Reply to “Comment on ‘Natural Bond Orbitals and the Nature of the Hydrogen Bond’”

Importance of Noncovalent Interactions Involving Sulfur Atoms in Thiopeptide Antibiotics─Glycothiohexide α and Nocathiacin I

Noncovalent interactions involving sulfur atoms play essential roles in protein structure and function by significantly contributing to protein stability, folding, and biological activity. Sulfur is a highly polarizable atom that can participate in many types of noncovalent interactions including hydrogen bonding, sulfur-π interactions, and S-lone pair interactions, but the impact of these sulfur-based interactions on molecular recognition and drug design is still often underappreciated. Here, we examine, using quantum chemical calculations, the roles of sulfur-based noncovalent interactions in complex naturally occurring molecules representative of thiopeptide antibiotics: glycothiohexide α and its close structural analogue nocathiacin I. While donor-acceptor orbital interactions make only very small contributions, electrostatic and dispersion contributions are predicted to be significant in many cases. In pursuit of understanding the magnitudes and nature of these noncovalent interactions, we made potential structural modifications that could significantly expand the chemical space of effective thiopeptide antibiotics.

Physical mechanisms of intermolecular interactions from symmetry-adapted perturbation theory

Symmetry-adapted perturbation theory (SAPT) is a method for computational studies of noncovalent interactions between molecules. This method will be discussed here from the perspective of establishing the paradigm for understanding mechanisms of intermolecular interactions. SAPT interaction energies are obtained as sums of several contributions. Each contribution possesses a clear physical interpretation as it results from some specific physical process. It also exhibits a specific dependence on the intermolecular separation R. The four major contributions are the electrostatic, induction, dispersion, and exchange energies, each due to a different mechanism, valid at any R. In addition, at large R, SAPT interaction energies are seamlessly connected with the corresponding terms in the asymptotic multipole expansion of interaction energy in inverse powers of R. Since such expansion explicitly depends on monomers' multipole moments and polarizabilities, this connection provides additional insights by rigorously relating interaction energies to monomers' properties.

Chameleonic Metal-bound Isocyanides: π-Donating CuI-center Imparts a Nucleophilicity to the Isocyanide Carbon toward Halogen Bonding

In the structures of the isostructural cocrystals [CuI3(CNXyl)3]·CHX3 (X = Br, I), two adjacent CuI-bound isocyanide groups, whose carbon lone pairs are blocked by the ligation, exhibit nucleophilic properties induced...

Bonding analysis of water clusters using quasi-atomic orbitals

The quasi-atomic orbital (QUAO) bonding analysis introduced by Ruedenberg and co-workers is used to develop an understanding of the hydrogen bonds in small water clusters, from the dimer through the hexamer (bag, boat, book, cyclic, prism and cage conformers). Using kinetic bond orders as a metric, it is demonstrated that as the number of waters in simple cyclic clusters increases, the hydrogen bonds strengthen, from the dimer through the cyclic hexamer. However, for the more complex hexamer isomers, the strength of the hydrogen bonds varies, depending on whether the cluster contains double acceptors and/or double donors. The QUAO analysis also reveals the three-center bonding nature of hydrogen bonds in water clusters.

Electrostatics, Charge Transfer, and the Nature of the Halide-Water Hydrogen Bond

Binary halide-water complexes X^-(H₂O) are examined by means of symmetry-adapted perturbation theory, using charge-constrained promolecular reference densities to extract a meaningful charge-transfer component from the induction energy. As is known, the X^-(H₂O) potential energy surface (for X = F, Cl, Br, or I) is characterized by symmetric left and right hydrogen bonds separated by a C_2v-symmetric saddle point, with a tunneling barrier height that is <2 kcal/mol except in the case of F^-(H₂O). Our analysis demonstrates that the charge-transfer energy is correspondingly small (<2 kcal/mol except for X = F), considerably smaller than the electrostatic interaction energy. Nevertheless, charge transfer plays a crucial role determining the conformational preferences of X^-(H₂O) and provides a driving force for the formation of quasi-linear X··· H-O hydrogen bonds. Charge-transfer energies correlate well with measured O-H vibrational redshifts for the halide-water complexes and also for OH^-(H₂O) and NO₂^-(H₂O), providing some indication of a general mechanism.

