Performance of Non-Local and Atom-Pairwise Dispersion Corrections to DFT for Structural Parameters of Molecules with Noncovalent Interactions

Extension of the D3 and D4 London dispersion corrections to the full actinides series

Efficient dispersion corrections are an indispensable component of modern density functional theory, semi-empirical quantum mechanical, and even force field methods. In this work, we extend the well established D3 and D4 London dispersion corrections to the full actinides series, francium, and radium. To keep consistency with the existing versions, the original parameterization strategy of the D4 model was only slightly modified. This includes improved reference Hirshfeld atomic partial charges at the ωB97M-V/ma-def-TZVP level to fit the required electronegativity equilibration charge (EEQ) model. In this context, we developed a new actinide data set called AcQM, which covers the most common molecular actinide compound space. Furthermore, the efficient calculation of dynamic polarizabilities that are needed to construct CAB6 dispersion coefficients was implemented into the ORCA program package. The extended models are assessed for the computation of dissociation curves of actinide atoms and ions, geometry optimizations of crystal structure cutouts, gas-phase structures of small uranium compounds, and an example extracted from a small actinide complex protein assembly. We found that the novel parameterizations perform on par with the computationally more demanding density-dependent VV10 dispersion correction. With the presented extension, the excellent cost-accuracy ratio of the D3 and D4 models can now be utilized in various fields of computational actinide chemistry and, e.g., in efficient composite DFT methods such as r2SCAN-3c. They are implemented in our freely available standalone codes (dftd4, s-dftd3) and the D4 version will be also available in the upcoming ORCA 6.0 program package.

Structure and stability of the sH binary hydrate cavity and host-guest versus guest-guest interactions therein: A DFT approach

The intrinsic ability of clathrate hydrates to encage gaseous molecules is explored. Encapsulation ability depends on the cavity size and the type of guest gaseous species in addition to the physical parameters, temperature and pressure. Here we have reported the structure, stability and nature of interaction in dissimilar guest occupied sH hydrate cavity. Diatomic gas molecules and small polyatomic hydrocarbons are considered as guests. The irregular icosahedron (5¹² 6⁸ ) cavity of sH hydrate is the host. Different thermodynamic parameters for the guest molecules encapsulation were calculated using three different hybrid DFT functionals, B3LYP, M05-2X, M06, and moreover using dispersion correction (PBE0-D3). With the consideration of large H-bonded systems the 6-31G* and cc-pVTZ basis sets were used for two set of computations. To disclose the nature of interaction between the host-guest systems as well as the interaction between the guest molecules inside the host the non-covalent interaction (NCI) indices and energy decomposition analysis (EDA) were done. Impact of host-guest and guest-guest interactions are discussed.

Cocrystals; basic concepts, properties and formation strategies

Cocrystallization is an old technique and remains the focus of several research groups working in the field of Chemistry and Pharmacy. This technique is basically in field for improving physicochemical properties of material which can be active pharmaceutical ingredients (APIs) or other chemicals with poor profile. So this review article has been presented in order to combine various concepts for scientists working in the field of chemistry, pharmacy or crystal engineering, also it was attempt to elaborate concepts belonging to crystal designing, their structures and applications. A handsome efforts have been made to bring scientists together working in different fields and to make chemistry easier for a pharmacist and pharmacy for chemists pertaining to cocrystals. Various aspects of chemicals being used as co-formers have been explored which predict the formation of co-crystals or molecular salts and even inorganic cocrystals.

