“Mindless” DFT Benchmarking

Quantum Mechanical Calculation of Noncovalent Interactions: A Large-Scale Evaluation of PMx, DFT, and SAPT Approaches

Quantum mechanical (QM) calculations of noncovalent interactions are uniquely useful as tools to test and improve molecular mechanics force fields and to model the forces involved in biomolecular binding and folding. Because the more computationally tractable QM methods necessarily include approximations, which risk degrading accuracy, it is essential to evaluate such methods by comparison with high-level reference calculations. Here, we use the extensive Benchmark Energy and Geometry Database (BEGDB) of CCSD(T)/CBS reference results to evaluate the accuracy and speed of widely used QM methods for over 1200 chemically varied gas-phase dimers. In particular, we study the semiempirical PM6 and PM7 methods; density functional theory (DFT) approaches B3LYP, B97-D, M062X, and ωB97X-D; and symmetry-adapted perturbation theory (SAPT) approach. For the PM6 and DFT methods, we also examine the effects of post hoc corrections for hydrogen bonding (PM6-DH+, PM6-DH2), halogen atoms (PM6-DH2X), and dispersion (DFT-D3 with zero and Becke–Johnson damping). Several orders of the SAPT expansion are also compared, ranging from SAPT0 up to SAPT2+3, where computationally feasible. We find that all DFT methods with dispersion corrections, as well as SAPT at orders above SAPT2, consistently provide dimer interaction energies within 1.0 kcal/mol RMSE across all systems. We also show that a linear scaling of the perturbative energy terms provided by the fast SAPT0 method yields similar high accuracy, at particularly low computational cost. The energies of all the dimer systems from the various QM approaches are included in the Supporting Information, as are the full SAPT2+(3) energy decomposition for a subset of over 1000 systems. The latter can be used to guide the parametrization of molecular mechanics force fields on a term-by-term basis.

The Houk–List transition states for organocatalytic mechanisms revisited

The ten year old Houk–List model for rationalising the origin of stereoselectivity in the organocatalysed intermolecular aldol addition is revisited, using a variety of computational techniques that have been introduced or improved since the original study.

Receding mechanism of NLO response of polyanion [M8O26]4− (M = Cr, Mo, W) and the closed loops theory analysis

The second hyperpolarizability of six octa-poly-oxo anions [M₈O₂₆]⁴⁻ (M = Cr, Mo, W) were studied by DFT/TDDFT method.

Calculation of Heats of Formation for Zn Complexes: Comparison of Density Functional Theory, Second Order Perturbation Theory, Coupled-Cluster and Complete Active Space Methods

Heats of formation were predicted for nine ZnX complexes (X= Zn, H, O, F2, S, Cl, Cl2, CH3, (CH3)2) using fourteen density functionals, MP2 calculations and the CCSD and CCSD(T) coupled-cluster methods. Calculations utilized the correlation consistent cc-pVTZ and aug-cc-pVTZ basis sets. Heats of formation were most accurately predicted by the TPSSTPSS and TPSSKCIS density functionals, and the BLYP, B3LYP, MP2, CCSD and CCSD(T) levels were among the poorest performing methods based on accuracy. A wide range of Zn2 equilibrium bond distances were predicted, indicating that many of the studied levels of theory may be unable to adequately describe this transition metal dimer. To further benchmark the accuracy of the density functional methods, high-level CASSCF and CASPT2 calculations were performed to estimate bond dissociation energies, equilibrium bond lengths and heats of formation for the diatomic Zn complexes and the latter two quantities were compared with the results of DFT, MP2 and coupled-cluster calculations as well as experimental values.

An assessment of DFT methods for predicting the thermochemistry of ion-molecule reactions of group 14 elements (Si, Ge, Sn)

Experimental mass-spectrometry data on thermochemistry of methide transfer reactions (CH₃)₃M(+) + M'(CH₃)₄ ↔ M(CH₃)₄ + (CH₃)₃M'(+) (M, M' = Si, Ge or Sn) and the formation energy of the [(CH₃)₃Si-CH₃-Si(CH₃)₃](+) complex are used as benchmarks for DFT methods (B3LYP, BMK, M06L, and ωB97XD). G2 and G3 theory methods are also used for the prediction of thermochemical data. BMK, M06L, and ωB97XD methods give the best fit to experimental data (close to chemical accuracy) as well as to G2 and G3 results, while B3LYP demonstrates poor performance. From the first three methods M06L gives the best overall result. Structures and formation energies of intermediate "mixed" [(CH₃)₃M-CH₃- M'(CH₃)₃] complexes not observed in experiment are predicted. Their structures, better described as M(CH₃)₄ [M'(CH₃)₃](+) complexes, explain their fast decompositions.

