Basis Set Superposition Errors Are Partly Basis Set Imbalances

When calculating fragment interaction energies by electronic structure methods employing medium-sized atom-centered basis sets, it is often observed that the effect is systematically overestimated. The common interpretation is that the systematic error arises because the basis set for the complex is more complete than for the isolated fragments, and this is denoted basis set superposition errors. It has been observed, however, that the interaction energy in some cases is underestimated, which defies the interpretation in terms of basis set completeness, and instead suggests that the effect partly is due to basis set imbalance. The imbalance can be removed by explicit optimization of the basis sets for each structure, and it is shown that this to a significant extent reduces the systematic overestimation attributed to basis set superposition error.

Conformational energies of reference organic molecules: benchmarking of common efficient computational methods against coupled cluster theory

We selected 145 reference organic molecules that include model fragments used in computer-aided drug design. We calculated 158 conformational energies and barriers using force fields, with wide applicability in commercial and free softwares and extensive application on the calculation of conformational energies of organic molecules, e.g. the UFF and DREIDING force fields, the Allinger's force fields MM3-96, MM3-00, MM4-8, the MM2-91 clones MMX and MM+, the MMFF94 force field, MM4, ab initio Hartree-Fock (HF) theory with different basis sets, the standard density functional theory B3LYP, the second-order post-HF MP2 theory and the Domain-based Local Pair Natural Orbital Coupled Cluster DLPNO-CCSD(T) theory, with the latter used for accurate reference values. The data set of the organic molecules includes hydrocarbons, haloalkanes, conjugated compounds, and oxygen-, nitrogen-, phosphorus- and sulphur-containing compounds. We reviewed in detail the conformational aspects of these model organic molecules providing the current understanding of the steric and electronic factors that determine the stability of low energy conformers and the literature including previous experimental observations and calculated findings. While progress on the computer hardware allows the calculations of thousands of conformations for later use in drug design projects, this study is an update from previous classical studies that used, as reference values, experimental ones using a variety of methods and different environments. The lowest mean error against the DLPNO-CCSD(T) reference was calculated for MP2 (0.35 kcal mol-1), followed by B3LYP (0.69 kcal mol-1) and the HF theories (0.81-1.0 kcal mol-1). As regards the force fields, the lowest errors were observed for the Allinger's force fields MM3-00 (1.28 kcal mol-1), ΜΜ3-96 (1.40 kcal mol-1) and the Halgren's MMFF94 force field (1.30 kcal mol-1) and then for the MM2-91 clones MMX (1.77 kcal mol-1) and MM+ (2.01 kcal mol-1) and MM4 (2.05 kcal mol-1). The DREIDING (3.63 kcal mol-1) and UFF (3.77 kcal mol-1) force fields have the lowest performance. These model organic molecules we used are often present as fragments in drug-like molecules. The values calculated using DLPNO-CCSD(T) make up a valuable data set for further comparisons and for improved force field parameterization.

Quantifying Intramolecular Basis Set Superposition Errors

We show that medium-sized Gaussian basis sets lead to significant intramolecular basis set superposition errors at Hartree-Fock and density functional levels of theory, with artificial stabilization of compact over extended conformations for a 186 atom deca-peptide. Errors of ∼80 and ∼10 kJ/mol are observed, with polarized double zeta and polarized triple zeta quality basis sets, respectively. Two different procedures for taking the basis set superposition error into account are tested. While both reduce the error, it appears that polarized quadruple zeta basis sets are required to reduce the error below a few kJ/mol. Alternatively, the basis set superposition error can be eliminated using multiresolution methods based on Multiwavelets.

Intramolecular O-H⋯O and C-H⋯O hydrogen bond cooperativity in D-glucopyranose and D-galactopyranose-A DFT/GIAO, QTAIM/IQA, and NCI approach

Density functional theory calculations are used to compute proton nuclear magnetic resonance (NMR) chemical shifts, interatomic distances, atom-atom interaction energies, and atomic charges for partial structures and conformers of α-D-glucopyranose, β-D-glucopyranose, and α-D-galactopyranose built up by introducing OH groups into 2-methyltetrahydropyran stepwisely. For the counterclockwise conformers, the most marked effects on the NMR shift and the charge on the OH1 proton are produced by OH2, those of OH3 and OH4 being somewhat smaller. This argues for a diminishing cooperative effect. The effect of OH6 depends on the configuration of the hydroxymethyl group and the position, axial or equatorial, of OH4, which controls hydrogen bonding in the 1,3-diol motif. Variations in the interaction energies reveal that a "new" hydrogen bond is sometimes formed at the expense of a preexisting one, probably due to geometrical constraints. Whereas previous work showed that complexing a conformer with pyridine affects only the nearest neighbour, successive OH groups increase the interaction energy of the N⋯H1 hydrogen bond and reduce its length. Analogous results are obtained for the clockwise conformers. The interaction energies for C-H⋯OH hydrogen bonding between axial CH protons and OH groups in certain conformers are much smaller than for O-H⋯OH bonds but they are largely covalent, whereas those of the latter are predominantly coulombic. These interactions are modified by complexation with pyridine in the same way as O-H⋯OH interactions: the computed NMR shifts of the CH protons increase, the atom-atom distances are shorter, and interaction energies are enhanced.