A comprehensive benchmark investigation of quantum chemical methods for carbocations

The application of various density functional approximations (DFAs) and an emphasis on popular methods without any consensus have prevailed in computational studies dedicated to carbocations. More importantly, an extensive and rigorous benchmark investigation on density functionals for the class is still lacking. To close this gap, we present a comprehensive benchmark study of quantum chemical methods on a series of classical and nonclassical carbocations, the CARBO33 dataset. We evaluate a total of 107 DFT methods from all rungs giving particular attention to double hybrid density functionals as the potential of the class has been largely undermined in the context of carbocations. To support our findings, DLPNO-CCSD(T) at the complete basis set (CBS) limit and W1-F12 are used as reference methods. Our results indicate that the composite CBS-QB3 method performs poorly and should not be adopted for target energies. Oftentimes, the tested DFAs of a lower rung perform better than several DFAs in a higher rung of Perdew's "Jacob's ladder". Nonetheless, double hybrids DSD-PBEP86-NL and ωB97X-2-D3(BJ) stand out by showing the overall best performance. Among the hybrids evaluated, about half of them show mean absolute deviation (MAD) below 1.1 kcal mol^-1, including the popular hybrids M06-2X and mPW1PW91. In this family, MN15-D3(BJ) performs particularly well (MAD = 0.77 kcal mol^-1) displaying reliable results across various tests. Highly popular B3LYP exhibited one of the worst performances (MAD = 4.74 kcal mol^-1), and we do not recommend its application to carbocations. We also assess the 24 general-purpose basis sets of single- up to quadruple-ζ quality. The best compromise between accuracy and computational cost is achieved with cc-pVTZ followed by def2-TZVP. Computations on larger structures of general interest, including terpene carbocations, are also presented for selected DFT methods confirming general trends in the results.

Quantification of secondary electrostatic interactions in H-bonded complexes

The H-bonding properties of compounds that contain multiple functional groups are difficult to predict, because there are through-bond polarisation effects and long-range secondary electrostatic interactions that have significant effects on the interactions with solvents and other molecules. Here we use experimental measurements of association constants for formation of 1 : 1 H-bonded complexes that contain a single well-defined H-bond and a single well-defined secondary electrostatic interaction to quantify the magnitude of this effect. The results were used to develop a computational method for calculating functional group H-bond parameters that accurately reproduce the magnitudes of both primary H-bonding interaction and secondary electrostatic interactions. The effects of secondary electrostatic interactions are observed in calculations of ab initio Molecular Electrostatic Potential (MEP) values, but at the van der Waals surface, the magnitude of the effect is highly overestimated. MEP values calculated on electron density isosurfaces that lie closer to the nuclei provide a more accurate description of the experimental observations. H-bond parameters calculated using this approach successfully account for the properties of arrays of multiple H-bond donor and acceptor groups in different configurations. The results provide insight into the factors that govern the interaction properties of molecules that contain multiple functional groups and provide an accurate method for prediction of solution phase complexation free energies based on gas phase calculations of individual molecules.

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.

Benchmarking London dispersion corrected density functional theory for noncovalent ion-π interactions

The strongly attractive noncovalent interactions of charged atoms or molecules with π-systems are important binding motifs in many chemical and biological systems. These so-called ion-π interactions play a major role in enzymes, molecular recognition, and for the structure of proteins. In this work, a molecular test set termed IONPI19 is compiled for inter- and intramolecular ion-π interactions, which is well balanced between anionic and cationic systems. The IONPI19 set includes interaction energies of significantly larger molecules (up to 133 atoms) than in other ion-π test sets and covers a broad range of binding motifs. Accurate (local) coupled cluster values are provided as reference. Overall, 19 density functional approximations, including seven (meta-)GGAs, eight hybrid functionals, and four double-hybrid functionals combined with three different London dispersion corrections, are benchmarked for interaction energies. DFT results are further compared to wave function based methods such as MP2 and dispersion corrected Hartree-Fock. Also, the performance of semiempirical QM methods such as the GFNn-xTB and PMx family of methods is tested. It is shown that dispersion-uncorrected DFT underestimates ion-π interactions significantly, even though electrostatic interactions dominate the overall binding. Accordingly, the new charge dependent D4 dispersion model is found to be consistently better than the standard D3 correction. Furthermore, the functional performance trend along Jacob's ladder is generally obeyed and the reduction of the self-interaction error leads to an improvement of (double) hybrid functionals over (meta-)GGAs, even though the effect of the SIE is smaller than expected. Overall, the double-hybrids PWPB95-D4/QZ and revDSD-PBEP86-D4/QZ turned out to be the most reliable among all assessed methods for the description of ion-π interactions, which opens up new perspectives for systems where coupled cluster calculations are no longer computationally feasible.

