Dangers of counterpoise corrected hypersurfaces. Advantages of basis set superposition improvement

The effect of midbond functions on interaction energies computed using MP2 and CCSD(T)

In this article we use MP2 and CCSD(T) calculations for the A24 and S66 data sets to explore how midbond functions can be used to generate cost effective counterpoise corrected supramolecular interaction energies of noncovalent complexes. We use the A24 data set to show that the primary role of midbond functions is not to approach the complete basis set limit, but rather to ensure a balanced description of the molecules and the interaction region (unrelated to the basis set superposition error). The need for balance is a consequence of using atom centered basis sets. In the complete basis set limit, the error will disappear, but reaching the complete basis set limit is not feasible beyond small systems. For S66 we investigate the need for increasing the number of midbond centers. Results show that adding a second midbond center increases the accuracy, but the effect is secondary to changing the atom centered basis set. Further, by comparing calculations using the 3s3p2d1f1g midbond set with using aug-cc-pVDZ and aug-cc-pVTZ as midbond sets, we see that the requirements for the midbond set to be effective, is not just that it contains diffuse functions, but also that high angular momentum functions are included. By comparing two approaches for placing midbond centers we show that results are not particularly sensitive to placement as long as the placement is reasonable.

Ab Initio Nonadiabatic Surface-Hopping Trajectory Simulations of Photocatalytic Water Oxidation and Hydrogen Evolution with the Heptazine Chromophore

In the past decade, polymeric carbon nitrides consisting of heptazine (Hz) building blocks emerged as highly promising materials for photocatalytic hydrogen evolution from water or sacrificial electron donors with near-ultraviolet light. However, the complexity of these materials and their poor characterization at the atomic level are detrimental to the unraveling of the detailed mechanisms of the reactions leading to hydrogen evolution. Recently, it has been shown that a derivative of the Hz molecule, trianisole-heptazine (TAHz), is a potent photobase, which readily oxidizes various derivatives of phenol and even water by an excited-state proton-coupled electron-transfer (PCET) reaction. Energy profiles along minimum-energy reaction paths and relaxed PCET potential-energy surfaces, which previously were computed with ab initio electronic-structure methods for complexes of Hz and TAHz with protic substrates, led to qualitative insights. To obtain more quantitative insight, reaction dynamics simulations are required. In the present work, the time scales of the electron and proton transfer processes and the branching ratios of competing channels were explored with ab initio on-the-fly quasiclassical surface-hopping trajectory simulations for the hydrogen-bonded Hz-H₂O complex. By the analysis of representative trajectories, detailed insight into the interplay of various nonadiabatic electronic transitions, electron transfer, proton transfer, and vibrational energy relaxation is obtained. The HzH radicals which are formed by the photoreduction of Hz can disproportionate to Hz and HzH₂ in an exothermic reaction with a low reaction barrier. The time scales and branching ratios of competing channels in H-atom photodetachment from the HzH₂ molecule also were explored with ab initio surface-hopping simulations. These results delineate for the first time a quantitatively supported scenario of water oxidation and hydrogen evolution with a molecular carbon nitride photocatalyst.

Ab Initio Simulation of the IR Spectrum of Hydrated Kaolinite

The hydration of the basal surfaces of kaolinite is studied by theoretical methods. The cluster method was used to simulate the positions of atoms. The positions of the atoms of the basal surfaces of dry and hydrated minerals are optimized by minimizing the total energy in the Hartree–Fock approximation. The adsorption energies of water molecules were calculated taking into account the fourth-order correlation corrections of Møller–Plesset perturbation theory. The formation of the IR spectrum of kaolinite in the range of wave numbers 2500–4500 cm−1 is studied. The experimentally observed effect of the change in relative intensity and position of the band with a change in the moisture content of the sample is interpreted.

CHAL336 Benchmark Set: How Well Do Quantum-Chemical Methods Describe Chalcogen-Bonding Interactions?

We present the CHAL336 benchmark set-the most comprehensive database for the assessment of chalcogen-bonding (CB) interactions. After careful selection of suitable systems and identification of three high-level reference methods, the set comprises 336 dimers each consisting of up to 49 atoms and covers both σ- and π-hole interactions across four categories: chalcogen-chalcogen, chalcogen-π, chalcogen-halogen, and chalcogen-nitrogen interactions. In a subsequent study of DFT methods, we re-emphasize the need for using proper London dispersion corrections when treating noncovalent interactions. We also point out that the deterioration of results and systematic overestimation of interaction energies for some dispersion-corrected DFT methods does not hint at problems with the chosen dispersion correction but is a consequence of large density-driven errors. We conclude this work by performing the most detailed DFT benchmark study for CB interactions to date. We assess 109 variations of dispersion-corrected and dispersion-uncorrected DFT methods and carry out a detailed analysis of 80 of them. Double-hybrid functionals are the most reliable approaches for CB interactions, and they should be used whenever computationally feasible. The best three double hybrids are SOS0-PBE0-2-D3(BJ), revDSD-PBEP86-D3(BJ), and B2NCPLYP-D3(BJ). The best hybrids in this study are ωB97M-V, PW6B95-D3(0), and PW6B95-D3(BJ). We do not recommend using the popular B3LYP functional nor the MP2 approach, which have both been frequently used to describe CB interactions in the past. We hope to inspire a change in computational protocols surrounding CB interactions that leads away from the commonly used, popular methods to the more robust and accurate ones recommended herein. We would also like to encourage method developers to use our set for the investigation and reduction of density-driven errors in new density functional approximations.

