Phenylacetylene-based [2]rotaxanes were synthesized by a covalent-template approach by aminolysis of the corresponding prerotaxanes. The wheel and the bulky stoppers are made of phenylene–ethynylene–butadiynylene macrocycles of the same size. The stoppers are large enough to enable the synthesis and purification of the rotaxane. However, the wheel unthreads from the axle at elevated temperatures. The deslipping kinetics and the activation parameters were determined. We described theoretically the unthreading by state-of-the-art DFT-based molecular-mechanics models and a string method for the simulation of rare events. This approach enabled us to characterize in detail the unthreading mechanism, which involves the folding of the stopper during its passage through the wheel opening, a process that defies intuitive geometrical considerations. The conformational and energetic features of the transition allowed us to infer the molecular residues controlling the disassembly timescale.

In quantum chemical computations the combination of Hartree–Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods.

The electronic circular dichroism (ECD) spectrum of the recently synthesized [16]helicene and a derivative comprising two triisopropylsilyloxy protection groups was computed by means of the very efficient simplified time-dependent density functional theory (sTD-DFT) approach. Different from many previous ECD studies of helicenes, nonequilibrium structure effects were accounted for by computing ECD spectra on "snapshots" obtained from a molecular dynamics (MD) simulation including solvent molecules. The trajectories are based on a molecule specific classical potential as obtained from the recently developed quantum chemically derived force field (QMDFF) scheme. The reduced computational cost in the MD simulation due to the use of the QMDFF (compared to ab-initio MD) as well as the sTD-DFT approach make realistic spectral simulations feasible for these compounds that comprise more than 100 atoms. While the ECD spectra of [16]helicene and its derivative computed vertically on the respective gas phase, equilibrium geometries show noticeable differences, these are “washed” out when nonequilibrium structures are taken into account. The computed spectra with two recommended density functionals (ωB97X and BHLYP) and extended basis sets compare very well with the experimental one. In addition we provide an estimate for the missing absolute intensities of the latter. The approach presented here could also be used in future studies to capture nonequilibrium effects, but also to systematically average ECD spectra over different conformations in more flexible molecules. Chirality 28:365–369, 2016. © 2016 Wiley Periodicals, Inc.

Low-temperature generation of P-nitroxyl phosphane 2 (Ph₂POTEMP), which was obtained by the reaction of Ph₂PH (1) with two equivalents of TEMPO, is presented. Upon warming, phosphane 2 decomposed to give P-nitroxyl phosphane P-oxide 3 (Ph₂P(O)OTEMP) as one of the final products. This facile synthetic protocol also enabled access to P-sulfide and P-borane derivatives 7 and 13, respectively, by using Ph₂P(S)H (6) or Ph₂P(BH₃)H (11) and TEMPO. Phosphane sulfide 7 revealed a rearrangement to phosphane oxide 8 (Ph₂P(O)STEMP) in CDCl₃ at ambient temperature, whereas in THF, thermal decomposition of sulfide 7 yielded salt 10 ([TEMP-H₂][Ph₂P(S)O]). As well as EPR and detailed NMR kinetic studies, indepth theoretical studies provided an insight into the reaction pathways and spin-density distributions of the reactive intermediates.

Phenylacetylene-based [2]rotaxanes were synthesized by a covalent-template approach by aminolysis of the corresponding prerotaxanes. The wheel and the bulky stoppers are made of phenylene–ethynylene–butadiynylene macrocycles of the same size. The stoppers are large enough to enable the synthesis and purification of the rotaxane. However, the wheel unthreads from the axle at elevated temperatures. The deslipping kinetics and the activation parameters were determined. We described theoretically the unthreading by state-of-the-art DFT-based molecular-mechanics models and a string method for the simulation of rare events. This approach enabled us to characterize in detail the unthreading mechanism, which involves the folding of the stopper during its passage through the wheel opening, a process that defies intuitive geometrical considerations. The conformational and energetic features of the transition allowed us to infer the molecular residues controlling the disassembly timescale.

