CBS extrapolation of Hartree-Fock energy: Pople and Dunning basis sets hand-to-hand on the endeavour

Quasiclassical Trajectory Study of the Si + SH Reaction on an Accurate Double Many-Body Expansion Potential Energy Surface

An accurate potential energy surface (PES) for the HSiS system based on MRCI+Q calculations extrapolated to the complete basis set limit is presented. Modeled with the double many-body expansion (DMBE) method, the PES provides an accurate description of the long-range interactions, including electrostatic and dispersion terms decaying as R^-4, R^-5, R^-6, R^-8, R^-10 that are predicted from dipole moments, quadrupole moments, and dipolar polarizabilities, which are also calculated at the MRCI+Q level. The novel PES is then used in quasiclassical trajectory calculations to predict the rate coefficients of the Si + SH → SiS + H reaction, which has been shown to be a major source of the SiS in certain regions of the interstellar medium. An account of the zero-point energy leakage based on various nonactive models is also given. It is shown that the reaction is dominated by long-range forces, with the mechanism Si + SH → SiSH → SSiH → SiS + H being the most important one for all temperatures studied. Although SSiH corresponds to the global minimum of the PES, the contribution from the direct reaction Si + SH → SSiH → SiS + H is less than 0.5% for temperatures higher than 500 K. The rovibrational distributions of the products are calculated using the momentum Gaussian binning method and show that as the temperature is increased the average vibrational quantum number decreases while the rotational distribution spreads up to larger values.

From six to eight Π-electron bare rings of group-XIV elements and beyond: can planarity be deciphered from the "quasi-molecules" they embed?

Ab initio molecular orbital theory is used to study the structures of six and eight π-electron bare rings of group-XIV elements, and even larger [n]annulenes up to C₁₈H₁₈, including some of their mono-, di-, tri-, and tetra-anions. While some of the above rings are planar, others are nonplanar. A much spotlighted case is cyclo-octatetraene (C₈H₈), which is predicted to be nonplanar together with its heavier group-XIV analogues Si₈H₈ and Ge₈H₈, with the solely planar members of its family having the stoichiometric formulas C₄Si₄H₈ and C₄Ge₄H₈. A similar situation arises with the six π-electron bare rings, where benzene and substituted ones up to C₃Si₃H₆ or so are planar, while others are not. However, the explanations encountered in the literature find support in ab initio calculations for such species, often rationalized from distinct calculated features. Using second-order Møller-Plesset perturbation theory and, when affordable (particularly tetratomics, which may allow even higher levels), the coupled-cluster method including single, double, and perturbative triple excitations, a common rationale is suggested based on a novel concept of quasi-molecules or the (3+4)-atom partition scheme. Any criticism of tautology is therefore avoided. The same analysis has also been successfully applied to even larger [n]annulenes, to their mixed family members involving silicon and germanium atoms, and to the C₁₈ carbon ring. Furthermore, it has been extended to annulene anions to check the criteria of the popular Hückel rule for planarity and aromaticity. Exploratory work on cycloarenes is also reported. Besides a partial study of the involved potential energy surfaces, equilibrium geometries and harmonic vibrational frequencies have been calculated anew, for both the parent and the actual prototypes of the quasi-molecules.

Molybdenum-Sulfur Bond: Electronic Structure of Low-Lying States of MoS

The molybdenum-sulfur bond plays an important role in many processes such as nitrogen-fixation, and it is found as a building block in layered materials such as MoS₂, known for its various shapes and morphologies. Here, we present an accurate theoretical and experimental investigation of the chemical bonding and the electronic structure of 20 low-lying states of the MoS molecule. Multireference and coupled cluster methodologies, namely, MRCISD, MRCISD + Q, RCCSD(T), and RCCSD[T], were employed in conjunction with basis sets up to aug-cc-pwCV5Z-PP/aug-cc-pwCV5Z for the study of these states. We note the significance of including the inner 4s²4p⁶ electrons of Mo and 2s²2p⁶ of S in the correlated space to obtain accurate results. Experimentally, the predissociation threshold of MoS was measured using resonant two-photon ionization spectroscopy, allowing for a precise measurement of the bond dissociation energy. Our extrapolated computational D₀ value for the ground state is 3.936 eV, in excellent agreement with our experimental measurement of 3.932 ± 0.004 eV. The largest calculated adiabatic D₀ (5.74 eV) and the largest dipole moment (6.50 D) were found for the ⁵Σ⁺ state, where a triple bond is formed. Finally, the connection of the chemical bonding of the isolated MoS species to the relevant solid, MoS₂, is emphasized. The low-lying septet states of the diatomic molecule are involved in the material as a building block, explaining the stability and the variety of the shapes and morphologies of the material.

Optimized Structural Data at the Complete Basis Set Limit via Successive Quadratic Minimizations

Two variants of a successive quadratic minimization method (SQM and c-SQM) are suggested to calculate the structural properties of molecular systems at the complete basis set (CBS) limit. When applied to H₃⁺, H₂O, CH₂O, SH₂, and SO₂, they revealed CBS/(x₁, x₂) structural parameters that significantly surpass the raw ones calculated at the x₂ basis set level. Such a performance has also been verified for the intricate case of the water dimer. Because the c-SQM method is system specific, thus showing somewhat enhanced results relative to the general SQM protocol, it can be of higher cost depending on the level of calibration used. Yet, it hardly surpasses the general quality of the results obtained with the cost-effective SQM method. Since the number of cycles required to reach convergence is relatively small, both schemes are simple to use and easily adaptable to any of the existing extrapolation schemes for the Hartree-Fock and correlation energies.

