Importance of London dispersion effects for the packing of molecular crystals: a case study for intramolecular stacking in a bis-thiophene derivative

Experimental and theoretical analysis of lp⋯π intermolecular interactions in derivatives of 1,2,4-triazoles

The calculations performed on the evaluation of the electrostatic potential provide deeper insights into the nature of lp⋯π interactions.

Dispersion-corrected density functional theory for aromatic interactions in complex systems

Aromatic interactions play a key role in many chemical and biological systems. However, even if very simple models are chosen, the systems of interest are often too large to be handled with standard wave function theory (WFT). Although density functional theory (DFT) can easily treat systems of more than 200 atoms, standard semilocal (hybrid) density functional approximations fail to describe the London dispersion energy, a factor that is essential for accurate predictions of inter- and intramolecular noncovalent interactions. Therefore dispersion-corrected DFT provides a unique tool for the investigation and analysis of a wide range of complex aromatic systems. In this Account, we start with an analysis of the noncovalent interactions in simple model dimers of hexafluorobenzene (HFB) and benzene, with a focus on electrostatic and dispersion interactions. The minima for the parallel-displaced dimers of HFB/HFB and HFB/benzene can only be explained when taking into account all contributions to the interaction energy and not by electrostatics alone. By comparison of saturated and aromatic model complexes, we show that increased dispersion coefficients for sp(2)-hybridized carbon atoms play a major role in aromatic stacking. Modern dispersion-corrected DFT yields accurate results (about 5-10% error for the dimerization energy) for the relatively large porphyrin and coronene dimers, systems for which WFT can provide accurate reference data only with huge computational effort. In this example, it is also demonstrated that new nonlocal, density-dependent dispersion corrections and atom pairwise schemes mutually agree with each other. The dispersion energy is also important for the complex inter- and intramolecular interactions that arise in the molecular crystals of aromatic molecules. In studies of hexahelicene, dispersion-corrected DFT yields "the right answer for the right reason". By comparison, standard DFT calculations reproduce intramolecular distances quite accurately in single-molecule calculations while inter- and intramolecular distances become too large when dispersion-uncorrected solid-state calculations are carried out. Dispersion-corrected DFT can fix this problem, and these results are in excellent agreement with experimental structure and energetic (sublimation) data. Uncorrected treatments do not even yield a bound crystal state. Finally, we present calculations for the formation of a cationic, quadruply charged dimer of a porphyrin derivative, a case where dispersion is required in order to overcome strong electrostatic repulsion. A combination of dispersion-corrected DFT with an adequate continuum solvation model can accurately reproduce experimental free association enthalpies in solution. As in the previous examples, consideration of the electrostatic interactions alone does not provide a qualitatively or quantitatively correct picture of the interactions of this complex.

XH/π (X = C, Si) Interactions in Graphene and Silicene: Weak in Strength, Strong in Tuning Band Structures

The lack of a band gap has greatly hindered the applications of graphene in electronic devices. By means of dispersion-corrected density functional theory computations, we demonstrated that considerable CH/π interactions exist between graphene and its fully (graphane) or patterned partially (C4H) hydrogenated derivatives. Due to the equivalence breaking of two sublattices of graphene, a 90 meV band gap is opened in the graphene/C4H bilayer. The band gap can be further increased to 270 meV by sandwiching graphene between two C4H layers. By taking advantage of the similar SiH/π interactions, a 120 meV band gap also can be opened for silicene. Interestingly, the high carrier mobility of graphene/silicene can be well-preserved. Our theoretical results suggest a rather practical solution for gap opening of graphene and silicene, which would allow them to serve as field effect transistors and other nanodevices.

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.