The first frustrated Lewis pair-catalyzed cycloisomerization of a series of 1,5-enynes was developed. The reaction proceeds via the π-activation of the alkyne and subsequent 5-endo-dig cyclization with the adjacent alkene. The presence of PPh₃ was of utmost importance on the one hand to prevent side reactions (for example, 1,1-carboboration) and on the other hand for the efficient protodeborylation to achieve the catalytic turnover. The mechanism is explained on the basis of quantum-chemical calculations, which are in full agreement with the experimental observations.

Die erste durch ein frustriertes Lewis-Paar katalysierte Cycloisomerisierung einer Reihe von 1,5-Eninen wurde entwickelt. Die Reaktion verläuft über die π-Aktivierung des Alkins mit anschließender 5-endo-dig-Cyclisierung. Die Gegenwart von PPh₃ als Lewis-Base war von besonderer Bedeutung, um einerseits Nebenreaktionen zu unterdrücken (z. B. 1,1-Carboborierung) und um andererseits die Protodeborylierung für die katalytische Reaktion zu erreichen. Der Mechanismus wurde durch quantenmechanische Rechnungen untersucht und ist im Einklang mit strukturchemischen und kinetischen Daten.

State-of-the-art quantum chemical methods have been applied to describe the association of two frustrated Lewis pairs (FLPs), B(C₆F₅)₃/PR₃ (1: R=2,4,6-Me₃C₆H₂; 2: R=CMe₃), with different steric demands of the base component. Interaction energies are calculated at the dispersion-corrected DFT, MP2 (second-order Møller-Plesset), and DLPNO-CCSD(T) (domain-based local pair natural orbital-coupled cluster, including single, double and perturbative triple excitations) levels of theory, combined with extended triple- or quadruple-ζ AO (atom-centered orbital) basis sets. Thermostatistical contributions to the free binding energy are calculated from harmonic frequencies at the efficient HF-3c (minimal basis Hartree-Fock with three corrections) level, while solvation effects in benzene are accounted for by the COSMO-RS (conductor-like screening model for realistic solvents) continuum model. Comparison with the recently measured experimental value for the free association energy of the FLP 1 reveals agreement between theory and experiment within the estimated error bars. The computed gas phase interaction energies for both FLPs are similar (about −13 kcal mol⁻¹), with only small variations (about ±3 kcal mol⁻¹) for various quantum chemical methods, when London dispersion interactions are accounted for properly. The association of the more “frustrated” FLP 1 is mainly driven by nondirectional dispersion forces, resulting in non-preferential orientations, which is in agreement with experimental results. On the other hand, in FLP 2 with the “smaller” base, the boron and phosphorous atoms face each other in the favored complex structure, indicating a weak PB donor-acceptor interaction. This conformation of 2 seems to be more suitable for small molecule (e.g., H₂) activations.

Es wird über eine übergangsmetallfreie Transferhydrierung von 1,1-disubstituierten Alkenen berichtet, in der ein Cyclohexa-1,4-dien die formale Diwasserstoffquelle darstellt. Der Prozess beginnt mit einer B(C₆F₅)₃-vermittelten Hydridabstraktion vom Diwasserstoffsurrogat unter Bildung eines Brønsted-sauren Wheland-Komplexes sowie [HB(C₆F₅)₃]⁻. Eine Abfolge aus Protonen- und Hydridübertragungen auf das Alkensubstrat liefert dann das Alkan. Obwohl mehrere Carbeniumionzwischenstufen beteiligt sind, werden konkurrierende Reaktionswege, beispielsweise Diwasserstofffreisetzung und kationische Dimerisierungen von Reaktanten, weitgehend unterdrückt. Dies wird durch den Einsatz von Cyclohexa-1,4-dienen mit Methylgruppen an den C1- und C5-Positionen sowie am C3-Kohlenstoffatom, an dem die Hydridabstraktion stattfindet, ermöglicht. Die Konzentration an Alken ist eine weitere entscheidende Einflussgröße. Die unterschiedlichen Reaktionspfade wurden berechnet, woraus sich ein mechanistisches Bild ergibt, das mit den experimentellen Beobachtungen vollständig in Einklang ist.

