Analysis of the NMR Spin−Spin Coupling Mechanism Across a H−Bond: Nature of the H-Bond in Proteins

Symmetry of Hydrogen Bonds: Application of NMR Method of Isotopic Perturbation and Relevance of Solvatomers

Short, strong, symmetric, low-barrier hydrogen bonds (H-bonds) are thought to be of special significance. We have been searching for symmetric H-bonds by using the NMR technique of isotopic perturbation. Various dicarboxylate monoanions, aldehyde enols, diamines, enamines, acid-base complexes, and two sterically encumbered enols have been investigated. Among all of these, we have found only one example of a symmetric H-bond, in nitromalonamide enol, and all of the others are equilibrating mixtures of tautomers. The nearly universal lack of symmetry is attributed to the presence of these H-bonded species as a mixture of solvatomers, meaning isomers (or stereoisomers or tautomers) that differ in their solvation environment. The disorder of solvation renders the two donor atoms instantaneously inequivalent, whereupon the hydrogen attaches to the less well solvated donor. We therefore conclude that there is no special significance to short, strong, symmetric, low-barrier H-bonds. Moreover, they have no heightened stability or else they would have been more prevalent.

Theoretical investigation on the improper hydrogen bond in κ-carrabiose⋯Y (Y = HF, HCl, HBr, NH3, H2O, and H2S) complexes

The nature of H-bonds in κ-carrabiose⋯Y (Y = HF, HCl, HBr, NH₃, H₂O, and H₂S) complexes was studied. For this aim, the structure of isolated κ-carrabiose was optimized using three global hybrids functional: B3LYP, PBE0, and M06-2X combined with 6-311G** basis set. Subsequently, the κ-carrabiose in the presence of HF, HCl, HBr, NH₃, H₂O, and H₂S was optimized using the CBS-4 M method. NBO analyses were then carried out at the MP2/6-311G** level of theory. A particular interest was focused on C₍₁₈₎-H₍₃₄₎⋯Y bond. The results reveal that the C₍₁₈₎-H₍₃₄₎⋯Y bond is an improper H-bond since a significant contraction of C₍₁₈₎-H₍₃₄₎ was observed during the complexation leading to a significant blueshifted stretching frequency. The NBO analyses have shown that the formation of the improper H-bonds C₍₁₈₎-H₍₃₄₎⋯Y (Y = F, Cl, Br, N, O, and S) is principally due to the increase of the s-character of the hybrid orbital in carbon atom (rehybridization) in κ-carrabiose⋯Y complexes. Regarding the polarization, it was proved that more the H-bond center (carbon in C₍₁₈₎-H₍₃₄₎⋯Y) becomes less positive, the hydrogen more positive, and Y more negative; more the contraction of the C₍₁₈₎-H₍₃₄₎ bond is important. It was also confirmed for intramolecular H-bonds in κ-carrabiose⋯Y complexes that the rehybridization is responsible for H-bonds nature either proper or improper.

Hydrogen bonding from a valence bond theory perspective: the role of covalency

A valence bond theory based method has been developed to decompose hydrogen bond energies into contributions from geometry, electrostatics, polarization and charge transfer. This decomposition method has been carried out for F-HFH, F-HOH2, F-HNH3, HO-HOH2, HO-HNH3, and H2N-HNH3. Localized valence bond self-consistent field (L-VBSCF) and localized breathing orbital valence bond (L-BOVB) calculations were performed at the PBEPBE/aug-cc-pVDZ optimized geometries. It is shown that inclusion of valence bond structures that explicitly include charge transfer account for at least 32% (likely over half) of the hydrogen bond energy of all systems studied, indicating the dominant role of covalency. This is in agreement with calculated bond lengths, geometry deformation energies, and polarization energies. Electrostatic effects were found to play only a minor role in contrast to some widely held ideas regarding the nature of hydrogen bonding.

