Minimally Empirical Double-Hybrid Functionals Trained against the GMTKN55 Database: revDSD-PBEP86-D4, revDOD-PBE-D4, and DOD-SCAN-D4

Benefits of Range-Separated Hybrid and Double-Hybrid Functionals for a Large and Diverse Data Set of Reaction Energies and Barrier Heights

To better understand the thermochemical kinetics and mechanism of a specific chemical reaction, an accurate estimation of barrier heights (forward and reverse) and reaction energies is vital. Because of the large size of reactants and transition state structures involved in real-life mechanistic studies (e.g., enzymatically catalyzed reactions), density functional theory remains the workhorse for such calculations. In this paper, we have assessed the performance of 91 density functionals for modeling the reaction energies and barrier heights on a large and chemically diverse data set (BH9) composed of 449 organic chemistry reactions. We have shown that range-separated hybrid functionals perform better than the global hybrids for BH9 barrier heights and reaction energies. Except for the PBE-based range-separated nonempirical double hybrids, range separation of the exchange term helps improve the performance for barrier heights and reaction energies. The 16-parameter Berkeley double hybrid, ωB97M(2), performs remarkably well for both properties. However, our minimally empirical range-separated double hybrid functionals offer marginally better accuracy than ωB97M(2) for BH9 barrier heights and reaction energies.

Pericyclic reaction benchmarks: hierarchical computations targeting CCSDT(Q)/CBS and analysis of DFT performance

Hierarchical, convergent ab initio benchmark computations were performed followed by a systematic analysis of DFT performance for five pericyclic reactions comprising Diels-Alder, 1,3-dipolar cycloaddition, electrocyclic rearrangement, sigmatropic rearrangement, and double group transfer prototypes. Focal point analyses (FPA) extrapolating to the ab initio limit were executed via explicit quantum chemical computations with electron correlation treatments through CCSDT(Q) and correlation-consistent Gaussian basis sets up to aug'-cc-pV5Z. Optimized geometric structures and vibrational frequencies of all stationary points were obtained at the CCSD(T)/cc-pVTZ level of theory. The FPA reaction barriers and energies exhibit convergence to within a few tenths of a kcal mol-1. The FPA benchmarks were used to evaluate the performance of 60 density functionals (eight dispersion-corrected), covering the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. The meta-hybrid M06-2X functional provided the best overall performance [mean absolute error (MAE) of 1.1 kcal mol-1] followed closely by the double-hybrids B2K-PLYP, mPW2K-PLYP, and revDSD-PBEP86 [MAE of 1.4-1.5 kcal mol-1]. The regularly used GGA functional BP86 gave a higher MAE of 5.8 kcal mol-1, but it qualitatively described the trends in reaction barriers and energies. Importantly, we established that accurate yet efficient meta-hybrid or double-hybrid DFT potential energy surfaces can be acquired based on geometries from the computationally efficient and robust BP86/DZP level.

Exploring Structure-Property Relations of B,S-Doped Polycyclic Aromatic Hydrocarbons through the Trinity of Synthesis, Spectroscopy, and Theory

Polycyclic aromatic hydrocarbons (PAHs) are prominent lead structures for organic optoelectronic materials. This work describes the synthesis of three B,S-doped PAHs with heptacene-type scaffolds via nucleophilic aromatic substitution reactions between fluorinated arylborane precursors and 1,2-(Me₃SiS)₂C₆H₄/1,8-diazabicyclo[5.4.0]undec-7-ene (72-92% yield). All compounds contain tricoordinate B atoms at their 7,16-positions, kinetically protected by mesityl (Mes) substituents. PAHs 1/2 feature two/four S atoms at their 5,18-/5,9,14,18-positions; PAH 3 is a 6,8,15,17-tetrafluoro derivative of 2. For comparison, we also prepared the skewed naphtho[2,3-c]pentaphene-type isomer 4. The simultaneous presence of electron-accepting B atoms and electron-donating S atoms results in a redox-ambiphilic behavior; the radical cations [1^•]⁺ and [2^•]⁺ were characterized by electron paramagnetic resonance spectroscopy. Several low-lying charge-transfer states exist, some of which (especially S-to-B and Mes-to-B transitions) compete on the excited-state potential-energy surface. Consistent with the calculated state characters and oscillator strengths, this competition results in a spread of fluorescence quantum yields (2-27%). The optoelectronic properties of 1 change drastically upon addition of Ag⁺ ions: while the color of 1 in CH₂Cl₂ changes bathochromically from yellow to red (λ_max from 463 to 486 nm; -0.13 eV), the emission band shifts hypsochromically from 606 to 545 nm (+0.23 eV), and the fluorescence quantum yield increases from 12 to 43%. According to titration experiments, higher order adducts [Ag_n1_m]ⁿ⁺ are formed. As a suitable system for modeling Ag⁺ complexation, our calculations predict a dimer structure (n = m = 2) with Ag₂S₄ core, approximately linear S-Ag-S fragments, and Ag-Ag interaction. The computed optoelectronic properties of [Ag₂1₂]²⁺ agree well with the experimentally observed ones.

Unbiased disentanglement of conformational baths with the help of microwave spectroscopy, quantum chemistry and artificial intelligence: the puzzling case of homocysteine

An integrated experimental-computational strategy for the accurate characterization of the conformational landscape of flexible biomolecule building blocks is proposed. This is based on the combination of rotational spectroscopy with quantum-chemical computations guided by artificial intelligence tools. The first step of the strategy is the conformer search and relative stability evaluation performed by means of an evolutionary algorithm. In this step, last generation semiempirical methods are exploited together with hybrid and double-hybrid density functionals. Next, the barriers ruling the interconversion between the low-lying conformers are evaluated in order to unravel possible fast relaxation paths. The relative stabilities and spectroscopic parameters of the ``surviving' conformers are then refined using state-of-the-art composite schemes. The reliability of the computational procedure is further improved by the inclusion of vibrational and thermal effects. The final step of the strategy is the comparison between experiment and theory without any ad hoc adjustment, which allows an unbiased assignment of the spectroscopic features in terms of different conformers and their spectroscopic parameters. The proposed approach has been tested and validated for homocysteine, a highly flexible non-proteinogenic alpha-amino acid. The synergism of the integrated strategy allowed the characterization of five conformers stabilized by bifurcated N-H-O=C hydrogen bonds, together with an additional conformer involving a more conventional HNH-O hydrogen bond. The stability order estimated from the experimental intensities as well as the number and type of conformers observed in the gas phase are in full agreement with the theoretical predictions. Analogously, a good match has been found for the spectroscopic parameters.