Post-complete-basis-set extrapolation of conventional and explicitly correlated coupled-cluster energies: can the convergence to the CBS limit be diagnosed?

We assess benchmark correlation energies for 130 systems in test sets A24 and TS-106 both with the canonical CCSD(T) and explicitly correlated CCSD(T)-F12 methods. Aiming at enhanced accuracy, the calculated raw energies from both sets are CBS extrapolated to the complete basis set (CBS) limit and subsequently post-CBS extrapolated. Attention is focused at total energies, since their accuracy reflects on that of the interaction energies. Using up to triple-ζ basis sets for CBS and an additional quadruple-ζ for post-CBS, the mean and standard unsigned deviations with canonical CCSD(T) theory are 0.257 ± 0.25 kcal mol^-1, while the corresponding values for CCSD(T)-F12 in its F12a and F12b variants with specialized basis sets up to VQZ-F12 are 0.170 ± 0.13 kcal mol^-1 and 0.048 ± 0.04 kcal mol^-1. Although these show gains at post-CBS level that vary from 0.08 to 0.20 kcal mol^-1 relative to their CCSD(T)/VXZ analogues, the convergence is somewhat less clear when extending the basis up to V5Z-F12, the highest-rung available: 0.220 ± 0.17 kcal mol^-1 and 0.142 ± 0.08 kcal mol^-1, in the same order. An explanation for the up to one order of magnitude smaller deviations in energy differences is detailed. Based on energy differences involving basis set pairs employed for extrapolating to the CBS limit, a convergence diagnostic is also suggested. Arising from irregularities in the basis set that directly correlate with non-dynamical correlation, the new diagnostic may complement popular ones that feature other aspects of correlation.

Extrapolation in quantum chemistry: Insights on energetics and reaction dynamics

Since there is no exact solution for problems in physics and chemistry, extrapolation methods may assume a key role in quantitative quantum chemistry. Two topics where it bears considerable impact are addressed, both at the heart of computational quantum chemistry: electronic structure and reaction dynamics. In the first, the problem of extrapolating the energy obtained by solving the electronic Schrödinger equation to the limit of the complete one-electron basis set is addressed. With the uniform-singlet-and-triplet-extrapolation (USTE) scheme at the focal point, the emphasis is on recent updates covering from the energy itself to other molecular properties. The second topic refers to extrapolation of quantum mechanical reactive scattering probabilities from zero total angular momentum to any of the values that it may assume when running quasiclassical trajectories, QCT/QM-[Formula: see text]J. With the extrapolation guided in both cases by physically motivated asymptotic theories, realism is seeked by avoiding unsecure jumps into the unknown. Although, mostly review oriented, a few issues are addressed for the first time here and there. Prospects for future work conclude the overview.

Basis Set Extrapolations for Density Functional Theory

Basis set extrapolation is a common technique in wavefunction theory used to squeeze better performance out of the highest affordable level of theory by combining it with lower quality calculations. In this work, I present analogous techniques for basis set extrapolation in density functional theory, focusing on [2,3]-ζ calculations and including double hybrid and dispersion-corrected functionals. My recommendations are based on basis set limit data from finite element calculations and estimates of basis set limits for double hybrid corrections, and they are validated using the GMTKN55 and NCDT datasets. A short review of extrapolation methods for Hartree-Fock calculations based on modern finite element data is carried out to inform this work. Extrapolation of [2,3]-ζ calculations in def2-Xzvpd and cc-pvXz-pp basis sets with the proposed recipes routinely matches and sometimes outperforms 4-ζ calculations at a fraction of the cost. The methods are implemented in Psi4, allowing for an automated and intuitive application.

Kinetics and Thermodynamics of Reactions Involving Criegee Intermediates: An Assessment of Density Functional Theory and Ab Initio Methods Through Comparison with CCSDT(Q)/CBS Data

Reactions involving Criegee intermediates (CIs, R₁ R₂ COO) are important in atmospheric ozonolysis models. In recent years, density functional theory (DFT) and CCSD(T)-based ab initio methods are increasingly being used for modeling reaction profiles involving CIs. We obtain highly accurate CCSDT(Q)/CBS reaction energies and barrier heights for ring-closing reactions involving atmospherically important CIs (R₁ /R₂ = H, Me, OH, OMe, F, CN, cyclopropene, ethylene, acetaldehyde, and acrolein). We use this benchmark data to evaluate the performance of DFT, double-hybrid DFT (DHDFT), and ab initio methods for the kinetics and thermodynamics of these reactions. We find that reaction energies are more challenging for approximate theoretical procedures than barrier heights. Overall, taking both reaction energies and barrier heights into account, only one of the 58 considered DFT methods (the meta-GGA MN12-L) attains near chemical accuracy, with root-mean-square deviations (RMSDs) of 3.5 (barrier heights) and 4.7 (reaction energies) kJ mol^-1 . Therefore, MN12-L is recommended for investigations where CCSD(T)-based methods are not computationally feasible. For reaction barrier heights performance does not strictly follow Jacob's Ladder, for example, DHDFT methods do not perform better than conventional DFT methods. Of the ab initio methods, the cost-effective CCSD(T)/CBS(MP2) approach gives the best performance for both reaction energies and barrier heights, with RMSDs of 1.7 and 1.4 kJ mol^-1 , respectively. All the considered Gaussian-n methods show good performance with RMSDs below the threshold of chemical accuracy for both reaction energies and barrier heights, where G4(MP2) shows the best overall performance with RMSDs of 2.9 and 1.5 kJ mol^-1 , respectively. © 2019 Wiley Periodicals, Inc.