Coupled Cluster Theory and Multireference Configuration Interaction Study of FO, F2O, FO2, and FOOF

Scalable Ab Initio Electronic Structure Methods with Near Chemical Accuracy for Main Group Chemistry

This study evaluates the precision of widely recognized quantum chemical methodologies, CCSD(T), DLPNO-CCSD(T), and localized ph-AFQMC, for determining the thermochemistry of main group elements. DLPNO-CCSD(T) and localized ph-AFQMC, which offer greater scalability compared to canonical CCSD(T), have emerged over the past decade as pivotal in producing precise benchmark chemical data. Our investigation includes closed-shell, neutral molecules, focusing on their heat of formation and atomization energy sourced from four specific small molecule data sets. First, we selected molecules from the G2 and G3 data sets, noted for their reliable experimental heat of formation data. Additionally, we incorporate molecules from the W4-11 and W4-17 sets, which provide high-level theoretical reference values for atomization energy at 0 K. Our findings reveal that both DLPNO-CCSD(T) and ph-AFQMC methods are capable of achieving a root-mean-square deviation of less than 1 kcal/mol across the combined data set, aligning with the threshold for chemical accuracy. Moreover, we make efforts to confine the maximum deviations within 2 kcal/mol, a degree of precision that significantly broadens the applicability of these methods in fields such as biology and materials science.

Density Functional Geometries and Zero-Point Energies in Ab Initio Thermochemical Treatments of Compounds with First-Row Atoms (H, C, N, O, F)

Density functionals are often used in ab initio thermochemistry to provide optimized geometries for single-point evaluations at a high level and to supply estimates of anharmonic zero-point energies (ZPEs). Their use is motivated by relatively high accuracy at a modest computational expense, but a thorough assessment of geometry-related error seems to be lacking. We have benchmarked 53 density functionals, focusing on approximations of the first four rungs and on relatively small basis sets for computational efficiency. Optimized geometries of 279 neutral first-row molecules (H, C, N, O, F) are judged by energy penalties relative to the best available geometries, using the composite model ATOMIC/B5 as energy probe. Only hybrid functionals provide good accuracy with root-mean-square errors around 0.1 kcal/mol and maximum errors below 1.0 kcal/mol, but not all of them do. Conspicuously, first-generation hybrids with few or no empirical parameters tend to perform better than highly parameterized ones. A number of them show good accuracy already with small basis sets (6-31G(d), 6-311G(d)). As is standard practice, anharmonic ZPEs are estimated from scaled harmonic values. Statistics of the latter show less performance variation among functionals than observed for geometry-related error, but they also indicate that ZPE error will generally dominate. We have selected PBE0-D3/6-311G(d) for the next version of the ATOMIC protocol (ATOMIC-2) and studied it in more detail. Empirical expressions have been calibrated to estimate bias corrections and 95% uncertainty intervals for both geometry-related error and scaled ZPEs.

Domain-based local pair natural orbital methods within the correlation consistent composite approach

Ab initio composite approaches have been utilized to model and predict main group thermochemistry within 1 kcal mol^-1 , on average, from well-established reliable experiments, primarily for molecules with less than 30 atoms. For molecules of increasing size and complexity, such as biomolecular complexes, composite methodologies have been limited in their application. Therefore, the domain-based local pair natural orbital (DLPNO) methods have been implemented within the correlation consistent composite approach (ccCA) framework, namely DLPNO-ccCA, to reduce the computational cost (disk space, CPU (central processing unit) time, memory) and predict energetic properties such as enthalpies of formation, noncovalent interactions, and conformation energies for organic biomolecular complexes including one of the largest molecules examined via composite strategies, within 1 kcal mol^-1 , after calibration with 119 molecules and a set of linear alkanes. © 2019 Wiley Periodicals, Inc.

Accurate theoretical characterization of dioxygen difluoride: a problem resolved

Determination of the minimum structure on a very flat surface is problematic. If r_e(OO) is changed by 0.0025 Å around the minimum, r_e(OF) is changed by 0.01 Å. Vibrational averaging is required.