Supramolecular cis-“Bis(Chelation)” of [M(CN)6]3− (M = CrIII, FeIII, CoIII) by Phloroglucinol (H3PG)

Studies on molecular co-crystal type materials are important in the design and preparation of easy-to-absorb drugs, non-centrosymmetric, and chiral crystals for optical performance, liquid crystals, or plastic phases. From a fundamental point of view, such studies also provide useful information on various supramolecular synthons and molecular ordering, including metric parameters, molecular matching, energetical hierarchy, and combinatorial potential, appealing to the rational design of functional materials through structure–properties–application schemes. Co-crystal salts involving anionic d-metallate coordination complexes are moderately explored (compared to the generality of co-crystals), and in this context, we present a new series of isomorphous co-crystalline salts (PPh4)3[M(CN)6](H3PG)2·2MeCN (M = Cr, 1; Fe, 2; Co 3; H3PG = phloroglucinol, 1,3,5-trihydroxobenzene). In this study, 1–3 were characterized experimentally using SC XRD, Hirshfeld analysis, ESI-MS spectrometry, vibrational IR and Raman, 57Fe Mössbauer, electronic absorption UV-Vis-NIR, and photoluminescence spectroscopies, and theoretically with density functional theory calculations. The two-dimensional square grid-like hydrogen-bond {[M(CN)6]3−;(H3PG)2}∞ network features original {[M(CN)6]3−;(H3PG)4} supramolecular cis-bis(chelate) motifs involving: (i) two double cyclic hydrogen bond synthons M(-CN⋅⋅⋅HO-)2Ar, {[M(CN)6]3−;H2PGH}, between cis-oriented cyanido ligands of [M(CN)6]3− and resorcinol-like face of H3PG, and (ii) two single hydrogen bonds M-CN⋅⋅⋅HO-Ar, {[M(CN)6]3−;HPGH2}, involving the remaining two cyanide ligands. The occurrence of the above tectonic motif is discussed with regard to the relevant data existing in the CCDC database, including the multisite H-bond binding of [M(CN)6]3− by organic species, mononuclear coordination complexes, and polynuclear complexes. The physicochemical and computational characterization discloses notable spectral modifications under the regime of an extended hydrogen bond network.

Analytic Gradients for the Long-Range-Corrected XYG3 Type of Doubly Hybrid Density Functionals: Theory, Implementation, and Assessment

An analytic gradient algorithm for the long-range-corrected (lrc-) XYG3 type of doubly hybrid functionals has been derived and implemented. Due to the introduction of a long-range second-order perturbation (lrPT2) as the correction, the Z-vector equations need to be modified, where the construction of a unique total Lagrangian of the method is required. Geometry optimizations using lrc-XYG3 and lrc-XYGJ-OS have then been applied to the A21 data set that consists of 21 noncovalently interacting systems with CCSD(T) reference data for structures, in order to testify the idea of introducing lrPT2 for a better description of intermolecular interactions. While lrc-XYG3 was observed to offer a better description in dispersion-dominant systems as compared to the XYG3 functional, lrc-XYGJ-OS stands out with an overall better balanced performance in reproducing intermolecular geometries.

Non-covalent interactions atlas benchmark data sets 4: σ-hole interactions

The SH250×10 dataset presented here extends the Non-Covalent Interactions Atlas database (https://www.nciatlas.org) to complexes bound by σ-hole interactions - halogen, chalcogen and pnictogen bonds. It comprises 250 complexes where Cl, Br, I, S, Se, P and As interact with diverse electron donors. An accurate CCSD(T)/CBS benchmark is provided for ten points along a dissociation curve of each complex. The SH250×10 set is used in testing a wide variety of DFT functionals and semiempirical quantum-mechanical methods. In DFT calculations, the new data set exposes large errors of some functionals related to exaggerated charge transfer. The size and diversity of the data set have also been exploited in the reparametrization of a halogen-bond correction for the PM6 semiempirical method.

Conformational Energy Benchmark for Longer n-Alkane Chains

We present the first benchmark set focusing on the conformational energies of highly flexible, long n-alkane chains, termed ACONFL. Unbranched alkanes are ubiquitous building blocks in nature, so the goal is to be able to calculate their properties most accurately to improve the modeling of, e.g., complex (biological) systems. Very accurate DLPNO-CCSD(T1)/CBS reference values are provided, which allow for a statistical meaningful evaluation of even the best available density functional methods. The performance of established and modern (dispersion corrected) density functionals is comprehensively assessed. The recently introduced r²SCAN-V functional shows excellent performance, similar to efficient composite DFT methods like B97-3c and r²SCAN-3c, which provide an even better cost-accuracy ratio, while almost reaching the accuracy of much more computationally demanding hybrid or double hybrid functionals with large QZ AO basis sets. In addition, we investigated the performance of common wave function methods, where MP2/CBS surprisingly performs worse compared to the simple D4 dispersion corrected Hartree-Fock. Furthermore, we investigate the performance of several semiempirical and force field methods, which are commonly used for the generation of conformational ensembles in multilevel workflows or in large scale molecular dynamics studies. Outstanding performance is obtained by the recently introduced general force field, GFN-FF, while other commonly applied methods like the universal force field yield large errors. We recommend the ACONFL as a helpful benchmark set for parametrization of new semiempirical or force field methods and machine learning potentials as well as a meaningful validation set for newly developed DFT or dispersion methods.

