Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds

A meta-GGA level screened range-separated hybrid functional by employing short range Hartree–Fock with a long range semilocal functional

The range-separated hybrid density functionals are very successful in describing a wide range of molecular and solid-state properties accurately.

‘Diet GMTKN55’ offers accelerated benchmarking through a representative subset approach

The GMTKN55 benchmarking protocol allows comprehensive analysis and ranking of density functional approximations with diverse chemical behaviours. This work reports diet versions of GMTKN55 which reproduce key properties of the full protocol at substantially reduced numerical cost. ‘Diet GMTKN55’ can thus be used for benchmarking expensive methods, or in combination with solid state benchmarks.

NMR shielding constants in group 15 trifluorides

By combining large basis and complete basis set (CBS) extrapolations of the coupled-cluster equilibrium geometry results with rovibrational and relativistic corrections, we demonstrate that it is possible to achieve near-quantitative accuracy for the NMR shielding constants in three group 15 trifluorides – NF₃, PF₃ and AsF₃.

Ground-State Gas-Phase Structures of Inorganic Molecules Predicted by Density Functional Theory Methods

We tested a battery of density functional theory (DFT) methods ranging from generalized gradient approximation (GGA) via meta-GGA to hybrid meta-GGA schemes as well as Møller-Plesset perturbation theory of the second order and a single and double excitation coupled-cluster (CCSD) theory for their ability to reproduce accurate gas-phase structures of di- and triatomic molecules derived from microwave spectroscopy. We obtained the most accurate molecular structures using the hybrid and hybrid meta-GGA approximations with B3PW91, APF, TPSSh, mPW1PW91, PBE0, mPW1PBE, B972, and B98 functionals, resulting in lowest errors. We recommend using these methods to predict accurate three-dimensional structures of inorganic molecules when intramolecular dispersion interactions play an insignificant role. The structures that the CCSD method predicts are of similar quality although at considerably larger computational cost. The structures that GGA and meta-GGA schemes predict are less accurate with the largest absolute errors detected with BLYP and M11-L, suggesting that these methods should not be used if accurate three-dimensional molecular structures are required. Because of numerical problems related to the integration of the exchange-correlation part of the functional and large scattering of errors, most of the Minnesota models tested, particularly MN12-L, M11, M06-L, SOGGA11, and VSXC, are also not recommended for geometry optimization. When maintaining a low computational budget is essential, the nonseparable gradient functional N12 might work within an acceptable range of error. As expected, the DFT-D3 dispersion correction had a negligible effect on the internuclear distances when combined with the functionals tested on nonweakly bonded di- and triatomic inorganic molecules. By contrast, the dispersion correction for the APF-D functional has been found to shorten the bonds significantly, up to 0.064 Å (AgI), in Ag halides, BaO, BaS, BaF, BaCl, Cu halides, and Li and Na halides and hydrides. These results do not agree well with very accurate structures derived from microwave spectroscopy; we therefore believe that the dispersion correction in the APF-D method should be reconsidered. Finally, we found that inaccurate structures can easily lead to errors of few kcal/mol in single-point energies.

Reaction of Methyl Fluoroformyl Peroxycarbonate (FC(O)OOC(O)OCH3) with Cl Atoms: Formation of Hydro-ChloroFluoro-Peroxides

The products following Cl atom initiated reactions of FC(O)OOC(O)OCH₃ in 50-760 Torr of N₂ at 296 K were investigated using FTIR. Reaction of Cl atoms with methyl fluoroformyl peroxycarbonate proceeds mainly via attack at the methyl group, forming FC(O)OOC(O)OCH₂^• radicals. Further reaction of this kind of radical with Cl₂ forms three new compounds: FC(O)OOC(O)OCH₂Cl, FC(O)OOC(O)OCHCl₂, and FC(O)OOC(O)OCCl₃, whose existence was characterized experimentally by FTIR spectroscopy assisted by ab initio calculations at the B3LYP/6-31++G(d,p) level. Relative rate techniques were used to measure k_{(Cl+FC(O)OOC(O)OCH3)} = (4.0 ± 0.4) × 10^-14 cm³ molecule^-1 s^-1 and k_{(Cl+FC(O)OOC(O)OCH2Cl)} = (3.2 ± 0.3) × 10^-14 cm³ molecule^-1 s^-1. When the reaction is run in the presence of oxygen, the paths giving chlorinated peroxide formation are suppressed, and oxidation to (mainly) CO₂ and HCl takes place through highly oxidized intermediates with lifetimes long enough to be detected by FTIR spectroscopy.

