A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

Comparison of some dispersion-corrected and traditional functionals with CCSD(T) and MP2 ab initio methods: dispersion, induction, and basis set superposition error

We compare dispersion and induction interactions for noble gas dimers and for Ne, methane, and 2-butyne with HF and LiF using a variety of functionals (including some specifically parameterized to evaluate dispersion interactions) with ab initio methods including CCSD(T) and MP2. We see that inductive interactions tend to enhance dispersion and may be accompanied by charge-transfer. We show that the functionals do not generally follow the expected trends in interaction energies, basis set superposition errors (BSSE), and interaction distances as a function of basis set size. The functionals parameterized to treat dispersion interactions often overestimate these interactions, sometimes by quite a lot, when compared to higher level calculations. Which functionals work best depends upon the examples chosen. The B3LYP and X3LYP functionals, which do not describe pure dispersion interactions, appear to describe dispersion mixed with induction about as accurately as those parametrized to treat dispersion. We observed significant differences in high-level wavefunction calculations in a basis set larger than those used to generate the structures in many of the databases. We discuss the implications for highly parameterized functionals based on these databases, as well as the use of simple potential energy for fitting the parameters rather than experimentally determinable thermodynamic state functions that involve consideration of vibrational states.

A reinvestigation of the dimer of para-benzoquinone and pyrimidine with MP2, CCSD(T), and DFT using functionals including those designed to describe dispersion

We reevaluate the interaction of pyridine and p-benzoquinone using functionals designed to treat dispersion. We compare the relative energies of four different structures: stacked, T-shaped (identified for the first time), and two planar H-bonded geometries using these functionals (B97-D, ωB97x-D, M05, M05-2X, M06, M06L, and M06-2X), other functionals (PBE1PBE, B3LYP, X3LYP), MP2, and CCSD(T) using basis sets as large as cc-pVTZ. The functionals designed to treat dispersion behave erratically as the predictions of the most stable structure vary considerably. MP2 predicts the experimentally observed structure (H-bonded) to be the least stable, while single-point CCSD(T) at the MP2 optimized geometry correctly predicts the observed structure to be the most stable. We have confirmed the assignment of the experimental structure using new calculations of the vibrational frequency shifts previously used to identify the structure. The MP2/cc-pVTZ vibrational calculations are in excellent agreement with the observations. All methods used to calculate the energies provide vibrational shifts that agree with the observed structure even though most do not predict this structure to be most stable. The implications for evaluating possible π-stacking in biologically important systems are discussed.

Can a C-H···O interaction be a determinant of conformation?

Whether nonconventional hydrogen bonds, such as the C-H···O interaction, are a consequence or a determinant of conformation is a long-running and unresolved issue. Here we outline a solid-state and quantum mechanical study designed to investigate whether a C-H···O interaction can override the significant trans-planar conformational preferences of α-fluoroamide substituents. A profound change in dihedral angle from trans-planar((OCCF)) to cis-planar((OCCF)) observed on introducing an acceptor group for a C-H···O hydrogen bond is consistent with this interaction functioning as a determinant of conformation in certain systems. This testifies to the potential influence of the C-H···O hydrogen bond and is consistent with the assignment of this interaction as a contributor to overall conformation in both model and natural systems.

Density functional theory study of β-hairpins in antiparallel β-sheets, a new classification based upon H-bond topology

We present a new classification of β-turns specific to antiparallel β-sheets based upon the topology of H-bond formation. This classification results from ONIOM calculations using B3LYP/D95** density functional theory and AM1 semiempirical calculations as the high and low levels, respectively. We chose acetyl(Ala)(6)NH(2) as a model system as it is the simplest all-alanine system that can form all the H-bonds required for a β-turn in a sheet. Of the 10 different conformations we have found, the most stable structures have C(7) cyclic H-bonds in place of the C(10) interactions specified in the classic definition. Also, the chiralities specified for residues i + 1 and i + 2 in the classic definition disappear when the structures are optimized using our techniques, as the energetic differences among the four diastereomers of each structure are not substantial for 8 of the 10 conformations.

Aqueous solvation of polyalanine α-helices with specific water molecules and with the CPCM and SM5.2 aqueous continuum models using density functional theory

We present density functional theory (DFT) calculations at the X3LYP/D95(d,p) level on the solvation of polyalanine α-helices in water. The study includes the effects of discrete water molecules and the CPCM and AMSOL SM5.2 solvent continuum model both separately and in combination. We find that individual water molecules cooperatively hydrogen-bond to both the C- and N-termini of the helix, which results in increases in the dipole moment of the helix/water complex to more than the vector sum of their individual dipole moments. These waters are found to be more stable than in bulk solvent. On the other hand, individual water molecules that interact with the backbone lower the dipole moment of the helix/water complex to below that of the helix itself. Small clusters of waters at the termini increase the dipole moments of the helix/water aggregates, but the effect diminishes as more waters are added. We discuss the somewhat complex behavior of the helix with the discrete waters in the continuum models.

