for isolated monohalogenated methanes, but its agreement for transition structures significantly depends on the halogen element. The performance of TD-DFTB/PCM is evaluated for the excited-state intramolecular proton transfer (ESIPT) reaction of 3-hydroxyflavone (3HF) in ethanol. TD-DFTB/PCM reproduces the barrier height of the ESIPT reaction in terms of geometry and energy relatively well, but it fails to reproduce the experimental absorption and fluorescence energies as a consequence of the absence of long-range corrections. Computational timings with and without PCM show that the additional cost of PCM for C500H502 is only 10% greater than the corresponding calculation in vacuum. Furthermore, the potential applications of TD-DFTB/PCM are highlighted by applying it to a double-stranded DNA complexed with dye (PDB ID 108D ). We conclude that TD-DFTB/PCM single-point calculations and geometry optimizations for systems consisting of more than 1000 and 500 atoms, respectively, is now manageable and that properties predicted with TD-DFTB must be interpreted with care.

MN15: A Kohn-Sham global-hybrid exchange-correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions.

Kohn-Sham density functionals are widely used; however, no currently available exchange-correlation functional can predict all chemical properties with chemical accuracy. Here we report a new functional, called MN15, that has broader accuracy than any previously available one. The properties considered in the parameterization include bond energies, atomization energies, ionization potentials, electron affinities, proton affinities, reaction barrier heights, noncovalent interactions, hydrocarbon thermochemistry, isomerization energies, electronic excitation energies, absolute atomic energies, and molecular structures. When compared with 82 other density functionals that have been defined in the literature, MN15 gives the second smallest mean unsigned error (MUE) for 54 data on inherently multiconfigurational systems, the smallest MUE for 313 single-reference chemical data, and the smallest MUE on 87 noncovalent data, with MUEs for these three categories of 4.75, 1.85, and 0.25 kcal mol-1, respectively, as compared to the average MUEs of the other 82 functionals of 14.0, 4.63, and 1.98 kcal mol-1. The MUE for 17 absolute atomic energies is 7.4 kcal mol-1 as compared to an average MUE of the other 82 functionals of 34.6 kcal mol-1. We further tested MN15 for 10 transition-metal coordination energies, the entire S66x8 database of noncovalent interactions, 21 transition-metal reaction barrier heights, 69 electronic excitation energies of organic molecules, 31 semiconductor band gaps, seven transition-metal dimer bond lengths, and 193 bond lengths of 47 organic molecules. The MN15 functional not only performs very well for our training set, which has 481 pieces of data, but also performs very well for our test set, which has 823 data that are not in our training set. The test set includes both ground-state properties and molecular excitation energies. For the latter MN15 achieves simultaneous accuracy for both valence and Rydberg electronic excitations when used with linear-response time-dependent density functional theory, with an MUE of less than 0.3 eV for both types of excitations.

Silane-initiated nucleation in chemically active plasmas: validation of density functionals, mechanisms, and pressure-dependent variational transition state calculations.

The growth of anionic silicon hydride clusters is a critically important process in nanodusty plasmas. In the current study, we focus on the formation of homologs of silylene (Sin+1H2n+2(-), n = 3, 4) and silyl (SinH2n+1(-), n = 4, 5) anions via anion-neutral reaction pathways. Species like silyl or silylene anions and their related elementary reactions, which are involved in the formation of silicon hydride clusters, were not used in developing exchange-correlation (xc) density functionals (i.e., they were not included in the training set of semiempirical density functionals); therefore, we explored the accuracy of various widely used xc density functionals based on reaction energies and barrier heights. Among the 21 density functionals we tested, M06-2X has the best performance for a hybrid functional, and MN15-L has the best performance for a local functional. Thermal rate constants of the elementary reactions involved in the reaction mechanism are calculated using M06-2X and multistructural canonical variational transition state theory with the small-curvature tunneling approximation (MS-CVT/SCT). The pressure dependence of unimolecular isomerization reactions is treated with system-specific quantum RRK theory (SS-QRRK) and the Lindemann-Hinshelwood mechanism.