A reliable and efficient resonance theory based on analysis of DFT wave functions

Due to methodological difficulties and limitations of applicability, a quantitative bonding analysis based on the theory of resonance is presently not as convenient and popular as that based on the molecular orbital (MO) methods. Here, we propose an efficient quantitative resonance theory by expanding the DFT wave function in terms of a complete set of Lewis structures. By rigorously separating the resonance subsystem represented by a set of localized MOs, this approach is able to treat large molecules, nonplanar π-conjugate systems, and bonding systems mixing both σ and π electrons. Assessment in 2c-2e systems suggests a new projection-weighted symmetric orthogonalization method to evaluate the weights of resonance contributors, which overcomes the drawbacks of other weighting schemes. Applications to benzene, naphthalene and chlorobenzene show that the present method is insensitive to the basis set employed in the DFT calculations, and to the choices of the independent Lewis set determined by Rumer's rule. Advanced applications to diverse chemical problems provide unique and valuable insights into the understanding of hydrogen bonding, the π substituent effect on benzene, and the mechanism of Diels-Alder reactions.

Comparison of Chemical and Interpretative Methods: the Carbon-Boron π-Bond as a Test Case*

Quantum chemical calculations and NBO, ETS-NOCV, QTAIM and ELF interpretative approaches have been carried out on C-donor ligand-stabilized dihydrido borenium cations. Numerous descriptors of the C-B π-bond strength obtained from orbital localization, energy partitioning or topological methods as well as from structural and chemical parameters have been calculated for 39 C-donor ligands including N-heterocyclic carbenes and carbones. Comparison of the results allows the identification of relative and absolute descriptors of the π interaction. For both families of descriptors excellent correlations are obtained. This enables the establishment of a π-donation capability scale and shows that the interpretative methods, despite their conceptual differences, describe the same chemical properties. These results also reveal noticeable shortcomings in these popular methods, and some precautions that need to be taken to interpret their results adequately.

Chemical Bonding: The Journey from Miniature Hooks to Density Functional Theory

Our modern understanding of chemistry is predicated upon bonding interactions between atoms and ions resulting in the assembly of all of the forms of matter that we encounter in our daily life. It was not always so. This review article traces the development of our understanding of bonding from prehistory, through the debates in the 19th century C.E. bearing on valence, to modern quantum chemical models and beyond.

Quantitative decomposition of resonance-assisted hydrogen bond energy in β-diketones into resonance and hydrogen bonding (π- and σ-) components using molecular tailoring and function-based approaches

Using the molecular tailoring and function-based approaches allows one to divide the energy of the O─H⋯O═C resonance-assisted hydrogen bond in a series of the β-diketones into resonance and hydrogen bonding components. The magnitude of the resonance component is assessed as about 6 kcal mol^-1 . This value increases by ca. 1 kcal mol^-1 on going from the weak to strong resonance-assisted hydrogen bonding. The magnitude of the hydrogen bonding component varies in the wide range from 2 to 20 kcal mol^-1 depending on the structure of the β-diketone in question.

Rationalizing the diversity of amide-amide H-bonding in peptides using the natural bond orbital method

Natural bond orbital (NBO) analysis of electron delocalization in a series of capped isolated peptides is used to diagnose amide-amide H-bonding and backbone-induced hyperconjugative interactions, and to rationalize their spectral effects. The sum of the stabilization energies corresponding to the interactions between NBOs that are involved in the H-bonding is demonstrated as an insightful indicator for the H-bond strength. It is then used to decouple the effect of the H-bond distance from that, intrinsic, of the donor/acceptor relative orientation, i.e., the geometrical approach. The diversity of the approaches given by the series of peptides studied enables us to illustrate the crucial importance of the approach when the acceptor is a carbonyl group, and emphasizes that efficient approaches can be achieved despite not matching the usual picture of a proton donor directly facing a lone pair of the proton acceptor, i.e., that encountered in intermolecular H-bonds. The study also illustrates the role of backbone flexibility, partly controlled by backbone-amide hyperconjugative interactions, in influencing the equilibrium structures, in particular by frustrating or enhancing the HB for a given geometrical approach. Finally, the presently used NBO-based HB strength indicator enables a fair prediction of the frequency of the proton donor amide NH stretching mode, but this simple picture is blurred by ubiquitous hyperconjugative effects between the backbone and amide groups, whose magnitude can be comparable to that of the weakest H-bonds.

