Density-functional theory vs density-functional fits

Molecular mechanism of saturated aldehyde oxidation: A DFT insight into volatiles forming from decanal thermal oxidation

Decanal is one of the main products of lipid oxidation. It has been shown that decanal can oxidize to form volatiles with shorter carbon chains during heating, but the mechanism is still unclear. In this study, volatile compounds formed in the decanal thermal oxidation were verified using thermal-desorption cryo-trapping combined with GC-MS. A total of 32 volatile compounds were identified. The oxidation mechanism of decanal was studied by applying density functional theory. Results revealed that the carbonyl carbon atom was the thermal oxidation site of decanal and two pathways of peroxide oxidation were determined: the ortho‑carbon and the meta‑carbon oxidation. The ortho‑carbon oxidation pathway is superior to the occurrence of the meta‑carbon oxidation pathway. The oxidative mechanism of decanal was finally summarized as the peroxide oxidation based on radical attack on the carbonyl carbon, which would provide a theoretical basis for exploring the oxidation mechanism of other saturated aldehydes.

Machine learning for accuracy in density functional approximations

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. Here, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

Deciphering molecular structures: NMR spectroscopy and quantum mechanical insights of halogenated 4H-Chromenediones

Sesquiterpene lactones (SL) represent a class of secondary metabolites found in the Asteraceae family, notable for their unique structures. The SL α-santonin (1) and its derivatives are worthy of mention due to their diverse biological properties. Additionally, 4H-chromenes and 4H-chromones are appealing frameworks holding the capability to be used as structural motifs for new drugs. Furthermore, unambiguous structural elucidation is crucial for developing novel compounds for diverse applications. In this context, it is common to find in the literature molecules erroneously assigned. Therefore, the use of quantum mechanical calculations to simulate NMR chemical shifts has emerged as a valuable strategy. In this work, we conceived the synthesis of two halogenated 4H-chromenediones derived from photosantonic acid (2), a photoproduct arising from irradiation of α-santonin (1) in the ultraviolet region. The structure of the chlorinated and brominated products was determined by NMR analysis, with the aid of quantum mechanical calculations at the B3LYP/6-311 + G(2d,p)//M062x/6-31 + G(d,p) level of theory. All analyses were in agreement and led to the assignment of the brominated 4H-chromene-2,7-dione as (3S,3aS,5aR,9bS)-5a-(2-bromopropan-2-yl)-3-methyl-3,3a,5,5a,8,9b-hexahydro-4H-furo[2,3-f]chromene-2,7-dione (11b) and of the chlorinated 4H-chromene-2,7-dione as (3S,3aS,5aR,9bS)-5a-(2-chloropropan-2-yl)-3-methyl-3,3a,5,5a,8,9b-hexahydro-4H-furo[2,3-f]chromene-2,7-dione (12b). The diastereoselectivities of the reactions were explained based on products and intermediates formation energy calculated using B3LYP/6-31 + G(d,p) as the level of theory. Structures 11b and 12b were identified as the thermodynamic and kinetic products of the reaction among all candidates. Consequently, the strategy utilized in this study is robust and successfully illustrates the use of quantum mechanical calculations in the structural elucidation of new compounds with potential applications as novel drugs or products.

Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density

ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional. Its exact form is unknown, or better "unknowable", and therefore the derivation of ever more accurate yet efficiently applicable approximate functionals is the "holy grail" in the field. In this context, the simultaneous minimization of so-called delocalization errors and static correlation errors is the greatest challenge that needs to be overcome as we move toward more accurate yet computationally efficient methods. In many cases, an improvement on one of these two aspects (also often termed fractional-charge and fractional-spin errors, respectively) generates a deterioration in the other one. Here we report on recent notable progress in escaping this so-called "zero-sum-game" by constructing new functionals based on the exact-exchange energy density. In particular, local hybrid and range-separated local hybrid functionals are discussed that incorporate additional terms that deal with static correlation as well as with delocalization errors. Taking hints from other coordinate-space models of nondynamical and strong electron correlations (the B13 and KP16/B13 models), position-dependent functions that cover these aspects in real space have been devised and incorporated into the local-mixing functions determining the position-dependence of exact-exchange admixture of local hybrids as well as into the treatment of range separation in range-separated local hybrids. While initial functionals followed closely the B13 and KP16/B13 frameworks, meanwhile simpler real-space functions based on ratios of semilocal and exact-exchange energy densities have been found, providing a basis for relatively simple and numerically convenient functionals. Notably, the correction terms can either increase or decrease exact-exchange admixture locally in real space (and in interelectronic-distance space), leading even to regions with negative admixture in cases of particularly strong static correlations. Efficient implementations into a fast computer code (Turbomole) using seminumerical integration techniques make such local hybrid and range-separated local hybrid functionals promising new tools for complicated composite systems in many research areas, where simultaneously small delocalization errors and static correlation errors are crucial. First real-world application examples of the new functionals are provided, including stretched bonds, symmetry-breaking and hyperfine coupling in open-shell transition-metal complexes, as well as a reduction of static correlation errors in the computation of nuclear shieldings and magnetizabilities. The newest versions of range-separated local hybrids (e.g., ωLH23tdE) retain the excellent frontier-orbital energies and correct asymptotic exchange-correlation potential of the underlying ωLH22t functional while improving substantially on strong-correlation cases. The form of these functionals can be further linked to the performance of the recent impactful deep-neural-network "black-box" functional DM21, which itself may be viewed as a range-separated local hybrid.

A microscopic mechanism study of the effect of binary surfactants on the flotation of Wiser bituminous coal

Investigating surfactant effects on the floatability of Wiser bituminous coal holds significant importance in improving coal cleanliness and utilization value. Using density functional theory and molecular dynamics simulation methods, this study constructed models of Wiser bituminous coal and examined the impact of different surfactants, including the anionic surfactant sodium dodecyl benzene sulfonate, the cationic surfactant hexadecyl trimethyl ammonium bromide (CTAB), and the non-ionic surfactant fatty alcohol ethoxylated ether. The focus was on investigating the charge distribution characteristics of these molecules and the modifying effect of binary surfactants on the hydrophobicity of bituminous coal. Results revealed that the maximum electrostatic potential was concentrated near oxygen/nitrogen/sulfur-containing functional groups like sulfonic acid groups, quaternary ammonium cations, ethylene oxide, hydroxyl groups, carboxyl groups, and sulfur bonds. These functional groups exhibited a propensity for accepting/delivering electrons to form hydrogen bonds. Among the surfactants tested, CTAB revealed the slightest difference in frontier orbital energy, measuring 3.187 eV, thereby demonstrating a superior trapping ability compared with the other two surfactants. Adsorption reactions within the system were determined to be spontaneous, with over 60% of the interaction force attributed to electrostatic forces. Moreover, the repulsive force magnitude with water molecules followed the trend: sulfonate group (2.20 Å) < ethylene oxide (2.43 Å) < quaternary ammonium cation (2.57 Å), indicating more excellent water repellency of CTAB. Findings showed that CTAE binary surfactants proved most effective in modifying the hydrophobicity of bituminous coal. This study offers valuable insights into reducing waste, pollution, and resource wastage.

A remarkably simple dispersion damping scheme and the DH24 double hybrid density functional

In recent papers, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] and then Becke [J. Chem. Phys. 159, 241101 (2023)] have developed a novel double hybrid density functional, "DH23," whose terms are based on good local physics. Its 12 coefficients are trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.73 kcal/mol for the revDH23 variant). Here, we simplify DH23 by introducing a dispersion damping scheme involving atomic numbers only and one global parameter. The resulting new functional, "DH24," performs as well as its predecessors.

My life in science: Lessons for yours?

Because of an acquired obsession to understand as much as possible in a limited but important area of science and because of optimism, luck, and help from others, my life in science turned out to be much better than I or others could have expected or planned. This is the story of how that happened, and also the story of the groundstate density functional theory of electronic structure, told from a personal perspective.

Doubling down on density-functional theory

In a recent paper, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] presented a novel double hybrid density functional, "DH23," whose terms are based on good physics. Its 12 coefficients were trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.76 kcal/mol). Here, we make some revisions to DH23 and test its efficacy on reference data beyond GMTKN55, namely, organometallic reaction energies and barrier heights. The results confirm that DH23 is robust outside its training set. In the process, a slightly smaller GMTKN55 WTMAD2 of 1.73 kcal/mol is achieved.