Neutron Crystallography for the Study of Hydrogen Bonds in Macromolecules

The hydrogen bond (H bond) is one of the most important interactions that form the foundation of secondary and tertiary protein structure. Beyond holding protein structures together, H bonds are also intimately involved in solvent coordination, ligand binding, and enzyme catalysis. The H bond by definition involves the light atom, H, and it is very difficult to study directly, especially with X-ray crystallographic techniques, due to the poor scattering power of H atoms. Neutron protein crystallography provides a powerful, complementary tool that can give unambiguous information to structural biologists on solvent organization and coordination, the electrostatics of ligand binding, the protonation states of amino acid side chains and catalytic water species. The method is complementary to X-ray crystallography and the dynamic data obtainable with NMR spectroscopy. Also, as it gives explicit H atom positions, it can be very valuable to computational chemistry where exact knowledge of protonation and solvent orientation can make a large difference in modeling. This article gives general information about neutron crystallography and shows specific examples of how the method has contributed to structural biology, structure-based drug design; and the understanding of fundamental questions of reaction mechanisms.

Dispersion-corrected energy decomposition analysis for intermolecular interactions based on the BLW and dDXDM methods

As the simplest variant of the valence bond (VB) theory, the block-localized wave function (BLW) method defines the intermediate electron-localized state self-consistently at the DFT level and can be used to explore the nature of intermolecular interactions in terms of several physically intuitive energy components. Yet, it is unclear how the dispersion interaction affects such a kind of energy decomposition analysis (EDA) as standard density functional approximations neglect the long-range dispersion attractive interactions. Three electron densities corresponding to the initial electron-localized state, optimal electron-localized state, and final electron-delocalized state are involved in the BLW-ED approach; a density-dependent dispersion correction, such as the recently proposed dDXDM approach, can thus uniquely probe the impact of the long-range dispersion effect on EDA results computed at the DFT level. In this paper, we incorporate the dDXDM dispersion corrections into the BLW-ED approach and investigate a range of representative systems such as hydrogen-bonding systems, acid-base pairs, and van der Waals complexes. Results show that both the polarization and charge-transfer energies are little affected by the inclusion of the long-range dispersion effect, which thus can be regarded as an independent energy component in EDA.

Theoretical description of hydrogen bonding in oxalic acid dimer and trimer based on the combined extended-transition-state energy decomposition analysis and natural orbitals for chemical valence (ETS-NOCV)

In the present study we have analyzed hydrogen bonding in dimer and trimer of oxalic acid, based on a recently proposed charge and energy decomposition scheme (ETS-NOCV). In the case of a dimer, two conformations, α and β, were considered. The deformation density contributions originating from NOCV's revealed that the formation of hydrogen bonding is associated with the electronic charge deformation in both the σ-(Δρ(σ)) and π-networks (Δρ(π)). It was demonstrated that σ-donation is realized by electron transfer from the lone pair of oxygen on one monomer into the empty P*(H-O) orbital of the second oxalic acid fragment. In addition, a covalent contribution is observed by the density transfer from hydrogen of H-O group in one oxalic acid monomer to the oxygen atom of the second fragment. The resonance assisted component (Δρ(π)), is based on the transfer of electron density from the π-orbital localized on the oxygen of OH on one oxalic acid monomer to the oxygen atom of the other fragment. ETS-NOCV allowed to conclude that the σ(O---HO) component is roughly eight times as important as π (RAHB) contribution in terms of energetic estimation. The electrostatic factor (ΔE(elstat)) is equally as important as orbital interaction term (ΔE(orb)). Finally, comparing β-dimer of oxalic acid with trimer we found practically no difference concerning each of the O---HO bonds, neither qualitative nor quantitative.

Characterizing the Cooperativity in H-Bonded Amino Structures

Density functional theory calculations were used to examine the effect of H-bond cooperativity on the magnitude of the NMR chemical shifts and spin-spin coupling constants in a C4h-symmetric G-quartet and in structures consisting of six cyanamide monomers. These included two ring structures (a planar C6h-symmetric structure and a nonplanar S6-symmetric structure) and two linear chain structures (a fully optimized planar Cs-symmetric chain and a planar chain structure where all intra- and intermolecular parameters were constrained to be identical). The NMR parameters were computed for the G-quartet and cyanamide structures, as well as for shorter fragments derived from these assemblies without reoptimization. In the ring structures and the chain with identical monomers, the intra- and intermolecular geometries of the cyanamides were identical, thereby allowing the study of cooperative effects in the absence of geometry changes. The magnitude of the |1JNH| coupling, 1H and 15N chemical shifts of the H-bonding amino N-H group, and the |h2JNN| H-bond coupling increased, whereas the size of the |1JNH| coupling of the non-H-bonded amino N-H bonds of the first amino group in the chain, which are roughly perpendicular to the H-bonding network, decreased in magnitude when H-bonding monomers were progressively added to extending ring or chain structures. These effects are attributed to electron redistribution induced by the presence of the nearby H-bonding guanine or cyanamide molecules.