Nitrato-Functionalized Task-Specific Ionic Liquids as Attractive Hypergolic Rocket Fuels

Hypergolic ionic liquids (HILs) as potential replacements for hydrazine derivatives have attracted increasing interest over the last decade. Previous studies on HILs have mostly concentrated on the anionic innovations of ionic liquids to shorten the ignition delay (ID) time, but little attention has been paid to cationic modifications and their structure-property relationships. In this work, we present a new strategy of cationic functionalization by introducing the energetic nitrato group into the cationic units of HILs. Interestingly, the introduction of oxygen-rich nitrato groups into the cationic structure significantly improved the combustion performance of HILs with larger flame diameters and duration times. The density-specific impulse (ρI_sp ) of these novel HILs are all above 279.0 s g cm^-3 , much higher than that of UDMH (215.7 s g cm^-3 ). In addition, the densities of these HILs are in the range of 1.22-1.39 g cm^-3 , which is much higher than that of UDMH (0.79 g cm^-3 ), showing their higher loading capacity than hydrazine-derived fuels in a propellant tank. This promising strategy of introducing nitrato groups into the cationic structures has provided a new platform for developing high-performing HILs with improved combustion properties.

Bias-Free Chemically Diverse Test Sets from Machine Learning

Current benchmarking methods in quantum chemistry rely on databases that are built using a chemist's intuition. It is not fully understood how diverse or representative these databases truly are. Multivariate statistical techniques like archetypal analysis and K-means clustering have previously been used to summarize large sets of nanoparticles however molecules are more diverse and not as easily characterized by descriptors. In this work, we compare three sets of descriptors based on the one-, two-, and three-dimensional structure of a molecule. Using data from the NIST Computational Chemistry Comparison and Benchmark Database and machine learning techniques, we demonstrate the functional relationship between these structural descriptors and the electronic energy of molecules. Archetypes and prototypes found with topological or Coulomb matrix descriptors can be used to identify smaller, statistically significant test sets that better capture the diversity of chemical space. We apply this same method to find a diverse subset of organic molecules to demonstrate how the methods can easily be reapplied to individual research projects. Finally, we use our bias-free test sets to assess the performance of density functional theory and quantum Monte Carlo methods.

How to computationally calculate thermochemical properties objectively, accurately, and as economically as possible

We have developed the WnX series of quantum chemistry composite protocols for the computation of highly-accurate thermochemical quantities with advanced efficiency and applicability. The W1X-type methods have a general accuracy of ~3–4 kJ mol−1 and they can currently be applied to systems with ~20–30 atoms. Higher-level methods include W2X, W3X and W3X-L, with the most accurate of these being W3X-L. It can be applied to molecules with ~10–20 atoms and is generally accurate to ~1.5 kJ mol−1. The WnX procedures have opened up new possibilities for computational chemists in pursue of accurate thermochemical values in a highly-productive manner.

Computational study of azole salts as high-energy materials

The crystal densities, heats of formation (HOFs), detonation properties, and impact sensitivities of a series of azole salts were investigated by the density functional theory and volume-based thermodynamics calculations. The HOFs of cations and anions and lattice energies were obtained based on the Born–Haber energy cycles. The detonation parameters (Q, D, and P) of 18 energetic salts have been calculated by the Kamlet–Jacobs equations with the calculated density and HOFs. The outcomes reflected that the hydroxylammonium cation has greater impact on the density and detonation properties of the azole salts than the hydrazine cation. Among all of the series salts under investigation, 2-amino-3-nitroamino-4,5-dinitropyrazole and 3-nitroamino-4,5-dinitropyrazole anions have greater HOFs and better detonation performances than other anions. In summary, the incorporations of all the cations studied here with the 2-amino-3-nitroamino-4,5-dinitropyrazole or 3-nitroamino-4,5-dinitropyrazole anions can be considered as potential high-energy salts.

