Jan Gerit Brandenburg

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).

Report on the sixth blind test of organic crystal structure prediction methods

The results of the sixth blind test of organic crystal structure prediction methods are presented and discussed, highlighting progress for salts, hydrates and bulky flexible molecules, as well as on-going challenges.

Accurate Modeling of Organic Molecular Crystals by Dispersion-Corrected Density Functional Tight Binding (DFTB)

The ambitious goal of organic crystal structure prediction challenges theoretical methods regarding their accuracy and efficiency. Dispersion-corrected density functional theory (DFT-D) in principle is applicable, but the computational demands, for example, to compute a huge number of polymorphs, are too high. Here, we demonstrate that this task can be carried out by a dispersion-corrected density functional tight binding (DFTB) method. The semiempirical Hamiltonian with the D3 correction can accurately and efficiently model both solid- and gas-phase inter- and intramolecular interactions at a speed up of 2 orders of magnitude compared to DFT-D. The mean absolute deviations for interaction (lattice) energies for various databases are typically 2-3 kcal/mol (10-20%), that is, only about two times larger than those for DFT-D. For zero-point phonon energies, small deviations of <0.5 kcal/mol compared to DFT-D are obtained.

Geometrical Correction for the Inter- and Intramolecular Basis Set Superposition Error in Periodic Density Functional Theory Calculations

We extend the previously developed geometrical correction for the inter- and intramolecular basis set superposition error (gCP) to periodic density functional theory (DFT) calculations. We report gCP results compared to those from the standard Boys-Bernardi counterpoise correction scheme and large basis set calculations. The applicability of the method to molecular crystals as the main target is tested for the benchmark set X23. It consists of 23 noncovalently bound crystals as introduced by Johnson et al. (J. Chem. Phys. 2012, 137, 054103) and refined by Tkatchenko et al. (J. Chem. Phys. 2013, 139, 024705). In order to accurately describe long-range electron correlation effects, we use the standard atom-pairwise dispersion correction scheme DFT-D3. We show that a combination of DFT energies with small atom-centered basis sets, the D3 dispersion correction, and the gCP correction can accurately describe van der Waals and hydrogen-bonded crystals. Mean absolute deviations of the X23 sublimation energies can be reduced by more than 70% and 80% for the standard functionals PBE and B3LYP, respectively, to small residual mean absolute deviations of about 2 kcal/mol (corresponding to 13% of the average sublimation energy). As a further test, we compute the interlayer interaction of graphite for varying distances and obtain a good equilibrium distance and interaction energy of 6.75 Å and -43.0 meV/atom at the PBE-D3-gCP/SVP level. We fit the gCP scheme for a recently developed pob-TZVP solid-state basis set and obtain reasonable results for the X23 benchmark set and the potential energy curve for water adsorption on a nickel (110) surface.

Dispersion Corrected Hartree–Fock and Density Functional Theory for Organic Crystal Structure Prediction

We present and evaluate dispersion corrected Hartree-Fock (HF) and Density Functional Theory (DFT) based quantum chemical methods for organic crystal structure prediction. The necessity of correcting for missing long-range electron correlation, also known as van der Waals (vdW) interaction, is pointed out and some methodological issues such as inclusion of three-body dispersion terms are discussed. One of the most efficient and widely used methods is the semi-classical dispersion correction D3. Its applicability for the calculation of sublimation energies is investigated for the benchmark set X23 consisting of 23 small organic crystals. For PBE-D3 the mean absolute deviation (MAD) is below the estimated experimental uncertainty of 1.3 kcal/mol. For two larger π-systems, the equilibrium crystal geometry is investigated and very good agreement with experimental data is found. Since these calculations are carried out with huge plane-wave basis sets they are rather time consuming and routinely applicable only to systems with less than about 200 atoms in the unit cell. Aiming at crystal structure prediction, which involves screening of many structures, a pre-sorting with faster methods is mandatory. Small, atom-centered basis sets can speed up the computation significantly but they suffer greatly from basis set errors. We present the recently developed geometrical counterpoise correction gCP. It is a fast semi-empirical method which corrects for most of the inter- and intramolecular basis set superposition error. For HF calculations with nearly minimal basis sets, we additionally correct for short-range basis incompleteness. We combine all three terms in the HF-3c denoted scheme which performs very well for the X23 sublimation energies with an MAD of only 1.5 kcal/mol, which is close to the huge basis set DFT-D3 result.

Unidirectional Molecular Stacking of Tribenzotriquinacenes in the Solid State: A Combined X‐ray and Theoretical Study

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 C3v 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.

Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs

Water in different phases under various external conditions is very important in bio-chemical systems and for material science at surfaces. Density functional theory methods and approximations thereof have to be tested system specifically to benchmark their accuracy regarding computed structures and interaction energies. In this study, we present and test a set of ten ice polymorphs in comparison to experimental data with mass densities ranging from 0.9 to 1.5 g/cm(3) and including explicit corrections for zero-point vibrational and thermal effects. London dispersion inclusive density functionals at the generalized gradient approximation (GGA), meta-GGA, and hybrid level as well as alternative low-cost molecular orbital methods are considered. The widely used functional of Perdew, Burke and Ernzerhof (PBE) systematically overbinds and overall provides inconsistent results. All other tested methods yield reasonable to very good accuracy. BLYP-D3(atm) gives excellent results with mean absolute errors for the lattice energy below 1 kcal/mol (7% relative deviation). The corresponding optimized structures are very accurate with mean absolute relative deviations (MARDs) from the reference unit cell volume below 1%. The impact of Axilrod-Teller-Muto (atm) type three-body dispersion and of non-local Fock exchange is small but on average their inclusion improves the results. While the density functional tight-binding model DFTB3-D3 performs well for low density phases, it does not yield good high density structures. As low-cost alternative for structure related problems, we recommend the recently introduced minimal basis Hartree-Fock method HF-3c with a MARD of about 3%.

Spin Crossover in Fe(II) and Co(II) Complexes with the Same Click-Derived Tripodal Ligand

The complexes [Fe(tbta)2](BF4)2·2EtOH (1), [Fe(tbta)2](BF4)2·2CH3CN (2), [Fe(tbta)2](BF4)2·2CHCl3 (3), and [Fe(tbta)2](BF4)2 (4) were synthesized from the respective metal salts and the click-derived tripodal ligand tris[(1-benzyl-1H-1,2,3-triazol-4-yl)methyl]amine (tbta). Structural characterization of these complexes (at 100 or 133 K) revealed Fe-N bond lengths for the solvent containing compounds 1-3 that are typical of a high spin (HS) Fe(II) complex. In contrast, the solvent-free compound 4 show Fe-N bond lengths that are characteristic of a low spin (LS) Fe(II) state. The Fe center in all complexes is bound to two triazole and one amine N atom from each tbta ligand, with the third triazole arm remaining uncoordinated. The benzyl substituents of the uncoordinated triazole arms and the triazole rings engage in strong intermolecular and intramolecular noncovalent interactions. These interactions are missing in the solvent containing molecules 1, 2, and 3, where the solvent molecules occupy positions that hinder these noncovalent interactions. The solvent-free complex (4) displays spin crossover (SCO) with a spin transition temperature T1/2 near room temperature, as revealed by superconducting quantum interference device (SQUID) magnetometric and Mössbauer spectroscopic measurements. The complexes 1, 2, and 3 remain HS throughout the investigated temperature range. Different torsion angles at the metal centers, which are influenced by the noncovalent interactions, are likely responsible for the differences in the magnetic behavior of these complexes. The corresponding solvent-free Co(II) complex (6) is also LS at lower temperatures and displays SCO with a temperature T1/2 near room temperature. Theoretical calculations at molecular and periodic DFT-D3 levels for 1-4 qualitatively reproduce the experimental findings, and corroborate the importance of intermolecular and intramolecular noncovalent interactions for the magnetic properties of these complexes. The present work thus represents rare examples of SCO complexes where the use of identical ligand sets produces SCO in Fe(II) as well as Co(II) complexes.

Small Atomic Orbital Basis Set First-Principles Quantum Chemical Methods for Large Molecular and Periodic Systems: A Critical Analysis of Error Sources

Abstract 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.

Assessment of Different Quantum Mechanical Methods for the Prediction of Structure and Cohesive Energy of Molecular Crystals

A comparative assessment of the accuracy of different quantum mechanical methods for evaluating the structure and the cohesive energy of molecular crystals is presented. In particular, we evaluate the performance of the semiempirical HF-3c method in comparison with the B3LYP-D* and the Local MP2 (LMP2) methods by means of a fully periodic approach. Three benchmark sets have been investigated: X23, G60, and the new K7; for a total of 82 molecular crystals. The original HF-3c method performs well but shows a tendency at overbinding molecular crystals, in particular for weakly bounded systems. For the X23 set, the mean absolute error for the cohesive energies computed with the HF-3c method is comparable to the LMP2 one. A refinement of the HF-3c has been attempted by tuning the dispersion term in the HF-3c energy. While the performance on cohesive energy prediction slightly worsens, optimized unit cell volumes are in excellent agreement with experiment. Overall, the B3LYP-D* method combined with a TZP basis set gives the best results. For cost-effective calculations on molecular crystals, we propose to compute cohesive energies at the B3LYP-D*/TZP level of theory on the dispersion-scaled HF-3c optimized geometries (i.e., B3LYP-D*/TZP//HF-3c(0.27) also dubbed as SP-B3LYP-D*). Besides, for further benchmarking on molecular crystals, we propose to combine the three test sets in a new one denoted as MC82.