Quantum Mechanical Assessment of Protein-Ligand Hydrogen Bond Strength Patterns: Insights from Semiempirical Tight-Binding and Local Vibrational Mode Theory.

Hydrogen bonds (HB)s are the most abundant motifs in biological systems. They play a key role in determining protein-ligand binding affinity and selectivity. We designed two pharmaceutically beneficial HB databases, database A including ca. 12,000 protein-ligand complexes with ca. 22,000 HBs and their geometries, and database B including ca. 400 protein-ligand complexes with ca. 2200 HBs, their geometries, and bond strengths determined via our local vibrational mode analysis. We identified seven major HB patterns, which can be utilized as a de novo QSAR model to predict the binding affinity for a specific protein-ligand complex. Glycine was reported as the most abundant amino acid residue in both donor and acceptor profiles, and N-H⋯O was the most frequent HB type found in database A. HBs were preferred to be in the linear range, and linear HBs were identified as the strongest. HBs with HB angles in the range of 100-110°, typically forming intramolecular five-membered ring structures, showed good hydrophobic properties and membrane permeability. Utilizing database B, we found a generalized Badger's relationship for more than 2200 protein-ligand HBs. In addition, the strength and occurrence maps between each amino acid residue and ligand functional groups open an attractive possibility for a novel drug-design approach and for determining drug selectivity and affinity, and they can also serve as an important tool for the hit-to-lead process.

Critical assessment of the FeC and CO bond strength in carboxymyoglobin: a QM/MM local vibrational mode study.

The interplay between FeC and CO bonding in carboxymyoglobin (MbCO) and the role of potential hydrogen bonding between the CO moiety and the side chains of the surrounding protein amino acids have been the subject of numerous experimental and theoretical studies. In this work, we present a quantitative measure for the intrinsic FeC and CO bond strength in MbCO, as well as for CO⋯H bonding, based on the local vibrational mode analysis, originally developed by Konkoli and Cremer. We investigated a gas phase model, two models of the wild-type protein, and 17 protein mutations that change the distal polarity of the heme pocket, as well as two protein mutations of the heme porphyrin ring. Based on local mode force constants, we could quantify for the first time the suggested inverse relationship between the CO and FeC bond strength, the strength of CO⋯H bonding, and how it weakens the CO bond. Combined with the natural orbital analysis, we could also confirm the key role of π back donation between Fe and the CO moiety in determining the FeC bond strength. We further clarified that CO and FeC normal modes couple with other protein motions in the protein environment. Therefore, normal mode frequencies/force constants are not suited as bond strength descriptors and instead their local mode counterparts should be used. Our comprehensive results provide new guidelines for the fine-tuning of existing and the design of MbCO models with specific FeC, CO, and CO⋯H bond strengths.Graphical abstract.

In Situ Assessment of Intrinsic Strength of X-I⋯OA-Type Halogen Bonds in Molecular Crystals with Periodic Local Vibrational Mode Theory.

Periodic local vibrational modes were calculated with the rev-vdW-DF2 density functional to quantify the intrinsic strength of the X-I⋯OA-type halogen bonding (X = I or Cl; OA: carbonyl, ether and N-oxide groups) in 32 model systems originating from 20 molecular crystals. We found that the halogen bonding between the donor dihalogen X-I and the wide collection of acceptor molecules OA features considerable variations of the local stretching force constants (0.1-0.8 mdyn/Å) for I⋯O halogen bonds, demonstrating its powerful tunability in bond strength. Strong correlations between bond length and local stretching force constant were observed in crystals for both the donor X-I bonds and I⋯O halogen bonds, extending for the first time the generalized Badger's rule to crystals. It is demonstrated that the halogen atom X controlling the electrostatic attraction between the σ -hole on atom I and the acceptor atom O dominates the intrinsic strength of I⋯O halogen bonds. Different oxygen-containing acceptor molecules OA and even subtle changes induced by substituents can tweak the n → σ ∗ (X-I) charge transfer character, which is the second important factor determining the I⋯O bond strength. In addition, the presence of the second halogen bond with atom X of the donor X-I bond in crystals can substantially weaken the target I⋯O halogen bond. In summary, this study performing the in situ measurement of halogen bonding strength in crystalline structures demonstrates the vast potential of the periodic local vibrational mode theory for characterizing and understanding non-covalent interactions in materials.

Quantitative Assessment of B-B-B, B-Hb -B, and B-Ht Bonds: From BH3 to B12 H122.

We report the thermodynamic stabilities and the intrinsic strengths of three-center-two-electron B-B-B and B-Hb -B bonds ( Hb : bridging hydrogen), and two-center-two-electron B-Ht bonds ( Ht : terminal hydrogen) which can be served as a new, effective tool to determine the decisive role of the intermediates of hydrogenation/dehydrogenation reactions of borohydride. The calculated heats of formation were obtained with the G4 composite method and the intrinsic strengths of B-B-B, B-Hb -B, and B-Ht bonds were derived from local stretching force constants obtained at the B3LYP-D2/cc-pVTZ level of theory for 21 boron-hydrogen compounds, including 19 intermediates. The Quantum Theory of Atoms in Molecules (QTAIM) was used to deepen the inside into the nature of B-B-B, B-Hb -B, and B-Ht bonds. We found that all of the experimentally identified intermediates hindering the reversibility of the decomposition reactions are thermodynamically stable and possess strong B-B-B, B-Hb -B, and B-Ht bonds. This proves that thermodynamic data and intrinsic B-B-B, B-Hb -B, and B-Ht bond strengths form a new, effective tool to characterize new (potential) intermediates and to predict their role for the reversibility of the hydrogenation/dehydrogenation reactions.

