Benchmark ab Initio Conformational Energies for the Proteinogenic Amino Acids through Explicitly Correlated Methods. Assessment of Density Functional Methods

Structure of Diferrocenyl Thioketone: From Molecule to Crystal

Ferrocenyl-functionalized thioketones have recently been recognized as useful building blocks for sulfur-containing compounds with potential applications in materials chemistry. This work is devoted to a single representative of such thioketones, namely diferrocenyl thioketone (Fc₂CS), whose structure has been determined here for the first time. Both X-ray crystallography and a wide variety of quantum-chemical methods were used to explore the structure of Fc₂CS. In addition to the X-ray structure determination, intermolecular interactions occurring in the crystal structure of Fc₂CS were examined in detail by quantum-chemical methods. These methods were also an invaluable tool in studying the molecular structure of Fc₂CS, from the gas phase to solutions and to its crystal. Intramolecular interactions governing the conformational behavior of an isolated Fc₂CS molecule were deduced from quantum-chemical analyses carried out in orbital space and real space. Our experimental and theoretical results indicate that the main structural features of an isolated Fc₂CS molecule in its lowest-energy geometry are retained both upon solvation and in the crystal. The tilt of ferrocenyl groups is only slightly affected by crystal packing forces that are dominated by dispersion. Nonetheless, a network of intermolecular interactions, such as H···H, C···H and S···H, was detected in the Fc₂CS crystal but each of them is fairly weak.

Computational prediction of chiroptical properties in structure elucidation of natural products

Covering: up to 2019This review covers the current status of the quantum mechanical prediction of chiroptical properties, such as electronic CD and optical rotation, as needed for stereochemical assignments in new natural products. The reliability of the prediction of chiroptical properties is steadily increasing, with a parallel decrease in the required computational resources. Now, quantum mechanical calculations for a medium-sized natural product can be reliably performed by natural product chemists on a mainstream PC. This review is aimed to guide natural product chemists through the numerous steps involved in such calculations. Through a concise, but comprehensive, discussion of the current computational practice, enriched by a few illustrative examples, this review provides readers with the theoretical background and practical knowledge needed to select the most appropriate parameters for performing the calculations, to anticipate possible problems, and to critically evaluate the reliability of their computational results. Common reasons for mistakes are also discussed; in particular, the importance of the correct evaluation of conformational ensembles of flexible molecules (an aspect often overlooked in current research) is stressed.

Minimally Empirical Double-Hybrid Functionals Trained against the GMTKN55 Database: revDSD-PBEP86-D4, revDOD-PBE-D4, and DOD-SCAN-D4

We present a family of minimally empirical double-hybrid DFT functionals parametrized against the very large and diverse GMTKN55 benchmark. The very recently proposed ωB97M(2) empirical double hybrid (with 16 adjustable parameters) has the lowest WTMAD2 (weighted mean absolute deviation over GMTKN55) ever reported at 2.19 kcal/mol. However, refits of the DSD-BLYP and DSD-PBEP86 spin-component-scaled, dispersion-corrected double hybrids can achieve WTMAD2 values as low as 2.33 with the very recent D4 dispersion correction (2.42 kcal/mol with the D3(BJ) dispersion term) using just a handful of adjustable parameters. If we use full DFT correlation in the initial orbital evaluation, the xrevDSD-PBEP86-D4 functional reaches WTMAD2 = 2.23 kcal/mol, statistically indistinguishable from ωB97M(2) but using just four nonarbitrary adjustable parameters (and three semiarbitrary ones). The changes from the original DSD parametrizations are primarily due to noncovalent interaction energies for large systems, which were undersampled in the original parametrization set. With the new parametrization, same-spin correlation can be eliminated at minimal cost in performance, which permits revDOD-PBEP86-D4 and revDOD-PBE-D4 functionals that scale as N⁴ or even N³ with the size of the system. Dependence of WTMAD2 for DSD functionals on the percentage of HF exchange is roughly quadratic; it is sufficiently weak that any reasonable value in the 64% to 72% range can be chosen semiarbitrarily. DSD-SCAN and DOD-SCAN double hybrids involving the SCAN nonempirical meta-GGA as the semilocal component have also been considered and offer a good alternative if one wishes to eliminate either the empirical dispersion correction or the same-spin correlation component. noDispSD-SCAN66 achieves WTMAD2 = 3.0 kcal/mol, compared to 2.7 kcal/mol for DOD-SCAN66-D4. However, the best performance without dispersion corrections (WTMAD2 = 2.8 kcal/mol) is reached by revωB97X-2, a slight reparametrization of the Chai–Head-Gordon range-separated double hybrid. Finally, in the context of double-hybrid functionals, the very recent D4 dispersion correction is clearly superior over D3(BJ).