Structure investigations on oxygen fluorides

The solid state structures of O₂F₂ and OF₂ resemble those in the gaseous state. Attempts to isolate the proposed (O₂⁺)₂PdF₆²⁻ from O₂F in HF result in the formation of (O₂⁺H₃Pd₂F₁₂⁻)_n.

Theoretical study on the ground electronic state of FO(+) and FO(-)

The equilibrium structures of the ground electronic states for molecular ions FO(+) and FO(-) have been calculated by using the multi-reference configuration interaction method in combination with the augmented correlation-consistent basis sets up through sextuple zeta quality. The equilibrium parameters, potential energy curves and spectroscopic constants are derived for both species. The extrapolation schemes are adopted to estimate the complete basis set limit. The corrections of core-valence correlation and relativistic effect are included to improve the accuracy of the calculations. The vibrational energy levels as well as rotational and centrifugal distortion constants of the ground electronic states for both systems are obtained by solving the radial Schrödinger equation of nuclear motion. The computations on neutral FO radical are also carried out to investigate the ionization potentials and the electron affinities.

Gas phase structures of peroxides: experiments and computational problems

Gas-phase structures of several organic and inorganic peroxides X-O-O-X and X-O-O-X', which have been determined experimentally by gas electron diffraction and/or microwave spectroscopy, are discussed. The OO bond length in these peroxides varies from 1.481(8) Å in Me3 SiOOSiMe3 to 1.214(2) Å in FOOF and the dihedral angle ϕ(XO-OX) between 0° in HC(O)O-OH and near 180° in Bu(t) O-OBu(t) . Some of the peroxides cause problems for quantum chemistry, since several computational methods fail to reproduce the experimental structures. Extreme examples are MeO-OMe and FO-OF. In the case of MeO-OMe only about half of the more than 100 computational methods reported in the literature reproduce the experimentally determined double-minimum shape of the torsional potential around the OO bond correctly. For FO-OF only a small number of close to 200 computational methods reproduce the OO and OF bond lengths better than ±0.02 Å.

Explicitly Correlated Methods within the ccCA Methodology

The prediction of energetic properties within "chemical accuracy" (1 kcal mol(-1) from well-established experiment) can be a major challenge in computational quantum chemistry due to the computational requirements (computer time, memory, and disk space) needed to achieve this level of accuracy. Methodologies such as coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) combined with very large basis sets are often required to reach this level of accuracy. Unfortunately, such calculations quickly become cost prohibitive as system size increases. Our group has developed an ab initio composite method, the correlation consistent Composite Approach (ccCA), which enables such accuracy to be possible, on average, but at reduced computational cost as compared with CCSD(T) in combination with a large basis set. While ccCA has proven quite useful, computational bottlenecks still occur. In this study, the means to reduce the computational cost of ccCA without compromising accuracy by utilizing explicitly correlated methods within ccCA have been considered, and an alternative formulation is described.

High-level ab initio enthalpies of formation of 2,5-dimethylfuran, 2-methylfuran, and furan

A high-level ab initio thermochemical technique, known as the Feller-Petersen-Dixon method, is used to calculate the total atomization energies and hence the enthalpies of formation of 2,5-dimethylfuran, 2-methylfuran, and furan itself as a means of rationalizing significant discrepancies in the literature. In order to avoid extremely large standard coupled cluster theory calculations, the explicitly correlated CCSD(T)-F12b variation was used with basis sets up to cc-pVQZ-F12. After extrapolating to the complete basis set limit and applying corrections for core/valence, scalar relativistic, and higher order effects, the final Δ(f)H° (298.15 K) values, with the available experimental values in parentheses are furan -34.8 ± 3 (-34.7 ± 0.8), 2-methylfuran -80.3 ± 5 (-76.4 ± 1.2), and 2,5-dimethylfuran -124.6 ± 6 (-128.1 ± 1.1) kJ mol(-1). The theoretical results exhibit a compelling internal consistency.