CHAL336 Benchmark Set: How Well Do Quantum-Chemical Methods Describe Chalcogen-Bonding Interactions?

We present the CHAL336 benchmark set-the most comprehensive database for the assessment of chalcogen-bonding (CB) interactions. After careful selection of suitable systems and identification of three high-level reference methods, the set comprises 336 dimers each consisting of up to 49 atoms and covers both σ- and π-hole interactions across four categories: chalcogen-chalcogen, chalcogen-π, chalcogen-halogen, and chalcogen-nitrogen interactions. In a subsequent study of DFT methods, we re-emphasize the need for using proper London dispersion corrections when treating noncovalent interactions. We also point out that the deterioration of results and systematic overestimation of interaction energies for some dispersion-corrected DFT methods does not hint at problems with the chosen dispersion correction but is a consequence of large density-driven errors. We conclude this work by performing the most detailed DFT benchmark study for CB interactions to date. We assess 109 variations of dispersion-corrected and dispersion-uncorrected DFT methods and carry out a detailed analysis of 80 of them. Double-hybrid functionals are the most reliable approaches for CB interactions, and they should be used whenever computationally feasible. The best three double hybrids are SOS0-PBE0-2-D3(BJ), revDSD-PBEP86-D3(BJ), and B2NCPLYP-D3(BJ). The best hybrids in this study are ωB97M-V, PW6B95-D3(0), and PW6B95-D3(BJ). We do not recommend using the popular B3LYP functional nor the MP2 approach, which have both been frequently used to describe CB interactions in the past. We hope to inspire a change in computational protocols surrounding CB interactions that leads away from the commonly used, popular methods to the more robust and accurate ones recommended herein. We would also like to encourage method developers to use our set for the investigation and reduction of density-driven errors in new density functional approximations.

Assessing the Applicability of the Geometric Counterpoise Correction in B2PLYP/Double-ζ Calculations for Thermochemistry, Kinetics, and Noncovalent Interactions

We present a proof-of-concept study of the suitability of Kruse and Grimme’s geometric counterpoise correction (gCP) for basis set superposition errors (BSSEs) in double-hybrid density functional calculations with a double-ζ basis set. The gCP approach only requires geometrical information as an input and no orbital/density information is needed. Therefore, this correction is practically free of any additional cost. gCP is trained against the Boys and Bernardi counterpoise correction across a set of 528 noncovalently bound dimers. We investigate the suitability of the approach for the B2PLYP/def2-SVP level of theory, and reveal error compensation effects—missing London dispersion and the BSSE—associated with B2PLYP/def2-SVP calculations, and present B2PLYP-gCP-D3(BJ)/def2-SVP with the reparametrised DFT-D3(BJ) and gCP corrections as a more balanced alternative. Benchmarking results on the S66x8 benchmark set for noncovalent interactions and the GMTKN55 database for main-group thermochemistry, kinetics, and noncovalent interactions show a statistical improvement of the B2PLYP-gCP-D3(BJ) scheme over plain B2PLYP and B2PLYP-D3(BJ). B2PLYP-D3(BJ) shows significant overestimation of interaction energies, barrier heights with larger deviations from the reference values, and wrong relative stabilities in conformers, all of which can be associated with BSSE. We find that the gCP-corrected method represents a significant improvement over B2PLYP-D3(BJ), particularly for intramolecular noncovalent interactions. These findings encourage future developments of efficient double-hybrid DFT strategies that can be applied when double-hybrid calculations with large basis sets are not feasible due to system size.