1,2-Carboboration of Arylallenes by In Situ Generated Alkenylboranes for the Synthesis of 1,4-Dienes

We herein report a novel method for the coupling of unactivated alkynes and arylallenes, which relies on an unprecedented and regioselective 1,2-carboboration of the allene by an alkenylborane. The alkenylborane is conveniently prepared in situ by hydroboration of an alkyne with Piers' borane, i. e., HB(C6 F5 )2 . The boryl-substituted 1,4-dienes that are formed by this carboboration are well-suited for a subsequent Suzuki-Miyaura coupling with aryl iodides. This allowed us to develop a three-step, one-pot protocol for the synthesis of aryl-substituted 1,4-dienes. The generality of the reaction was demonstrated by the synthesis of twenty dienes with modular variations of all three reaction partners. The mechanism of the new 1,2-carboboration was investigated using dispersion corrected double-hybrid DFT computations that allowed us to rationalize the chemo- and regioselectivity of this key step.

Dipolar 1,3-cycloaddition of thioformaldehyde S-methylide (CH2 SCH2 ) to ethylene and acetylene. A comparison with (valence) isoelectronic O3 , SO2 , CH2 OO and CH2 SO

Methods rooted in the density functional theory and in the coupled cluster ansatz were employed to investigate the cycloaddition reactions to ethylene and acetylene of 1,3-dipolar species including ozone and the derivatives issued from replacement of the central oxygen atom by the valence-isoelectronic sulfur atom, and/or of one or both terminal oxygen atoms by the isoelectronic CH₂ group. This gives rise to five different 1,3-dipolar compounds, namely ozone itself (O₃ ), sulfur dioxide (SO₂ ), the simplest Criegee intermediate (CH₂ OO), sulfine (CH₂ SO), and thioformaldehyde S-methylide (CH₂ SCH₂ , TSM). The experimental and accurate theoretical data available for some of those molecules were employed to assess the accuracy of two last-generation composite methods employing conventional or explicitly correlated post-Hartree-Fock contributions (jun-Cheap and SVECV-f12, respectively), which were then applied to investigate the reactivity of TSM. The energy barriers provided by both composite methods are very close (the average values for the two composite methods are 7.1 and 8.3 kcal mol^-1 for the addition to ethylene and acetylene, respectively) and comparable to those ruling the corresponding additions of ozone (4.0 and 7.7 kcal mol^-1 , respectively). These and other evidences strongly suggest that, at least in the case of cycloadditions, the reactivity of TSM is similar to that of O₃ and very different from that of SO₂ .

Spectroscopic Characterization of 3-Aminoisoxazole, a Prebiotic Precursor of Ribonucleotides

The processes and reactions that led to the formation of the first biomolecules on Earth play a key role in the highly debated theme of the origin of life. Whether the first chemical building blocks were generated on Earth (endogenous synthesis) or brought from space (exogenous delivery) is still unanswered. The detection of complex organic molecules in the interstellar medium provides valuable support to the latter hypothesis. To gather more insight, here we provide the astronomers with accurate rotational frequencies to guide the interstellar search of 3-aminoisoxazole, which has been recently envisaged as a key reactive species in the scenario of the so-called RNA-world hypothesis. Relying on an accurate computational characterization, we were able to register and analyze the rotational spectrum of 3-aminoisoxazole in the 6–24 GHz and 80–320 GHz frequency ranges for the first time, exploiting a Fourier-transform microwave spectrometer and a frequency-modulated millimeter/sub-millimeter spectrometer, respectively. Due to the inversion motion of the −NH₂ group, two states arise, and both of them were characterized, with more than 1300 lines being assigned. Although the fit statistics were affected by an evident Coriolis interaction, we were able to produce accurate line catalogs for astronomical observations of 3-aminoisoxazole.

Noncovalently bound excited-state dimers: a perspective on current time-dependent density functional theory approaches applied to aromatic excimer models

Excimers are supramolecular systems whose binding strength is influenced by many factors that are ongoing challenges for computational methods, such as charge transfer, exciton coupling, and London dispersion interactions. Treating the various intricacies of excimer binding at an adequate level is expected to be particularly challenging for Time-Dependent Density Functional Theory (TD-DFT) methods. In addition to well-known limitations for some TD-DFT methods in the description of charge transfer or exciton coupling, the inherent London dispersion problem from ground-state DFT translates to TD-DFT. While techniques to appropriately treat dispersion in DFT are well-developed for electronic ground states, these dispersion corrections remain largely untested for excited states. Herein, we aim to shed light on current TD-DFT methods, including some of the newest developments. The binding of four model excimers is studied across nine density functionals with and without the application of additive dispersion corrections against a wave function reference of SCS-CC2/CBS(3,4) quality, which approximates select CCSDR(3)/CBS data adequately. To our knowledge, this is the first study that presents single-reference wave function dissociation curves at the complete basis set level for the assessed model systems. It is also the first time range-separated double-hybrid density functionals are applied to excimers. In fact, those functionals turn out to be the most promising for the description of excimer binding followed by global double hybrids. Range-separated and global hybrids-particularly with large fractions of Fock exchange-are outperformed by double hybrids and yield worse dissociation energies and inter-molecular equilibrium distances. The deviation between each assessed functional and reference increases with system size, most likely due to missing dispersion interactions. Additive dispersion corrections of the DFT-D3(BJ) and DFT-D4 types reduce the average errors for TD-DFT methods but do so inconsistently and therefore do not offer a black-box solution in their ground-state parametrised form. The lack of appropriate description of dispersion effects for TD-DFT methods is likely hindering the practical application of the herein identified more efficient methods. Dispersion corrections parametrised for excited states appear to be an important next step to improve the applicability of TD-DFT methods and we hope that our work assists with the future development of such corrections.

Double Hybrids and Noncovalent Interactions: How Far Can We Go?

