Junwei Lucas Bao

Hydrogen Abstraction Reactions from Phenolic Compounds by Peroxyl Radicals: Multireference Character and Density Functional Theory Rate Constants.

An assessment of multireference character in transition states is considered to be an important component in establishing the expected reliability of various electronic structure methods. In the present work, the multireference characters of the transition states and the forming and breaking of bonds for a large set of hydrogen abstraction reactions from phenolic compounds by peroxyl radicals have been analyzed using the T1, M, B1, and GB1 diagnostics. The extent of multireference character depends on the system and on the conditions under which the reaction takes place, and some systematic trends are observed. In particular, the multireference character is found to be reduced by solvation, the size of the phenolic compound, and deprotonation in aqueous solution. However, the deviations of calculated rate constants from experimental ones are not correlated with the extent of multireference character. The performance of single-determinant density functional theory was investigated for the kinetics of these reactions by comparing calculated rate constants to experimental data; the results from these analyses showed that the M05 functional performs well for the task at hand.

Kinetics of Hydrogen Radical Reactions with Toluene Including Chemical Activation Theory Employing System-Specific Quantum RRK Theory Calibrated by Variational Transition State Theory

Pressure-dependent reactions are ubiquitous in combustion and atmospheric chemistry. We employ a new calibration procedure for quantum Rice-Ramsperger-Kassel (QRRK) unimolecular rate theory within a chemical activation mechanism to calculate the pressure-falloff effect of a radical association with an aromatic ring. The new theoretical framework is applied to the reaction of H with toluene, which is a prototypical reaction in the combustion chemistry of aromatic hydrocarbons present in most fuels. Both the hydrogen abstraction reactions and the hydrogen addition reactions are calculated. Our system-specific (SS) QRRK approach is adjusted with SS parameters to agree with multistructural canonical variational transition state theory with multidimensional tunneling (MS-CVT/SCT) at the high-pressure limit. The new method avoids the need for the usual empirical estimations of the QRRK parameters, and it eliminates the need for variational transition state theory calculations as a function of energy, although in this first application we do validate the falloff curves by comparing SS-QRRK results without tunneling to multistructural microcanonical variational transition state theory (MS-μVT) rate constants without tunneling. At low temperatures, the two approaches agree well with each other, but at high temperatures, SS-QRRK tends to overestimate falloff slightly. We also show that the variational effect is important in computing the energy-resolved rate constants. Multiple-structure anharmonicity, torsional-potential anharmonicity, and high-frequency-mode vibrational anharmonicity are all included in the rate computations, and torsional anharmonicity effects on the density of states are investigated. Branching fractions, which are both temperature- and pressure-dependent (and for which only limited data is available from experiment), are predicted as a function of pressure.

Correlated-Participating-Orbitals Pair-Density Functional Method and Application to Multiplet Energy Splittings of Main-Group Divalent Radicals.

Predicting the singlet-triplet splittings of divalent radicals is a challenging task for electronic structure theory. In the present work, we investigate the performance of multiconfiguration pair-density functional theory (MC-PDFT) for computing the singlet-triplet splitting for small main-group divalent radicals for which accurate experimental data are available. In order to define theoretical model chemistries that can be assessed consistently, we define three correlated participating orbitals (CPO) schemes (nominal, moderate, and extended, abbreviated as nom, mod, and ext) to define the constitution of complete active spaces, and we test them systematically. Broken-symmetry Kohn-Sham DFT calculations have also been carried out for comparison. We found that the extended CPO-PDFT scheme with translated on-top pair-density functionals have smaller mean unsigned errors than weighted-average broken-symmetry Kohn-Sham DFT with the corresponding exchange-correlation functional. The accuracy of the translated Perdew-Burke-Ernzerhof (tPBE) on-top pair-density functionals with ext-CPO active space is even better than some of the more accurately parametrized exchange-correlation density functionals that we tested; this is very encouraging for MC-PDFT theory.

Path-dependent variational effects and multidimensional tunneling in multi-path variational transition state theory: rate constants calculated for the reactions of HO2 with tert-butanol by including all 46 paths for abstraction at C and all six paths for abstraction at O

Multi-path variational transition state theory (MP-VTST) provides a conformationally complete framework for calculating gas-phase rate constants. For reactions in which the transition state has distinguishable torsional minima (which include most reactions), there are multiple possible reaction paths. In principle MP-VTST includes the contributions from all the reaction paths, and it should explicitly treat the variational and tunneling effects of each path, but in practice one may need to truncate the number of paths included in MP-VTST calculations in order to achieve a balance between computational cost and accuracy. In this work, we present calculations including all paths for two prototype combustion reactions, namely the two hydrogen abstraction reactions from tert-butanol by HO2 radical. For both reactions we included all the reaction paths. Since abstraction at C has 46 paths, it provided a good opportunity to carry out a case study in which we investigated the errors introduced by truncating the number of paths. For the reaction studied, we found that the variational and multidimensional tunneling transmission coefficients are very different for different reaction paths, which provides new evidence that MP-VTST is necessary for treating path-dependent variational effects and multidimensional tunneling. We found that tunneling transmission coefficients can be much larger for higher-energy paths than for lower-energy ones. Interestingly, the simple hypothesis that higher barriers are narrower does not explain this finding in the present case; we found instead that the effect is due to higher-energy barriers having the possibility of tunneling at energies farther below the barrier top. We also show that a previously applied criterion for judging convergence with respect to the number of paths may not be reliable at low temperature.