Dispersion-driven conformational preference in the gas phase: Microwave spectroscopic and theoretical study of allyl isocyanate

The conformations of allyl isocyanate (CH₂=CHCH₂N=C=O) were explored in the gas phase by combining theoretical calculations and Fourier transform microwave spectroscopy, including the chirped pulse and Balle-Flygare types. Three conformers (I, II, and III) were predicted using D3(BJ) dispersion-corrected B3LYP and MP2 methods; however, the lowest energy conformer (conf. I) was absent at the standard B3LYP level. The observed microwave spectra are consistent with the presence of both conf. I and III in the supersonic jet, and surprisingly, this is the first report of the global minimum conf. I both experimentally and theoretically. Rotational transitions from the parent species of both conformers as well as their minor isotopologues (¹³C, ¹⁵N, and ¹⁸O) in natural abundance were assigned allowing experimental geometries to be derived. For conf. I, in addition to the typical splitting pattern due to the ¹⁴N quadrupole nucleus, the transitions show a tunneling splitting which arises from the interconversion motion between its two mirror images. The experimental observation of conf. I and the absence of conf. II in the jet are rationalized using quantum-chemical calculations to explore the importance of electron correlation and in particular, demonstrate the necessity of including dispersion effects in density functional theory calculations even for seemingly small molecules.

Secondary Electrostatic Interaction Model Revised: Prediction Comes Mainly from Measuring Charge Accumulation in Hydrogen-Bonded Monomers

The secondary electrostatic interaction (SEI) model is often used to predict and explain relative hydrogen bond strengths of self-assembled systems. The SEI model oversimplifies the hydrogen-bonding mechanisms by viewing them as interacting point charges, but nevertheless experimental binding strengths are often in line with the model’s predictions. To understand how this rudimentary model can be predictive, we computationally studied two tautomeric quadruple hydrogen-bonded systems, DDAA-AADD and DADA-ADAD. Our results reveal that when the proton donors D (which are electron-donating) and the proton acceptors A (which are electron-withdrawing) are grouped together as in DDAA, there is a larger accumulation of charge around the frontier atoms than when the proton donor and acceptor groups are alternating as in DADA. This accumulation of charge makes the proton donors more positive and the proton acceptors more negative, which enhances both the electrostatic and covalent interactions in the DDAA dimer. The SEI model is thus predictive because it provides a measure for the charge accumulation in hydrogen-bonded monomers. Our findings can be understood from simple physical organic chemistry principles and provide supramolecular chemists with meaningful understanding for tuning hydrogen bond strengths and thus for controlling the properties of self-assembled systems.

Planar rings in nano-Saturns and related complexes

Nitrogen substitution into the ortho positions in polyaryl macrocycles creates planar or ribbon structures leading to such structures as this nano-Saturn with a flat ring.

Improved general-purpose five-point model for water: TIP5P/2018

A new five point potential for liquid water, TIP5P/2018, is presented along with the techniques used to derive its charges from ab initio per-molecule electrostatic potentials in the liquid phase using the split charge equilibration of Nistor et al. [J. Chem. Phys. 125, 094108 (2006)]. By taking the density and diffusion dependence on temperature as target properties, significant improvements to the behavior of isothermal compressibility were achieved along with improvements to other thermodynamic and rotational properties. While exhibiting a dipole moment close to ab initio values, TIP5P/2018 suffers from a too small quadrupole moment due to the charge assignment procedure and results in an overestimation of the dielectric constant.

Semi-empirical or non-empirical double-hybrid density functionals: which are more robust?

