Benchmark Energy & Geometry Database

These are a set of global and local minima of water clusters containing 2-10 waters. The geometry of each isomer was optimized using RI-MP2/aug-cc-pVDZ. The RI-MP2/CBS binding energy was calculated by extrapolating the RI-MP2/aug-cc-pVDZ//aug-cc-pVDZ, RI-MP2/aug-cc-pVTZ//aug-cc-pVDZ, and RI-MP2/aug-cc-pVQZ//aug-cc-pVDZ energies to their complete basis set limit using a 4-5 inverse 4-5 polynomial scheme that has been used extensively for water clusters. ΔCCSD(T) correction using aug-cc-pVDZ basis set was added to estimate the CCSD(T)/CBS binding energy. Zero-point vibrational energy and finite temperature corrections within the ideal-gas-rigid-rotor-harmonic-oscillator (IGRRHO) model using scaled and unscaled harmonic vibrational frequencies can be found in the published article.

Data set of large noncovalent complexes featuring mainly dispersion interactions (both pi-pi stacking and interaction of aliphatic hydrocarbons). The reference binding energies were determined by extrapolating the MP2 binding energies to the complete basis set limit and adding a ΔQCISD(T)/6-31G*(0.25) correction term in the case of CBH, C3A, C3GC, GGG and PHE complexes; whereas in the case of C2C2PD and GCGC complexes the Δ correction term was determined at the QCISD(T)/”aug”-cc-pVDZ (cf. Mol.Phys 2010, 108, 249-257) and CCSD(T)/6-31G**(0.25,0.15) level of theory, respectively.

A set of 24 small noncovalent complexes featuring a variety of interaction motifs. The geometries had been optimized at the CCSD(T)/CBS level. CCSD(T) interaction energies had been extrapolated from a series of aug-cc-pV(T,Q,5) basis sets. The contributions of core correlation and scalar relativistic effects (4th order DKH amiltonian) had been determined at CCSD(T) level. Finally, an estimate of higher-order contributions to correlation energy had been calculated using CCSDT(Q) in 6-31G**(0.25,0.15) basis set.

A set of 40 noncovalent complexes of organic halides, halohydrides and halogen molecules where the halogens participate in a variety of interaction types. The set, named X40, covers electrostatic interactions, London dispersion, hydrogen bonds, halogen bonding, halogen-π interactions and stacking of halogenated aromatic molecules. Interaction energies at equilibrium geometries were calculated using a composite CCSD(T)/CBS scheme where the CCSD(T) contribution is calculated using triple-zeta basis sets with diffuse functions on all atoms but hydrogen.

Geometries were constructed by scaling the closest intermolecular distance in the complexes by a factor of 0.8, 0.85, 0.9, 0.95, 1.0, 1.05, 1.1, 1.25, 1.5 and 2.0, starting from MP2/cc-pVTZ geometry. The benchmark CCSD(T)/CBS interaction energies are based on MP2/CBS calculations in aug-cc-pVTZ and aug-cc-pVQZ basis sets and CCSD(T) correction calculated in aug-cc-pVDZ basis set.

The set was developed for parameterization of hydrogen bonding correction for semiempirical QM methods. Geometries were constructed by scaling the closest intermolecular distance in the complexes by a factor of 0.9, 0.95, 1.0, 1.05, 1.1, 1.25, 1.5 and 2.0, starting from MP2/cc-pVTZ geometry. The benchmark CCSD(T)/CBS interaction energies are based on MP2/CBS calculations in aug-cc-pVTZ and aug-cc-pVQZ basis sets and CCSD(T) correction calculated in aug-cc-pVDZ basis set.

Geometries were constructed by scaling the closest intermolecular distance in the complexes by a factor of 0.9, 0.95, 1.0, 1.05, 1.1, 1.25, 1.5 and 2.0, starting from MP2/cc-pVTZ geometry. The benchmark CCSD(T)/CBS interaction energies are based on MP2/CBS calculations in aug-cc-pVTZ and aug-cc-pVQZ basis sets and CCSD(T) correction calculated in aug-cc-pVDZ basis set.
Full text of the paper is available: S66.pdf
More data for download

"The set contains 23 hydrogen bonds featuring all possible combionations of the most common donor and acceptor groups; 23 dispersion-dominated complexes covering pi-pi, aliphatic-aliphatic and pi-aliphatic interactions; and 20 complexes with mixed electrostatic/dispersion interaction. The benchmark CCSD(T)/CBS interaction energies are based on MP2/CBS calculations in aug-cc-pVTZ and aug-cc-pVQZ basis sets and CCSD(T) correction calculated in aug-cc-pVDZ basis set.
Full text of the paper is available: S66.pdf
More data for download
Update: More accurate CCSD(T)/CBS calculations from JCTC 7, 3466 (2011) available - CCSD(T) contribution in heavy-aug-ccPVTZ and extrapolated from heavy-aug-ccPV(D,T)Z. To distinguish the different CCSD(T)/CBS setups in the table, the basis set is listed in parenthesis."