A transition-metal-free transfer hydrogenation of 1,1-disubstituted alkenes with cyclohexa-1,4-dienes as the formal source of dihydrogen is reported. The process is initiated by B(C₆F₅)₃-mediated hydride abstraction from the dihydrogen surrogate, forming a Brønsted acidic Wheland complex and [HB(C₆F₅)₃]⁻. A sequence of proton and hydride transfers onto the alkene substrate then yields the alkane. Although several carbenium ion intermediates are involved, competing reaction channels, such as dihydrogen release and cationic dimerization of reactants, are largely suppressed by the use of a cyclohexa-1,4-diene with methyl groups at the C1 and C5 as well as at the C3 position, the site of hydride abstraction. The alkene concentration is another crucial factor. The various reaction pathways were computationally analyzed, leading to a mechanistic picture that is in full agreement with the experimental observations.

The inclusion of dynamical and static electron correlation (SEC) is mandatory for accurate quantum chemistry (QC). SEC is particularly difficult to calculate and hence a qualitative understanding is important to judge the applicability of approximate QC methods. Existing scalar SEC diagnostics, however, lack the important information where the SEC effects occur in a molecule. We introduce an analysis tool based on a fractional occupation number weighted electron density (ρ^FOD) that is plotted in 3D for a pre-defined contour surface value. The scalar field is obtained by finite-temperature DFT calculations with pre-defined electronic temperature (e.g. TPSS at 5000 K). FOD plots only show the contribution of the “hot” (strongly correlated) electrons. We discuss illustrative plots for a broad range of chemical systems from small molecules to large conjugated molecules with polyradicaloid character. Spatial integration yields a single number which can be used to globally quantify SEC.

Die Einbeziehung von dynamischer und statischer Elektronenkorrelation (SEK) ist unerlässlich für hochgenaue quantenchemische (QC) Berechnungen, wobei die SEK besonders schwierig zu beschreiben ist. Daher ist ein qualitatives Verständnis wichtig, um die Anwendbarkeit von approximativen QC-Methoden zu beurteilen. Bereits vorhandenen SEK-Diagnostiken fehlt jedoch die wichtige Information, wo in einem Molekül SEK-Effekte auftreten. Wir stellen ein Analysewerkzeug vor, welches auf einer mit gebrochenzahlig besetzten Orbitalen gewichteten Elektronendichte (ρ^FOD, “fractional occupation density”) basiert und in 3D mit einem vordefinierten Konturwert als Isofläche dargestellt wird. Dieses Skalarfeld wird aus einer Dichtefunktionaltheorie(DFT)-Rechnung mit einer festen elektronischen Temperatur (z. B. TPSS mit 5000 K) erhalten. FOD-Visualisierungen zeigen nur die Beiträge “heißer” (stark korrelierter) Elektronen. Wir diskutieren FOD-Abbildungen für eine breite Palette von typischen chemischen Systemen, angefangen von kleinen Molekülen bis hin zu großen, konjugierten Molekülen mit Polyradikalcharakter. Durch räumliche Integration der ρ^FOD erhält man eine Maßzahl, welche zur weiteren Quantifizierung der SEK benutzt werden kann.

Reliable thermochemical measurements and theoretical predictions for reactions involving large transition metal complexes in which long-range intramolecular London dispersion interactions contribute significantly to their stabilization are still a challenge, particularly for reactions in solution. As an illustrative and chemically important example, two reactions are investigated where a large dipalladium complex is quenched by bulky phosphane ligands (triphenylphosphane and tricyclohexylphosphane). Reaction enthalpies and Gibbs free energies were measured by isotherm titration calorimetry (ITC) and theoretically ‘back-corrected’ to yield 0 K gas-phase reaction energies (ΔE). It is shown that the Gibbs free solvation energy calculated with continuum models represents the largest source of error in theoretical thermochemistry protocols. The (‘back-corrected’) experimental reaction energies were used to benchmark (dispersion-corrected) density functional and wave function theory methods. Particularly, we investigated whether the atom-pairwise D3 dispersion correction is also accurate for transition metal chemistry, and how accurately recently developed local coupled-cluster methods describe the important long-range electron correlation contributions. Both, modern dispersion-corrected density functions (e.g., PW6B95-D3(BJ) or B3LYP-NL), as well as the now possible DLPNO-CCSD(T) calculations, are within the ‘experimental’ gas phase reference value. The remaining uncertainties of 2–3 kcal mol⁻¹ can be essentially attributed to the solvation models. Hence, the future for accurate theoretical thermochemistry of large transition metal reactions in solution is very promising.