The accurate evaluation of weak noncovalent interactions in large, that is those containing up to thousand atoms, molecular systems represents a difficult challenge for any quantum chemical method. Indeed, some approximations are often introduced to render affordable these calculations. Here, we consider the PBE-QIDH/DH-SVPD protocol, combining a nonempirical double hybrid functional (PBE-QIDH) with a small basis set (DH-SVPD) tailored for noncovalent interactions with a double aim: (i) explore the robustness and accuracy of this protocol with respect to other Density Functional Approximations; (ii) illustrate how its performances are affected by the computational parameters underlying the calculation of the exact exchange and the Coulomb contribution, as well as the perturbative term. To this end, we consider three data sets, namely S66, L7, and CiM13, incorporating molecules of increasing size. On the bright side, our results suggest that the PBE-QIDH/DH-SVPD protocol is particularly accurate for large systems such as those contained in the CiM13 set (up to more than 1000 atoms and 14 000 basis functions), for which the DLPNO approximation leads to a significant speed-up for the evaluation of the perturbative correlation term. However, our analysis also points out the limit of this statistical exercise, when the quality of the reference data cannot be easily assessed, due to the size of the molecular complexes involved, and when the number of molecules is limited.

Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and versatile tools in elucidating molecular structures. To eliminate ambiguities of experimental assignments, accurate calculations of NMR spectra are of great importance. Here, a method for theoretical evaluation of the NMR shielding constants by analytic derivatives using gauge including atomic orbitals (GIAO) has been implemented for the XYG3 type of doubly hybrid density functionals (xDH), namely, the GIAO-xDH method. Benchmark calculations on shielding constants and chemical shifts demonstrate the remarkable accuracy of the GIAO-xDH method, compared to the accurate CCSD(T) references. It is shown here that the XYGJ-OS functional is able to give a mean absolute deviation (MAD) of ∼3.0 ppm in the calculated shielding constants for ¹³C, ¹⁵N, ¹⁷O, ¹⁹F, while both XYGJ-OS and xDH-PBE0 functionals are able to provide a satisfactory estimation of chemical shifts with MADs of ∼0.03 and 1.0 ppm for ¹H and ¹³C, respectively. The basis set influence upon the method has been examined and a computational scheme considering both accuracy and efficiency has been proposed and tested to predict the experimental ¹³C chemical shifts of five medium-sized natural product molecules, yielding a MAD of ∼1.0 ppm, which demonstrates the practical feasibility of the GIAO-xDH method.

Do Double-Hybrid Functionals Benefit from Regularization in the PT2 Term? Observations from an Extensive Benchmark

We put to the test a recent suggestion [Shee, J., et al. J. Phys. Chem. Lett. 2021, 12 (50), 12084-12097] that MP2 regularization might improve the performance of double-hybrid density functionals. Using the very large and chemically diverse GMTKN55 benchmark, we find that κ-regularization is indeed beneficial at lower percentages of Hartree-Fock exchange, especially if spin-component scaling is not applied [such as in B2GP-PLYP or ωB97M(2)]. This benefit dwindles for DSD and DOD functionals and vanishes entirely in the ∼70% HF exchange region optimal for them.

Accurate Quantum Chemical Spectroscopic Characterization of Glycolic Acid: A Route Toward its Astrophysical Detection

The first step to shed light on the abiotic synthesis of biochemical building blocks, and their further evolution toward biological systems, is the detection of the relevant species in astronomical environments, including earthlike planets. To this end, the species of interest need to be accurately characterized from structural, energetic, and spectroscopic viewpoints. This task is particularly challenging when dealing with flexible systems, whose spectroscopic signature is ruled by the interplay of small- and large-amplitude motions (SAMs and LAMs, respectively) and is further tuned by the conformational equilibrium. In such instances, quantum chemical (QC) calculations represent an invaluable tool for assisting the interpretation of laboratory measurements or even observations. In the present work, the role of QC results is illustrated with reference to glycolic acid (CH2OHCOOH), a molecule involved in photosynthesis and plant respiration and a precursor of oxalate in humans, which has been detected in the Murchison meteorite but not yet in the interstellar medium or in planetary atmospheres. In particular, the equilibrium structure of the lowest-energy conformer is derived by employing the so-called semiexperimental approach. Then, accurate yet cost-effective QC calculations relying on composite post-Hartree-Fock schemes and hybrid coupled-cluster/density functional theory approaches are used to predict the structural and ro-vibrational spectroscopic properties of the different conformers within the framework of the second-order vibrational perturbation theory. A purposely tailored discrete variable representation anharmonic approach is used to treat the LAMs related to internal rotations. The computed spectroscopic data, particularly those in the infrared region, complement the available experimental investigations, thus enhancing the possibility of an astronomical detection of this molecule.

Modeling the Conformational Preference of the Lignocellulose Interface and Its Interaction with Weak Acids

We have examined the conformational space of model systems for the hydrogen-bonded and covalent linkages between the sugar and lignin components of lignocellulose. Specifically, glucose and paracoumaryl alcohol moieties are used in our models. Multistage screening protocols are used to identify and validate a set of lowest-energy isomers. We found a cost-effective screening process involving an initial screening with DFTB3/3ob using a 20 kJ mol^-1 threshold, a refinement with the SCANh/6-31+G(2d,p) method with a 10 kJ mol^-1 cutoff, a third step at the DSD-PBEP86/ma-def2-TZVP//MS1-D3/6-31+G(2d,p) level with the same 10 kJ mol^-1 threshold, and a last step at the CCSD(T)/CBS//B3LYP/cc-pVTZ level with a tighter 5 kJ mol^-1 threshold. The use of machine learning (with the London and Axilrod-Teller-Muto potential) can further accelerate the screening process. In general, all low-energy conformers are characterized by hydrogen bonding between the sugar and lignin moieties. We examined the interactions of covalently bonded sugar-lignin models with weak acids (HSO₃^-, H₂PO₃^-, HSeO₃^-, H₂citrate^-, etc.) and found that they interacted strongly with the oxygen of the sugar-O-lignin linkage. Our results suggest that acids such as dihydrogen citrate may be attractive alternatives to the commonly used HSO₃^- for lignocellulose processing.