Water in protein hydration and ligand recognition

This review describes selected basics of water in biomolecular recognition. We focus on a qualitative understanding of the most important physical aspects, how these change in magnitude between bulk water and protein environment, and how the roles that water plays for proteins arise from them. These roles include mechanical support, thermal coupling, dielectric screening, mass and charge transport, and the competition with a ligand for the occupation of a binding site. The presence or absence of water has ramifications that range from the thermodynamic binding signature of a single ligand up to cellular survival. The large inhomogeneity in water density, polarity and mobility around a solute is hard to assess in experiment. This is a source of many difficulties in the solvation of protein models and computational studies that attempt to elucidate or predict ligand recognition. The influence of water in a protein binding site on the experimental enthalpic and entropic signature of ligand binding is still a point of much debate. The strong water‐water interaction in enthalpic terms is counteracted by a water molecule's high mobility in entropic terms. The complete arrest of a water molecule's mobility sets a limit on the entropic contribution of a water displacement process, while the solvent environment sets limits on ligand reactivity.

Nine questions on energy decomposition analysis

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

Electrostatics and Dispersion in X-H···Y (X = C, N, O; Y = N, O) Hydrogen Bonds and Their Role in X-H Vibrational Frequency Shifts

The frequency shifts of donor stretching vibration in X-H···Y (X = C, N, O; Y = N, O) hydrogen-bonded complexes of phenylacetylene, indole, and phenol are linearly correlated with the electrostatic component of the interaction energy. This linear correlation suggests that the electrostatic component, which is the first-order perturbative correction to the stabilization energy, is essentially localized on the X-H group. The linear correlation suggests that the electrostatic tuning rate, which is a measure of the X-H oscillator to undergo shifts upon hydrogen bonding per unit increase in the electrostatic component of the stabilization energy, was found to be in the order of O-H > N-H > C-H. Interestingly, for each of the donor groups, viz., C-H, N-H, and O-H, the vibrational frequency shifts were inversely correlated to the dipole moment of the acceptor separately, which is counterintuitive vis-à-vis the electrostatic component. This implies that extrapolation to zero dipole moment of the acceptor will yield very large shifts in the hydrogen-bonded X-H stretching frequencies. The trends in the variation of the dispersion and exchange-repulsion components and the total interaction energy vis-à-vis frequency shifts of donor stretching vibration are similar for hydrogen-bonded complexes of phenylacetylene, indole, and phenol. Furthermore, it was observed that the vibrational frequency shifts of all of the complexes are linearly correlated with the charge transfer from the filled orbital of the hydrogen acceptor to the vacant antibonding (σ*) orbital of the X-H donor group on the basis of natural bonding orbital calculations.

On the Computational Characterization of Charge-Transfer Effects in Noncovalently Bound Molecular Complexes

Charge-transfer (CT) is an important binding force in the formation of intermolecular complexes, and there have been a variety of theoretical models proposed to quantify this effect. These approaches, which typically rely on a definition of a "CT-free" state based on a partition of the system, sometimes yield significantly different results for a given intermolecular complex. Two widely used definitions of the "CT-free" state, the absolutely localized molecular orbitals (ALMO) method (where only on-fragment orbital mixings are permitted) and the constrained density functional theory (CDFT) approach (where fragment electron populations are fixed), are carefully examined in this work. Natural bond orbital (NBO) and the regularized symmetry-adapted perturbation theory (SAPT) are also briefly considered. Results for the ALMO and CDFT definitions of CT are compared on a broad range of model systems, including hydrogen-bonding systems, borane complexes, metal-carbonyl complexes, and complexes formed by water and metal cations. For most of these systems, CDFT yields a much smaller equilibrium CT energy compared to that given by the ALMO-based definition. This is mainly because the CDFT population constraint does not fully inhibit CT, which means that the CDFT "CT-free" state is in fact CT-contaminated. Examples of this contamination include (i) matching forward and backward donation (e.g., formic acid dimer) and (ii) unidirectional CT without changing fragment populations. The magnitude of the latter effect is quantified in systems such as the water dimer by employing a 3-space density constraint in addition to the orbital constraint. Furthermore, by means of the adiabatic EDA, it is shown that several observable effects of CT, such as the "pyramidalization" of the planar BH₃ molecule upon the complexation with Lewis bases, already appear on the "CT-free" CDFT surface. These results reveal the essential distinctions between the ALMO and CDFT definitions of CT and suggest that the former is more consistent with accepted understanding of the role of CT in intermolecular binding.