Theoretical study of the auto-catalyzed hydrolysis reaction of sulfur dioxide

The hydrolysis reaction of sulfur dioxide (SO2) to form sulfurous acid involving additional sulfurous acid (H2SO3) was investigated using high-level computational methods. With H2SO3, the reaction takes place via a double proton transfer process with a cage-like structure, which is different from the planar ring structure involved in a corresponding process with an additional water molecule (served as a catalyst). Our results show that H2SO3 is a better catalyst than water, as the barrier height for the H2SO3-catalyzed reaction is only 5.5kcal/mol, compared to over 25.0 and 15.0kcal/mol for the reaction without a catalyst and the H2O-catalyzed reaction, respectively. In addition, the sulfurous acid dimer from the H2SO3-catalyzed reaction is more stable than hydrated H2SO3 from the H2O-catalyzed reaction. Considering the existence of sulfurous acid in the aqueous phase and acidic aerosols, as well as the importance of SO2 and H2O in the atmosphere, our results will have potentially significant implications on the homogeneous and heterogeneous nucleation processes.

Multistate density function theory and the construction of diabatic and adiabatic potential energy surfaces

A multistate density function theory( MSDFT) based on valence bond theory was introduced. As an application,the MSDFT method was illustrated by the bond dissociation of H2 and the proton transfer between HNO3 and a water molecule. In the dissociation of H2,the MSDFT method yields a correct behavior as the two H atoms stretch to infinity,and gives a potential well in accord with second-order perturbation using complete active space( CASPT2). For the proton transfer process of HNO3,MSDFT can be used to yield both diabatic and adiabatic potential energy curves as a function of the proton transfer reaction coordinate. For the reaction barrier height,the inclusion of an ionic state in a three-state model can significantly improve the accuracy in barrier height in comparison with the high-level results.

Substrate Vibrations as Promoters of Chemical Reactivity on Metal Surfaces.

Studies exploring how vibrational energy (Evib) promotes chemical reactivity most often focus on molecular reagents, leaving the role of substrate atom motion in heterogeneous interfacial chemistry underexplored. This combined theoretical and experimental study of methane dissociation on Ni(111) shows that lattice atom motion modulates the reaction barrier height during each surface atom's vibrational period, which leads to a strong variation in the reaction probability (S0) with surface temperature (Tsurf). State-resolved beam-surface scattering studies at Tsurf = 90 K show a sharp threshold in S0 at translational energy (Etrans) = 42 kJ/mol. When Etrans decreases from 42 kJ/mol to 34 kJ/mol, S0 decreases 1000-fold at Tsurf = 90 K, but only 2-fold at Tsurf = 475 K. Results highlight the mechanism for this effect, provide benchmarks for DFT calculations, and suggest the potential importance of surface atom induced barrier height modulation in heterogeneously catalyzed reactions, particularly on structurally labile nanoscale particles and defect sites.

Toward a Database of Chemically Accurate Barrier Heights for Reactions of Molecules with Metal Surfaces

Being able to calculate reaction barrier heights to within chemical accuracy (errors < 1 kcal/mol) is crucial to the accurate modeling of chemical reactions. Although accurate databases exist that can help theorists with benchmarking new electronic structure theories on gas-phase chemical reactions, no such databases exist for reactions of molecules with metal surfaces. Nonetheless, most chemicals are made in heterogeneously catalyzed processes, of which many take place over metal particles. Presently, barrier heights for molecule-metal surface reactions have been determined with chemical accuracy for only two systems, that is, H2 + Cu(111) and H2 + Cu(100). This has been done with semiempirically determined density functionals, which were fitted through comparisons of dynamics results with molecular beam sticking probabilities. The prospects of extending the database with chemically accurate data for other molecule-metal reactions, either with the use of semiempirical density functional theory or with first-principles theory, are discussed.

Kinetics of the Hydrogen Abstraction Reaction From 2-Butanol by OH Radical.

The kinetics of the hydrogen abstraction from 2-butanol by hydroxyl radical have been studied using multipath variational transition-state theory with the multidimensional small curvature tunneling approximation. The rate constants for each of the five hydrogen abstraction sites (C1, C2, C3, C4, and O) and the overall reaction have been computed by direct dynamics based on M08-HX/6-311+G(2df,2p) electronic structure calculations. We show that multistructural torsional anharmonicity, anharmonicity differences of high-frequency modes between the transition structures and the reactants, and reaction-path dependence of multiple reaction paths are all important factors for determining accurate reaction rates and branching fractions for this problem. The reaction barrier heights for abstraction from various sites follow the order C2 < C3 < C4 < C1 < O, but the reactivities of the various sites do not precisely follow the inverse order of barrier heights, and the order of reactivities depends on temperature. The abstractions from C2 and C3 have the largest contribution to the total reaction rate from 200 to 2000 K.