Towards highly accurate ab initio thermochemistry of larger systems: benzene

The high accuracy extrapolated ab initio thermochemistry (HEAT) protocol is applied to compute the total atomization energy (TAE) and the heat of formation of benzene. Large-scale coupled-cluster calculations with more than 1500 basis functions and 42 correlated electrons as well as zero-point energies based on full cubic and (semi)diagonal quartic force fields obtained with the coupled-cluster singles and doubles with perturbative treatment of the triples method and atomic natural orbital (ANO) triple- and quadruple-zeta basis sets are presented. The performance of modifications to the HEAT scheme and the scaling properties of its contributions with respect to the system size are investigated. A purely quantum-chemical TAE and associated conservative error bar of 5463.0 ± 3.1 kJ mol(-1) are obtained, while the corresponding 95% confidence interval, based on a statistical analysis of HEAT results for other and related molecules, is ± 1.8 kJ mol(-1). The heat of formation of benzene is determined to be 101.5 ± 2.0 kJ mol(-1) and 83.9 ± 2.1 kJ mol(-1) at 0 K and 298.15 K, respectively.

Structures and heats of formation of simple alkali metal compounds: hydrides, chlorides, fluorides, hydroxides, and oxides for Li, Na, and K

Geometry parameters, frequencies, heats of formation, and bond dissociation energies are predicted for simple alkali metal compounds (hydrides, chlorides, fluorides, hydroxides and oxides) of Li, Na, and K from coupled cluster theory [CCSD(T)] calculations including core-valence correlation with the aug-cc-pwCVnZ basis set (n = D, T, Q, and 5). To accurately calculate the heats of formation, the following additional correction were included: scalar relativistic effects, atomic spin-orbit effects, and vibrational zero-point energies. For calibration purposes, the properties of some of the lithium compounds were predicted with iterative triple and quadruple excitations via CCSDT and CCSDTQ. The calculated geometry parameters, frequencies, heats of formation, and bond dissociation energies were compared with all available experimental measurements and are in excellent agreement with high-quality experimental data. High-level calculations are required to correctly predict that K(2)O is linear and that the ground state of KO is (2)Sigma(+), not (2)Pi, as in LiO and NaO. This reliable and consistent set of calculated thermodynamic data is appropriate for use in combustion and atmospheric simulations.

Heats of formation of XeF(3)(+), XeF(3)(-), XeF(5)(+), XeF(7)(+), XeF(7)(-), and XeF(8) from high level electronic structure calculations

Atomization energies at 0 K and heats of formation at 0 and 298 K are predicted for XeF(3)(+), XeF(3)(-), XeF(5)(+), XeF(7)(+), XeF(7)(-), and XeF(8) from coupled cluster theory (CCSD(T)) calculations with effective core potential correlation-consistent basis sets for Xe and including correlation of the nearest core electrons. Additional corrections are included to achieve near chemical accuracy of +/-1 kcal/mol. Vibrational zero point energies were computed at the MP2 level of theory. Unlike the other neutral xenon fluorides, XeF(8) is predicted to be thermodynamically unstable with respect to loss of F(2) with the reaction calculated to be exothermic by 22.3 kcal/mol at 0 K. XeF(7)(+) is also predicted to be thermodynamically unstable with respect to the loss of F(2) by 24.1 kcal/mol at 0 K. For XeF(3)(+), XeF(5)(+), XeF(3)(-), XeF(5)(-), and XeF(7)(-), the reactions for loss of F(2) are endothermic by 14.8, 37.8, 38.2, 59.6, and 31.9 kcal/mol at 0 K, respectively. The F(+) affinities of Xe, XeF(2), XeF(4), and XeF(6) are predicted to be 165.1, 155.3, 172.7, and 132.5 kcal/mol, and the corresponding F(-) affinities are 6.3, 19.9, 59.1, and 75.0 kcal/mol at 0 K, respectively.

