Comprehensive Benchmarking of a Density-Dependent Dispersion Correction

Molecular adsorption at Pt(111). How accurate are DFT functionals?

Recent DFT functionals including van der Waals contributions are benchmarked against micro calorimetric measurement for chemisorption on Pt(111). OptPBE-vdW and PBE-dDsC are found to be the most accurate, especially for unsaturated molecules where large errors can be committed with other functionals as PBE.

Effects of density functionals and dispersion interactions on geometries, bond energies and harmonic frequencies of EUX3 (E=N, P, CH; X=H, F, Cl)

Quantum-chemical calculations have been performed to evaluate the geometries, bonding nature and harmonic frequencies of the compounds [EUX3] at DFT, DFT-D3, DFT-D3(BJ) and DFT-dDSc levels using different density functionals BP86, BLYP, PBE, revPBE, PW91, TPSS and M06-L. The stretching frequency of UN bond in [NUF3] calculated with DFT/BLYP closely resembles with the experimental value. The performance of different density functionals for accurate UN vibrational frequencies follows the order BLYP>revPBE>BP86>PW91>TPSS>PBE>M06-L. The BLYP functional gives accurate value of the UE bond distances. The uranium atom in the studied compounds [EUX3] is positively charged. Upon going from [EUF3] to [EUCl3], the partial Hirshfeld charge on uranium atom decreases because of the lower electronegativity of chlorine compared to flourine. The Gopinathan-Jug bond order for UE bonds ranges from 2.90 to 3.29. The UE bond dissociation energies vary with different density functionals as M06-L<TPSS<BLYP<revPBE<BP86<PBE≈PW91. The orbital interactions ΔEorb, in all studied compounds [EUX3] are larger than the electrostatic interaction ΔEelstat, which means the UN bonds in these compound have greater degree of covalent character (in the range 63.8-77.2%). The UE σ-bonding interaction is the dominant bonding interaction in the nitride and methylidyne complexes while it is weaker in [PUX3]. The dispersion energy contributions to the total bond dissociation energies are rather small. Compared to the Grimme's D3(BJ) corrections, the Corminboeuf's dispersion corrections are larger with metaGGA functionals (TPSS, M06-L) while smaller with GGA functionals.

Fast and highly chemoselective alkynylation of thiols with hypervalent iodine reagents enabled through a low energy barrier concerted mechanism

Among all functional groups, alkynes occupy a privileged position in synthetic and medicinal chemistry, chemical biology, and materials science. Thioalkynes, in particular, are highly useful, as they combine the enhanced reactivity of the triple bond with a sulfur atom frequently encountered in bioactive compounds and materials. Nevertheless, general methods to access these compounds are lacking. In this article, we describe the mechanism and full scope of the alkynylation of thiols using ethynyl benziodoxolone (EBX) hypervalent iodine reagents. Computations led to the discovery of a new, three-atom concerted transition state with a very low energy barrier, which rationalizes the high reaction rate. On the basis of this result, the scope of the reaction was extended to the synthesis of aryl- and alkyl-substituted alkynes containing a broad range of functional groups. New sulfur nucleophiles such as thioglycosides, thioacids, and sodium hydrogen sulfide were also alkynylated successfully to lead to the most general and practical method yet reported for the synthesis of thioalkynes.

Minimizing density functional failures for non-covalent interactions beyond van der Waals complexes