The development of non-empirical double-hybrid density functionals (DHDFs) is a very active research area with the number of approaches in this field having increased rapidly. At the same time, there is a lack of published work that provides a fair assessment and comparison between non-empirical and semi-empirical DHDFs on an equal footing. Herein, we close this gap and present a thorough analysis of both classes of DHDFs on the large GMTKN55 benchmark database for general main-group thermochemistry, kinetics, and noncovalent interactions [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184-32215]. In total, 115 variations of dispersion-corrected and -uncorrected DHDFs are tested, which will be condensed to an in-depth assessment of 31 methods: 19 non-empirical and 12 semi-empirical DHDFs. As such, our study represents the largest DHDF study ever conducted and can serve as an important benchmark informing method developers and users alike. Our results show that semi-empirical DHDFs are the most robust density functional approximations and more reliable and accurate than non-empirical ones. In fact, some non-empirical approaches are even outperformed by hybrid approaches or even dispersion-corrected and -uncorrected MP2 and SCS-MP2. SOS0-PBE0-2-D3(BJ) is the only exception and the only non-empirical DHDF that we can safely recommend for general applicability. However, it is still outperformed by six semi-empirical DHDFs, of which we would like to particularly recommend the following five: ωB97X-2-D3(BJ), DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), B2NC-PLYP-D3(BJ), and B2GPPLYP-D3(BJ). Our findings seriously question current trends in the field and they highlight that novel strategies have to be found in order to outperform the currently best density functional theory methods on the market. We hope that our study can function as an important cornerstone inspiring such a change of direction in the field.

Improving the first hyperpolarizability of anthracene through interaction with HX molecules (XF, Cl, Br): A theoretical study

The variations in nonlinear optical activity (NLO) of anthracene (C₁₄H₁₀) was investigated via intermolecular interactions between C₁₄H₁₀ and HX molecules (XF, Cl and Br) using B3LYP-D3 method at 6-311++G(d,p) basis set. The stabilization of those complexes was investigated via vibrational analysis, quantum theory of atoms in molecules, molecular electrostatic potential, natural bond orbitals and symmetry-adapted perturbation theory (SAPT) analysis. Furthermore, the optical spectra and the first hyperpolarizabilities of C₁₄H₁₀⋯HX complexes were computed. The adsorption of hydrogen halide through C₁₄H₁₀⋯HX complex formation, didn't change much the linear optical activities of C₁₄H₁₀ molecule, but the magnitude of the first hyperpolarizability of the C₁₄H₁₀⋯HX complexes to be as much as that of urea.

Nature of Intramolecular Resonance Assisted Hydrogen Bonding in Malonaldehyde and Its Saturated Analogue

The nature of resonance-assisted hydrogen bonds (RAHB) is still subject of an ongoing debate. We therefore analyzed the σ and π charge redistributions associated with the formation of intramolecular hydrogen bonds in malonaldehyde (MA) and its saturated analogue 3-hydroxypropanal (3-OH) and addressed the question whether there is a resonance assistance phenomenon in the sense of a synergistic interplay between the σ and π electron systems. Our quantum chemical calculations at the BP86/TZ2P level of theory show that the π charge flow is indeed in line with the Lewis structure as proposed by the RAHB model. This typical rearrangement of charge is only present in the unsaturated system, and not in its saturated analogue. Resonance in the π electron system assists the intramolecular hydrogen bond by reducing the hydrogen bond distance, and by providing an additional stabilizing component to the net bonding energy. The σ orbital interaction plays an important role in the enhanced hydrogen bond strength in MA as well. However, there is no resonance assistance in the sense of an interplay between σ charge transfer and π polarization; σ and π contribute independently from each other.

Computational insight into magnetic behavior and properties of the transition metal complexes with redox-active ligands: a DFT approach

Various aspects related to the use of DFT method for the study of magnetic, geometry and energetic properties of transition metal complexes with redox-active ligands are considered. Particular attention is given to the correct choice of model compounds and methodology of the calculations.

Tuning the affinity of catechols and salicylic acids towards Al(iii): characterization of Al–chelator interactions

Aluminum is a non-essential element in the human body with unclear harmful effects; therefore, the design and tuning of new and efficient Al(iii) chelating agents is a subject of paramount importance nowadays.