Assessment of the CCSD and CCSD(T) coupled-cluster methods in calculating heats of formation for Zn complexes

Heats of formation were calculated using coupled-cluster methods for a series of zinc complexes. The calculated values were evaluated against previously conducted computational studies using density functional methods as well as experimental values. Heats of formation for nine neutral ZnX(n) complexes [X = -Zn, -H, -O, -F2, -S, -Cl, -Cl2, -CH3, (-CH3)2] were determined at the CCSD and CCSD(T) levels using the 6-31G** and TZVP basis sets as well as the LANL2DZ-6-31G** (LACVP**) and LANL2DZ-TZVP hybrid basis sets. The CCSD(T)/6-31G** level of theory was found to predict the heat of formation for the nonalkyl Zn complexes most accurately. The alkyl Zn species were problematic in that none of the methods that were tested accurately predicted the heat of formation for these complexes. In instances where experimental geometric parameters were available, these were most accurately predicted by the CCSD/6-31G** level of theory; going to CCSD(T) did not improve agreement with the experimental values. Coupled-cluster methods did not offer a systemic improvement over DFT calculations for a given functional/basis set combination. With the exceptions of ZnH and ZnF2, there are multiple density functionals that outperform coupled-cluster calculations with the 6-31G** basis set.

Highly accurate first-principles benchmark data sets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics

We present a number of near-exact, nonrelativistic, Born-Oppenheimer reference data sets for the parametrization of more approximate methods (such as DFT functionals). The data were obtained by means of the W4 ab initio computational thermochemistry protocol, which has a 95% confidence interval well below 1 kJ/mol. Our data sets include W4-08, which are total atomization energies of over 100 small molecules that cover varying degrees of nondynamical correlations, and DBH24-W4, which are W4 theory values for Truhlar's set of 24 representative barrier heights. The usual procedure of comparing calculated DFT values with experimental atomization energies is hampered by comparatively large experimental uncertainties in many experimental values and compounds errors due to deficiencies in the DFT functional with those resulting from neglect of relativity and finite nuclear mass. Comparison with accurate, explicitly nonrelativistic, ab initio data avoids these issues. We then proceed to explore the performance of B2x-PLYP-type double hybrid functionals for atomization energies and barrier heights. We find that the optimum hybrids for hydrogen-transfer reactions, heavy-atoms transfers, nucleophilic substitutions, and unimolecular and recombination reactions are quite different from one another: out of these subsets, the heavy-atom transfer reactions are by far the most sensitive to the percentages of Hartree-Fock-type exchange y and MP2-type correlation x in an (x, y) double hybrid. The (42,72) hybrid B2K-PLYP, as reported in a preliminary communication, represents the best compromise between thermochemistry and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochemistry and the DBH24-W4 data set, however, we find a new (36,65) hybrid which we term B2GP-PLYP. At a slight expense in performance for hydrogen-transfer barrier heights and nucleophilic substitutions, we obtain substantially better performance for the other reaction types. Although both B2K-PLYP and B2GP-PLYP are capable of 2 kcal/mol quality thermochemistry, B2GP-PLYP appears to be the more robust toward nondynamical correlation and strongly polar character. We additionally find that double-hybrid functionals display excellent performance for such problems as hydrogen bonding, prototype late transition metal reactions, pericyclic reactions, prototype cumulene-polyacetylene system, and weak interactions.

Density Functional Study of Structures and Electron Affinities of BrO4F/BrO4F-

The structures, electron affinities and bond dissociation energies of BrO₄F/BrO₄F⁻ species have been investigated with five density functional theory (DFT) methods with DZP++ basis sets. The planar F-Br…O₂…O₂ complexes possess ³A′ electronic state for neutral molecule and ⁴A′ state for the corresponding anion. Three types of the neutral-anion energy separations are the adiabatic electron affinity (EA_ad), the vertical electron affinity (EA_vert), and the vertical detachment energy (VDE). The EA_ad value predicted by B3LYP method is 4.52 eV. The bond dissociation energies D_e (BrO₄F → BrO_4-mF + O_m) (m = 1–4) and D_e⁻ (BrO₄F⁻ → BrO_4-mF⁻ + O_m and BrO₄F⁻ → BrO_4-mF + O_m⁻) are predicted. The adiabatic electron affinities (EA_ad) were predicted to be 4.52 eV for F-Br…O₂…O₂ (³A′←⁴A′) (B3LYP method).