Toward a correct treatment of core properties with local hybrid functionals

In local hybrid functionals (LHs), a local mixing function (LMF) determines the position-dependent exact-exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt-LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn-Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high-density and iso-orbital limits relevant for the innermost core region. Using TDDFT calculations for a set of K-shell core excitations of second- and third-period systems including accurate state-of-the-art relativistic orbital corrections, the core part of the LMF is optimized, while the valence part is optimized as previously reported for test sets of atomization energies and reaction barriers (Haasler et al., J Chem Theory Comput 2020, 16, 5645). The LHs are completed by a calibration function that minimizes spurious nondynamical correlation effects caused by the gauge ambiguities of exchange-energy densities, as well as by B95c meta-GGA correlation. The resulting LH23pt functional relates to the previous LH20t functional but specifically improves upon the core region.

The difference between molecules and materials: Reassessing the role of exact conditions in density functional theory

Exact conditions have long been used to guide the construction of density functional approximations. However, hundreds of empirical-based approximations tailored for chemistry are in use, of which many neglect these conditions in their design. We analyze well-known conditions and revive several obscure ones. Two crucial distinctions are drawn: that between necessary and sufficient conditions and that between all electronic densities and the subset of realistic Coulombic ground states. Simple search algorithms find that many empirical approximations satisfy many exact conditions for realistic densities and non-empirical approximations satisfy even more conditions than those enforced in their construction. The role of exact conditions in developing approximations is revisited.

Cobalt Hydrogen-Bonded Organic Framework as a Visible Light-Driven Photocatalyst for CO2 Cycloaddition Reaction

A novel cobalt hydrogen-bonded organic framework (Co-HOF, C24H14CoN4O8) was synthesized from a mixed linker, that is, 2,5-pyridinedicarboxylic acid (PDC) and 2,2'-bipyridyl (BPY) linkers and cobalt ion through a simple, one-pot, low-cost, and scalable solvothermal method. The Co-HOF was fully characterized using several analytical and spectroscopic techniques including single-crystal X-ray diffraction, diffuse reflectance spectroscopy, Fourier transform infrared spectroscopy, scanning electron microscopy, energy-dispersive X-ray, and X-ray photoelectron spectroscopy. The Co-HOF exhibits high thermal and chemical stabilities compared to previously reported HOF materials. Moreover, Co-HOF shows excellent photocatalytic activity under visible light irradiation due to its narrow band gap of 2.05 eV. The cycloaddition reaction of CO2 to variable epoxides was investigated to evaluate the photocatalytic performance of Co-HOF under visible light radiation and was found to produce the corresponding cyclic carbonates in yields up to 99.9%.

A double-hybrid density functional based on good local physics with outstanding performance on the GMTKN55 database

In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and A. D. Becke, J. Chem. Phys. 157, 234102 (2022)], we compared two Kohn-Sham density functionals based on physical modeling and theory with the best density-functional power-series fits in the literature. The best error statistics reported to date for a hybrid functional on the general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)] were obtained. In the present work, additional second-order perturbation-theory terms are considered. The result is a 12-parameter double-hybrid density functional with the lowest GMTKN55 WTMAD2 "weighted total mean absolute deviation" error (1.76 kcal/mol) yet seen for any hybrid or double-hybrid density-functional approximation. We call it "DH23."

Full Implementation, Optimization, and Evaluation of a Range-Separated Local Hybrid Functional with Wide Accuracy for Ground and Excited States

We report the first full and efficient implementation of range-separated local hybrid functionals (RSLHs) into the TURBOMOLE program package. This enables the computation of ground-state energies and nuclear gradients as well as excitation energies. Regarding the computational effort, RSLHs scale like regular local hybrid functionals (LHs) with system or basis set size and increase timings by a factor of 2-3 in total. An advanced RSLH, ωLH22t, has been optimized for atomization energies and reaction barriers. It is an extension of the recent LH20t local hybrid and is based on short-range PBE and long-range HF exchange-energy densities, a pig2 calibration function to deal with the gauge ambiguity of exchange-energy densities, and reoptimized B95c correlation. ωLH22t has been evaluated for a wide range of ground-state and excited-state quantities. It further improves upon the already successful LH20t functional for the GMTKN55 main-group energetics test suite, and it outperforms any global hybrid while performing close to the top rung-4 functional, ωB97M-V, for these evaluations when augmented by D4 dispersion corrections. ωLH22t performs excellently for transition-metal reactivity and provides good balance between delocalization errors and left-right correlation for mixed-valence systems, with a somewhat larger bias toward localized states compared to LH20t. It approaches the accuracy of the best local hybrids to date for core, valence singlet and triplet, and Rydberg excitation energies while improving strikingly on intra- and intermolecular charge-transfer excitations, comparable to the most successful range-separated hybrids available.