Molecular Dynamics Simulations Enforcing Nonperiodic Boundary Conditions: New Developments and Application to the Solvent Shifts of Nitroxide Magnetic Parameters

Multiscale methods combining quantum mechanics and molecular mechanics (QM/MM) have become the most suitable and effective strategies for the investigation of the spectroscopic properties of medium-to-large size chromophores in condensed phases. In this context, we are developing a novel workflow aimed at improving the generality, reliability, and ease of use of the available computational tools. In this paper, we report our latest developments with specific reference to a general protocol based on atomistic simulations, carried out under nonperiodic boundary conditions (NPBC). In particular, we add to our in house MD engine a new efficient treatment of mean field electrostatic contributions to energy and forces, together with the capability of performing the simulations either in the canonical (NVT) or in the isothermal–isobaric (NPT) ensemble. Next, we provide convincing evidence that the NBPC approach enhanced by specific tweaks for rigid body propagation, allows for the simulation of solute–solvent systems with a minimum number of degrees of freedom and large integration time step. After its validation, this new approach is applied to the challenging case of solvatochromic effects on the electron paramagnetic resonance (EPR) spectrum of a prototypical nitroxide radical. To this end, we propose and validate also an automated protocol to extract and weight simulation snapshots, making use of a continuous description of the strength of solute–solvent hydrogen bridges. While further developments are being worked on, the effectiveness of our approach, even in its present form, is demonstrated by the accuracy of the results obtained through an unsupervised approach characterized by a strongly reduced computational cost as compared to that of conventional QM/MM models, without any appreciable deterioration of accuracy.

A general justification for hybrid functionals in DFT by means of linear response theory

In the present work, resorting to linear response theory, we examine the plausibility of postulating Kohn-Sham (KS)-type equations which contain, by definition, an effective hybrid potential made up by some arbitrary mixture of local and non-local terms. In this way a general justification for the construction of hybrid functionals is provided without resorting to arguments based on the adiabatic connection, the generalized KS theory or the Levy's constrained search (or its variations). In particular, we examine the cases of single-hybrid functionals, derived from non-local exchange and of double-hybrid functionals, emerging from non-local second-order expressions obtained from the KS perturbation theory. A further generalization for higher-order hybrid functionals is also included.

Piers' Borane-Induced Tetramerization of Arylacetylenes

We herein report that the reaction of Piers' borane, i. e. HB(C6 F5 )2 , with an excess of arylacetylenes at room temperature leads to tetramerization of the acetylene and the diastereoselective formation of boryl-substituted tetra-aryl-tetrahydropentalenes. The reaction mechanism was investigated by isotope labeling experiments and DFT computations. These investigations indicate that a series of 1,2-carboboration reactions form an octatetraene that undergoes an electrocyclization. Two skeletal rearrangements then presumably lead to the formation of the tetrahydropentalene core. Overall, this intricate and unprecedented transformation comprises five carbon-carbon bond formations in a single reaction.

Vibrational Spectra and Molecular Vibrational Behaviors of Dibenzyl Disulfide, Dibenzyl Sulphide and Bibenzyl

The vibration spectroscopy (Raman and infrared) of widely concerned molecules in sulfur corrosion phenomenon (Dibenzyl Disulfide, Dibenzyl Sulphide, and Bibenzyl) is detailedly analyzed based on density functional theory and experimental measurement. The dominant conformations of these molecules are determined according to Boltzmann distribution in relative Gibbs free energy. Additionally, noncovalent interaction analysis is conducted to indicate intramolecular interaction. Vibration normal mode is assigned based on potential energy distribution, which comprehensively reveals the molecular vibrational behaviors. Conformations weighted spectra are obtained and compared with experimentally measured spectra. We found that experimental spectra are in good agreement with the theoretical spectra in B3LYP-D3(BJ)/6-311G** level with a frequency correction factor. Furthermore, the divergence among these molecules is discussed. The vibrational behavior of the methylene group in the molecule shows a trend with the presence of the sulfur atom.

Accurate Spectral Properties within Double-Hybrid Density Functional Theory: A Spin-Scaled Range-Separated Second-Order Algebraic-Diagrammatic Construction-Based Approach

Our second-order algebraic-diagrammatic construction [ADC(2)]-based double-hybrid (DH) ansatz (J. Chem. Theory Comput. 2019, 15, 4440. DOI: 10.1021/acs.jctc.9b00391) is combined with range-separation techniques. In the present scheme, both the exchange and the correlation contributions are range-separated, while spin-scaling approaches are also applied. The new methods are thoroughly tested for the most popular benchmark sets including 250 singlet and 156 triplet excitations, as well as 80 oscillator strengths. It is demonstrated that the range separation for the correlation contributions is highly recommended for both the genuine and the ADC(2)-based DH approaches. Our results show that the latter scheme slightly but consistently outperforms the former one for single excitation dominated transitions. Furthermore, states with larger fractions of double excitations are assessed as well, and challenging charge-transfer excitations are also discussed, where the recently proposed spin-scaled long-range corrected DHs fail. The suggested iterative fourth-power scaling RS-PBE-P86/SOS-ADC(2) method, using only three adjustable parameters, provides the most robust and accurate excitation energies within the DH theory. In addition, the relative error of the oscillator strengths is reduced by 65% compared to the best genuine DH functionals.

The Adsorption of Small Molecules on the Copper Paddle-Wheel: Influence of the Multi-Reference Ground State

We report a theoretical study of the adsorption of a set of small molecules (C2H2, CO, CO2, O2, H2O, CH3OH, C2H5OH) on the metal centers of the "copper paddle-wheel"-a key structural motif of many MOFs. A systematic comparison between DFT of different rungs, single-reference post-HF methods (MP2, SOS-MP2, MP3, DLPNO-CCSD(T)), and multi-reference approaches (CASSCF, DCD-CAS(2), NEVPT2) is performed in order to find a methodology that correctly describes the complicated electronic structure of paddle-wheel structure together with a reasonable description of non-covalent interactions. Apart from comparison with literature data (experimental values wherever possible), benchmark calculations with DLPNO-MR-CCSD were also performed. Despite tested methods show qualitative agreement in the majority of cases, we showed and discussed reasons for quantitative differences as well as more fundamental problems of specific cases.

