Comprehensive Benchmark of Association (Free) Energies of Realistic Host–Guest Complexes

The S12L test set for supramolecular Gibbs free energies of association Δ<i>G</i>_<i>a</i> (Grimme, S. Chem. Eur. J. 2012, 18, 9955−9964) is extended to 30 complexes (S30L), featuring more diverse interaction motifs, anions, and higher charges (−1 up to +4) as well as larger systems with up to 200 atoms. Various typical noncovalent interactions like hydrogen and halogen bonding, π–π stacking, nonpolar dispersion, and CH−π and cation–dipolar interactions are represented by “real” complexes. The experimental Gibbs free energies of association (Δ<i>G</i>_<i>a</i>^<i>exp</i>) cover a wide range from −0.7 to −24.7 kcal mol^–1. In order to obtain a theoretical best estimate for Δ<i>G</i>_<i>a</i>, we test various dispersion corrected density functionals in combination with quadruple-ζ basis sets for calculating the association energies in the gas phase. Further, modern semiempirical methods are employed to obtain the thermostatistical corrections from energy to Gibbs free energy, and the COSMO-RS model with several parametrizations as well as the SMD model are used to include solvation contributions. We investigate the effect of including counterions for the charged systems (S30L-CI), which is found to overall improve the results. Our best method combination consists of PW6B95-D3 (for neutral and charged systems) or ωB97X-D3 (for systems with counterions) energies, HF-3c thermostatistical corrections, and Gibbs free energies of solvation obtained with the COSMO-RS 2012 parameters for nonpolar solvents and 2013-fine for water. This combination gives a mean absolute deviation for Δ<i>G</i>_<i>a</i> of only 2.4 kcal mol^–1 (S30L) and 2.1 kcal mol^–1 (S30L-CI), with a mean deviation of almost zero compared to experiment. Regarding the relative Gibbs free energies of association for the 13 pairs of complexes which share the same host, the correct trend in binding affinities could be reproduced except for two cases. The MAD compared to experiment amounts to 1.2 kcal mol^–1, and the MD is almost zero. The best-estimate theoretical corrections are used to back-correct the experimental Δ<i>G</i>_<i>a</i> values in order to get an empirical estimate for the “experimental”, zero-point vibrational energy exclusive, gas phase binding energies. These are then utilized to benchmark the performance of various “low-cost” quantum chemical methods for noncovalent interactions in large systems. The performance of other common DFT methods as well as the use of semiempirical methods for structure optimizations is discussed

DFT-D3 Study of Some Molecular Crystals

We investigate the performance of the dispersion correction D3 with and without an explicit three-body dispersion term for the energetic and structural properties of rare gas and molecular crystals. Therefore, the two- and three-body gradient of the dispersion energy is implemented in the periodic plane-wave program VASP. It is combined with different density functionals at the level of the general gradient approximation (GGA) and hybrid functionals. Cohesive energies and lattice parameters for the rare gas crystals Ar, Kr, and Xe and a set of 23 molecular crystals are calculated and compared to experimental reference values. In general, all tested methods yield very good results. For the molecular crystals the mean absolute deviation of lattice energies from reference data (about 1–2 kcal/mol) is close to or below their uncertainties. The influence of the three-body Axilrod–Teller–Muto dispersion term on energy and structure is found to be rather small. While on a GGA level cohesive energies become slightly worse, for hybrid functionals the three-body term improves the results

Performance of Non-Local and Atom-Pairwise Dispersion Corrections to DFT for Structural Parameters of Molecules with Noncovalent Interactions