The performance of 23 density functionals, including one LDA, four GGAs, three meta-GGAs, three hybrid GGAs, eight hybrid meta-GGAs, and ten double-hybrid functionals, was investigated for the computation of activation energies of various covalent main-group single bonds by four catalysts: Pd, PdCl⁻, PdCl₂, and Ni (all in the singlet state). A reactant complex, the barrier, and reaction energy were considered, leading to 164 energy data points for statistical analysis. Extended Gaussian AO basis sets were used in all calculations. The best functional for the complete benchmark set relative to estimated CCSD(T)/CBS reference data is PBE0-D3, with an MAD value of 1.1 kcal mol⁻¹ followed by PW6B95-D3, the double hybrid PWPB95-D3, and B3LYP-D3 (1.9 kcal mol⁻¹ each). The other tested hybrid meta-GGAs perform less well (M06-HF: 7.0 kcal mol⁻¹; M06-2X: 6.3 kcal mol⁻¹; M06: 4.9 kcal mol⁻¹) for the investigated reactions. In the Ni case, some double hybrids show larger errors due to partial breakdown of the perturbative treatment for the correlation energy in cases with difficult electronic structures (partial multi-reference character). Only double hybrids either with very low amounts of perturbative correlation (e.g., PBE0-DH) or that use the opposite-spin correlation component only (e.g., PWPB95) seem to be more robust. We also investigated the effect of the D3 dispersion correction. While the barriers are not affected by this correction, significant and mostly positive results were observed for reaction energies. Furthermore, six very recently proposed double-hybrid functionals were analyzed regarding the influence of the amount of Fock exchange as well as the type of perturbative correlation treatment. According to these results, double hybrids with <50–60 % of exact exchange and ∼30 % perturbative correlation perform best.

A combined X-ray diffraction and theoretical study of the solid-state molecular and crystal structures of tribenzotriquinacene (TBTQ, 2) and its centro-methyl derivative (3) is presented. The molecular structure of the parent hydrocarbon displays C_3v symmetry and the three indane wings adopt mutually orthogonal orientations, similar to the case in its previously reported methyl derivative (3). Also similarly to the latter structure, the bowl-shaped molecules of compound 2 form infinite molecular stacks with perfectly axial, face-to-back (convex–concave) packing and with parallel and unidirectional orientation of the stacks. The experimentally determined intra-stack molecular distance is 4.75 Å for compound 2 and 5.95 Å for compound 3. Whereas the molecules of compound 2 show a slight alternating rotation (±6°) about the common axis of each stack, those of compound 3 show perfect translational symmetry within the stacks. We used dispersion-corrected density functional theory to compute the crystal structures of tribenzotriquinacenes 2 and 3. The London dispersion correction was crucial for obtaining an accurate description of the crystallization of both analyzed systems and the calculated results agreed excellently with the experimental measurements. We also obtained reasonable sublimation energies for both compounds. In addition, the geometries and dimerization energies of oligomeric stacks of compound 2 were computed and showed smooth convergence to the properties of the infinite polymeric stack.

Direct CH phenylation of 2-ethylthiophene and 2-chlorothiophene with PhPdI(bipy) complex to form either the corresponding 4-phenyl or 5-phenylthiophene derivative is studied under stoichiometric conditions using various Lewis acids as additives. It is shown that reactions occur via the corresponding cationic Pd complex (PhPdbipy⁺) and that the counteranion determines the regioselectivity. High-level DFT calculations reveal that CC bond formation occurs via a carbopalladation pathway and not via electrophilic palladation. These calculations give some indications regarding the regioselectivity of the thiophene arylation.

