Prototypical π-π dimers re-examined by means of high-level CCSDT(Q) composite ab initio methods

Another Angle on Benchmarking Noncovalent Interactions

For noncovalent interactions, the CCSD(T)-coupled cluster method is widely regarded as the "gold standard". With localized orbital approximations, benchmarks for ever larger complexes are being published, yet FN-DMC (fixed-node quantum Monte Carlo) intermolecular interaction energies diverge to a progressively larger degree from CCSD(T) as the system size grows, particularly when π-stacking is involved. Unfortunately, post-CCSD(T) methods like CCSDT(Q) are cost-prohibitive, which requires us to consider alternative means of estimating post-CCSD(T) contributions. In this work, we take a step back by considering the evolution of the correlation energy with respect to the number of subunits for such π-stacked sequences as acene dimers and alkadiene dimers. We show it to be almost perfectly linear and propose the slope of the line as a probe for the behavior of a given electron correlation method. By going further into the coupled cluster expansion and comparing with CCSDT(Q) results for benzene and naphthalene dimers, we show that CCSD(T) does slightly overbind but not as strongly as suggested by the FN-DMC results.

Canonical coupled cluster binding benchmark for nanoscale noncovalent complexes at the hundred-atom scale

In this study, we introduce two datasets for nanoscale noncovalent binding, featuring complexes at the hundred-atom scale, benchmarked using coupled cluster with single, double, and perturbative triple [CCSD(T)] excitations extrapolated to the complete basis set (CBS) limit. The first dataset, L14, comprises 14 complexes with canonical CCSD(T)/CBS benchmarks, extending the applicability of CCSD(T)/CBS binding benchmarks to systems as large as 113 atoms. The second dataset, vL11, consists of 11 even larger complexes, evaluated using the local CCSD(T)/CBS method with stringent thresholds, covering systems up to 174 atoms. We compare binding energies obtained from local CCSD(T) and fixed-node diffusion Monte Carlo (FN-DMC), which have previously shown discrepancies exceeding the chemical accuracy threshold of 1 kcal/mol in large complexes, with the new canonical CCSD(T)/CBS results. While local CCSD(T)/CBS agrees with canonical CCSD(T)/CBS within binding uncertainties, FN-DMC consistently underestimates binding energies in π-π complexes by over 1 kcal/mol. Potential sources of error in canonical CCSD(T)/CBS are discussed, and we argue that the observed discrepancies are unlikely to originate from CCSD(T) itself. Instead, the fixed-node approximation in FN-DMC warrants further investigation to elucidate these binding discrepancies. Using these datasets as reference, we evaluate the performance of various electronic structure methods, semi-empirical approaches, and machine learning potentials for nanoscale complexes. Based on computational accuracy and stability across system sizes, we recommend MP2+aiD(CCD), PBE0+D4, and ωB97X-3c as reliable methods for investigating noncovalent interactions in nanoscale complexes, maintaining their promising performance observed in smaller systems.

An Assessment of Dispersion-Corrected DFT Methods for Modeling Nonbonded Interactions in Protein Kinase Inhibitor Complexes

Accurate modeling of nonbonded interactions between protein kinases and their small molecule inhibitors is essential for structure-based drug design. Quantum chemical methods such as density functional theory (DFT) hold significant promise for quantifying the strengths of these key protein-ligand interactions. However, the accuracy of DFT methods can vary substantially depending on the choice of exchange-correlation functionals and associated basis sets. In this study, a comprehensive benchmarking of nine widely used DFT methods was carried out to identify an optimal approach for quantitative modeling of nonbonded interactions, balancing both accuracy and computational efficiency. From a database of 2139 kinase-inhibitor crystal structures, a diverse library of 49 nonbonded interaction motifs was extracted, encompassing CH-π, π-π stacking, cation-π, hydrogen bonding, and salt bridge interactions. The strengths of nonbonded interaction energies for all 49 motifs were calculated at the advanced CCSD(T)/CBS level of theory, which serve as references for a systematic benchmarking of BLYP, TPSS, B97, ωB97X, B3LYP, M062X, PW6B95, B2PLYP, and PWPB95 functionals with D3BJ dispersion correction alongside def2-SVP, def2-TZVP, and def2-QZVP basis sets. The RI, RIJK, and RIJCOSX approximations were used for selected functionals. It was found that the B3LYP/def2-TZVP and RIJK RI-B2PLYP/def2-QZVP methods delivered the best combination of accuracy and computational efficiency, making them well-suited for efficient modeling of nonbonded interactions responsible for molecular recognition of protein kinase inhibitors in their targets.