Unification of the W1X and G4(MP2)-6X Composite Protocols

We have devised the composite procedures WG and WGh to unify the W1X and the (computationally more economical) G4(MP2)-6X protocols. The WG procedure employs a combination of MP2, MP2-F12, CCSD-F12b, and CCSD(T) to approximate the all-electron scalar-relativistic CCSD(T)/CBS energy. In addition, it incorporates features such as the scaling of the energy components and an empirical "higher-level-correction" term. The WGh protocol represents a somewhat more economical variant of WG with partial removal of diffuse functions. Our benchmark shows that, in general, both WG and WGh have similar performance to that for W1X-2, with WGh (predictably) performing somewhat less well for electron affinities. In terms of computational efficiency, WG is approximately an order of magnitude less costly than W1X-2, while WGh gives not only a further slight savings in computer time but also a notably reduced disk requirement.

Efficient DLPNO–CCSD(T)-Based Estimation of Formation Enthalpies for C-, H-, O-, and N-Containing Closed-Shell Compounds Validated Against Critically Evaluated Experimental Data

An accurate and cost-efficient methodology for the estimation of the enthalpies of formation for closed-shell compounds composed of C, H, O, and N atoms is presented and validated against critically evaluated experimental data. The computational efficiency is achieved through the use of the resolution-of-identity (RI) and domain-based local pair-natural orbital coupled cluster (DLPNO-CCSD(T)) approximations, which results in a drastic reduction in both the computational cost and the number of necessary steps for a composite quantum chemical method. The expanded uncertainty for the proposed methodology evaluated using a data set of 45 thoroughly vetted experimental values for molecules containing up to 12 heavy atoms is about 3 kJ·mol-1, competitive with those of typical calorimetric measurements. For the compounds within the stated scope, the methodology is shown to be superior to a representative, more general, and widely used composite quantum chemical method, G4.

Performance of a nonempirical density functional on molecules and hydrogen-bonded complexes

Recently, Tao and Mo derived a meta-generalized gradient approximation functional based on a model exchange-correlation hole. In this work, the performance of this functional is assessed on standard test sets, using the 6-311++G(3df,3pd) basis set. These test sets include 223 G3/99 enthalpies of formation, 99 atomization energies, 76 barrier heights, 58 electron affinities, 8 proton affinities, 96 bond lengths, 82 harmonic vibrational frequencies, 10 hydrogen-bonded molecular complexes, and 22 atomic excitation energies. Our calculations show that the Tao-Mo functional can achieve high accuracy for most properties considered, relative to the local spin-density approximation, Perdew-Burke-Ernzerhof, and Tao-Perdew-Staroverov-Scuseria functionals. In particular, it yields the best accuracy for proton affinities, harmonic vibrational frequencies, hydrogen-bond dissociation energies and bond lengths, and atomic excitation energies.

G4CEP: A G4 theory modification by including pseudopotential for molecules containing first-, second- and third-row representative elements

The G4CEP composite method was developed from the respective G4 all-electron version by considering the implementation of compact effective pseudopotential (CEP). The G3/05 test set was used as reference to benchmark the adaptation by treating in this work atoms and compounds from the first and second periods of the periodic table, as well as representative elements of the third period, comprising 440 thermochemical data. G4CEP has not reached a so high level of accuracy as the G4 all-electron theory. G4CEP presented a mean absolute error around 1.09 kcal mol(-1), while the original method presents a deviation corresponding to 0.83 kcal mol(-1). The similarity of the optimized molecular geometries between G4 and G4CEP indicates that the core-electron effects and basis set adjustments may be pointed out as a significant factor responsible for the large discrepancies between the pseudopotential results and the experimental data, or even that the all-electron calculations are more efficient either in its formulation or in the cancellation of errors. When the G4CEP mean absolute error (1.09 kcal mol(-1)) is compared to 1.29 kcal mol(-1) from G3CEP, it does not seem so efficient. However, while the G3CEP uncertainty is ±4.06 kcal mol(-1), the G4CEP deviation is ±2.72 kcal mol(-1). Therefore, the G4CEP theory is considerably more reliable than any previous combination of composite theory and pseudopotential, particularly for enthalpies of formation and electron affinities.

When does a functional correctly describe both the structure and the energy of the transition state?

Requiring that several properties are well reproduced is a severe test on density functional approximations. This can be assessed through the estimation of joint and conditional success probabilities. An example is provided for a small set of molecules, for properties characterizing the transition states (geometries and energies).