Construction and application of a new dual-hybrid random phase approximation.

The direct random phase approximation (dRPA) combined with Kohn-Sham reference orbitals is among the most promising tools in computational chemistry and applicable in many areas of chemistry and physics. The reason for this is that it scales as N(4) with the system size, which is a considerable advantage over the accurate ab initio wave function methods like standard coupled-cluster. dRPA also yields a considerably more accurate description of thermodynamic and electronic properties than standard density-functional theory methods. It is also able to describe strong static electron correlation effects even in large systems with a small or vanishing band gap missed by common single-reference methods. However, dRPA has several flaws due to its self-correlation error. In order to obtain accurate and precise reaction energies, barriers and noncovalent intra- and intermolecular interactions, we construct a new dual-hybrid dRPA (hybridization of exact and semilocal exchange in both the energy and the orbitals) and test the performance of this new functional on isogyric, isodesmic, hypohomodesmotic, homodesmotic, and hyperhomodesmotic reaction classes. We also use a test set of 14 Diels-Alder reactions, six atomization energies (AE6), 38 hydrocarbon atomization energies, and 100 reaction barrier heights (DBH24, HT-BH38, and NHT-BH38). For noncovalent complexes, we use the NCCE31 and S22 test sets. To test the intramolecular interactions, we use a set of alkane, cysteine, phenylalanine-glycine-glycine tripeptide, and monosaccharide conformers. We also discuss the delocalization and static correlation errors. We show that a universally accurate description of chemical properties can be provided by a large, 75% exact exchange mixing both in the calculation of the reference orbitals and the final energy.

Reaction barrier heights for cycloreversion of heterocyclic rings: An Achilles’ heel for DFT and standard ab initio procedures

We introduce a database of 20 accurate cycloreversion barrier heights of 5-membered heterocyclic rings (to be known as the CRBH20 database). In these reactions, dioxazole and oxathiazole rings are fragmented to form isocyanates, isothiocyanates, and carbonyls. The reference reaction barrier heights are obtained by means of the high-level, ab initio W1-F12 and W1w thermochemical protocols. We evaluate the performance of 65 contemporary density functional theory (DFT) and double-hybrid DFT (DHDFT) procedures. The CRBH20 database represents an extremely challenging test for these methods. Most of the conventional DFT functionals (74%) result in root-mean-square deviations (RMSDs) between 10 and 81kJmol−1. The rest of the DFT functionals attain RMSDs=5−10kJmol−1. Of the 12 tested DHDFT functionals, only five result in RMSDs<10kJmol−1. The CRBH20 dataset also proves to be a surprisingly challenging target for composite and standard ab initio procedures.

Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights.

We consider several spin-unrestricted random-phase approximation (RPA) variants for calculating correlation energies, with and without range separation, and test them on datasets of atomization energies and reaction barrier heights. We show that range separation greatly improves the accuracy of all RPA variants for these properties. Moreover, we show that a RPA variant with exchange, hereafter referred to as RPAx-SO2, first proposed by Szabo and Ostlund [J. Chem. Phys. 67, 4351 (1977)] in a spin-restricted closed-shell formalism, and extended here to a spin-unrestricted formalism, provides on average the most accurate range-separated RPA variant for atomization energies and reaction barrier heights. Since this range-separated RPAx-SO2 method had already been shown to be among the most accurate range-separated RPA variants for weak intermolecular interactions [J. Toulouse et al., J. Chem. Phys. 135, 084119 (2011)], this works confirms range-separated RPAx-SO2 as a promising method for general chemical applications.

Assessment of Orbital-Optimized MP2.5 for Thermochemistry and Kinetics: Dramatic Failures of Standard Perturbation Theory Approaches for Aromatic Bond Dissociation Energies and Barrier Heights of Radical Reactions.