The equilibrium association free enthalpies ΔG_a for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG_a values in the range 0 to −21 kcal mol⁻¹ (on average −6 kcal mol⁻¹) are investigated. The theoretical approach employs a (nondynamic) single-structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT-D3) with extended basis sets (triple-ζ and quadruple-ζ quality) is used to determine structures and gas-phase interaction energies (ΔE), the COSMO-RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro-vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low-lying vibrational modes are treated by a free-rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range −5 to −60 kcal mol⁻¹ (up to 200 % of ΔE). Inclusion of three-body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG_a values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG_a values with errors of only 2 kcal mol⁻¹ on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300–400 atoms. The various contributions to binding and enthalpy–entropy compensations are discussed.

Dispersion-corrected density functional theory calculations (DFT-D3) were performed for the adsorption of CO on MgO and C₂H₂ on NaCl surfaces. An extension of our non-empirical scheme for the computation of atom-in-molecules dispersion coefficients is proposed. It is based on electrostatically embedded M₄X₄ (MNa, Mg) clusters that are used in TDDFT calculations of dynamic dipole polarizabilities. We find that the dispersion coefficients for bulk NaCl and MgO are reduced by factors of about 100 and 35 for Na and Mg, respectively, compared to the values of the free atoms. These are used in periodic DFT calculations with the revPBE semi-local density functional. As demonstrated by calculations of adsorption potential energy curves, the new C₆ coefficients lead to much more accurate energies (E_ads) and molecule–surface distances than with previous DFT-D schemes. For NaCl/C₂H₂ we obtained at the revPBE-D3(BJ) level a value of E_ads=−7.4 kcal mol⁻¹ in good agreement with experimental data (−5.7 to −7.1 kcal mol⁻¹). Dispersion-uncorrected DFT yields an unbound surface state. For the MgO/CO system, the computed revPBE-D3(BJ) value of E_ads=−4.1 kcal mol⁻¹ is also in reasonable agreement with experimental results (−3.0 kcal mol⁻¹) when thermal corrections are taken into account. Our new dispersion correction also improves computed lattice constants of the bulk systems significantly compared to plain DFT or previous DFT-D results. The extended DFT-D3 scheme also provides accurate non-covalent interactions for ionic systems without empirical adjustments and is suggested as a general tool in surface science.

Dispersion-corrected density functional theory is assessed on the new S66 and S66x8 benchmark sets for non-covalent interactions. In total, 17 different density functionals are evaluated. Two flavors of our latest additive London-dispersion correction DFT-D3 and DFT-D3(BJ), which differ in their short-range damping functions, are tested. In general, dispersion corrections are again shown to be crucial to obtain reliable non-covalent interaction energies and equilibrium distances. The corrections strongly diminish the performance differences between the functionals, and in summary most dispersion-corrected methods can be recommended. DFT-D3 and DFT-D3(BJ) also yield similar results but for most functionals and intermolecular distances, the rational Becke–Johnson scheme performs slightly better. Particularly, the statistical analysis for S66x8, which covers also non-equilibrium complex geometries, shows that the Minnesota class of functionals is also improved by the D3 scheme. The best methods on the (meta-)GGA or hybrid- (meta-)GGA level are B97-D3, BLYP-D3(BJ), PW6B95-D3, MPW1B95-D3 and LC-ωPBE-D3. Double-hybrid functionals are the most accurate and robust methods, and in particular PWPB95-D3 and B2-PLYP-D3(BJ) can be recommended. The best DFT-D3 and DFT-D3(BJ) approaches are competitive to specially adapted perturbation methods and clearly outperform standard MP2. Comparisons between S66, S22 and parts of the GMTKN30 database show that the S66 set provides statistically well-behaved data and can serve as a valuable tool for, for example, fitting purposes or cross-validation of other benchmark databases.