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Accurate Theoretical Thermochemistry for Fluoroethyl Radicals

An accurate coupled-cluster (CC) based model chemistry was applied to calculate reliable thermochemical quantities for hydrofluorocarbon derivatives including radicals 1-fluoroethyl (CH₃-CHF), 1,1-difluoroethyl (CH₃-CF₂), 2-fluoroethyl (CH₂F-CH₂), 1,2-difluoroethyl (CH₂F-CHF), 2,2-difluoroethyl (CHF₂-CH₂), 2,2,2-trifluoroethyl (CF₃-CH₂), 1,2,2,2-tetrafluoroethyl (CF₃-CHF), and pentafluoroethyl (CF₃-CF₂). The model chemistry used contains iterative triple and perturbative quadruple excitations in CC theory, as well as scalar relativistic and diagonal Born-Oppenheimer corrections. To obtain heat of formation values with better than chemical accuracy perturbative quadruple excitations and scalar relativistic corrections were inevitable. Their contributions to the heats of formation steadily increase with the number of fluorine atoms in the radical reaching 10 kJ/mol for CF₃-CF₂. When discrepancies were found between the experimental and our values it was always possible to resolve the issue by recalculating the experimental result with currently recommended auxiliary data. For each radical studied here this study delivers the best heat of formation as well as entropy data.

Theoretical study on homolytic B–B cleavages of diboron(4) compounds

The B–B BDEs of diboron(4) compounds and the Pt–B and Cu–B BDEs of their corresponding complexes were investigated by SOGGA11-X method.

A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions

We present the updated and extended GMTKN55 benchmark database for more accurate and extensive energetic evaluation of density functionals and other electronic structure methods with detailed guidelines for method users.

Improving the cyclability performance of lithium-ion batteries by introducing lithium difluorophosphate (LiPO2F2) additive

The cyclability of lithium-ion batteries (LIBs) is often affected by the components of the solid electrolyte interphase (SEI) layer which is generated from electrochemical decomposition of electrolyte.

Understanding the influence of low-frequency vibrations on the hydrogen bonds of acetic acid and acetamide dimers

Low-frequency vibrations coupled to high-frequency modes are known to influence the hydrogen bond strengths in a weakly interacting dimer.

Computational study on C–B homolytic bond dissociation enthalpies of organoboron compounds

The theoretical study of three hybridized C–B BDEs with different substituents can provide corresponding guidance to experimental research studies.

The INV24 test set: how well do quantum-chemical methods describe inversion and racemization barriers?

For years, there has been ongoing interest in experimentally and theoretically understanding inversion and racemization processes. However, to the best of our knowledge, there has been no computational study that systematically investigated how well low-level quantum-chemical methods predict inversion barriers. Herein, we provide an answer to this question and we present the INV24 benchmark set of 24 high-level, ab initio inversion barriers. INV24 covers inversion in triatomics, in pyramidal molecules, in one cyclic system, and in various helical and bowl-shaped compounds. Our results indicate that previously applied DFT approximations combined with small basis sets are not reliable enough and that at least a triple-ζ basis is needed for meaningful results. Moreover, we show that intramolecular London dispersion influences the barriers by 2 kcal/mol or more and that dispersion corrections should always be applied to DFT results. With our analysis of 34 DFT approximations, we can reproduce the well-known Jacob’s Ladder scheme with (meta-)generalized-gradient-approximation methods underestimating barriers and global-hybrid DFT functionals performing better. Range-separated hybrids or Minnesota-type hybrids are not particularly superior to more conventional methods, such as B3LYP-D3. The by far best results are achieved with dispersion-corrected double hybrids, which give results below the chemical accuracy target of 1 kcal/mol. They also outperform wave-function second-order perturbation theory approaches and we recommend using them whenever possible. Given that our systematic study of INV24 is the first of its kind, our findings have the potential to change common practice in this field and they will guide future investigations of inversion processes.

Enhanced Basicity of Push-Pull Nitrogen Bases in the Gas Phase

Nitrogen bases containing one or more pushing amino-group(s) directly linked to a pulling cyano, imino, or phosphoimino group, as well as those in which the pushing and pulling moieties are separated by a conjugated spacer (C═X)_n, where X is CH or N, display an exceptionally strong basicity. The n-π conjugation between the pushing and pulling groups in such systems lowers the basicity of the pushing amino-group(s) and increases the basicity of the pulling cyano, imino, or phosphoimino group. In the gas phase, most of the so-called push-pull nitrogen bases exhibit a very high basicity. This paper presents an analysis of the exceptional gas-phase basicity, mostly in terms of experimental data, in relation with structure and conjugation of various subfamilies of push-pull nitrogen bases: nitriles, azoles, azines, amidines, guanidines, vinamidines, biguanides, and phosphazenes. The strong basicity of biomolecules containing a push-pull nitrogen substructure, such as bioamines, amino acids, and peptides containing push-pull side chains, nucleobases, and their nucleosides and nucleotides, is also analyzed. Progress and perspectives of experimental determinations of GBs and PAs of highly basic compounds, termed as "superbases", are presented and benchmarked on the basis of theoretical calculations on existing or hypothetical molecules.