Hydrogen-Bond Strength of CC and GG Pairs Determined by Steric Repulsion: Electrostatics and Charge Transfer Overruled

Theoretical and experimental studies have elucidated the bonding mechanism in hydrogen bonds as an electrostatic interaction, which also exhibits considerable stabilization by charge transfer, polarization, and dispersion interactions. Therefore, these components have been used to rationalize the differences in strength of hydrogen‐bonded systems. A completely new viewpoint is presented, in which the Pauli (steric) repulsion controls the mechanism of hydrogen bonding. Quantum chemical computations on the mismatched DNA base pairs CC and GG (C=cytosine, G=guanine) show that the enhanced stabilization and shorter distance of GG is determined entirely by the difference in the Pauli repulsion, which is significantly less repulsive for GG than for CC. This is the first time that evidence is presented for the Pauli repulsion as decisive factor in relative hydrogen‐bond strengths and lengths.

Partnering dispersion corrections with modern parameter-free double-hybrid density functionals

The PBE-QIDH and SOS1-PBE-QIDH double-hybrid density functionals are merged with a pair of dispersion corrections, namely the pairwise additive D3(BJ) and the non-local correlation functional VV10, leading to the corresponding dispersion-corrected models.

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.

A theoretical study of π-stacking interactions in C-substituted tetrazoles

The π-stacking effects of benzene ring (Ben) with 1H- and 2H-tetrazole derivatives (1H-TZ-X and 2H-TZ-X) substituted at C5 (where X is Cl, COH, NO, NO2, CN, NH2, OH, OCH3, SH and H) has been investigated by the quantum mechanical calculations at the M06-2X/6-311++G** level. The results indicate the 1H-TZ-X||Ben complexes (|| donates π-stacking interaction) are more stable than 2H-TZ-X||Ben while in unstacked forms, 1H-TZ-X is less stable than 2H-TZ-X. All substituents enhance the π-stacking interaction relative to the unsubstituted ones and enhancement is higher for the electron-withdrawing substituents (EWSs). Also, investigation of the local and direct effect of substituents in stacking interaction showed that all substituents regardless of whether are electron donating or electron withdrawing have an additive effect in π-stacking interaction. Excellent correlations were found between the binding energies of the complexes and combination of substituent constant terms. The results showed that the electrostatic interaction alone is not responsible for stacking stabilization but charge penetration is important. Furthermore, analysis of aromaticity, AIM, ESP and NPA were investigated to obtain aromaticity index, non-bonding interactions, chemical reactivity and polarity (dipole moment), respectively.

Stabilizing and Modulating Color by Copigmentation: Insights from Theory and Experiment

Natural anthocyanin pigments/dyes and phenolic copigments/co-dyes form noncovalent complexes, which stabilize and modulate (in particular blue, violet, and red) colors in flowers, berries, and food products derived from them (including wines, jams, purees, and syrups). This noncovalent association and their electronic and optical implications constitute the copigmentation phenomenon. Over the past decade, experimental and theoretical studies have enabled a molecular understanding of copigmentation. This review revisits this phenomenon to provide a comprehensive description of the nature of binding (the dispersion and electrostatic components of π-π stacking, the hydrophobic effect, and possible hydrogen-bonding between pigment and copigment) and of spectral modifications occurring in copigmentation complexes, in which charge transfer plays an important role. Particular attention is paid to applications of copigmentation in food chemistry.