The Spectroscopic Characterization of Halogenated Pollutants through the Interplay between Theory and Experiment: Application to R1122

In the last decade, halogenated ethenes have seen an increasing interest for different applications; in particular, in refrigeration, air-conditioning and heat pumping. At the same time, their adverse effects as atmospheric pollutants require environmental monitoring, especially by remote sensing spectroscopic techniques. For this purpose, an accurate characterization of the spectroscopic fingerprint—in particular, those of relevance for rotational–vibrational spectroscopy—of the target molecules is strongly needed. This work provides an integrated computational–theoretical investigation on R1122 (2-Chloro-1,1-difluoro-ethylene, ClHC=CF2), a compound widely employed as a key intermediate in different chemical processes. State-of-the-art quantum chemical calculations relying on CCSD(T)-based composite schemes and hybrid CCSD(T)/DFT approaches are used to obtain an accurate prediction of the structural, rotational and vibrational spectroscopic properties. In addition, the equilibrium geometry is obtained by exploiting the semi-experimental method. The theoretical predictions are used to guide the analysis of the experimentally recorded gas-phase infrared spectrum, which is assigned in the 400–6500 cm−1 region. Furthermore, absorption cross sections are accurately determined over the same spectral range. Finally, by using the obtained spectroscopic data, a first estimate of the global warming potential of R1122 vibrational spectra is obtained.

Exploiting the “Lego brick” approach to predict accurate molecular structures of PAHs and PANHs

Polycyclic aromatic hydrocarbons (PAHs) and polycyclic aromatic nitrogen heterocycles (PANHs) are important and ubiquitous species in space. However, their accurate structural and spectroscopic characterization is often missing. To fill this...

Modulation of π character upon complexation captured by molecular rotation spectra

Two configurations of the furan–CF3Cl complex have been observed by high-resolution rotational spectroscopy. One is characterized by a dominant Cl lone pairs∙∙∙π*aromatic interaction and the other is stabilized by a...

Reliable prediction of association (free) energies of supramolecular complexes with heavy main group elements – the HS13L benchmark set

We introduce a set of 13 supramolecular complexes featuring diverse non-covalent interactions with heavy main group elements (Zn, As, Se, Te, Br, I), high charges (−2 up to +4), and large systems with up to 266 atoms (HS13L).

Exploring the evolution patterns of melem from thermal synthesis of melamine to graphitic carbon nitride

In the exploration of synthesizing graphitic carbon nitride (g-C₃N₄), the existence of secondary anime bridging units shows the incompleteness of related theories. Thus, taking the thermal synthesis of melamine as an example, this work finds a possible reaction path with Density Functional Theory (DFT) for forming melem during the thermal synthesis of g-C₃N₄. Combined with transition state theory (TST), it indicates that the formation of melem results from the condensation of melamine and isomerization of melam. Meanwhile, the weak signal near 2135 cm⁻¹ in the Fourier Transform Infrared Spectra (FTIR) corresponds to the vibration of carbodi-imines (–N Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> CN–), which further proves the proposed reaction path. Thus, this work can explain the formation of g-C₃N₄ and its monomer, which may contribute to the successful formation of ideal g-C₃N₄ in the future.

In the exploration of synthesizing graphitic carbon nitride (g-C₃N₄), the existence of secondary anime bridging units shows the incompleteness of related theories.

S66x8 noncovalent interactions revisited: new benchmark and performance of composite localized coupled-cluster methods

The S66x8 noncovalent interactions benchmark has been re-evaluated at the “sterling silver” level. Against this, a selection of computationally more economical alternatives has been assayed, ranging from localized CC to double hybrids and SAPT(DFT).

Spin-component-scaled and dispersion-corrected second-order Møller-Plesset perturbation theory: A path toward chemical accuracy

Second-order Moller-Plesset perturbation theory (MP2) provides a valuable alternative to density functional theory for modeing problems in organic and biological chemistry. However, MP2 suffers from known limitations in the description...

Spiers Memorial Lecture: theory of unimolecular reactions

One hundred years ago, at an earlier Faraday Discussion meeting, Lindemann presented a mechanism that provides the foundation for contemplating the pressure dependence of unimolecular reactions. Since that time, our...

Non-Covalent Interactions Atlas Benchmark Data Sets 5: London Dispersion in an Extended Chemical Space

The Non-Covalent Interactions Atlas (www.nciatlas.org) has been extended with two data sets of benchmark interaction energies in complexes dominated by London dispersion. The D1200 data set of equilibrium geometries provides...

Pure and Hybrid SCAN, rSCAN, and r2SCAN: Which One Is Preferred in KS- and HF-DFT Calculations, and How Does D4 Dispersion Correction Affect This Ranking?

Using the large and chemically diverse GMTKN55 dataset, we have tested the performance of pure and hybrid KS-DFT and HF-DFT functionals constructed from three variants of the SCAN meta-GGA exchange-correlation functional: original SCAN, rSCAN, and r2SCAN. Without any dispersion correction involved, HF-SCANn outperforms the two other HF-DFT functionals. In contrast, among the self-consistent variants, SCANn and r2SCANn offer essentially the same performance at lower percentages of HF-exchange, while at higher percentages, SCANn marginally outperforms r2SCANn and rSCANn. However, with D4 dispersion correction included, all three HF-DFT-D4 variants perform similarly, and among the self-consistent counterparts, r2SCANn-D4 outperforms the other two variants across the board. In view of the much milder grid dependence of r2SCAN vs. SCAN, r2SCAN is to be preferred across the board, also in HF-DFT and hybrid KS-DFT contexts.

Pure and Hybrid SCAN, rSCAN, and r2SCAN: Which One Is Preferred in KS- and HF-DFT Calculations, and How Does D4 Dispersion Correction Affect This Ranking?