The Topology of Molecules with Twelve Fused Phenyl Rings ([12]Circulenes): Rings, Infinitenes, and Möbius Infinitenes

Following the recent preparation of infinitene (J. Am. Chem. Soc. 2022, 144, 862-871), a computational (ωB97XD/6-311G(d)) exploration of 42 isomeric compounds with 12 fused phenyl rings identified structures with linking number of zero (ring, saddle, and ribbon shapes), two (infinitene-like shape), and one (Möbius infinitene shape) is reported. An infinitene isomer composed of two [5]helicene fragments connected to two stacked phenyl rings and a Möbius infinitene isomer are identified that are more stable than the known infinitene. The energies of the structures are examined by assessing their macrocyclization (strain) energies, π-stacking, and possible aromaticity. Examples of fused phenyl molecules with linking numbers of 3, 4, 5, and 6 are shown, indicating the potential topological range that these molecules can possess.

A critical comparison of CH⋯π versus π⋯π interactions in the benzene dimer: obtaining benchmarks at the CCSD(T) level and assessing the accuracy of lower scaling methods

We have established CCSD(T)/CBS (Complete Basis Set) limits for 3 stationary points on the benzene dimer potential energy surface, corresponding to the π⋯π (parallel displaced or PD(C_2h), minimum) and CH⋯π (T-shaped or T(C_2v), transition state) and tilted T-shaped (or TT(C_s), minimum) bonding scenarios considering both the structure and binding energy. The CCSD(T)/CBS binding energies are -2.65 ± 0.02 (PD), -2.74 ± 0.03 (T), and -2.83 ± 0.01 kcal mol^-1 (TT). To this end, the CH⋯π is ∼0.2 kcal mol^-1 stronger than the π⋯π interaction, whereas the tilting of the CH donating benzene molecule with respect to the other benzene is worth 0.1 kcal mol^-1. As previously discussed in the literature, the MP2 level of theory does not provide a close match for either the energy or structure, yet the SCS-MP2 yields structures in excellent agreement with respect to the CCSD(T) result. It is found that the SCS-MI-MP2 also gives optimized structures very close to SCS-MP2 (within ∼0.01 Å of the benchmark). Despite the closer match in structure, the spin-biased MP2 methods (SCS-, SCS-MI-, and SOS-MP2) incorrectly predict the relative stabilities of the isomers. That said, none of the spin biased MP2 methods offers a good compromise between energy and structure for the systems examined. Finally, the CCSD(T)/CBS benchmarks were used to assess the performance of 13 DFT functionals selected from different rungs of Jacob's ladder. Several functionals such as TPSS-D3, B3LYP-D3, B97-D, B97-D3, and B2PLYP-D3 provided a good description of the binding energies for both CH⋯π and π⋯π interactions, yielding values within 6% of the CCSD(T)/CBS benchmark values. Unlike the MP2 methods, these functionals correctly predict the relative stability of the PD(C_2h) and T(C_2v) dimers. Further, we find that there is no systematic improvement as Jacob's ladder is ascended (increased complexity of functional). The best functionals that result in a good compromise between structure and energy accuracy are B97-D3 and B2PLYP-D3 for both the CH⋯π and π⋯π interaction. Despite the impressive performance of these functionals, a challenge that remains is ensuring the transferability of these density functionals in accurately describing the interaction between dimers of larger aromatic molecules, the latter requiring high-level benchmarks for these systems.

Addressing the System-Size Dependence of the Local Approximation Error in Coupled-Cluster Calculations

Over the last two decades, the local approximation has been successfully used to extend the range of applicability of the "gold standard" singles and doubles coupled-cluster method with perturbative triples CCSD(T) to systems with hundreds of atoms. The local approximation error grows in absolute value with the increasing system size, i.e., by increasing the number of electron pairs in the system. In this study, we demonstrate that the recently introduced two-point extrapolation scheme for approaching the complete pair natural orbital (PNOs) space limit in domain-based pair natural orbital CCSD(T) calculations drastically reduces the dependence of the error on the system size, thus opening up unprecedented opportunities for the calculation of benchmark quality relative energies for large systems.

junChS and junChS-F12 Models: Parameter-free Efficient yet Accurate Composite Schemes for Energies and Structures of Noncovalent Complexes

A recently developed model chemistry (denoted as junChS [Alessandrini, S.; et al. J. Chem. Theory Comput. 2020, 16, 988-1006]) has been extended to the employment of explicitly correlated (F12) methods. This led us to propose a family of effective, reliable, and parameter-free schemes for the computation of accurate interaction energies of molecular complexes ruled by noncovalent interactions. A thorough benchmark based on a wide range of interactions showed that the so-called junChS-F12 model, which employs cost-effective revDSD-PBEP86-D3(BJ) reference geometries, has an improved performance with respect to its conventional counterpart and outperforms well-known model chemistries. Without employing any empirical parameter and at an affordable computational cost, junChS-F12 reaches subchemical accuracy. Accurate characterizations of molecular complexes are usually limited to energetics. To take a step forward, the conventional and F12 composite schemes developed for interaction energies have been extended to structural determinations. A benchmark study demonstrated that the most effective option is to add MP2-F12 core-valence correlation corrections to fc-CCSD(T)-F12/jun-cc-pVTZ geometries without the need of recovering the basis set superposition error and the extrapolation to the complete basis set.