GFN2-xTB-An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions

An extended semiempirical tight-binding model is presented, which is primarily designed for the fast calculation of structures and noncovalent interaction energies for molecular systems with roughly 1000 atoms. The essential novelty in this so-called GFN2-xTB method is the inclusion of anisotropic second order density fluctuation effects via short-range damped interactions of cumulative atomic multipole moments. Without noticeable increase in the computational demands, this results in a less empirical and overall more physically sound method, which does not require any classical halogen or hydrogen bonding corrections and which relies solely on global and element-specific parameters (available up to radon, Z = 86). Moreover, the atomic partial charge dependent D4 London dispersion model is incorporated self-consistently, which can be naturally obtained in a tight-binding picture from second order density fluctuations. Fully analytical and numerically precise gradients (nuclear forces) are implemented. The accuracy of the method is benchmarked for a wide variety of systems and compared with other semiempirical methods. Along with excellent performance for the "target" properties, we also find lower errors for "off-target" properties such as barrier heights and molecular dipole moments. High computational efficiency along with the improved physics compared to its precursor GFN-xTB makes this method well-suited to explore the conformational space of molecular systems. Significant improvements are furthermore observed for various benchmark sets, which are prototypical for biomolecular systems in aqueous solution.

PEPCONF, a diverse data set of peptide conformational energies

We present an extensive and diverse database of peptide conformational energies. Our database contains five different classes of model geometries: dipeptides, tripeptides, and disulfide-bridged, bioactive, and cyclic peptides. In total, the database consists of 3775 conformational energy data points and 4530 conformer geometries. All the reference energies have been calculated at the LC-ωPBE-XDM/aug-cc-pVTZ level of theory, which is shown to yield conformational energies with an accuracy in the order of tenths of a kcal/mol when compared to complete-basis-set coupled-cluster reference data. The peptide conformational data set (PEPCONF) is presented as a high-quality reference set for the development and benchmarking of molecular-mechanics and semi-empirical electronic structure methods, which are the most commonly used techniques in the modeling of medium to large proteins.

Aggregation of lactic acid in cold rare-gas matrices and the link to solution: a matrix isolation-vibrational circular dichroism study

Crucial insight into lactic acid self-aggregation in solution is obtained by following its unique VCD spectral features in cold matrices.

Statistically representative databases for density functional theory via data science

Cluster analysis applied to quantum chemistry: a new broad database of chemical properties with a reasonable computational cost.

Thermochemistry of Guanine Tautomers Re-Examined by Means of High-Level CCSD(T) Composite Ab Initio Methods

