Christoph Bannwarth

Dispersion-Corrected Mean-Field Electronic Structure Methods

Mean-field electronic structure methods like Hartree-Fock, semilocal density functional approximations, or semiempirical molecular orbital (MO) theories do not account for long-range electron correlation (London dispersion interaction). Inclusion of these effects is mandatory for realistic calculations on large or condensed chemical systems and for various intramolecular phenomena (thermochemistry). This Review describes the recent developments (including some historical aspects) of dispersion corrections with an emphasis on methods that can be employed routinely with reasonable accuracy in large-scale applications. The most prominent correction schemes are classified into three groups: (i) nonlocal, density-based functionals, (ii) semiclassical C6-based, and (iii) one-electron effective potentials. The properties as well as pros and cons of these methods are critically discussed, and typical examples and benchmarks on molecular complexes and crystals are provided. Although there are some areas for further improvement (robustness, many-body and short-range effects), the situation regarding the overall accuracy is clear. Various approaches yield long-range dispersion energies with a typical relative error of 5%. For many chemical problems, this accuracy is higher compared to that of the underlying mean-field method (i.e., a typical semilocal (hybrid) functional like B3LYP).

Combinations of ethers and B(C6F5)3 function as hydrogenation catalysts.

It works ether way: Labile adducts of dialkyl ethers with the electrophilic borane B(C6F5)3 are shown to scramble HD to H2 and D2 and catalyze the hydrogenation of 1,1-diphenylethylene.

A Robust and Accurate Tight-Binding Quantum Chemical Method for Structures, Vibrational Frequencies, and Noncovalent Interactions of Large Molecular Systems Parametrized for All spd-Block Elements (Z = 1–86)

We propose a novel, special purpose semiempirical tight binding (TB) method for the calculation of structures, vibrational frequencies, and noncovalent interactions of large molecular systems with 1000 or more atoms. The functional form of the method is related to the self-consistent density functional TB scheme and mostly avoids element-pair-specific parameters. The parametrization covers all spd-block elements and the lanthanides up to Z = 86 using reference data at the hybrid density functional theory level. Key features of the Hamiltonian are the use of partially polarized Gaussian-type orbitals, a double-ζ orbital basis for hydrogen, atomic-shell charges, diagonal third-order charge fluctuations, coordination number-dependent energy levels, a noncovalent halogen-bond potential, and the well-established D3 dispersion correction. The accuracy of the method, called Geometry, Frequency, Noncovalent, eXtended TB (GFN-xTB), is extensively benchmarked for various systems in comparison with existing semiempirical approaches, and the method is applied to a few representative structural problems in chemistry.

The Thermochemistry of London Dispersion-Driven Transition Metal Reactions: Getting the ‘Right Answer for the Right Reason’

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.

Enantiotopos‐Selective CH Oxygenation Catalyzed by a Supramolecular Ruthenium Complex

Spirocyclic oxindoles undergo an enantioselective oxygenation reaction (nine examples; e.r. up to 97:3) upon catalysis by a chiral ruthenium porphyrin complex (1 mol %). The catalyst exhibits a lactam ring, which is responsible for substrate association through hydrogen bonds, and an active ruthenium center, which is in a defined spatial relationship to the oxygenation substrate. DFT calculations illustrate the perfect alignment of the active site with the reactive C-H bond and suggest--in line with the kinetic isotope effect--an oxygen rebound mechanism for the reaction.

Ultra-fast computation of electronic spectra for large systems by tight-binding based simplified Tamm-Dancoff approximation (sTDA-xTB)

The computational bottleneck of the extremely fast simplified Tamm-Dancoff approximated (sTDA) time-dependent density functional theory procedure [S. Grimme, J. Chem. Phys. 138, 244104 (2013)] for the computation of electronic spectra for large systems is the determination of the ground state Kohn-Sham orbitals and eigenvalues. This limits such treatments to single structures with a few hundred atoms and hence, e.g., sampling along molecular dynamics trajectories for flexible systems or the calculation of chromophore aggregates is often not possible. The aim of this work is to solve this problem by a specifically designed semi-empirical tight binding (TB) procedure similar to the well established self-consistent-charge density functional TB scheme. The new special purpose method provides orbitals and orbital energies of hybrid density functional character for a subsequent and basically unmodified sTDA procedure. Compared to many previous semi-empirical excited state methods, an advantage of the ansatz is that a general eigenvalue problem in a non-orthogonal, extended atomic orbital basis is solved and therefore correct occupied/virtual orbital energy splittings as well as Rydberg levels are obtained. A key idea for the success of the new model is that the determination of atomic charges (describing an effective electron-electron interaction) and the one-particle spectrum is decoupled and treated by two differently parametrized Hamiltonians/basis sets. The three-diagonalization-step composite procedure can routinely compute broad range electronic spectra (0-8 eV) within minutes of computation time for systems composed of 500-1000 atoms with an accuracy typical of standard time-dependent density functional theory (0.3-0.5 eV average error). An easily extendable parametrization based on coupled-cluster and density functional computed reference data for the elements H-Zn including transition metals is described. The accuracy of the method termed sTDA-xTB is first benchmarked for vertical excitation energies of open- and closed-shell systems in comparison to other semi-empirical methods and applied to exemplary problems in electronic spectroscopy. As side products of the development, a robust and efficient valence electron TB method for the accurate determination of atomic charges as well as a more accurate calculation scheme of dipole rotatory strengths within the Tamm-Dancoff approximation is proposed.