CONSPECTUS: Kohn-Sham density functional theory offers a powerful and robust formalism for investigating the electronic structure of many-body systems while providing a practical balance of accuracy and computational cost unmatched by other methods. Despite this success, the commonly used semilocal approximations have difficulties in properly describing attractive dispersion interactions that decay with R(-6) at large intermolecular distances. Even in the short to medium range, most semilocal density functionals fail to give an accurate description of weak interactions. The omnipresence of dispersion interactions, which are neglected in the most popular electronic structure framework, has stimulated intense developments during the past decade. In this Account, we summarize our effort to develop and implement dispersion corrections that dramatically reduce the failures of both inter- and intramolecular interaction energies. The proposed schemes range from improved variants of empirical atom pairwise dispersion correction (e.g., dD10) to robust formulations dependent upon the electron density. Emphasis has been placed on introducing more physics into a modified Tang and Toennies damping function and deriving accurate dispersion coefficients. Our most sophisticated and established density-dependent correction, dDsC, is based on a simple generalized gradient approximation (GGA)-like reformulation of the exchange hole dipole moment introduced by Becke and Johnson. Akin to its empirical precursor, dDsC dramatically improves the interaction energy of a variety of standard density functionals simultaneously for typical intermolecular complexes and shorter-range interactions occurring within molecules. The broad applicability and robustness of the dDsC scheme is demonstrated on various representative reaction energies, geometries, and molecular dynamic simulations. The suitability of the a posteriori correction is also established through comparisons with the more computationally demanding self-consistent implementation. The proposed correction is then exploited to identify the key factors at the origin of the errors in thermochemistry beyond van der Waals complexes. Particular focus is placed on charge-transfer and mixed-valence complexes, which are relevant to the field of organic electronics. These types of complexes represent insightful examples for which the delocalization error may partially counterbalance the missing dispersion. Our devised methodology reveals the true performance of standard density functional approximations and the subtle interplay between the two types of errors. The analysis presented provides guidance for future functional development that could further improve the modeling of the structures and properties of molecular materials. Overall, the proposed state-of-the-art approaches have contributed to stress the crucial role of dispersion and improve their description in both straightforward van der Waals complexes and more challenging chemical situations. For the treatment of the latter, we have also provided relevant insights into which type of density functionals to favor.

Modeling adsorption and reactions of organic molecules at metal surfaces

CONSPECTUS: The understanding of adsorption and reactions of (large) organic molecules at metal surfaces plays an increasingly important role in modern surface science and technology. Such hybrid inorganic/organic systems (HIOS) are relevant for many applications in catalysis, light-emitting diodes, single-molecule junctions, molecular sensors and switches, and photovoltaics. Obviously, the predictive modeling and understanding of the structure and stability of such hybrid systems is an essential prerequisite for tuning their electronic properties and functions. At present, density-functional theory (DFT) is the most promising approach to study the structure, stability, and electronic properties of complex systems, because it can be applied to both molecules and solids comprising thousands of atoms. However, state-of-the-art approximations to DFT do not provide a consistent and reliable description for HIOS, which is largely due to two issues: (i) the self-interaction of the electrons with themselves arising from the Hartree term of the total energy that is not fully compensated in approximate exchange-correlation functionals, and (ii) the lack of long-range part of the ubiquitous van der Waals (vdW) interactions. The self-interaction errors sometimes lead to incorrect description of charge transfer and electronic level alignment in HIOS, although for molecules adsorbed on metals these effects will often cancel out in total energy differences. Regarding vdW interactions, several promising vdW-inclusive DFT-based methods have been recently demonstrated to yield remarkable accuracy for intermolecular interactions in the gas phase. However, the majority of these approaches neglect the nonlocal collective electron response in the vdW energy tail, an effect that is particularly strong in condensed phases and at interfaces between different materials. Here we show that the recently developed DFT+vdW(surf) method that accurately accounts for the collective electronic response effects enables reliable modeling of structure and stability for a broad class of organic molecules adsorbed on metal surfaces. This method was demonstrated to achieve quantitative accuracy for aromatic hydrocarbons (benzene, naphthalene, anthracene, and diindenoperylene), C60, and sulfur/oxygen-containing molecules (thiophene, NTCDA, and PTCDA) on close-packed and stepped metal surfaces, leading to an overall accuracy of 0.1 Å in adsorption heights and 0.1 eV in binding energies with respect to state-of-the-art experiments. An unexpected finding is that vdW interactions contribute more to the binding of strongly bound molecules on transition-metal surfaces than for molecules physisorbed on coinage metals. The accurate inclusion of vdW interactions also significantly improves tilting angles and adsorption heights for all the studied molecules, and can qualitatively change the potential-energy surface for adsorbed molecules with flexible functional groups. Activation barriers for molecular switches and reaction precursors are modified as well.

Origin of the enantioselectivity in organocatalytic Michael additions of β-ketoamides to α,β-unsaturated carbonyls: a combined experimental, spectroscopic and theoretical study

The organocatalytic enantioselective conjugate addition of secondary β-ketoamides to α,β-unsaturated carbonyl compounds is reported. Use of bifunctional Takemoto's thiourea catalyst allows enantiocontrol of the reaction leading either to simple Michael adducts or spirocyclic aminals in up to 99 % ee. The origin of the enantioselectivity has been rationalised based on combined DFT calculations and kinetic analysis. This study provides a deeper understanding of the reaction mechanism, which involves a predominant role of the secondary amide proton, and clarifies the complex interactions occurring between substrates and the catalyst.