Theoretical Study of Spin Crossover in 30 Iron Complexes

Iron complexes are important spin crossover (SCO) systems with vital roles in oxidative metabolism and promising technological potential. The SCO tendency depends on the free energy balance of high- and low-spin states, which again depends on physical effects such as dispersion, relativistic effects, and vibrational entropy. This work studied 30 different iron SCO systems with experimentally known thermochemical data, using 12 different density functionals. Remarkably general entropy-enthalpy compensation across SCO systems was identified (R = 0.82, p = 0.002) that should be considered in rational SCO design. Iron(II) complexes displayed higher ΔH and ΔS values than iron(III) complexes and also less steep compensation effects. First-coordination sphere ΔS values computed from numerical frequencies reproduce most of the experimental entropy and should thus be included when modeling spin-state changes in inorganic chemistry (R = 0.52, p = 3.4 × 10(-3); standard error in TΔS ≈ 4.4 kJ/mol at 298 K vs 16 kJ/mol of total TΔS on average). Zero-point energies favored high-spin states by 9 kJ/mol on average. Interestingly, dispersion effects are surprisingly large for the SCO process (average: 9 kJ/mol, but up to 33 kJ/mol) and favor the more compact low-spin state. Relativistic effects favor low-spin by ∼9 kJ/mol on average, but up to 24 kJ/mol. B3LYP*, TPSSh, B2PLYP, and PW6B95 performed best for the typical calculation scheme that includes ZPE. However, if relativistic and dispersion effects are included, only B3LYP* remained accurate. On average, high-spin was favored by LYP by 11-15 kJ/mol relative to other correlation functionals, and by 4.2 kJ/mol per 1% HF exchange in hybrids. 13% HF exchange was optimal without dispersion, and 15% was optimal with all effects included for these systems.

Reactive p-block cations stabilized by weakly coordinating anions

The chemistry of the p-block elements is a huge playground for fundamental and applied work. With their bonding from electron deficient to hypercoordinate and formally hypervalent, the p-block elements represent an area to find terra incognita. Often, the formation of cations that contain p-block elements as central ingredient is desired, for example to make a compound more Lewis acidic for an application or simply to prove an idea. This review has collected the reactive p-block cations (rPBC) with a comprehensive focus on those that have been published since the year 2000, but including the milestones and key citations of earlier work. We include an overview on the weakly coordinating anions (WCAs) used to stabilize the rPBC and give an overview to WCA selection, ionization strategies for rPBC-formation and finally list the rPBC ordered in their respective group from 13 to 18. However, typical, often more organic ion classes that constitute for example ionic liquids (imidazolium, ammonium, etc.) were omitted, as were those that do not fulfill the - naturally subjective -"reactive"-criterion of the rPBC. As a rule, we only included rPBC with crystal structure and only rarely refer to important cations published without crystal structure. This collection is intended for those who are simply interested what has been done or what is possible, as well as those who seek advice on preparative issues, up to people having a certain application in mind, where the knowledge on the existence of a rPBC that might play a role as an intermediate or active center may be useful.

Beyond energies: geometry predictions with the XYG3 type of doubly hybrid density functionals

The scaled mean absolute deviations (s-MADs) of the optimized geometric parameters for covalent bondings (the CCse set), nonbonded interactions (the S22G30 set) and the transition state structures (the TSG36 set), with Tot referring to the averaged s-MAD for general performances.

Consistent structures and interactions by density functional theory with small atomic orbital basis sets

A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calculations conducted for molecular crystals to test structures (including cell volumes) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calculations. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust "high-speed" computational tool in theoretical chemistry and physics.

Competitive lithium solvation of linear and cyclic carbonates from quantum chemistry

The composition of the lithium cation (Li(+)) solvation shell in mixed linear and cyclic carbonate-based electrolytes has been re-examined using Born-Oppenheimer molecular dynamics (BOMD) as a function of salt concentration and cluster calculations with ethylene carbonate:dimethyl carbonate (EC:DMC)-LiPF6 as a model system. A coordination preference for EC over DMC to a Li(+) was found at low salt concentrations, while a slightly higher preference for DMC over EC was found at high salt concentrations. Analysis of the relative binding energies of the (EC)n(DMC)m-Li(+) and (EC)n(DMC)m-LiPF6 solvates in the gas-phase and for an implicit solvent (as a function of the solvent dielectric constant) indicated that the DMC-containing Li(+) solvates were stabilized relative to (EC4)-Li(+) and (EC)3-LiPF6 by immersing them in the implicit solvent. Such stabilization was more pronounced in the implicit solvents with a high dielectric constant. Results from previous Raman and IR experiments were reanalyzed and reconciled by correcting them for changes of the Raman activities, IR intensities and band shifts for the solvents which occur upon Li(+) coordination. After these correction factors were applied to the results of BOMD simulations, the composition of the Li(+) solvation shell from the BOMD simulations was found to agree well with the solvation numbers extracted from Raman experiments. Finally, the mechanism of the Li(+) diffusion in the dilute (EC:DMC)LiPF6 mixed solvent electrolyte was studied using the BOMD simulations.