Extension of the D3 dispersion coefficient model

A new model, termed D4, for the efficient computation of molecular dipole-dipole dispersion coefficients is presented. As in the related, well established D3 scheme, these are obtained as a sum of atom-in-molecule dispersion coefficients over atom pairs. Both models make use of dynamic polarizabilities obtained from first-principles time-dependent density functional theory calculations for atoms in different chemical environments employing fractional atomic coordination numbers for interpolation. Different from the D3 model, the coefficients are obtained on-the-fly by numerical Casimir-Polder integration of the dynamic, atomic polarizabilities α(iω). Most importantly, electronic density information is now incorporated via atomic partial charges computed at a semi-empirical quantum mechanical tight-binding level, which is used to scale the polarizabilities. Extended statistical measures show that errors for dispersion coefficients with the proposed D4 method are significantly lower than with D3 and other, computationally more involved schemes. Alongside, accurate isotropic charge and hybridization dependent, atom-in-molecule static polarizabilities are obtained with an unprecedented efficiency. Damping function parameters are provided for three standard density functionals, i.e., TPSS, PBE0, and B3LYP, allowing evaluation of the new DFT-D4 model for common non-covalent interaction energy benchmark sets.

An Octanuclear Metallosupramolecular Cage Designed To Exhibit Spin-Crossover Behavior

By employing the subcomponent self-assembly approach utilizing 5,10,15,20-tetrakis(4-aminophenyl)porphyrin or its zinc(II) complex, 1H-4-imidazolecarbaldehyde, and either zinc(II) or iron(II) salts, we were able to prepare O-symmetric cages having a confined volume of ca. 1300 Å3 . The use of iron(II) salts yielded coordination cages in the high-spin state at room temperature, manifesting spin-crossover in solution at low temperatures, whereas corresponding zinc(II) salts led to the corresponding diamagnetic analogues. The new cages were characterized by synchrotron X-ray crystallography, high-resolution mass spectrometry, and NMR, Mössbauer, IR, and UV/Vis spectroscopy. The cage structures and UV/Vis spectra were independently confirmed by state-of-the-art DFT calculations. A remarkably high-spin-stabilizing effect through encapsulation of C70 was observed. The spin-transition temperature T1/2 is lowered by 20 K in the host-guest complex.

Fully Automated Quantum-Chemistry-Based Computation of Spin–Spin-Coupled Nuclear Magnetic Resonance Spectra

Abstract We present a composite procedure for the quantum‐chemical computation of spin–spin‐coupled 1H NMR spectra for general, flexible molecules in solution that is based on four main steps, namely conformer/rotamer ensemble (CRE) generation by the fast tight‐binding method GFN‐xTB and a newly developed search algorithm, computation of the relative free energies and NMR parameters, and solving the spin Hamiltonian. In this way the NMR‐specific nuclear permutation problem is solved, and the correct spin symmetries are obtained. Energies, shielding constants, and spin–spin couplings are computed at state‐of‐the‐art DFT levels with continuum solvation. A few (in)organic and transition‐metal complexes are presented, and very good, unprecedented agreement between the theoretical and experimental spectra was achieved. The approach is routinely applicable to systems with up to 100–150 atoms and may open new avenues for the detailed (conformational) structure elucidation of, for example, natural products or drug molecules.

Electronic Circular Dichroism of Highly Conjugated π-Systems: Breakdown of the Tamm–Dancoff/Configuration Interaction Singles Approximation

We show that the electronic circular dichroism (ECD) of delocalized π-systems represents a worst-case scenario for Tamm-Dancoff approximated (TDA) linear response methods. We mainly consider density functional theory (TDA-DFT) variants together with range-separated hybrids, but the conclusions also apply for other functionals as well as the configuration interaction singles (CIS) approaches. We study the effect of the TDA for the computation of ECD spectra in some prototypical extended π-systems. The C76 fullerene, a chiral carbon nanotube fragment, and [11]helicene serve as model systems for inherently chiral, π-chromophores. Solving the full linear response problem is inevitable in order to obtain accurate ECD spectra for these systems. For the C76 fullerene and the nanotube fragment, TDA and CIS approximated methods yield spectra in the origin-independent velocity gauge formalism of incorrect sign which would lead to the assignment of the opposite (wrong) absolute configuration. As a counterexample, we study the ECD of an α-helix polypeptide chain. Here, the lowest-energy transitions are dominated by localized excitations within the individual peptide units, and TDA methods perform satisfactorily. The results may have far-reaching implications for simple semiempirical methods which often employ TDA and CIS for huge molecules. Our recently presented simplified time-dependent DFT approach proves to be an excellent low-cost linear response method which together with range-separated density functionals like ωB97X-D3 produces ECD spectra in very good agreement with experiment.