Density-functional theory vs density-functional fits: The best of both

In a recent paper [A. D. Becke, J. Chem. Phys. 156, 214101 (2022)], we compared two Kohn-Sham density functionals based on physical modeling and theory with the best density-functional power series fits in the literature. With only a handful of physically motivated pre-factors, our functionals matched, and even slightly exceeded, the performance of the best power-series functionals on the general main group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. This begs the question: how much can their performance be improved by adding power-series terms of our own? We address this question in the present work. First, we describe a series expansion variable that we believe contains more local physics than any other variable considered to date. Then we undertake modest, one-dimensional fits to the GMTKN55 data with our theory-based functional corrected by power-series exchange and dynamical correlation terms. We settle on 12 power-series terms (plus six parent terms) and achieve the lowest GMTKN55 "WTMAD2" error yet reported, by a substantial margin, for a hybrid Kohn-Sham density functional. The new functional is called "B22plus."

Local Hybrid Functional Applicable to Weakly and Strongly Correlated Systems

The recent idea (Wodyński, A.; Arbuznikov, A. V.; Kaupp M. J. Chem. Phys. 2021, 155, 144101) to augment local hybrid functionals by a strong-correlation (sc) factor obtained from the adiabatic connection in the spirit of the KP16 model has been extended and applied to generate the accurate sc-corrected local hybrid functional scLH22t. By damping small values of the ratio between nondynamical and dynamical correlation entering the correction factor, it has become possible to avoid double counting of nondynamical correlation for weakly correlated situations and thereby preserve the excellent accuracy of the underlying LH20t local hybrid for such cases almost perfectly. On the other hand, scLH22t improves substantially over LH20t in reducing fractional-spin errors (FSEs), in providing improved spin-restricted bond dissociation curves, and in treating some typical systems with multireference character. The obtained FSEs are similar to those of the KP16/B13 model and slightly larger than for B13, but performance for weakly correlated systems is better than for these two related methods, which are also difficult to use self-consistently. The recent DM21 functional based on the training of a deep neural network still performs somewhat better than scLH22t but allows no physical insights into the origins of reduced FSEs. Examination of local mixing functions (LMFs) for the corrected scLH22t and uncorrected LH20t functionals provides further insights: in weakly correlated situations, the LMF remains essentially unchanged. Strong-correlation effects manifest in a reduction of the LMF values in certain regions of space, even to the extent of producing negative LMF values. It is suggested that this is the mechanism by which also DM21, which may be viewed as a range-separated local hybrid, is able to reduce FSEs.

A Local Hybrid Exchange Functional Approximation from First Principles

Local hybrid functionals are a more flexible class of density functional approximations allowing for a position-dependent admixture of exact exchange. This additional flexibility, however, comes with a more involved mathematical form and a more complicated design. A common denominator for previously constructed local hybrid funtionals is usage of thermochemical benchmark data to construct these functionals. Herein, we design a local hybrid functional without relying on benchmark data. Instead, we construct it in a more ab initio manner, following the principles of modern meta-generalized gradient approximations and considering theoretical constrains. To achieve this, we make use of the density matrix expansion and a local mixing function based on an approximate correlation length. The accuracy of the developed density functional approximation is assessed for thermochemistry, excitation energies, polarizabilities, magnetizabilities, NMR spin-spincoupling constants, NMR shieldings and shifts, as well as EPR g-tensors and hyperfine coupling constants. Here, the new exchange functional shows a robust performance and is especially well suited for atomization energies, barrier heights, excitation energies, NMR coupling constants, and EPR properties, whereas it looses some ground for the NMR shifts.Therefore, the designed functional is a major step forwards for functionals that have been designed from first principles.