Hydrophobicity: effect of density and order on water's rotational slowing down

Ab initio molecular dynamics (AIMD) simulations of over 4.5 ns were performed in the temperature range of T = 260-350 K with van der Waals corrections to investigate the relationship between local water density and tetrahedral order in bulk water and in the presence of a hydrophobe, tetramethylurea (TMU). We demonstrate that in bulk water, defects consisting of 5- and higher coordinated water are a major contributor to dynamics. Close to a hydrophobe, 3-coordinated defects take over. The co-existence of these defects gives rise to very different local densities. We propose that the slowing down of rotational motion close to a hydrophobe is induced by an interplay between density and order with the slowing down decreasing in the following order: (i) low-density ordered-water, (ii) normal-density ordered-water, (iii) high-density ordered-water and (iv) disordered-water. The proportions of these water environments vary with temperature. These local environments also support the idea of water's polymorphism, i.e., the existence of the high- and low-density states in supercooled water.

Quantum chemical benchmark study on 46 RNA backbone families using a dinucleotide unit

We have created a benchmark set of quantum chemical structure-energy data denoted as UpU46, which consists of 46 uracil dinucleotides (UpU), representing all known 46 RNA backbone conformational families. Penalty-function-based restrained optimizations with COSMO TPSS-D3/def2-TZVP ensure a balance between keeping the target conformation and geometry relaxation. The backbone geometries are close to the clustering-means of their respective RNA bioinformatics family classification. High-level wave function methods (DLPNO-CCSD(T) as reference) and a wide-range of dispersion-corrected or inclusive DFT methods (DFT-D3, VV10, LC-BOP-LRD, M06-2X, M11, and more) are used to evaluate the conformational energies. The results are compared to the Amber RNA bsc0χOL3 force field. Most dispersion-corrected DFT methods surpass the Amber force field significantly in accuracy and yield mean absolute deviations (MADs) for relative conformational energies of ∼0.4-0.6 kcal/mol. Double-hybrid density functionals represent the most accurate class of density functionals. Low-cost quantum chemical methods such as PM6-D3H+, HF-3c, DFTB3-D3, as well as small basis set calculations corrected for basis set superposition errors (BSSEs) by the gCP procedure are also tested. Unfortunately, the presently available low-cost methods are struggling to describe the UpU conformational energies with satisfactory accuracy. The UpU46 benchmark is an ideal test for benchmarking and development of fast methods to describe nucleic acids, including force fields.

London dispersion in molecular chemistry--reconsidering steric effects

London dispersion, which constitutes the attractive part of the famous van der Waals potential, has long been underappreciated in molecular chemistry as an important element of structural stability, and thus affects chemical reactivity and catalysis. This negligence is due to the common notion that dispersion is weak, which is only true for one pair of interacting atoms. For increasingly larger structures, the overall dispersion contribution grows rapidly and can amount to tens of kcal mol(-1) . This Review collects and emphasizes the importance of inter- and intramolecular dispersion for molecules consisting mostly of first row atoms. The synergy of experiment and theory has now reached a stage where dispersion effects can be examined in fine detail. This forces us to reconsider our perception of steric hindrance and stereoelectronic effects. The quantitation of dispersion energy donors will improve our ability to design sophisticated molecular structures and much better catalysts.