A Density Functional Theory Evaluation of Hydrophobic Solvation: Ne, Ar and Kr in a 50-Water Cluster. Implications for the Hydrophobic Effect

The physical explanation for the hydrophobic effect has been the subject of disagreement. Physical organic chemists tend to use a explanation related to pressure, while many biochemists prefer an explanation that involves decreased entropy of the aqueous solvent. We present DFT calculations at the B3LYP/6-31G(d,p) and X3LYP/6-31G(d,p) levels on the solvation of three noble gases (Ne, Ar, and Kr) in clusters of 50 waters. Vibrational analyses show no substantial decreases in the vibrational entropies of the waters in any of the three clusters. The observed positive free energies of transfer from the gas phase or from nonpolar solvents to water appear to be due to the work needed to make a suitable hole in the aqueous solvent. We distinguish between hydrophobic solvations (explicitly studied here) and the hydrophobic effect that occurs when a solute (or transition state) can decrease its volume through conformational change (which is not possible for the noble gases).

Comparison of β-sheets of capped polyalanine with those of the tau-amyloid structures VQIVYK and VQIINK. A density functional theory study

We present ONIOM calculations using B3LYP/d95(d,p) as the high and AM1 as the low level on parallel β-sheets containing from two to ten strands of Ac-VQIVYK-NHMe and Ac-VQIINK-NHMe, as well as both parallel and antiparallel Ac-AAAAAA-NHMe. We find that the first two sequences form more stable sheets due to the additional H-bonding between the Q's in the side chains of both and the N's in the side chain of Ac-VQIINK-NHMe. However, the H-bonds in the amyloid chains are significantly weakened by attractive strain, which prevents all the interstrand H-bonds from achieving their optimal geometries simultaneously and requires high distortion energies for the individual strands in the sheets. The antiparallel Ac-AAAAAA-NHMe's are generally more stable and more cooperative than the parallel sheets, principally due to the higher distortion energies of the latter.

The Effects of Regularly Spaced Glutamine Substitutions on Alpha-Helical Peptide Structures. A DFT/ONIOM Study

The side-chains of the residues of glutamine (Q) and asparagine (N) contain amide groups. These can H-bond to each other in patterns similar to those of the backbone amides in α-helices. We show that mutating multiple Q's for alanines (A's) in a polyalanine helix stabilizes the helical structure, while similar mutations with multiple N's do not. We suggest that modification of peptides by incorporating Q's in such positions can make more robust helices that can be used to test the effects of secondary structures in biochemical experiments linked to proteins with variable structures such as tau and α-synuclein.

The effect of polarization on multiple hydrogen-bond formation in models of self-assembling materials

We report density functional theory calculations at the B3LYP/D95(d,p) level on several different cyclic H-bonding dimers, where the monomers of each are connected by a pair of N-H···O=C H-bonding interactions, and the H-bonding donors and acceptors on each monomer are separated by polarizable spacers. Depending on the structures, the individual H-bonds vary in strength (enthalpy) by over a factor of four, from 2.41 to 10.99 kcal/mol. We attribute most of the variation in interaction energies to differences in the extent of polarization due to each of the H-bonds, which can either combine constructively or destructively. The dipole-dipole interactions between the pair of H-bonds also contribute somewhat to the relative stabilities. The relevance of these results to the design of self-assembling materials is discussed.

Aggregation of capped hexaglycine strands into hydrogen-bonding motifs representative of pleated and rippled β-sheets, collagen, and polyglycine I and II crystal structures. A density functional theory study

We compare the energies and enthalpies of inter-action of three- and seven-stranded capped polyglycine aggregates in both the pleated and rippled antiparallel and parallel β-sheet structures as well as the collagenic (three-strand) or polyglycine II-like (seven-strand) forms using density functional theory at the B3LYP/D95(d,p) level. We present the overall interaction energies as broken down into pure H-bonding between the strands at the geometries they assume in the aggregates and the distortion energies required to achieve those geometries starting from the fully relaxed single strands. While the antiparallel sheets represent the most stable structures for both the three- and seven-strand structures, the pure H-bonding interactions are the smallest for these structures. The overall interaction energies are dominated by the energy required to distort the relaxed polyglycine strands rather than the H-bonding energies. The antiparallel β-sheet constrained to C(s) symmetry has a lower enthalpy, but higher energy, of interaction than the fully optimized structure.