Conformational Shifts of Stacked Heteroaromatics: Vacuum vs. Water Studied by Machine Learning

Stacking interactions play a crucial role in drug design, as we can find aromatic cores or scaffolds in almost any available small molecule drug. To predict optimal binding geometries and enhance stacking interactions, usually high-level quantum mechanical calculations are performed. These calculations have two major drawbacks: they are very time consuming, and solvation can only be considered using implicit solvation. Therefore, most calculations are performed in vacuum. However, recent studies have revealed a direct correlation between the desolvation penalty, vacuum stacking interactions and binding affinity, making predictions even more difficult. To overcome the drawbacks of quantum mechanical calculations, in this study we use neural networks to perform fast geometry optimizations and molecular dynamics simulations of heteroaromatics stacked with toluene in vacuum and in explicit solvation. We show that the resulting energies in vacuum are in good agreement with high-level quantum mechanical calculations. Furthermore, we show that using explicit solvation substantially influences the favored orientations of heteroaromatic rings thereby emphasizing the necessity to include solvation properties starting from the earliest phases of drug design.

STACKED - Solvation Theory of Aromatic Complexes as Key for Estimating Drug Binding

The use of fragments to biophysically characterize a protein binding pocket and determine the strengths of certain interactions is a computationally and experimentally commonly applied approach. Almost all drug like molecules contain at least one aromatic moiety forming stacking interactions in the binding pocket. In computational drug design, the strength of stacking and the resulting optimization of the aromatic core or moiety is usually calculated using high level quantum mechanical approaches. However, as these calculations are performed in a vacuum, solvation properties are neglected. We close this gap by using Grid Inhomogeneous Solvation Theory (GIST) to describe the properties of individual heteroaromatics and complexes and thereby estimate the desolvation penalty. In our study, we investigated the solvation free energies of heteroaromatics frequently occurring in drug design projects in complex with truncated side chains of phenylalanine, tyrosine, and tryptophan. Furthermore, we investigated the properties of drug-fragments crystallized in a fragment-based lead optimization approach investigating PDE-10-A. We do not only find good correlation for the estimated desolvation penalty and the experimental binding free energy, but our calculations also allow us to predict prominent interaction sites. We highlight the importance of including the desolvation penalty of the respective heteroaromatics in stacked complexes to explain the gain or loss in affinity of potential lead compounds.

Testing the CP-correction procedure with different DFT methods on H-bonding complexes of κ-carrabiose with water molecules

Interaction of water molecules with κ-carrabiose disaccharide, within three H-bonding complexes, was investigated. Particular interest was focused on the way with which the BSSE correction has to be performed. Two strategies were used, either performing BSSE correction during or after optimization. For this aim, several DFT-functionals (hybrid GGA and hybrid meta-GGA) and 6-31 + G* basis set were considered. The results demonstrated the uselessness of including of BSSE-CP correction during optimization for all complexes. From a structural point of view, a proper H-bonding description was obtained using the PBE0 functional for all complexes. The basis set effect on the BSSE using B3LYP functional was also investigated. The reliability of B3LYP/6-31 + G** and B3LYP/6-31++G** models for the complexes involving one or two water molecules was reported while the use of B3LYP/6-311 + G** or B3LYP/6-311++G** levels was shown to be more appropriate for larger complexes equivalent to that involving three water molecules. CP-corrected interaction energies were demonstrated to be closer to CBS-4 M interaction energies than the uncorrected ones. Graphical abstract Functional and basis set effects on BSSE.