We obtained accurate gas-phase tautomerization energies for a set of 14 guanine tautomers by means of high-level thermochemical procedures approximating the CCSD(T) energy at the complete basis set (CBS) limit. For the five low-lying tautomers, we use the computationally demanding W1-F12 composite method for obtaining the tautomerization energies. The relative W1-F12 tautomerization enthalpies at 298K are: 0.00 (1), 2.37 (2), 2.63 (3), 4.03 (3′), and 14.31 (4) kJmol−1. Thus, as many as four tautomers are found within a small energy window of less than 1.0kcalmol−1 (1kcalmol−1=4.184kJmol−1). We use these highly accurate W1-F12 tautomerization energies to evaluate the performance of a wide range of lower-level composite ab initio procedures. The Gn composite procedures (G4, G4(MP2), G4(MP2)-6X, G3, G3B3, G3(MP2), and G3(MP2)B3) predict that the enol tautomer (3) is more stable than the keto tautomer (2) by amounts ranging from 0.36 (G4) to 1.28 (G3(MP2)) kJmol−1. We also find that an approximated CCSD(T)/CBS energy calculated as HF/jul-cc-pV{D,T}Z+CCSD/jul-cc-pVTZ+(T)/jul-cc-pVDZ results in a root-mean-square deviation (RMSD) of merely 0.11kJmol−1 relative to the W1-F12 reference values. We use this approximated CCSD(T)/CBS method to obtain the tautomerization energies of 14 guanine tautomers. The relative tautomerization enthalpies at 298K are: 0.00 (1), 2.20 (2), 2.51 (3), 4.06 (3′), 14.30 (4), 25.65 (5), 43.78 (4′), 53.50 (6′), 61.58 (6), 77.37 (7), 82.52 (8′), 86.02 (9), 100.70 (10), and 121.01 (8) kJmol−1. Using these tautomerization enthalpies, we evaluate the performance of standard and composite methods for the entire set of 14 guanine tautomers. The best-performing procedures emerge as (RMSDs are given in parentheses): G4(MP2)-6X (0.51), CCSD(T)+ΔMP2/CBS (0.52), and G4(MP2) (0.64kJmol−1). The worst performers are CCSD(T)/AVDZ (1.05), CBS-QB3 (1.24), and CBS-APNO (1.38kJmol−1).

Do CCSD and approximate CCSD-F12 variants converge to the same basis set limits? The case of atomization energies

While the title question is a clear "yes" from purely theoretical arguments, the case is less clear for practical calculations with finite (one-particle) basis sets. To shed further light on this issue, the convergence to the basis set limit of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) has been investigated in detail for the W4-17 thermochemical benchmark. Near the CBS ([1-particle] complete basis set) limit, CCSD and CCSD(F12^*) agree to within their respective uncertainties (about ±0.04 kcal/mol) due to residual basis set incompleteness error, but a nontrivial difference remains between CCSD-F12b and CCSD(F12^*), which is roughly proportional to the degree of static correlation. The observed basis set convergence behavior results from the superposition of a rapidly converging, attractive, CCSD[F12]-CCSD-F12b difference (consisting mostly of third-order terms) and a more slowly converging, repulsive, fourth-order difference between CCSD(F12^*) and CCSD[F12]. For accurate thermochemistry, we recommend CCSD(F12^*) over CCSD-F12b if at all possible. There are some indications that the nZaPa family of basis sets exhibits somewhat smoother convergence than the correlation consistent family.

Semi-empirical or non-empirical double-hybrid density functionals: which are more robust?

The development of non-empirical double-hybrid density functionals (DHDFs) is a very active research area with the number of approaches in this field having increased rapidly. At the same time, there is a lack of published work that provides a fair assessment and comparison between non-empirical and semi-empirical DHDFs on an equal footing. Herein, we close this gap and present a thorough analysis of both classes of DHDFs on the large GMTKN55 benchmark database for general main-group thermochemistry, kinetics, and noncovalent interactions [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184-32215]. In total, 115 variations of dispersion-corrected and -uncorrected DHDFs are tested, which will be condensed to an in-depth assessment of 31 methods: 19 non-empirical and 12 semi-empirical DHDFs. As such, our study represents the largest DHDF study ever conducted and can serve as an important benchmark informing method developers and users alike. Our results show that semi-empirical DHDFs are the most robust density functional approximations and more reliable and accurate than non-empirical ones. In fact, some non-empirical approaches are even outperformed by hybrid approaches or even dispersion-corrected and -uncorrected MP2 and SCS-MP2. SOS0-PBE0-2-D3(BJ) is the only exception and the only non-empirical DHDF that we can safely recommend for general applicability. However, it is still outperformed by six semi-empirical DHDFs, of which we would like to particularly recommend the following five: ωB97X-2-D3(BJ), DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), B2NC-PLYP-D3(BJ), and B2GPPLYP-D3(BJ). Our findings seriously question current trends in the field and they highlight that novel strategies have to be found in order to outperform the currently best density functional theory methods on the market. We hope that our study can function as an important cornerstone inspiring such a change of direction in the field.