An assessment of orbital-optimized MP2.5 (OMP2.5) [ Bozkaya, U.; Sherrill, C. D. J. Chem. Phys. 2014, 141, 204105 ] for thermochemistry and kinetics is presented. The OMP2.5 method is applied to closed- and open-shell reaction energies, barrier heights, and aromatic bond dissociation energies. The performance of OMP2.5 is compared with that of the MP2, OMP2, MP2.5, MP3, OMP3, CCSD, and CCSD(T) methods. For most of the test sets, the OMP2.5 method performs better than MP2.5 and CCSD, and provides accurate results. For barrier heights of radical reactions and aromatic bond dissociation energies OMP2.5-MP2.5, OMP2-MP2, and OMP3-MP3 differences become obvious. Especially, for aromatic bond dissociation energies, standard perturbation theory (MP) approaches dramatically fail, providing mean absolute errors (MAEs) of 22.5 (MP2), 17.7 (MP2.5), and 12.8 (MP3) kcal mol(-1), while the MAE values of the orbital-optimized counterparts are 2.7, 2.4, and 2.4 kcal mol(-1), respectively. Hence, there are 5-8-folds reductions in errors when optimized orbitals are employed. Our results demonstrate that standard MP approaches dramatically fail when the reference wave function suffers from the spin-contamination problem. On the other hand, the OMP2.5 method can reduce spin-contamination in the unrestricted Hartree-Fock (UHF) initial guess orbitals. For overall evaluation, we conclude that the OMP2.5 method is very helpful not only for challenging open-shell systems and transition-states but also for closed-shell molecules. Hence, one may prefer OMP2.5 over MP2.5 and CCSD as an O(N(6)) method, where N is the number of basis functions, for thermochemistry and kinetics. The cost of the OMP2.5 method is comparable with that of CCSD for energy computations. However, for analytic gradient computations, the OMP2.5 method is only half as expensive as CCSD.

Free-radical copolymerisation of acrylamides, acrylates, and α-olefins

We report the results of a joint theoretical and experimental investigation into the copolymerisation of acrylamides and acrylates with α-olefins in free-radical processes. The transition-state structures of models for free-radical homo- and copolymerisation involving acrylamide, methylacrylamide, methacrylate, methyl methacrylate, and ethylene have been determined using density functional theory. The reaction energies and barrier heights comport with the experimentally observed properties, including the prevalence of monomer alternation, the realised stereospecificity, and the reaction yield. Continuum solvation models have been applied to determine the sensitivity of the relative energies to the bulk solvent properties. Experimentally, a Lewis acid catalyst is demonstrated to increase the incorporation of nonpolar 1-alkenes in copolymerisations with polar acrylamides and acrylates. In the presence of the Lewis acid, scandium (III) trifluoromethanesulfonate, the copolymerisation of 1-hexene and acrylamide results in an 8.5 mol % incorporation, up from 3.9 mol % in the absence of the Lewis acid. Computations incorporating Mg2+ as a model Lewis acid elucidate the mechanism of this catalysis. In the addition of methacrylate to a methyl methacrylate radical terminated polymer, the Lewis acid binds to the carbonyls on both promoting isotactic addition, while for the addition of an alkene to the same polymer, the Lewis acid binds to the polymer, reducing the barrier for alkenyl addition inductively by withdrawing electron density. We have demonstrated the ability of computational studies to aid experimentalists in the synthesis of new copolymers with desired properties.

Final state-resolved mode specificity in HX + OH → X + H2O (X = F and Cl) reactions: A quasi-classical trajectory study

The state-to-state dynamics of the title reactions are investigated using a quasi-classical trajectory method on recently developed accurate global potential energy surfaces. Although both produce the H2O product, these two reactions have very different characteristics in the reaction energy, barrier location, and barrier height. It is shown that the H2O product is moderately excited in its three vibrational modes in the HF + OH reaction, but its stretching modes are highly excited in the HCl + OH reaction. For both reactions, the OH vibrational degree of freedom is essentially a spectator, which sequesters its energy throughout the reaction. On the other hand, the HF vibrational excitation has almost no impact on the H2O vibrational distribution while HCl converts some of its vibrational energy into the stretching modes of H2O. These mode specific correlations can be rationalized by the recently proposed Sudden Vector Projection model.

Assessment of multireference perturbation methods for chemical reaction barrier heights.