How surface reparation prevents catalytic oxidation of carbon monoxide on atomic gold at defective magnesium oxide surfaces

In this contribution, we study using first principles the co-adsorption and catalytic behaviors of CO and O2 on a single gold atom deposited at defective magnesium oxide surfaces. Using cluster models and point charge embedding within a density functional theory framework, we simulate the CO oxidation reaction for Au1 on differently charged oxygen vacancies of MgO(001) to rationalize its experimentally observed lack of catalytic activity. Our results show that: (1) co-adsorption is weakly supported at F(0) and F(2+) defects but not at F(1+) sites, (2) electron redistribution from the F(0) vacancy via the Au1 cluster to the adsorbed molecular oxygen weakens the O2 bond, as required for a sustainable catalytic cycle, (3) a metastable carbonate intermediate can form on defects of the F(0) type, (4) only a small activation barrier exists for the highly favorable dissociation of CO2 from F(0), and (5) the moderate adsorption energy of the gold atom on the F(0) defect cannot prevent insertion of molecular oxygen inside the defect. Due to the lack of protection of the color centers, the surface becomes invariably repaired by the surrounding oxygen and the catalytic cycle is irreversibly broken in the first oxidation step.

Counterpoise correction is not useful for short and Van der Waals distances but may be useful at long range

This article investigates the errors in supermolecule calculations for the helium dimer. In a full CI calculation, there are two errors. One is the basis set superposition error (BSSE), the other is the basis set convergence error (BSCE). Both of the errors arise from the incompleteness of the basis set. These two errors make opposite contributions to the interaction energies. The BSCE is by far the largest error in the short range and larger than (but much closer to) BSSE around the Van der Waals minimum. Only at the long range, the BSSE becomes the larger error. The BSCE and BSSE largely cancel each other over the Van der Waals well. Accordingly, it may be recommended to not include the BSSE for the calculation of the potential energy curve from short distance till well beyond the Van der Waals minimum, but it may be recommended to include the BSSE correction if an accurate tail behavior is required. Only if the calculation has used a very large basis set, one can refrain from including the counterpoise correction in the full potential range. These results are based on full CI calculations with the aug-cc-pVXZ (X = D, T, Q, 5) basis sets.

Theoretical prediction of hydrogen bond strength for use in molecular modeling

Hybrid density functional theory calculations are used to investigate the strength of hydrogen bonds of structurally different molecules in complex with a standard donor and acceptor in vacuo. B3LYP/aug-cc-pVDZ calculations with one angle constraint lead to excellent correlations with experimental data (R(2) = 0.94, s(y) = 0.45 for acceptors and R(2) = 0.77, s(y) = 0.88 for donors). Substitutions of aromatic systems by electron donating and -withdrawing groups show a reinforcement of the interaction when substituting an acceptor with electron donating groups and weakening by substitution with electron withdrawing groups. For donor systems the opposite effect can be observed. Drug design of novel ligands will be able to profit from the predictive power of the method established, as hydrogen bonds between receptor and drug molecules are an important criterion for binding affinities.

Ab initio studies of crystalline nitromethane under high pressure

We have studied the mechanical compressibility and band structure of solid nitromethane both in equilibrium and compressed states using Hartree-Fock and density functional theory (DFT) with atom-centered all-electron linear combination of atomic orbitals basis sets. Hartree-Fock calculations with a 6-21G basis set, uncorrected for basis set superposition error, gave the best agreement with experimental compression studies. These results may be due to the cancellation of basis set superposition error with dispersion force errors. The equilibrium DFT band gap is comparable to the lowest-energy feature in electron-impact spectroscopy of nitromethane but underpredicts the optical absorption gap; we interpret these features in terms of the presence of tightly bound excitons. Only minor changes in the gap are observed under hydrostatic compression.

Interaction and solvation energies of nonpolar DNA base analogues and their role in polymerase insertion fidelity

Although DNA polymerase fidelity has been mainly ascribed to Watson-Crick hydrogen bonds, two nonpolar isosteres for thymine (T) and adenine (A)--difluorotoluene (F) and benzimidazole (Z) --effectively mimic their natural counterparts in polymerization experiments with pol I (KF exo-) [JC Morales and ET Kool. Nature Struct Biol, 5, 950-954, 1998]. By ab initio quantum chemical gas phase methods (HF/6-31G* and MP2/6-31G**) and a solvent phase method (CPCM-HF/6-31G**), we find that the A-F interaction energy is 1/3 the A-T interaction energy in the gas phase and unstable in the solvent phase. The F-Z and T-Z interactions are very weak and T-Z is quite unstable in the solvent. Electrostatic solvation energy calculations on F, Z and toluene yield that Z is two times, and F and toluene are five times, less hydrophilic than the natural bases. Of the new "base-pairs" (F-Z, T-Z, and F-A), only F-A formed an A-T-like arrangement in unconstrained optimizations. F-Z and T-Z do not freely form planar arrangements, and constrained optimizations show that large amounts of energy are required to make these pairs fit the exact A-T geometry, suggesting that the polymerase does not require all bases to conform to the exact A-T geometry. We discuss a model for polymerase/nucleotide binding energies and investigate the forces and conformational range involved in the polymerase geometrical selection.