Survival of the most transferable at the top of Jacob's ladder: Defining and testing the ωB97M(2) double hybrid density functional

A meta-generalized gradient approximation, range-separated double hybrid (DH) density functional with VV10 non-local correlation is presented. The final 14-parameter functional form is determined by screening trillions of candidate fits through a combination of best subset selection, forward stepwise selection, and random sample consensus (RANSAC) outlier detection. The MGCDB84 database of 4986 data points is employed in this work, containing a training set of 870 data points, a validation set of 2964 data points, and a test set of 1152 data points. Following an xDH approach, orbitals from the ωB97M-V density functional are used to compute the second-order perturbation theory correction. The resulting functional, ωB97M(2), is benchmarked against a variety of leading double hybrid density functionals, including B2PLYP-D3(BJ), B2GPPLYP-D3(BJ), ωB97X-2(TQZ), XYG3, PTPSS-D3(0), XYGJ-OS, DSD-PBEP86-D3(BJ), and DSD-PBEPBE-D3(BJ). Encouragingly, the overall performance of ωB97M(2) on nearly 5000 data points clearly surpasses that of all of the tested density functionals. As a Rung 5 density functional, ωB97M(2) completes our family of combinatorially optimized functionals, complementing B97M-V on Rung 3, and ωB97X-V and ωB97M-V on Rung 4. The results suggest that ωB97M(2) has the potential to serve as a powerful predictive tool for accurate and efficient electronic structure calculations of main-group chemistry.

Density Functional Theory for Microwave Spectroscopy of Noncovalent Complexes: A Benchmark Study

In this work, we compare the results obtained with 89 computational methods for predicting noncovalent bond lengths in weakly bound complexes. Evaluations for the performance in noncovalent interaction energies and covalent bond lengths obtained from five other data sets are included. The overall best performing density functional is the ωB97M-V method, achieving balanced results across all three categories. For noncovalent geometries, the best methods include B97M-V, B3LYP-D3(BJ) and DSD-PBEPBE-D3(BJ). The effects of systematic improvement of the density functional approximation and of dispersion corrections are also discussed.

Reliable and Performant Identification of Low-Energy Conformers in the Gas Phase and Water

Prediction of compound properties from structure via quantitative structure-activity relationship and machine-learning approaches is an important computational chemistry task in small-molecule drug research. Though many such properties are dependent on three-dimensional structures or even conformer ensembles, the majority of models are based on descriptors derived from two-dimensional structures. Here we present results from a thorough benchmark study of force field, semiempirical, and density functional methods for the calculation of conformer energies in the gas phase and water solvation as a foundation for the correct identification of relevant low-energy conformers. We find that the tight-binding ansatz GFN-xTB shows the lowest error metrics and highest correlation to the benchmark PBE0-D3(BJ)/def2-TZVP in the gas phase for the computationally fast methods and that in solvent OPLS3 becomes comparable in performance. MMFF94, AM1, and DFTB+ perform worse, whereas the performance-optimized but far more expensive functional PBEh-3c yields energies almost perfectly correlated to the benchmark and should be used whenever affordable. On the basis of our findings, we have implemented a reliable and fast protocol for the identification of low-energy conformers of drug-like molecules in water that can be used for the quantification of strain energy and entropy contributions to target binding as well as for the derivation of conformer-ensemble-dependent molecular descriptors.

The S66 Non-Covalent Interactions Benchmark Reconsidered Using Explicitly Correlated Methods Near the Basis Set Limit

The S66 benchmark for non-covalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 ‘high-level corrections’ are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66×8 problem set in particular, and for accurate calculations on non-covalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, whereas half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost.