A DFT-D study of structural and energetic properties of TiO2 modifications

The structures and relative energies of the three naturally occurring modifications of titanium dioxide (rutile, brookite and anatase) were investigated. For an accurate description, atom-pairwise dispersion-corrected density functional theory (DFT-D) was applied. The DFT-D3 scheme was extended non-empirically to improve the description of Ti atoms in bulk systems. New dispersion coefficients were derived from TDDFT calculations for electrostatically embedded TiO(2) clusters. The dispersion coefficient [Formula: see text] is reduced by a factor of 18 compared to the free atom. The three TiO(2) modifications were optimized in periodic plane-wave calculations with dispersion-corrected GGA (PBE, revPBE) and hybrid density functionals (PBE0, revPBE0). The calculated lattice parameters are in good agreement with experimental data, in particular the dispersion-corrected PBE0 and revPBE0 hybrid functionals. Although the observed relative stabilities could not be reproduced in all cases, dispersion corrections improve the results. For an accurate description of bulk metal oxides, London dispersion is a prominent force that should not be neglected when energies and structures are computed with DFT. Additionally, the influence of dispersion interactions on the relaxation of the TiO(2)(110) surface is investigated.

Hydrogen bond dynamics in crystalline β-9-anthracene carboxylic acid--a combined crystallographic and spectroscopic study

We compare results from single crystal X-ray diffraction and FTIR spectroscopy to elucidate the nature of hydrogen bonding in β-9-anthracene carboxylic acid (β-9AC, C(15)H(10)O(2)). The crystallographic studies indicate a disorder for the protons in the cyclic hydrogen bond. This disorder allows the determination of the energy difference between two proton sites along the hydrogen bond. The temperature dependent Fourier transform infrared spectroscopy (FTIR) underpins the crystallographic results. The combination of both methods allows the estimation of a one-dimensional potential curve describing the OH-stretching motion. The dynamical properties of the proton transfer along the hydrogen bond are extracted from this potential. The work presented here has profound implication on future studies of photochemical dynamics of crystalline β-9AC, which can deliver a deeper understanding of the mechanism of photochemical driven molecular machines and the optical and electronic properties of molecular organic semiconductors.

Tuning Metal-Organic Frameworks with Open-Metal Sites and Its Origin for Enhancing CO2 Affinity by Metal Substitution

Reducing anthropogenic carbon emission is a problem that requires immediate attention. Metal-organic frameworks (MOFs) have emerged as a promising new materials platform for carbon capture, of which Mg-MOF-74 offers chemospecific affinity toward CO2 because of the open Mg sites. Here we tune the binding affinity of CO2 for M-MOF-74 by metal substitution (M = Mg, Ca, and the first transition metal elements) and show that Ti- and V-MOF-74 can have an enhanced affinity compared to Mg-MOF-74 by 6-9 kJ/mol. Electronic structure calculations suggest that the origin of the major affinity trend is the local electric field effect of the open metal site that stabilizes CO2, but forward donation from the lone-pair electrons of CO2 to the empty d-levels of transition metals as in a weak coordination bond makes Ti and V have an even higher binding strength than Mg, Ca, and Sc.

Proteogenic amino acids: chiral and racemic crystal packings and stabilities

Crystal structures of chiral and racemic proteogenic amino acids are compared, over a database of 40 crystal structures and 20 chiral-racemic pairs. Wallach's rule does not apply. Solubility data show that the racemates tend to be slightly more stable than their chiral counterparts. Lattice energies are calculated by semiempirical PIXEL methods and by several ab initio methods, which also yield molecular energies. Results, especially molecular energies, are sensitive to small structural differences and therefore depend on the crystal structure accuracy. Surface effects in crystals of zwitterionic molecules require special attention. Energy differences between chiral and racemic crystals are typically around 10 kJ mol(-1), roughly the limit of our calculations. These suggest, however, that crystal stability tends to increase with decreasing crystal density, a result possibly related to the strong directionality of hydrogen bonds. The analysis of interaction energies between molecules related by specific symmetry operations shows that stabilization in homochiral crystal structures comes mainly from formation of screw-symmetric ribbons, whereas racemic crystal structures preferentially exhibit strongly stabilizing centrosymmetric dimers.