Density Functional Investigation of the Adsorption of Isooctane, Ethanol, and Acetic Acid on a Water-Covered Fe(100) Surface

The presence of water in biofuels poses the question of how it affects the frictional performance of additives in fuels containing organic substances. To investigate the effect of water on the adsorption of molecules present in fuel and its additives we simulated within the framework of density functional theory the adsorption of ethanol, isooctane (2,2,4-trimethylpentane), and acetic acid on a bare and a water-covered Fe(100) surface. Van der Waals interactions are taken into account in our computations. In those molecules, where dispersion forces contribute significantly to the binding mechanism, the water layer has a stronger screening effect. Additionally, this effect can be enhanced by the presence of polar functional groups in the molecule. Thus, with the introduction of a water layer, the adsorption energy of isooctane and ethanol is reduced but it is increased in the case of the acetic acid. The adsorption configuration of ethanol is changed, while the one of acetic acid is moderately, and for isooctane only very slightly altered. Therefore, the effect of a water layer in the adsorption of organic molecules on an Fe(100) surface strongly depends on the type of bond and consequently, so do the tribological properties.

Effects of van der Waals Interactions in the Adsorption of Isooctane and Ethanol on Fe(100) Surfaces

van der Waals (vdW) forces play a fundamental role in the structure and behavior of diverse systems. Because of development of functionals that include nonlocal correlation, it is possible to study the effects of vdW interactions in systems of industrial and tribological interest. Here we simulated within the framework of density functional theory (DFT) the adsorption of isooctane (2,2,4-trimethylpentane) and ethanol on an Fe(100) surface, employing various exchange-correlation functionals to take vdW forces into account. In particular, this paper discusses the effect of vdW forces on the magnitude of adsorption energies, equilibrium geometries, and their role in the binding mechanism. According to our calculations, vdW interactions increase the adsorption energies and reduce the equilibrium distances. Nevertheless, they do not influence the spatial configuration of the adsorbed molecules. Their effect on the electronic density is a nonisotropic, delocalized accumulation of charge between the molecule and the slab. In conclusion, vdW forces are essential for the adsorption of isooctane and ethanol on a bcc Fe(100) surface.

Adjusting the Local Arrangement of π-Stacked Oligothiophenes through Hydrogen Bonds: A Viable Route to Promote Charge Transfer

We show that substituting quaterthiophene cores with strong H-bond aggregators, such as urea groups, provides an efficient way to adjust the mutual in-plane displacements of the semiconducting units and promote charge transfer. Our 2-D structure-property mapping reveals that the insertion of substituents induces up to 2.0 Å longitudinal and transversal displacements between the π-conjugated moieties. Some of these relative displacements lead to improved cofacial orbital overlaps that are otherwise inaccessible due to Pauli repulsion. Our results also emphasize that the fine-tuning of in-plane displacements is more effective than achieving "tighter" packing to promote charge-transfer properties.

Many-body van der Waals interactions in molecules and condensed matter

This work reviews the increasing evidence that many-body van der Waals (vdW) or dispersion interactions play a crucial role in the structure, stability and function of a wide variety of systems in biology, chemistry and physics. Starting with the exact expression for the electron correlation energy provided by the adiabatic connection fluctuation-dissipation theorem, we derive both pairwise and many-body interatomic methods for computing the long-range dispersion energy by considering a model system of coupled quantum harmonic oscillators within the random-phase approximation. By coupling this approach to density functional theory, the resulting many-body dispersion (MBD) method provides an accurate and efficient scheme for computing the frequency-dependent polarizability and many-body vdW energy in molecules and materials with a finite electronic gap. A select collection of applications are presented that ascertain the fundamental importance of these non-bonded interactions across the spectrum of intermolecular (the S22 and S66 benchmark databases), intramolecular (conformational energies of alanine tetrapeptide) and supramolecular (binding energy of the 'buckyball catcher') complexes, as well as molecular crystals (cohesive energies in oligoacenes). These applications demonstrate that electrodynamic response screening and beyond-pairwise many-body vdW interactions--both captured at the MBD level of theory--play a quantitative, and sometimes even qualitative, role in describing the properties considered herein. This work is then concluded with an in-depth discussion of the challenges that remain in the future development of reliable (accurate and efficient) methods for treating many-body vdW interactions in complex materials and provides a roadmap for navigating many of the research avenues that are yet to be explored.