Predicting Bond Dissociation Energies of Transition-Metal Compounds by Multiconfiguration Pair-Density Functional Theory and Second-Order Perturbation Theory Based on Correlated Participating Orbitals and Separated Pairs

We study the performance of multiconfiguration pair-density functional theory (MC-PDFT) and multireference perturbation theory for the computation of the bond dissociation energies in 12 transition-metal-containing diatomic molecules and three small transition-metal-containing polyatomic molecules and in two transition-metal dimers. The first step is a multiconfiguration self-consistent-field calculation, for which two choices must be made: (i) the active space and (ii) its partition into subspaces, if the generalized active space formulation is used. In the present work, the active space is chosen systematically by using three correlated-participating-orbitals (CPO) schemes, and the partition is chosen by using the separated-pair (SP) approximation. Our calculations show that MC-PDFT generally has similar accuracy to CASPT2, and the active-space dependence of MC-PDFT is not very great for transition-metal-ligand bond dissociation energies. We also find that the SP approximation works very well, and in particular SP with the fully translated BLYP functional SP-ftBLYP is more accurate than CASPT2. SP greatly reduces the number of configuration state functions relative to CASSCF. For the cases of FeO and NiO with extended-CPO active space, for which complete active space calculations are unaffordable, SP calculations are not only affordable but also of satisfactory accuracy. All of the MC-PDFT results are significantly better than the corresponding results with broken-symmetry spin-unrestricted Kohn-Sham density functional theory. Finally we test a perturbation theory method based on the SP reference and find that it performs slightly worse than CASPT2 calculations, and for most cases of the nominal-CPO active space, the approximate SP perturbation theory calculations are less accurate than the much less expensive SP-PDFT calculations.

Self-Interaction Error in Density Functional Theory: An Appraisal

Self-interaction error (SIE) is considered to be one of the major sources of error in most approximate exchange-correlation functionals for Kohn-Sham density-functional theory (KS-DFT), and it is large with all local exchange-correlation functionals and with some hybrid functionals. In this work, we consider systems conventionally considered to be dominated by SIE. For these systems, we demonstrate that by using multiconfiguration pair-density functional theory (MC-PDFT), the error of a translated local density-functional approximation is significantly reduced (by a factor of 3) when using an MCSCF density and on-top density, as compared to using KS-DFT with the parent functional; the error in MC-PDFT with local on-top functionals is even lower than the error in some popular KS-DFT hybrid functionals. Density-functional theory, either in MC-PDFT form with local on-top functionals or in KS-DFT form with some functionals having 50% or more nonlocal exchange, has smaller errors for SIE-prone systems than does CASSCF, which has no SIE.

Predicting pressure-dependent unimolecular rate constants using variational transition state theory with multidimensional tunneling combined with system-specific quantum RRK theory: a definitive test for fluoroform dissociation

Understanding the falloff in rate constants of gas-phase unimolecular reaction rate constants as the pressure is lowered is a fundamental problem in chemical kinetics, with practical importance for combustion, atmospheric chemistry, and essentially all gas-phase reaction mechanisms. In the present work, we use our recently developed system-specific quantum RRK theory, calibrated by canonical variational transition state theory with small-curvature tunneling, combined with the Lindemann-Hinshelwood mechanism, to model the dissociation reaction of fluoroform (CHF3), which provides a definitive test for falloff modeling. Our predicted pressure-dependent thermal rate constants are in excellent agreement with experimental values over a wide range of pressures and temperatures. The present validation of our methodology, which is able to include variational transition state effects, multidimensional tunneling based on the directly calculated potential energy surface along the tunneling path, and torsional and other vibrational anharmonicity, together with state-of-the-art reaction-path-based direct dynamics calculations, is important because the method is less empirical than models routinely used for generating full mechanisms, while also being simpler in key respects than full master equation treatments and the full reduced falloff curve and modified strong collision methods of Troe.