Density functional theory investigation of hydrogen bonding effects on the oxygen, nitrogen and hydrogen electric field gradient and chemical shielding tensors of anhydrous chitosan crystalline structure

A systematic computational investigation was carried out to characterize the 17O, 14N and 2H electric field gradient, EFG, as well as 17O, 15N, 13C and 1H chemical shielding tensors in the anhydrous chitosan crystalline structure. To include the hydrogen-bonding effects in the calculations, the most probable interacting molecules with the target molecule in the crystalline phase were considered through a hexameric cluster. The computations were performed with the B3LYP method and 6-311++G(d,p) and 6-31++G(d,p) standard basis sets using the Gaussian 98 suite of programs. Calculated EFG and chemical shielding tensors were used to evaluate the 17O, 14N and 2H nuclear quadrupole resonance, NQR, and 17O, 15N, 13C and 1H nuclear magnetic resonance, NMR, parameters in the hexameric cluster, which are in good agreement with the available experimental data. The difference between the calculated NQR and NMR parameters of the monomer and hexamer cluster shows how much hydrogen bonding interactions affect the EFG and chemical shielding tensors of each nucleus. These results indicate that both O(3)-H(33)...O(5-3) and N-H(22)...O(6-4) hydrogen bonding have a major influence on NQR and NMR parameters. Also, the quantum chemical calculations indicate that the intra- and intermolecular hydrogen bonding interactions play an essential role in determining the relative orientation of EFG and chemical shielding principal components in the molecular frame axes.

Calculation and analysis of NMR spin-spin coupling constants

The analysis of NMR spin-spin coupling leads to a unique insight into the electronic structure of closed-shell molecules, provided one is able to decode the different features of the spin-spin coupling mechanism. For this purpose, the physics of spin-spin coupling is described and the way how spin-spin coupling constants (SSCCs) can be quantum mechanically determined. Based on this insight, a set of requirements is derived that guide the development of a quantum mechanical analysis of spin-spin coupling. It is demonstrated that the J-OC-PSP (=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization) analysis method fulfills all requirements. J-OC-PSP makes it possible to partition the isotropic indirect SSCC J or its reduced analogue K as well as the four Ramsey terms (Fermi contact (FC), spin dipole (SD), diamagnetic spin orbit (DSO), paramagnetic spin orbit (PSO)) leading to J (or K) into Cartesian components (for the anisotropic Ramsey terms SD, DSO, PSO), orbital contributions or electron interaction terms. For the purpose of decoding the spin-spin coupling mechanism, FC, SD, DSO, and PSO coupling is discussed in detail and related to electronic and bonding features of the molecules in question. The myth of empirical and semiempirical relationships between SSCCs and bonding features is unveiled. It is found that most relationships are only of limited, partly dubious value, often arising from a fortuitous cancellation of terms that cannot be expected in general. These relationships are replaced by quantum chemical relations and descriptions that directly reflect the complex electronic processes leading to spin-spin coupling.

