Quantification of Geometric Errors Made Simple: Application to Main-Group Molecular Structures

Evaluating wavefunction methods, the counterpoise correction, and the frozen core approximation for the optimization of van der Waals dimers

A number of benchmarking studies have assessed the accuracy of various electronic structure methods for computing the interaction energies of van der Waals dimers, but fewer have systematically assessed the quality of dimer geometries obtained by these methods. We present optimized geometries of 21 van der Waals dimers using a highly accurate level of theory, namely coupled-cluster through perturbative triples at the complete basis set limit [CCSD(T)/CBS], and compare these results with optimizations performed at lower levels of theory. The lower levels of theory include variants of Møller-Plesset perturbation theory (MP2, MP2D, and MP2.5) and coupled-cluster theory [CCSD and CCSD(T)], with basis sets ranging from double- to quadruple-zeta. The accuracy of these methods is assessed by comparing errors in the least-root-mean-squared deviations (LRMSDs) of atomic coordinates, center-of-mass distances (ΔdCOM), interaction energies, and rotational constants. We also investigate the impact of the counterpoise correction and the frozen core approximation on the quality of the optimized geometries. Our findings show that increasing the basis set size beyond double-zeta significantly improves the accuracy of the geometries, while further improvements due to the basis set size depend on the method used. The frozen core approximation induces very small changes in geometries, while the counterpoise correction has a larger effect. For double-zeta basis sets, the counterpoise correction tends to degrade the quality of the optimized geometries, regardless of the method used. Several methods yield geometries with LRMSDs and ΔdCOM within 0.1 Å for all 21 dimers, and MP2D with the aug-cc-pVTZ basis set emerges as the most computationally efficient among these well-performing approaches with an average LRMSD and an absolute ΔdCOM of 0.02 Å.

Regularized and Opposite Spin-Scaled Functionals from Møller-Plesset Adiabatic Connection─Higher Accuracy at Lower Cost

Noncovalent interactions (NCIs) play a crucial role in biology, chemistry, material science, and everything in between. To improve pure quantum-chemical simulations of NCIs, we propose a methodology for constructing approximate correlation energies by combining an interpolation along the Møller-Plesset adiabatic connection (MP AC) with a regularization and spin-scaling strategy applied to MP2 correlation energies. This combination yields cosκos-SPL2, which exhibits superior accuracy for NCIs compared to any of the individual strategies. With the N4 formal scaling, cosκos-SPL2 is competitive or often outperforms more expensive dispersion-corrected double hybrids for NCIs. The accuracy of cosκos-SPL2 particularly shines for anionic halogen bonded complexes, where it surpasses standard dispersion-corrected DFT by a factor of 3 to 5.

Gas-Phase Interaction of CO, CO2, H2S, NH3, NO, NO2, and SO2 with Zn12O12 and Zn24 Atomic Clusters

Atmospheric pollutants pose a high risk to human health, and therefore it is necessary to capture and preferably remove them from ambient air. In this work, we investigate the intermolecular interaction between the pollutants such as CO, CO₂, H₂S, NH₃, NO, NO₂, and SO₂ gases with the Zn₂₄ and Zn₁₂O₁₂ atomic clusters, using the density functional theory (DFT) at the meta-hybrid functional TPSSh and LANl2Dz basis set. The adsorption energy of these gas molecules on the outer surfaces of both types of clusters has been calculated and found to have a negative value, indicating a strong molecular-cluster interaction. The largest adsorption energy has been observed between SO₂ and the Zn₂₄ cluster. In general, the Zn₂₄ cluster appears to be more effective for adsorbing SO₂, NO₂, and NO than Zn₁₂O₁₂, whereas the latter is preferable for the adsorption of CO, CO₂, H₂S, and NH₃. Frontier molecular orbital (FMO) analysis showed that Zn₂₄ exhibits higher stability upon adsorption of NH₃, NO, NO₂, and SO₂, with the adsorption energy falling within the chemisorption range. The Zn₁₂O₁₂ cluster shows a characteristic decrease in band gap upon adsorption of CO, H₂S, NO, and NO₂, suggesting an increase in electrical conductivity. Natural bond orbital (NBO) analysis also suggests the presence of strong intermolecular interactions between atomic clusters and the gases. This interaction was recognized to be strong and noncovalent, as determined by noncovalent interaction (NCI) and quantum theory of atoms in molecules (QTAIM) analyses. Overall, our results suggest that both Zn₂₄ and Zn₁₂O₁₂ clusters are good candidate species for promoting adsorption and, thus, can be employed in different materials and/or systems for enhancing interaction with CO, H₂S, NO, or NO₂.

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

Density functional theory (DFT) calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn-Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree-Fock density is enough. This Perspective explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.

A new double-reference correction scheme for accurate and efficient computation of NMR chemical shieldings

Our novel correction procedure yields high-accuracy DFT predictions of absolute NMR shieldings and enables outliers due to relativistic effects or manifestly inadequate modelling of electron correlation to be easily and unambiguously identified.