The Harvard organic photovoltaic dataset

The Harvard Organic Photovoltaic Dataset (HOPV15) presented in this work is a collation of experimental photovoltaic data from the literature, and corresponding quantum-chemical calculations performed over a range of conformers, each with quantum chemical results using a variety of density functionals and basis sets. It is anticipated that this dataset will be of use in both relating electronic structure calculations to experimental observations through the generation of calibration schemes, as well as for the creation of new semi-empirical methods and the benchmarking of current and future model chemistries for organic electronic applications.

How Accurate Are the Minnesota Density Functionals for Noncovalent Interactions, Isomerization Energies, Thermochemistry, and Barrier Heights Involving Molecules Composed of Main-Group Elements?

The 14 Minnesota density functionals published between the years 2005 and early 2016 are benchmarked on a comprehensive database of 4986 data points (84 data sets) involving molecules composed of main-group elements. The database includes noncovalent interactions, isomerization energies, thermochemistry, and barrier heights, as well as equilibrium bond lengths and equilibrium binding energies of noncovalent dimers. Additionally, the sensitivity of the Minnesota density functionals to the choice of basis set and integration grid is explored for both noncovalent interactions and thermochemistry. Overall, the main strength of the hybrid Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., M06-2X), barrier heights (e.g., M08-HX, M08-SO, MN15), and systems heavily characterized by self-interaction error (e.g., M06-2X, M08-HX, M08-SO, MN15), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-2X is recommended from the 10 hybrid Minnesota functionals). Similarly, the main strength of the local Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., MN15-L), barrier heights (e.g., MN12-L), and systems heavily characterized by self-interaction error (e.g., MN12-L and MN15-L), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-L is clearly the best from the four local Minnesota functionals). As an overall guide, M06-2X and MN15 are perhaps the most broadly useful hybrid Minnesota functionals, while M06-L and MN15-L are perhaps the most broadly useful local Minnesota functionals, although each has different strengths and weaknesses.

Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists

Density functional theory (DFT) emerged in the last two decades as the most reliable tool for the description and prediction of properties of molecular systems and extended materials, coupling in an unprecedented way high accuracy and reasonable computational cost. This success rests also on the development of more and more performing density functional approximations (DFAs). Indeed, the Achilles' heel of DFT is represented by the exchange-correlation contribution to the total energy, which, being unknown, must be approximated. Since the beginning of the 1990s, global hybrids (GH) functionals, where an explicit dependence of the exchange-correlation energy on occupied Kohn-Sham orbitals is introduced thanks to a fraction of Hartree-Fock-like exchange, imposed themselves as the most reliable DFAs for chemical applications. However, if these functionals normally provide results of sufficient accuracy for most of the cases analyzed, some properties, such as thermochemistry or dispersive interactions, can still be significantly improved. A possible way out is represented by the inclusion, into the exchange-correlation functional, of an explicit dependence on virtual Kohn-Sham orbitals via perturbation theory. This leads to a new class of functionals, called double-hybrids (DHs). In this Account, we describe our nonempirical approach to DHs, which, following the line traced by the Perdew-Burke-Ernzerhof approach, allows for the definition of a GH (PBE0) and a DH (QIDH) model. In such a way, a whole family of nonempirical functionals, spanning on the highest rungs of the Perdew's quality scale, is now available and competitive with other-more empirical-DFAs. Discussion of selected cases, ranging from thermochemistry and reactions to weak interactions and excitation energies, not only show the large range of applicability of nonempirical DFAs, but also underline how increasing the number of theoretical constraints parallels with an improvement of the DFA's numerical performances. This fact further consolidates the strong theoretical framework of nonempirical DFAs. Finally, even if nonempirical DH approaches are still computationally expensive, relying on the fact that they can benefit of all technical enhancements developed for speeding up post-Hartree-Fock methods, there is substantial hope for their near future routine application to the description and prediction of complex chemical systems and reactions.