Geometry Dependence of Spin–Spin Couplings in Cyanamide by DFT Analysis

There have been numerous theoretical and experimental investigations examining NMR parameters related to non-amino N-H...N H-bonded moieties in both biological and chemical contexts. In contrast, little information on the geometry dependence of NMR parameters related to the biologically important H-bond donor amino group is available. Herein, the geometric dependencies of the one-bond amino N-H spin-spin coupling constants [(1)J(NH)] in the cyanamide monomer and dimer have been computed with B3LYP and the aug-cc-pVTZ-su0 basis set. In an isolated planar cyanamide molecule, the |(1)J(NH)| couplings were found to increase as the N-H bond lengthened. In contrast, in the planar cyanamide dimer the size of the H-bonded amino N-H coupling (|(1)J(N(d)H(d))|) decreased with increasing N(d)H(d) bond length. The |(1)J(N(d)H(d))| coupling was larger than the |(1)J(N(d)H(free))| coupling for N(d)H(d) distances up to 1.18 A (for a fixed N(d)H(free) distance of 1.006 A). Hence, the decrease of |(1)J(NH)| with increasing N-H distance, as well as the larger value of |(1)J(N(d)H(d))| compared to |(1)J(N(d)H(free))|, were only observed for situations where the amino group is involved in an H-bonding interaction. This is attributed to electron redistribution induced by the presence of the second cyanamide molecule. Similar electron-redistribution effects are thought to be responsible for the observed distance dependence of computed (1)J(NH) couplings of H-bonded amino groups in near-planar G-quartet structures. Here, the |(1)J(NH)| couplings of the amino N-H bonds decreased with increasing N-H bond length whereas the |(1)J(N(d)H(d))| couplings are approximately 7 Hz larger than the |(1)J(N(d)H(free))| couplings, despite the longer N(d)-H(d) bond length.

How resonance assists hydrogen bonding interactions: An energy decomposition analysis

Block-localized wave function (BLW) method, which is a variant of the ab initio valence bond (VB) theory, was employed to explore the nature of resonance-assisted hydrogen bonds (RAHBs) and to investigate the mechanism of synergistic interplay between pi delocalization and hydrogen-bonding interactions. We examined the dimers of formic acid, formamide, 4-pyrimidinone, 2-pyridinone, 2-hydroxpyridine, and 2-hydroxycyclopenta-2,4-dien-1-one. In addition, we studied the interactions in beta-diketone enols with a simplified model, namely the hydrogen bonds of 3-hydroxypropenal with both ethenol and formaldehyde. The intermolecular interaction energies, either with or without the involvement of pi resonance, were decomposed into the Hitler-London energy (DeltaEHL), polarization energy (DeltaEpol), charge transfer energy (DeltaECT), and electron correlation energy (DeltaEcor) terms. This allows for the examination of the character of hydrogen bonds and the impact of pi conjugation on hydrogen bonding interactions. Although it has been proposed that resonance-assisted hydrogen bonds are accompanied with an increasing of covalency character, our analyses showed that the enhanced interactions mostly originate from the classical dipole-dipole (i.e., electrostatic) attraction, as resonance redistributes the electron density and increases the dipole moments in monomers. The covalency of hydrogen bonds, however, changes very little. This disputes the belief that RAHB is primarily covalent in nature. Accordingly, we recommend the term "resonance-assisted binding (RAB)" instead of "resonance-assisted hydrogen bonding (RHAB)" to highlight the electrostatic, which is a long-range effect, rather than the electron transfer nature of the enhanced stabilization in RAHBs.

CLOPPA-IPPP Analysis of Electronic Mechanisms of Intermolecular 1hJ(A,H) and 2hJ(A,D) Spin−Spin Coupling Constants in Systems with D−H···A Hydrogen Bonds

The electronic origin of intermolecular (2h)J(A,D) and (1h)J(A,H) couplings is discussed by means of the CLOPPA-IPPP approach in several model complexes with D-H...A hydrogen bonds. It is found that the origin of these couplings is mainly due to the interaction between the acceptor sigma lone pair and vacant molecular orbitals localized in the D-H...A moiety, regardless of the donor and acceptor nuclei. The problem of the larger absolute value of (2h)J(A,D) compared to (1h)J(A,H) is also addressed.

Elucidation of the Electronic Structure of Molecules with the Help of NMR Spin−Spin Coupling Constants: The FH Molecule

It is demonstrated how the one-bond NMR spin-spin coupling constant (SSCC) (1)J(FH) can be used as a source of information on the electronic structure of the FH molecule. For this purpose, the best possible agreement between measured and calculated SSCC is achieved by large basis set coupled perturbed density functional theory calculations. Then, the calculated value is dissected into its four Ramsey terms: Fermi contact, the paramagnetic spin-orbit term, the diamagnetic spin-orbit term, and the spin dipole term, which in turn are decomposed into orbital contributions and then described by their spin densities and orbital current densities. In this way, the SSCC gives detailed information about the electronegativity of F, the bond polarity, the bond polarizability, the volume and the polarizability of sigma and pi lone pair orbitals, the s- or p-character of the bond orbital, the nature of the LUMO, and the density distribution around F.