Using the large and chemically diverse GMTKN55 dataset, we have tested the performance of pure and hybrid KS-DFT and HF-DFT functionals constructed from three variants of the SCAN meta-GGA exchange-correlation functional: original SCAN, rSCAN, and r2SCAN. Without any dispersion correction involved, HF-SCANn outperforms the two other HF-DFT functionals. In contrast, among the self-consistent variants, SCANn and r2SCANn offer essentially the same performance at lower percentages of HF-exchange, while at higher percentages, SCANn marginally outperforms r2SCANn and rSCANn. However, with D4 dispersion correction included, all three HF-DFT-D4 variants perform similarly, and among the self-consistent counterparts, r2SCANn-D4 outperforms the other two variants across the board. In view of the much milder grid dependence of r2SCAN vs. SCAN, r2SCAN is to be preferred across the board, also in HF-DFT and hybrid KS-DFT contexts.

Symmetry Dilemma of Doubly Hybrid Density Functionals for Equilibrium Molecular Property Calculations

In electronic structure theory, when an approximate wavefunction tends to artifactually break the symmetry of the exact Hamiltonian, the corresponding method is referred to as having a "symmetry dilemma" problem. Such types of artifacts were often reported when Hartree-Fock (HF) and the low-level post-HF methods were used, while the traditional Kohn-Sham density functional theory (KS-DFT) methods were usually found to be more resistant to this breakdown. In this work, we present a systematic study on the reliability of the doubly hybrid (DH) DFT methods for several violable cases. Almost all the commonly used B2PLYP-type (bDH) functionals are shown to have a severe "symmetry dilemma" problem and yield dramatically unreliable molecular properties, such as dipole moment, vibrational frequency, and static polarizability at the equilibrium geometry. A one-parameter bDH functional model study demonstrates that such a problem is a combined effect of the inappropriate portion of the HF exchange (over 50%) for the self-consistent field (SCF) calculation and the augmentation of the second-order perturbative contribution. It is remarkable that the XYG3-type (xDH) functionals show a good capability to resist the artifactual symmetry breaking and yield reliable molecular properties when the same critical cases are calculated. In the xDH, there are two functionals of different purposes, namely, the SCF functional and the energy functional, which have different amounts of the HF exchange and different portions of the correlation contributions. The success of the xDHs can be attributed to this flexibility in xDH construction to avoid using an improperly large portion of the HF exchange in the SCF functional. The insights gained in this work are of significance for the development of an improved DH functional.

Structural and Energetic Properties of Amino Acids and Peptides Benchmarked by Accurate Theoretical and Experimental Data

Structural, energetic, and spectroscopic data derived in this work aim at the setup of an "experimentally validated" database for amino acids and polypeptides conformers. First, the "cheap" composite scheme (ChS, CCSD(T)/(CBS+CV)^MP2) is tested for evaluation of conformational energies of all eight stable conformers of glycine, by comparing to the more accurate CCSD(T)/CBS+CV computations (Phys. Chem. Chem. Phys. 2013, 15, 10094-10111 and J Mol. Model. 2020, 26, 129). The recently proposed jun-ChS (J. Chem. Theory and Comput. 2020, 16, 988-1006), employing the jun-cc-pVnZ basis set family for CCSD(T) computations and CBS extrapolation, yields conformational energies accurate to 0.2 kJ·mol^-1, at reduced computational cost with respect to aug-ChS employing aug-cc-pVnZ basis sets. The jun-ChS composite scheme is further applied to derive conformational energies for three dipeptide analogues Ac-Gly-NH₂, Ac-Ala-NH₂, and Gly-Gly. Finally, dipeptide conformational energies and semiexperimental equilibrium rotational constants along with the CCSD(T)/(CBS+CV)^MP2 structural parameters (J. Phys. Chem. Lett. 2014, 5, 534-540) stand as the reference for benchmarking of selected density functional methodologies. The double-hybrid functionals B2-PLYP-D3(BJ) and DSD-PBEP86, perform best for structural and energetic characterization of all dipeptide analogues. From hybrid functionals CAM-B3LYP-D3(BJ) and ωB97X-D3(BJ) represent promising methods applicable for larger peptide-based systems for which computations with double-hybrid functionals are not feasible.

Extending the Applicability of the Semi-experimental Approach by Means of "Template Molecule" and "Linear Regression" Models on Top of DFT Computations

The accurate determination of equilibrium structures for isolated molecules plays a central role in the evaluation and interpretation of stereoelectronic, thermodynamic, and spectroscopic properties. For small semi-rigid systems, state-of-the-art quantum-chemical computations can rival the most sophisticated experimental results. For larger molecules, cheaper yet accurate approaches need to be defined. The double-hybrid rev-DSD-PBEP86 functional already delivers remarkable results that can be further improved by means of a "Lego brick" model. This is based on the idea that a molecular system can be seen as formed by different fragments (the "Lego bricks"), whose accurate semi-experimental (SE) equilibrium geometries are available. The template molecule (TM) approach can be used to account for the modifications occurring when going from the isolated fragment to the molecular system under investigation, with the linear regression (LR) model employed to correct the linkage between the different fragments. The resulting TM-SE_LR approach has been tested with respect to available SE equilibrium structures and rotational constants. Indeed, the latter parameters straightforwardly depend on the equilibrium geometry of the system under consideration. The main outcome of our study is the reliability, robustness, and accuracy of this novel approach. The molecular systems considered for benchmarking the TM-SE_LR scheme are those formally issued from addition/elimination reactions of nucleophilic unsaturated radicals (e.g., CN, C2H, and phenyl) to alkenes, imines, and aldehydes, whose rotational spectra have been investigated, but accurate structural determinations are not yet available.

junChS and junChS-F12 Models: Parameter-free Efficient yet Accurate Composite Schemes for Energies and Structures of Noncovalent Complexes