Geometries of noncovalent complexes from the S22 dataset were displaced along intermolecular axis, forming one shortened and three elongated (0.9, 1.2, 1.5 and 2.0 times the original intermolecular distance) structures. The dataset also includes the original geometry (labeled 1.0). CCSD(T)/CBS interaction energies consistent with the original S22 work have been calculated.

A set of 24 pairs of amino acid side chain interactions based on X-ray crystal structures with resolution of 2.0 A or better. The pairs have been selected to represent the most typical interactions between side-chains in proteins. The side-chains were truncated at CA atom and only hydrogens were optimized with TPSS functional with TZVP basis. Interaction energies were calculated at various levels ranging from highly accurate ab initio methods CCSD(T)|CBS to forcefields Amber parm03 and OPLS-AA/L. The decomposition of interaction energies was done with DFT-SAPT method. The effect of solvent was studied with DFT-D method and PCM implicit solvent model.

A detailed quantum chemical study on five peptides (WG, WGG, FGG, GGF and GFA) containing the residues phenylalanyl (F), glycyl (G), tryptophyl (W) and alanyl (A)—where F and W are of aromatic character—is presented. When investigating isolated small peptides, the dispersion interaction is the dominant attractive force in the peptide backbone–aromatic side chain intramolecular interaction. Consequently, an accurate theoretical study of these systems requires the use of a methodology covering properly the London dispersion forces. For this reason we have assessed the performance of the MP2, SCS-MP2, MP3, TPSS-D, PBE-D, M06-2X, BH&H, TPSS, B3LYP, tight-binding DFT-D methods and ff99 empirical force field compared to CCSD(T)/complete basis set (CBS) limit benchmark data. All the DFT techniques with a ‘-D’ symbol have been augmented by empirical dispersion energy while the M06-2X functional was parameterized to cover the London dispersion energy. For the systems here studied we have concluded that the use of the ff99 force field is not recommended mainly due to problems concerning the assignment of reliable atomic charges. Tight-binding DFT-D is efficient as a screening tool providing reliable geometries. Among the DFT functionals, the M06-2X and TPSS-D show the best performance what is explained by the fact that both procedures cover the dispersion energy. The B3LYP and TPSS functionals—not covering this energy—fail systematically. Both, electronic energies and geometries obtained by means of the wave-function theory methods compare satisfactorily with the CCSD(T)/CBS benchmark data.Conformer energies are set relative to average for given peptide in each method.

These are the complexes of halogemethanes with substituted fluorohalomethanes with formaldehyde (H3CX…OCH2 and F3CX...OCH2, X=Cl, Br, I). Very high level binding energies have been obtained for these complexes, the highest level of theory described here is CCSD(T)/aug-cc-pVQZ. For complexes containing Bromine and Iodine the halogen atom is described using the aug-cc-pVQZ-PP basis set, which uses pseudopotentials to describe the atomic core. These pseudopotentials also implicitly include relativistic effects, which can be important for such large atoms.

These are the complexes that were added to the S22 set in order to have more single hydrogen bonding complexes. The methanol dimer and the methanol formaldehyde dimer were optimized at the MP2/cc-pVTZ level of theory. The structures for methyl amide dimer (α) and methyl amide dimer (β) are derived from the crystal structure of Rubredoxin (PDB ID 1RB9), where α came from an α-helix and β came from a β-sheet. Hydrogen atom positions for these two structures were optimized at the DFT/TPSS/TZVP level of theory, heavy (non-hydrogen) atoms were not allowed to move from their crystal structure positions. The reference binding energies were determined by extrapolating the MP2 binding energies to the complete basis set limit and adding a ΔCCSD(T) correction term that was obtained with the aug-cc-pVDZ basis set.

S22 set consists of small to relatively large (30 atoms) complexes of common molecules containing only C, N, O and H, and single, double and triple bonds. Most typical noncovalent interactions, such as hydrogen bonds (XHY), dispersion interactions (stacked parallel, T-shaped), and mixed electrostatic-dispersion interactions are represented. A total of 22 complexes are divided into three subgroups: (i) hydrogen bonded complexes; (ii) complexes with predominant dispersion stabilization; (iii) mixed complexes in which electrostatic and dispersion contributions are similar in magnitude. Cunterpoise-corrected gradient optimization was used to obtain the geometries. The smallest complexes were optimized by the CCSD(T) method (numerical gradients) using cc-pVTZ and cc-pVQZ basis sets without counterpoise correction. We believe that our S22 set will manage to represent non-covalent interactions in biological molecules in a balanced way and that it will help to design and test fast computational tools for biologically oriented applications.

A set of 124 nucleic bases complexes and 19 amino acid complexes compiled from several publications. All interaction energies are at the CCSD(T)/CBS level.