Decomposition of nuclear magnetic resonance spin–spin coupling constants into active and passive orbital contributions

The theory of the J-OC-PSP (decomposition of J into orbital contributions using orbital currents and partial spin polarization) method is derived to distinguish between the role of active, passive, and frozen orbitals on the nuclear magnetic resonance (NMR) spin-spin coupling mechanism. Application of J-OC-PSP to the NMR spin-spin coupling constants of ethylene, which are calculated using coupled perturbed density functional theory in connection with the B3LYP hybrid functional and a [7s,6p,2d/4s,2p] basis set, reveal that the well-known pi mechanism for Fermi contact (FC) spin coupling is based on passive pi orbital contributions. The pi orbitals contribute to the spin polarization of the sigma orbitals at the coupling nuclei by mediating spin information between sigma orbitals (spin-transport mechanism) or by increasing the spin information of a sigma orbital by an echo effect. The calculated FC(pi) value of the SSCC (1)J(CC) of ethylene is 4.5 Hz and by this clearly smaller than previously assumed.

Investigation of the NMR Spin−Spin Coupling Constants across the Hydrogen Bonds in Ubiquitin: The Nature of the Hydrogen Bond as Reflected by the Coupling Mechanism

The indirect scalar NMR spin-spin coupling constants across the H-bonds of the protein ubiquitin were calculated, including the Fermi contact, the diamagnetic spin-orbit, the paramagnetic spin-orbit, and the spin dipole term, employing coupled perturbed density functional theory in combination with the B3LYP functional and different basis sets: (9s,5p,1d/5s,1p)[6s,4p,1d/3s,1p] and (11s,7p,2d/5s,1p)[7s,6p,2d/4s,2p]. Four different models based on either the crystal or the aqueous solution structure of ubiquitin were used to describe H-bonding for selected residue pairs of ubiquitin. Calculated and measured 3hJ(NC') coupling constants differ depending on the model used, which is due to the fact that the geometry of ubiquitin is different in the solid state and in aqueous solution. Also, conformational averaging leads to a decrease of the magnitude of the measured 3hJ(NC') constants, which varies locally (larger for -sheets, smaller for -helix). Two different spin-spin coupling mechanisms were identified. While mechanism I transmits spin polarization via an electric field effect, mechanism II involves also electron delocalization from the lone pair of the carbonyl oxygen to the antibonding orbital of the N-H bond. Mechanism I is more important in the crystal structure of ubiquitin, while in aqueous solution, mechanism II plays a larger role. It is possible to set up simple relationships between the spin-spin coupling constants associated with the H bond in proteins and the geometrical features of these bonds. The importance of the 3hJ(NC') and 1J(N-H) constants as descriptors for the H-bond is emphasized.

One-electron versus electron–electron interaction contributions to the spin–spin coupling mechanism in nuclear magnetic resonance spectroscopy: Analysis of basic electronic effects

For the first time, the nuclear magnetic resonance (NMR) spin-spin coupling mechanism is decomposed into one-electron and electron-electron interaction contributions to demonstrate that spin-information transport between different orbitals is not exclusively an electron-exchange phenomenon. This is done using coupled perturbed density-functional theory in conjunction with the recently developed J-OC-PSP [=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization)] method. One-orbital contributions comprise Ramsey response and self-exchange effects and the two-orbital contributions describe first-order delocalization and steric exchange. The two-orbital effects can be characterized as external orbital, echo, and spin transport contributions. A relationship of these electronic effects to zeroth-order orbital theory is demonstrated and their sign and magnitude predicted using simple models and graphical representations of first order orbitals. In the case of methane the two NMR spin-spin coupling constants result from totally different Fermi contact coupling mechanisms. (1)J(C,H) is the result of the Ramsey response and the self-exchange of the bond orbital diminished by external first-order delocalization external one-orbital effects whereas (2)J(H,H) spin-spin coupling is almost exclusively mitigated by a two-orbital steric exchange effect. From this analysis, a series of prediction can be made how geometrical deformations, electron lone pairs, and substituent effects lead to a change in the values of (1)J(C,H) and (2)J(H,H), respectively, for hydrocarbons.