The nonlocal, electron density dependent dispersion correction of Vydrov and Van Voorhis (Vydrov, O. A.; Van Voorhis, T. <i>J. Chem. Phys.</i> <b>2010</b>, <i>133</i>, 244103), termed VV10 or DFT-NL, has been implemented for structural optimizations of molecules. It is tested in combination with the four (hybrid)­GGA density functionals TPSS, TPSS0, B3LYP, and revPBE38 for <i>inter</i>- and <i>intra</i>molecular noncovalent interactions (NCI) and compared to results from atom-pairwise dispersion corrected DFT-D3. The methods are applied to a wide range of different problems, namely the S22 and S66 test sets, large transition metal complexes, water hexamer clusters, hexahelicene, and four other difficult cases of intramolecular NCI. Critical interatomic distances are computed remarkably accurately by both dispersion corrections compared to theoretical or experimental reference data and inter- and intramolecular interactions are treated on equal footing. The methods can be recommended as reliable and robust tools for geometry optimizations of large systems in which long-range dispersion forces are crucial

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

Comprehensive Benchmark of Association (Free) Energies of Realistic Host–Guest Complexes

The S12L test set for supramolecular Gibbs free energies of association Δ<i>G</i>_<i>a</i> (Grimme, S. Chem. Eur. J. 2012, 18, 9955−9964) is extended to 30 complexes (S30L), featuring more diverse interaction motifs, anions, and higher charges (−1 up to +4) as well as larger systems with up to 200 atoms. Various typical noncovalent interactions like hydrogen and halogen bonding, π–π stacking, nonpolar dispersion, and CH−π and cation–dipolar interactions are represented by “real” complexes. The experimental Gibbs free energies of association (Δ<i>G</i>_<i>a</i>^<i>exp</i>) cover a wide range from −0.7 to −24.7 kcal mol^–1. In order to obtain a theoretical best estimate for Δ<i>G</i>_<i>a</i>, we test various dispersion corrected density functionals in combination with quadruple-ζ basis sets for calculating the association energies in the gas phase. Further, modern semiempirical methods are employed to obtain the thermostatistical corrections from energy to Gibbs free energy, and the COSMO-RS model with several parametrizations as well as the SMD model are used to include solvation contributions. We investigate the effect of including counterions for the charged systems (S30L-CI), which is found to overall improve the results. Our best method combination consists of PW6B95-D3 (for neutral and charged systems) or ωB97X-D3 (for systems with counterions) energies, HF-3c thermostatistical corrections, and Gibbs free energies of solvation obtained with the COSMO-RS 2012 parameters for nonpolar solvents and 2013-fine for water. This combination gives a mean absolute deviation for Δ<i>G</i>_<i>a</i> of only 2.4 kcal mol^–1 (S30L) and 2.1 kcal mol^–1 (S30L-CI), with a mean deviation of almost zero compared to experiment. Regarding the relative Gibbs free energies of association for the 13 pairs of complexes which share the same host, the correct trend in binding affinities could be reproduced except for two cases. The MAD compared to experiment amounts to 1.2 kcal mol^–1, and the MD is almost zero. The best-estimate theoretical corrections are used to back-correct the experimental Δ<i>G</i>_<i>a</i> values in order to get an empirical estimate for the “experimental”, zero-point vibrational energy exclusive, gas phase binding energies. These are then utilized to benchmark the performance of various “low-cost” quantum chemical methods for noncovalent interactions in large systems. The performance of other common DFT methods as well as the use of semiempirical methods for structure optimizations is discussed

Elucidation of Electron Ionization Induced Fragmentations of Adenine by Semiempirical and Density Functional Molecular Dynamics

The gas phase fragmentation pathways of the nucleobase adenine upon 70 eV electron ionization are investigated by means of a combined stochastic and first-principles based molecular dynamics approach. We employ no preconceived fragmentation channels in our calculations, which simulate standard electron ionization mass spectrometry (EI-MS) conditions. The reactions observed compare well to a wealth of experimental and theoretical data available for this important nucleic acid building block. All significant peaks in the experimental mass spectrum of adenine are reproduced. Additionally, the fragment ion connectivities obtained from our simulations at least partially concur with results from previous experimental studies on selectively isotope labeled adenines. Moreover, we are able to assign noncyclic structures that are entropically favored and have not been proposed in nondynamic quantum chemical studies before to the decomposition products, which result automatically from our molecular dynamics procedure. From simulations under various conditions it is evident that most of the fragmentation reactions even at low internal excess energy (<10 eV) occur very fast within a few picoseconds