On the viability of heterolytic peptide N-C(α) bond cleavage in electron capture and transfer dissociation mass spectrometry

While frequently employed as an experimental technique, the mechanistic picture surrounding the gas-phase dissociation of peptides carrying multiple positive charges during electron capture and electron transfer dissociation tandem mass spectrometry remains incomplete. Despite this mechanistic uncertainty, most proposals agree that the peptide backbone N-Cα bond located to the C-terminal (right) side of an aminoketyl radical formed in a peptide backbone during the electron capture process is homolytically cleaved. Recently, we introduced the "enol" mechanism, which proposes that a backbone N-Cα bond located to the N-terminal (left) side of an aminoketyl radical is cleaved heterolytically. Here, we further validate this mechanism using replica-exchange molecular dynamics to create unbiased representative sets of low-energy conformers for several model tryptic peptide systems (H-Alax-Lys-OH(2+), x = 3-5). Transition state barrier enthalpies for the cleavage of N-Cα bonds proceeding via the homolytic (right-side) and heterolytic (left-side) pathways, determined by density functional computations, identify the preferred cleavage route for each conformer. These findings support our original hypothesis that heterolytic N-Cα cleavage can exist in a competitive balance with homolytic cleavages, independent of the relative energy of the precursor dication species. Smaller peptide systems see decreased heterolytic N-Cα cleavage probabilities, likely resulting from an insufficient hydrogen-bonding network needed to stabilize and ultimately annihilate the transition state zwitterion. This observation may explain the early dismissal of left-side cleavage pathways based on computational studies employing small model systems.

Assessment of density functionals and paucity of non-covalent interactions in aminoylyne complexes of molybdenum and tungsten [(η5-C5H5)(CO)2MEN(SiMe3)(R)] (E = Si, Ge, Sn, Pb): a dispersion-corrected DFT study

Geometries, bonding analysis and dispersion interactions in aminoylyne complexes of molybdenum and tungsten have been investigated using different density functionals.

Absorption and fluorescence signatures of 1,2,3-triazole based regioisomers: challenging compounds for TD-DFT

Photophysical signatures of 1,2,3-triazole regioisomers: a surprisingly challenging problem for TD-DFT.

Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem

Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula upon invoking the random-phase approximation (RPA) or the full-potential approximation. Moreover, for a system of quantum harmonic oscillators coupled through a dipole-dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD-RPA correlation energy. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula, we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy.

Effects of local protein environment on the binding of diatomic molecules to heme in myoglobins. DFT and dispersion-corrected DFT studies

The heme-AB binding energies (AB = CO, O2) in a wild-type myoglobin (Mb) and two mutants (H64L, V68N) of Mb have been investigated in detail with both DFT and dispersion-corrected DFT methods, where H64L and V68N represent two different, opposite situations. Several dispersion correction approaches were tested in the calculations. The effects of the local protein environment were accounted for by including the five nearest surrounding residues in the calculated systems. The specific role of histidine-64 in the distal pocket was examined in more detail in this study than in other studies in the literature. Although the present calculated results do not change the previous conclusion that the hydrogen bonding by the distal histidine-64 residue plays a major role in the O2/CO discrimination by Mb, more details about the interaction between the protein environment and the bound ligand have been revealed in this study by comparing the binding energies of AB to a porphyrin and the various myoglobins. The changes in the experimental binding energies from one system to another are well reproduced by the calculations. Without constraints on the residues in geometry optimization, the dispersion correction is necessary, since it improves the calculated structures and energetic results significantly.

Pair-Wise and Many-Body Dispersive Interactions Coupled to an Optimally Tuned Range-Separated Hybrid Functional

We propose a nonempirical, pair-wise or many-body dispersion-corrected, optimally tuned range-separated hybrid functional. This functional retains the advantages of the optimal-tuning approach in the prediction of the electronic structure. At the same time, it gains accuracy in the prediction of binding energies for dispersively bound systems, as demonstrated on the S22 and S66 benchmark sets of weakly bound dimers.