W3X: A Cost-Effective Post-CCSD(T) Composite Procedure

We have formulated the W3X procedure by incorporating cost-effective post-CCSD(T) components (up to the CCSDT(Q) level) into the W1X-1 protocol, the latter representing a recently reported economical yet accurate approximation to CCSD(T)/CBS. For medium-sized systems, W3X is moderately more computationally demanding than W1X-1, but it is significantly less costly than the W3.2lite and (especially) W3.2 procedures. Because of the use of the cost-effective W1X-1 method as the underlying CCSD(T) component, W3X is also less expensive than the W2.2 protocol, which does not incorporate post-CCSD(T) excitations. We find that, for single-reference systems (the G2/97 set and most of the W4-11 set), W3X is comparable in accuracy to the underlying W1X-1 protocol, as might have been expected. For the more challenging cases of the multireference systems within the W4-11 set, the dissociation of F2 and the automerization of cyclobutadiene, W3X provides improved performance compared with the CCSD(T)-based procedures (W1X-1 and W2.2). Highly multireference chromium oxides CrO, CrO2, and CrO3 are still somewhat challenging for W3X (and even for the higher-level W3.2lite and W3.2 procedures), but the inclusion of the economical post-CCSD(T) terms in W3X already leads to a significant improvement over W1X-1. Thus, W3X provides a cost-effective means for treating systems with significant (but perhaps not excessive) multireference character that are otherwise not well-described by CCSD(T)-based methods.

Comparative analysis of the performance of commonly available density functionals in the determination of geometrical parameters for copper complexes

In this study, a set of 50 transition-metal complexes of Cu(I) and Cu(II), were used in the evaluation of 18 density functionals in geometry determination. In addition, 14 different basis sets were considered, including four commonly used Pople's all-electron basis sets; four basis sets including popular types of effective-core potentials: Los Alamos, Steven-Basch-Krauss, and Stuttgart-Dresden; and six triple-ζ basis sets. The results illustrate the performance of different methodological alternatives for the treatment of geometrical properties in relevant copper complexes, pointing out Double-Hybrid (DH) and Long-range Correction (LC) Generalized Gradient Approximation (GGA) methods as better descriptors of the geometry of the evaluated systems. These however, are associated with a computational cost several times higher than some of the other methods employed, such as the M06 functional, which has also demonstrated a comparable performance. Regarding the basis sets, 6-31+G(d) and 6-31+G(d,p) were the best performing approaches. In addition, the results show that the use of effective-core potentials has a limited impact, in terms of the accuracy in the determination of metal-ligand bond-lengths and angles in our dataset of copper complexes. Hence, these could become a good alternative for the geometrical description of these systems, particularly CEP-121G and SDD basis sets, if one is considering larger copper complexes where the computational cost could be an issue.

Benchmark study of the performance of density functional theory for bond activations with (ni,pd)-based transition-metal catalysts

The performance of 23 density functionals, including one LDA, four GGAs, three meta-GGAs, three hybrid GGAs, eight hybrid meta-GGAs, and ten double-hybrid functionals, was investigated for the computation of activation energies of various covalent main-group single bonds by four catalysts: Pd, PdCl⁻, PdCl₂, and Ni (all in the singlet state). A reactant complex, the barrier, and reaction energy were considered, leading to 164 energy data points for statistical analysis. Extended Gaussian AO basis sets were used in all calculations. The best functional for the complete benchmark set relative to estimated CCSD(T)/CBS reference data is PBE0-D3, with an MAD value of 1.1 kcal mol⁻¹ followed by PW6B95-D3, the double hybrid PWPB95-D3, and B3LYP-D3 (1.9 kcal mol⁻¹ each). The other tested hybrid meta-GGAs perform less well (M06-HF: 7.0 kcal mol⁻¹; M06-2X: 6.3 kcal mol⁻¹; M06: 4.9 kcal mol⁻¹) for the investigated reactions. In the Ni case, some double hybrids show larger errors due to partial breakdown of the perturbative treatment for the correlation energy in cases with difficult electronic structures (partial multi-reference character). Only double hybrids either with very low amounts of perturbative correlation (e.g., PBE0-DH) or that use the opposite-spin correlation component only (e.g., PWPB95) seem to be more robust. We also investigated the effect of the D3 dispersion correction. While the barriers are not affected by this correction, significant and mostly positive results were observed for reaction energies. Furthermore, six very recently proposed double-hybrid functionals were analyzed regarding the influence of the amount of Fock exchange as well as the type of perturbative correlation treatment. According to these results, double hybrids with <50–60 % of exact exchange and ∼30 % perturbative correlation perform best.