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

Why the Standard B3LYP/6-31G* Model Chemistry Should Not Be Used in DFT Calculations of Molecular Thermochemistry: Understanding and Correcting the Problem

We analyze the error compensations that are responsible for the relatively good performance of the popular B3LYP/6-31G* model chemistry for molecular thermochemistry. We present the B3LYP-gCP-D3/6-31G* scheme, which corrects for missing London dispersion and basis set superposition error (BSSE) in a physically sound manner. Benchmark results for the general main group thermochemistry, kinetics, and noncovalent interactions set (GMTKN30) are presented. A detailed look is cast on organic reactions of several arenes with C₆₀, Diels–Alder reactions, and barriers to [4 + 3] cycloadditions. We demonstrate the practical advantages of the new B3LYP-gCP-D3/6-31G* scheme and show its higher robustness over standard B3LYP/6-31G*. B3LYP-gCP-D3/6-31G* is meant to fully substitute standard B3LYP/6-31G* calculations in the same black-box sense at essentially no increase in computational cost. The energy corrections are made available by a Web service (http://www.thch.uni-bonn.de/tc/gcpd3) and by freely available software

Fast and Reasonable Geometry Optimization of Lanthanoid Complexes with an Extended Tight Binding Quantum Chemical Method

The recently developed tight binding electronic structure approach GFN-xTB is tested in a comprehensive and diverse lanthanoid geometry optimization benchmark containing 80 lanthanoid complexes. The results are evaluated with reference to high-quality X-ray molecular structures obtained from the Cambridge Structural Database and theoretical DFT-D3­(BJ) optimized structures for a few Pm (<i>Z</i> = 61) containing systems. The average structural heavy-atom root-mean-square deviation of GFN-xTB (0.65 Å) is smaller compared to its competitors, the Sparkle/PM6 (0.86 Å) and HF-3c (0.68 Å) quantum chemical methods. It is shown that GFN-xTB yields chemically reasonable structures, less outliers, and performs well in terms of overall computational speed compared to other low-cost methods. The good reproduction of large lanthanoid complex structures corroborates the wide applicability of the GFN-xTB approach and its value as an efficient low-cost quantum chemical method. Its main purpose is the search for energetically low-lying complex conformations in the elucidation of reaction mechanisms

Either Accurate Singlet–Triplet Gaps or Excited-State Structures: Testing and Understanding the Performance of TD-DFT for TADF Emitters

The energy gap between the lowest singlet and triplet excited states (ΔEST) is a key property of thermally activated delayed fluorescence (TADF) emitters, where these states are dominated by charge-transfer (CT) character. Despite its well-known shortcomings concerning CT states, time-dependent density functional theory (TD-DFT) is widely used to predict this gap and study TADF. Moreover, polar CT states exhibit a strong interaction with their molecular environment, which further complicates their computational description. Addressing these two major challenges, this work studies the performance of Tamm–Dancoff-approximated TD-DFT (TDA-DFT) on the recent STGABS27 benchmark set,1 exploring different strategies to include orbital and structural relaxation, as well as dielectric embedding. The results show that the best-performing strategy is to calculate ΔEST at the ground-state structure using functionals with a surprisingly small amount of Fock exchange of ≈10% and without a (complete) solvent model. However, as this approach heavily relies on error cancellation to mimic dielectric relaxation, it is not robust and exhibits large systematic deviations in excited state energies, state characters, and structures. More rigorous approaches, including state-specific solvation, do not share these systematic deviations, but their predicted ΔEST values exhibit larger statistical errors. We thus conclude that for the description of CT states in dielectric environments, none of the tested TDA-DFT methods is competitive with the recently presented ROKS/PCM approach regarding robustness, accuracy, and computational efficiency