Modelling the Effect of Conformation on Hydrogen-Atom Abstraction from Peptides

Computational quantum chemistry is used to examine the effect of conformation on the kinetics of hydrogen-atom abstraction by HO• from amides of glycine and proline as peptide models. In accord with previous findings, it is found that there are substantial variations possible in the conformations and the corresponding energies, with the captodative effect, hydrogen bonding, and solvation being some of the major features that contribute to the variations. The ‘minimum-energy-structure-pathway’ strategy that is often employed in theoretical studies of peptide chemistry with small models certainly provides valuable fundamental information. However, one may anticipate different reaction outcomes in structurally constrained systems due to modified reaction thermodynamics and kinetics, as demonstrated explicitly in the present study. Thus, using a ‘consistent-conformation-pathway’ approach may indeed be more informative in such circumstances, and in this regard theory provides information that would be difficult to obtain from experimental studies alone.

Partnering dispersion corrections with modern parameter-free double-hybrid density functionals

The PBE-QIDH and SOS1-PBE-QIDH double-hybrid density functionals are merged with a pair of dispersion corrections, namely the pairwise additive D3(BJ) and the non-local correlation functional VV10, leading to the corresponding dispersion-corrected models.

A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions

We present the updated and extended GMTKN55 benchmark database for more accurate and extensive energetic evaluation of density functionals and other electronic structure methods with detailed guidelines for method users.

How Accurate Are the Minnesota Density Functionals for Noncovalent Interactions, Isomerization Energies, Thermochemistry, and Barrier Heights Involving Molecules Composed of Main-Group Elements?

The 14 Minnesota density functionals published between the years 2005 and early 2016 are benchmarked on a comprehensive database of 4986 data points (84 data sets) involving molecules composed of main-group elements. The database includes noncovalent interactions, isomerization energies, thermochemistry, and barrier heights, as well as equilibrium bond lengths and equilibrium binding energies of noncovalent dimers. Additionally, the sensitivity of the Minnesota density functionals to the choice of basis set and integration grid is explored for both noncovalent interactions and thermochemistry. Overall, the main strength of the hybrid Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., M06-2X), barrier heights (e.g., M08-HX, M08-SO, MN15), and systems heavily characterized by self-interaction error (e.g., M06-2X, M08-HX, M08-SO, MN15), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-2X is recommended from the 10 hybrid Minnesota functionals). Similarly, the main strength of the local Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., MN15-L), barrier heights (e.g., MN12-L), and systems heavily characterized by self-interaction error (e.g., MN12-L and MN15-L), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-L is clearly the best from the four local Minnesota functionals). As an overall guide, M06-2X and MN15 are perhaps the most broadly useful hybrid Minnesota functionals, while M06-L and MN15-L are perhaps the most broadly useful local Minnesota functionals, although each has different strengths and weaknesses.

First-principles data set of 45,892 isolated and cation-coordinated conformers of 20 proteinogenic amino acids

We present a structural data set of the 20 proteinogenic amino acids and their amino-methylated and acetylated (capped) dipeptides. Different protonation states of the backbone (uncharged and zwitterionic) were considered for the amino acids as well as varied side chain protonation states. Furthermore, we studied amino acids and dipeptides in complex with divalent cations (Ca²⁺, Ba²⁺, Sr²⁺, Cd²⁺, Pb²⁺, and Hg²⁺). The database covers the conformational hierarchies of 280 systems in a wide relative energy range of up to 4 eV (390 kJ/mol), summing up to a total of 45,892 stationary points on the respective potential-energy surfaces. All systems were calculated on equal first-principles footing, applying density-functional theory in the generalized gradient approximation corrected for long-range van der Waals interactions. We show good agreement to available experimental data for gas-phase ion affinities. Our curated data can be utilized, for example, for a wide comparison across chemical space of the building blocks of life, for the parametrization of protein force fields, and for the calculation of reference spectra for biophysical applications.

The S66x8 benchmark for noncovalent interactions revisited: explicitly correlated ab initio methods and density functional theory

The S66x8 dataset for noncovalent interactions of biochemical relevance has been re-examined by means of CCSD(F12*)(T), DFT, and SAPT methods.

Screened exchange hybrid density functional for accurate and efficient structures and interaction energies

HSE-3c: a computationally efficient and numerically robust screened hybrid functional that can be applied to periodic small gap systems.