Unimolecular reaction of acetone oxide and its reaction with water in the atmosphere

Significance Obtaining rate constants and tropospheric lifetimes of Criegee intermediates is of critical significance for atmospheric modeling. We report calculations that can produce quantitative rate constants by variational transition state theory with corner-cutting tunneling based on implicit potential energy surfaces calibrated against high-level calculations. Demonstration of this capability is particularly significant because the calculations can fully cover the atmospheric conditions, which is hard to do by experiment. The present results also show the usefulness of the M11-L and MN15-L density functionals in describing this nominally multireference system. Modern quantum chemistry is now accurate enough to be used for atmospheric chemistry, and the present methods and strategies can be also be used to study other atmospherically important reactions of other medium-sized molecules. Criegee intermediates (i.e., carbonyl oxides with two radical sites) are known to be important atmospheric reagents; however, our knowledge of their reaction kinetics is still limited. Although experimental methods have been developed to directly measure the reaction rate constants of stabilized Criegee intermediates, the experimental results cover limited temperature ranges and do not completely agree well with one another. Here we investigate the unimolecular reaction of acetone oxide [(CH3)2COO] and its bimolecular reaction with H2O to obtain rate constants with quantitative accuracy comparable to experimental accuracy. We do this by using CCSDT(Q)/CBS//CCSD(T)-F12a/DZ-F12 benchmark results to select and validate exchange-correlation functionals, which are then used for direct dynamics calculations by variational transition state theory with small-curvature tunneling and torsional and high-frequency anharmonicity. We find that tunneling is very significant in the unimolecular reaction of (CH3)2COO and its bimolecular reaction with H2O. We show that the atmospheric lifetimes of (CH3)2COO depend on temperature and that the unimolecular reaction of (CH3)2COO is the dominant decay mode above 240 K, while the (CH3)2COO + SO2 reaction can compete with the corresponding unimolecular reaction below 240 K when the SO2 concentration is 9 × 1010 molecules per cubic centimeter. We also find that experimental results may not be sufficiently accurate for the unimolecular reaction of (CH3)2COO above 310 K. Not only does the present investigation provide insights into the decay of (CH3)2COO in the atmosphere, but it also provides an illustration of how to use theoretical methods to predict quantitative rate constants of medium-sized Criegee intermediates.

Multiconfiguration Pair-Density Functional Theory Is Free From Delocalization Error

Delocalization error has been singled out by Yang and co-workers as the dominant error in Kohn-Sham density functional theory (KS-DFT) with conventional approximate functionals. In this Letter, by computing the vertical first ionization energy for well separated He clusters, we show that multiconfiguration pair-density functional theory (MC-PDFT) is free from delocalization error. To put MC-PDFT in perspective, we also compare it with some Kohn-Sham density functionals, including both traditional and modern functionals. Whereas large delocalization errors are almost universal in KS-DFT (the only exception being the very recent corrected functionals of Yang and co-workers), delocalization error is removed by MC-PDFT, which bodes well for its future as a step forward from KS-DFT.

Dual-Level Method for Estimating Multistructural Partition Functions with Torsional Anharmonicity

For molecules with multiple torsions, an accurate evaluation of the molecular partition function requires consideration of multiple structures and their torsional-potential anharmonicity. We previously developed a method called MS-T for this problem, and it requires an exhaustive conformational search with frequency calculations for all the distinguishable conformers; this can become expensive for molecules with a large number of torsions (and hence a large number of structures) if it is carried out with high-level methods. In the present work, we propose a cost-effective method to approximate the MS-T partition function when there are a large number of structures, and we test it on a transition state that has eight torsions. This new method is a dual-level method that combines an exhaustive conformer search carried out by a low-level electronic structure method (for instance, AM1, which is very inexpensive) and selected calculations with a higher-level electronic structure method (for example, density functional theory with a functional that is suitable for conformational analysis and thermochemistry). To provide a severe test of the new method, we consider a transition state structure that has 8 torsional degrees of freedom; this transition state structure is formed along one of the reaction pathways of the hydrogen abstraction reaction (at carbon-1) of ketohydroperoxide (KHP; its IUPAC name is 4-hydroperoxy-2-pentanone) by OH radical. We find that our proposed dual-level method is able to significantly reduce the computational cost for computing MS-T partition functions for this test case with a large number of torsions and with a large number of conformers because we carry out high-level calculations for only a fraction of the distinguishable conformers found by the low-level method. In the example studied here, the dual-level method with 40 high-level optimizations (1.8% of the number of optimizations in a coarse-grained full search and 0.13% of the number of optimizations in a fine-grained full search) reproduces the full calculation of the high-level partition function within a factor of 1.0 to 2.0 from 200 to 1000 K. The error in the dual-level method can be further reduced to factors of 0.6 to 1.1 over the whole temperature interval from 200 to 2400 K by optimizing 128 structures (5.9% of the number of optimizations in a fine-grained full search and 0.41% of the number of optimizations in a fine-grained full search). These factor-of-two or better errors are small compared to errors up to a factor of 1.0 × 103 if one neglects multistructural effects for the case under study.