Selecting DFT methods for use in optimizations of enzyme active sites: applications to ONIOM treatments of DNA glycosylases

When using a hybrid methodology to treat an enzymatic reaction, many factors contribute to selecting the method for the high-level region, which can be complicated by the presence of dispersion-driven interactions such as π–π stacking. In addition, the proper treatment of the reaction center often requires a large number of heavy atoms to be included in the high-level region, precluding the use of ab initio methods such as MP2 as well as large basis sets, in the optimization step. In the present work, popular DFT methods were tested to identify an appropriate functional for treating the high-level region in ONIOM optimizations of reactions catalyzed by nonmetalloenzymes. Eight different DFT methods (B3LYP, B97-2, MPW1K, MPWB1K, BB1K, B1B95, M06-2X, and ωB97X-D) in combination with four double-ζ quality Pople basis sets were tested for their ability to optimize noncovalent interactions (hydrogen bonding and π–π) and characterize reactions (proton transfer, SN2 hydrolysis, and unimolecular cleavage). Although the primary focus of this study is accurate structure determination, energetics were also examined at both the optimization level of theory, and with triple-ζ quality basis set and select (M06-2X or ωB97X-D) methods. If dispersion-driven interactions exist within the active site, then MPWB1K/6-31G(d,p) or M06-2X/6-31+G(d,p) are recommended for the optimization step with subsequent triple-ζ quality single-point energies. However, since dispersion-corrected functionals (M06-2X and ωB97X-D) generally require diffuse functions to yield appropriate geometries, the possible size of the high-level region is greatly limited with these methods. In contrast, if the model is large enough to recover steric constraints on π–π interactions, then B3LYP with a small basis set performs comparatively well for the optimization step and is significantly less computationally expensive. Interestingly, the functionals that afford the best geometries often do not yield the best energetics, which emphasizes the importance of structural benchmark studies.

Nitrogen reactivity toward beryllium: surface reactions

Recent experiments with nitrogen as a seeding gas in fusion plasma devices together with the option of using beryllium as an armor material in the future ITER tokamak (International Thermonuclear Experimental Reactor) have raised new interest in the interactions of beryllium surfaces with nitrogen (atomic or molecular). The strong reactivity of nitrogen implies the formation of beryllium nitrite and, in conjunction with oxygen and other possible impurities, experimentalists have to consider the probability of generating various complex moieties such as imine, amine or oxyamine, and amide radicals. This chemistry would obviously dramatically perturb the plasma, and quantum investigations can be of great predictive help. Nitrogen adsorption on beryllium basal surfaces is investigated through quantum density functional theory. Different situations are examined: molecular or atomic nitrogen reactions; nitride radical adsorption or formation on surfaces; hydrogen retention on surfaces; combined nitrogen/oxygen reactivity and hydrogen retention. A tentative comparison with experiment is also proposed.

Electron-deficient η1-Indenyl,η3-allylpalladium(II) complexes stabilized by fluxional non-covalent interactions

Highly fluxional, solution-persistent, and formally electron-deficient (32e(-)) binuclear Pd(II)-C(0) complexes of 2-methyl-1H-indene were synthesized and structurally characterized by X-ray diffraction analysis. DFT investigations combined with a number of theoretical analyses of the bond framework suggest that the polar intermetallic interaction possesses no major covalent character. Instead of bearing a static metal-metal bond as suggested by structural X-ray diffraction analysis, the complexes display in solution significant fluxionality through haptotropy, i.e., a formal "oscillation" of the Pd(η(3)-allyl) moiety between two limiting η(1)-indenyl configurations.

A Density Functional with Spherical Atom Dispersion Terms

A new hybrid density functional, APF, is introduced, which avoids the spurious long-range attractive or repulsive interactions that are found in most density functional theory (DFT) models. It therefore provides a sound baseline for the addition of an empirical dispersion correction term, which is developed from a spherical atom model (SAM). The APF-D empirical dispersion model contains nine adjustable parameters that were selected based on a very small training set (15 noble gas dimers and 4 small hydrocarbon dimers), along with two computed atomic properties (ionization potential and effective atomic polarizability) for each element. APF-D accurately describes a large portion of the potential energy surfaces of complexes of noble gas atoms with various diatomic molecules involving a wide range of elements and of dimers of small hydrocarbons, and it reproduces the relative conformational energies of organic molecules. The accuracy for these weak interactions is comparable to that of CCSD(T)/aug-cc-pVTZ calculations. The accuracy in predicting the geometry of hydrogen bond complexes is competitive with other models involving DFT and empirical dispersion.