Quantitative Assessment of Tetrel Bonding Utilizing Vibrational Spectroscopy.

A set of 35 representative neutral and charged tetrel complexes was investigated with the objective of finding the factors that influence the strength of tetrel bonding involving single bonded C, Si, and Ge donors and double bonded C or Si donors. For the first time, we introduced an intrinsic bond strength measure for tetrel bonding, derived from calculated vibrational spectroscopy data obtained at the CCSD(T)/aug-cc-pVTZ level of theory and used this measure to rationalize and order the tetrel bonds. Our study revealed that the strength of tetrel bonds is affected by several factors, such as the magnitude of the σ-hole in the tetrel atom, the negative electrostatic potential at the lone pair of the tetrel-acceptor, the positive charge at the peripheral hydrogen of the tetrel-donor, the exchange-repulsion between the lone pair orbitals of the peripheral atoms of the tetrel-donor and the heteroatom of the tetrel-acceptor, and the stabilization brought about by electron delocalization. Thus, focusing on just one or two of these factors, in particular, the σ-hole description can only lead to an incomplete picture. Tetrel bonding covers a range of -1.4 to -26 kcal/mol, which can be strengthened by substituting the peripheral ligands with electron-withdrawing substituents and by positively charged tetrel-donors or negatively charged tetrel-acceptors.

Quantitative Assessment of Halogen Bonding Utilizing Vibrational Spectroscopy.

A total of 202 halogen-bonded complexes have been studied using a dual-level approach: ωB97XD/aug-cc-pVTZ was used to determine geometries, natural bond order charges, charge transfer, dipole moments, electron and energy density distributions, vibrational frequencies, local stretching force constants, and relative bond strength orders n. The accuracy of these calculations was checked for a subset of complexes at the CCSD(T)/aug-cc-pVTZ level of theory. Apart from this, all binding energies were verified at the CCSD(T) level. A total of 10 different electronic effects have been identified that contribute to halogen bonding and explain the variation in its intrinsic strength. Strong halogen bonds are found for systems with three-center-four-electron (3c-4e) bonding such as chlorine donors in interaction with substituted phosphines. If halogen bonding is supported by hydrogen bonding, genuine 3c-4e bonding can be realized. Perfluorinated diiodobenzenes form relatively strong halogen bonds with alkylamines as they gain stability due to increased electrostatic interactions.

Quantitative Assessment of Aromaticity and Antiaromaticity Utilizing Vibrational Spectroscopy.

Vibrational frequencies can be measured and calculated with high precision. Therefore, they are excellent tools for analyzing the electronic structure of a molecule. In this connection, the properties of the local vibrational modes of a molecule are best suited. A new procedure is described, which utilizes local CC stretching force constants to derive an aromaticity index (AI) that quantitatively determines the degree of π-delocalization in a cyclic conjugated system. Using Kekulé benzene as a suitable reference, the AIs of 30 mono- and polycyclic conjugated hydrocarbons are calculated. The AI turns out to describe π-delocalization in a balanced way by correctly describing local aromatic units, peripheral, and all-bond delocalization. When comparing the AI with the harmonic oscillator model of AI, the latter is found to exaggerate the antiaromaticity of true and potential 4n π-systems or to wrongly describe local aromaticity. This is a result of a failure of the Badger relationship (the shorter bond is always the stronger bond), which is only a rule and therefore cannot be expected to lead to an accurate description of the bond strength via the bond length. The AI confirms Clar's rule of disjoint benzene units in many cases, but corrects it in those cases where peripheral π-delocalization leads to higher stability. [5]-, [6]-, [7]-Circulene and Kekulene are found to be aromatic systems with varying degree of delocalization. Properties of the local vibrational modes provide an accurate description of π-delocalization and an accurate AI.

Quantitative assessment of the multiplicity of carbon-halogen bonds: carbenium and halonium ions with F, Cl, Br, and I.

CX (X = F, Cl, Br, I) and CE bonding (E = O, S, Se, Te) was investigated for a test set of 168 molecules using the local CX and CE stretching force constants k(a) calculated at the M06-2X/cc-pVTZ level of theory. The stretching force constants were used to derive a relative bond strength order (RBSO) parameter n. As alternative bond strength descriptors, bond dissociation energies (BDE) were calculated at the G3 level or at the two-component NESC (normalized elimination of the small component)/CCSD(T) level of theory for molecules with X = Br, I or E = Se, Te. RBSO values reveal that both bond lengths and BDE values are less useful when a quantification of the bond strength is needed. CX double bonds can be realized for Br- or I-substituted carbenium ions where as suitable reference the double bond of the corresponding formaldehyde homologue is used. A triple bond cannot be realized in this way as the diatomic CX(+) ions with a limited π-donor capacity for X are just double-bonded. The stability of halonium ions increases with the atomic number of X, which is reflected by a strengthening of the fractional (electron-deficient) CX bonds. An additional stability increase of up to 25 kcal/mol (X = I) is obtained when the X(+) ion can form a bridged halonium ion with ethene such that a more efficient 2-electron-3-center bonding situation is created.