A few flavors of multireference perturbation theory, two variants of the n-electron valence state perturbation theory and two of the complete active space perturbation theory, are here tested for the calculation of barrier heights for the set of chemical reactions included in the DBH24/08 database, for which very accurate values are available. The comparison of the results obtained with these approaches with those already published for other theoretical models indicates that multireference perturbation theory is a valuable tool for the description of a chemical reaction. Moreover, limiting the comparison to the perturbation theory approaches, one observes that the bad behavior found for single reference methods (such as Møller-Plesset to second and fourth order in the energy) is markedly improved upon moving to the multireference generalizations.

Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential.

A new non-empirical exchange energy functional of the generalized gradient approximation (GGA) type, which gives an exchange potential with the correct asymptotic behavior, is developed and explored. In combination with the Perdew-Burke-Ernzerhof (PBE) correlation energy functional, the new CAP-PBE (CAP stands for correct asymptotic potential) exchange-correlation functional gives 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 on standard test sets that are fully competitive with those obtained from other GGA-type functionals that do not have the correct asymptotic exchange potential behavior. Distinct from them, the new functional provides important improvements in quantities dependent upon response functions, e.g., static and dynamic polarizabilities and hyperpolarizabilities. CAP combined with the Lee-Yang-Parr correlation functional gives roughly equivalent results. Consideration of the computed dynamical polarizabilities in the context of the broad spectrum of other properties considered tips the balance to the non-empirical CAP-PBE combination. Intriguingly, these improvements arise primarily from improvements in the highest occupied and lowest unoccupied molecular orbitals, and not from shifts in the associated eigenvalues. Those eigenvalues do not change dramatically with respect to eigenvalues from other GGA-type functionals that do not provide the correct asymptotic behavior of the potential. Unexpected behavior of the potential at intermediate distances from the nucleus explains this unexpected result and indicates a clear route for improvement.

Accurate reaction barrier heights of pericyclic reactions: Surprisingly large deviations for the CBS-QB3 composite method and their consequences in DFT benchmark studies.

Accurate barrier heights are obtained for the 26 pericyclic reactions in the BHPERI dataset by means of the high-level Wn-F12 thermochemical protocols. Very often, the complete basis set (CBS)-type composite methods are used in similar situations, but herein it is shown that they in fact result in surprisingly large errors with root mean square deviations (RMSDs) of about 2.5 kcal mol(-1). In comparison, other composite methods, particularly G4-type and estimated coupled cluster with singles, doubles, and quasiperturbative triple excitations [CCSD(T)/CBS] approaches, show deviations well below the chemical-accuracy threshold of 1 kcal mol(-1). With the exception of SCS-MP2 and the herein newly introduced MP3.5 approach, all other tested Møller-Plesset perturbative procedures give poor performance with RMSDs of up to 8.0 kcal mol(-1). The finding that CBS-type methods fail for barrier heights of these reactions is unexpected and it is particularly troublesome given that they are often used to obtain reference values for benchmark studies. Significant differences are identified in the interpretation and final ranking of density functional theory (DFT) methods when using the original CBS-QB3 rather than the new Wn-F12 reference values for BHPERI. In particular, it is observed that the more accurate Wn-F12 benchmark results in lower statistical errors for those methods that are generally considered to be robust and accurate. Two examples are the PW6B95-D3(BJ) hybrid-meta-general-gradient approximation and the PWPB95-D3(BJ) double-hybrid functionals, which result in the lowest RMSDs of the entire DFT study (1.3 and 1.0 kcal mol(-1), respectively). These results indicate that CBS-QB3 should be applied with caution in computational modeling and benchmark studies involving related systems.

Ab initio study of guanine damage by hydroxyl radical.

Multiconfigurational ab initio methods are used in this study to examine two initial reactions that take place during the OH radical attack of the DNA base guanine: a ring opening reaction and a hydrogen transfer reaction. The same reactions are also studied in the presence of a single water molecule. The ring opening reaction has a moderate barrier height of ∼20-25 kcal/mol that is relatively insensitive to the presence of water. The barrier of the H-transfer reaction, on the other hand, is lowered from ∼50 to ∼22 kcal/mol when one water molecule is added, thus becoming comparable to the barrier height of the ring opening reaction.