Benchmark Study for the Cysteine-Histidine Proton Transfer Reaction in a Protein Environment: Gas Phase, COSMO, QM/MM Approaches

Proton transfer reactions are of crucial interest for the investigation of proteins. We have investigated the accuracy of commonly used quantum chemical methods for the description of proton transfer reactions in different environments (gas phase, COSMO, QM/MM) using the proton transfer between the catalytic dyad residues cysteine 145 and histidine 41 of SARS coronavirus main protease as a case study. The test includes thermodynamic, kinetic, and structural properties. The study comprises computationally demanding ab initio approaches (HF, CC2, MP2, SCS-CC2, SCS-MP2, CCSD(T)), popular density functional theories (BLYP, B3LYP, M06-2X), and semiempirical methods (MNDO/d, AM1, RM1, PM3, PM6). The approximated coupled cluster approach LCCSD(T) is taken as a reference method. We find that the robustness of the tested methods with respect to the environment correlates well with the level of theory. As an example HF, CC2, MP2, and their SCS variants show similar errors for gas phase, COSMO, or QM/MM computations. In contrast for semiempirical methods, the errors strongly diversify if one goes from gas phase to COSMO or QM/MM. Particular problems are observed for the recent semiempirical methods PM6 and RM1, which show the best performance for gas phase calculations but possess larger errors in conjunction with COSMO. Finally, a combination of SCS-MP2 and B3LYP or M06-2X allows reliable estimates about remaining errors.

JACOB: a dynamic database for computational chemistry benchmarking

JACOB (just a collection of benchmarks) is a database that contains four diverse benchmark studies, which in-turn included 72 data sets, with a total of 122,356 individual results. The database is constructed upon a dynamic web framework that allows users to retrieve data from the database via predefined categories. Additional flexibility is made available via user-defined text-based queries. Requested sets of results are then automatically presented as bar graphs, with parameters of the graphs being controllable via the URL. JACOB is currently available at www.wallerlab.org/jacob.

Theoretical study of the oxidation of histidine by singlet oxygen

Herein we present a theoretical study of the reaction of singlet oxygen with histidine performed both in the gas phase and in aqueous solution. The potential energy surface of the reactive system was explored at the B3LYP/cc-pVTZ level of theory and the electronic energies were refined by means of single-point CCSD(T)/cc-pVTZ(-f) calculations. Solvent effects were taken into account by using a solvent continuum model (COSMO) and by adding explicit water molecules. The results show that the first step in the reaction mechanism corresponds to a nearly symmetric Diels-Alder addition of the singlet oxygen molecule to the imidazole ring to yield an endoperoxide, in agreement with experimental evidence. The intermediate formed can evolve along two different reaction paths leading to two isomeric hydroperoxides and, eventually, to open-chain or internally cyclised oxidised products. Water plays a significant role in stabilising the reaction structures by solvation and by acting as a bifunctional catalyst in the elimination/addition reaction steps. Our results explain why substituents at the N1-imidazole ring can hamper the evolution of the initial endoperoxide and result in Gibbs energy barriers in solution similar to those experimentally measured and suggest a likely route to the formation of peptide aggregates during the oxidation of histidine by singlet molecular oxygen.

Formation of N-N cross-links in DNA by reaction of radiation-produced DNA base pair diradicals: a DFT study

This study employs DFT (density functional theory) to investigate the formation of hydrazine-like (N-N) cross-linked structures between DNA base pair diradicals that are likely to result from the interaction of high linear energy transfer (LET) radiation, such as ion-beam radiation, with DNA. In our calculations, we generated the guanine (G), cytosine (C), adenine (A), and thymine (T) radicals by removing one hydrogen atom from an N-H bond involved in the normal base pairing. The radical species formed are those that naturally result from one-electron oxidation of the bases followed by deprotonation. N-N cross-links between G and C or A and T diradicals were studied using the BHandHLYP, B3LYP, M06, and M06-2X density functionals and 6-31G* basis set. From a comparison to several test cases performed with the G3B3 method, which gives thermodynamically reliable values, we found that calculations employing the BHandHLYP/6-31G* method predict the best estimates of bonding energies for hydrazine-like structures. Our study shows that the N-N cross-link formed between guanine radical and a neutral cytosine is endothermic in nature but can form metastable structures. However, the reactions between two DNA base radicals (diradical) to form several N-N cross-linked structures are found to be highly exothermic in nature. The N-N cross-links formed between various G-C, G-G, and C-C diradicals have binding energies in the range of ca. -54 to -68, -41 to -47, and -67 to -75 kcal/mol, respectively, whereas A-T, A-A, and T-T have binding energies of -80, -60, and -98 kcal/mol, respectively. In all purine-pyrimidine N-N cross-linked structures, the highest occupied molecular orbital (HOMO) is found to be localized on the purine moiety and the lowest unoccupied molecular orbital (LUMO) is on the pyrimidine moiety.