A recently developed model chemistry (denoted as junChS [Alessandrini, S.; et al. J. Chem. Theory Comput. 2020, 16, 988-1006]) has been extended to the employment of explicitly correlated (F12) methods. This led us to propose a family of effective, reliable, and parameter-free schemes for the computation of accurate interaction energies of molecular complexes ruled by noncovalent interactions. A thorough benchmark based on a wide range of interactions showed that the so-called junChS-F12 model, which employs cost-effective revDSD-PBEP86-D3(BJ) reference geometries, has an improved performance with respect to its conventional counterpart and outperforms well-known model chemistries. Without employing any empirical parameter and at an affordable computational cost, junChS-F12 reaches subchemical accuracy. Accurate characterizations of molecular complexes are usually limited to energetics. To take a step forward, the conventional and F12 composite schemes developed for interaction energies have been extended to structural determinations. A benchmark study demonstrated that the most effective option is to add MP2-F12 core-valence correlation corrections to fc-CCSD(T)-F12/jun-cc-pVTZ geometries without the need of recovering the basis set superposition error and the extrapolation to the complete basis set.

Accurate Biomolecular Structures by the Nano-LEGO Approach: Pick the Bricks and Build Your Geometry

The determination of accurate equilibrium molecular structures plays a fundamental role for understanding many physical–chemical properties of molecules, ranging from the precise evaluation of the electronic structure to the analysis of the role played by dynamical and environmental effects in tuning their overall behavior. For small semi-rigid systems in the gas phase, state-of-the-art quantum chemical computations rival the most sophisticated experimental (from, for example, high-resolution spectroscopy) results. For larger molecules, more effective computational approaches must be devised. To this end, we have further enlarged the compilation of available semi-experimental (SE) equilibrium structures, now covering the most important fragments containing H, B, C, N, O, F, P, S, and Cl atoms collected in the new SE100 database. Next, comparison with geometries optimized by methods rooted in the density functional theory showed that the already remarkable results delivered by PW6B95 and, especially, rev-DSDPBEP86 functionals can be further improved by a linear regression (LR) approach. Use of template fragments (taken from the SE100 library) together with LR estimates for the missing interfragment parameters paves the route toward accurate structures of large molecules, as witnessed by the very small deviations between computed and experimental rotational constants. The whole approach has been implemented in a user-friendly tool, termed nano-LEGO, and applied to a number of demanding case studies.

Do Double-Hybrid Exchange-Correlation Functionals Provide Accurate Chemical Shifts? A Benchmark Assessment for Proton NMR

A benchmark density functional theory (DFT) study of ¹H NMR chemical shifts for data sets comprising 200 chemical shifts, including complex natural products, has been carried out to assess the performance of DFT methods. Two new benchmark data sets, NMRH33 and NMRH148, have been established. The meta-GGA revTPSS performs remarkably well against the NMRH33 benchmark set (mean absolute deviation (MAD), 0.10 ppm; maximum deviation (max), 0.26 ppm) with the smallest MAD of all evaluated functionals. The best-performing double-hybrid density functional (DHDF), revDSD-BLYP (MAD, 0.16 ppm; max, 0.35 ppm), performs similarly to hybrid-GGA methods (e.g., mPW1PW91/6-311G(d) (MAD, 0.15 ppm; max, 0.36 ppm)), but at a considerably higher computational cost. The results indicate that currently available double-hybrid DFT methods offer no benefit over GGA (including hybrid and meta) functionals in the calculation of ¹H NMR chemical shifts.

Coupled Cluster Benchmark of New DFT and Local Correlation Methods: Mechanisms of Hydroarylation and Oxidative Coupling Catalyzed by Ru(II, III) Chloride Carbonyls

We have evaluated a set of accurate canonical CCSD(T) energies for stationary points on the potential energy surface for Ru(II, III) chloride carbonyl catalysis of two competing reactions between benzene and methyl acrylate (MA), namely, hydroarylation and oxidative coupling. We have then applied this set to evaluate the performance of localized orbital coupled-cluster methods and several new and common density functionals. We find that (a) DLPNO-CCSD(T) with TightPNO cutoffs is an acceptable substitute for full canonical CCSD(T) calculations on this system; (b) for the closed-shell systems where it could be applied, LNO-CCSD(T) with tight convergence criteria is very close to the canonical results; (c) the recent ωB97X-V and ωB97M-V functionals exhibit superior performance to commonly used DFT functionals in both closed- and open-shell calculations; (d) the revDSD-PBEP86 revision of the DSD-PBEP86 double hybrid represents an improvement over the original, even though transition metals were not involved in its parametrization; and (e) DSD-SCAN and DOD-SCAN show comparable efficiency. Most tested (meta)-GGA and hybrid density functionals perform better for open-shell than for closed-shell complexes; this is not the case for the double hybrids considered.

Coupled Cluster Benchmark of New DFT and Local Correlation Methods: Mechanisms of Hydroarylation and Oxidative Coupling Catalyzed by Ru(II, III) Chloride Carbonyls

We have evaluated a set of accurate canonical CCSD(T) energies for stationary points on the potential energy surface for Ru(II, III) chloride carbonyl catalysis of two competing reactions between benzene and methyl acrylate (MA), namely, hydroarylation and oxidative coupling. We have then applied this set to evaluate the performance of localized orbital coupled-cluster methods and several new and common density functionals. We find that (a) DLPNO-CCSD(T) with TightPNO cutoffs is an acceptable substitute for full canonical CCSD(T) calculations on this system; (b) for the closed-shell systems where it could be applied, LNO-CCSD(T) with tight convergence criteria is very close to the canonical results; (c) the recent ωB97X-V and ωB97M-V functionals exhibit superior performance to commonly used DFT functionals in both closed- and open-shell calculations; (d) the revDSD-PBEP86 revision of the DSD-PBEP86 double hybrid represents an improvement over the original, even though transition metals were not involved in its parametrization; and (e) DSD-SCAN and DOD-SCAN show comparable efficiency. Most tested (meta)-GGA and hybrid density functionals perform better for open-shell than for closed-shell complexes; this is not the case for the double hybrids considered.