The nature of hydrogen bonds and conjugation in H-bonded systems

Analysis of the electron density distributions in the spatial regions of hydrogen bonds reveals the existence of both ?? and ?? binding. The ??-type electron density distribution is shown to be determined by occupied orbitals of both bonding and antibonding character. The ?? system can be conjugated and provides the predominant binding of molecules in nonplanar structures. The mutual orientation of the molecules involved in a hydrogen bond is found to be optimal when the X-H bond in the proton donor and the orbital of the acceptor, the main contributor to ?? binding, have a common axis of symmetry. The conjugated ?? electron system in molecular clusters determines the so-called cooperativity that is manifested in the deviation of the properties of hydrogen-bonded systems from pairwise additivity.     

Quantitative relationships between bond lengths,stretching vibrational frequencies,bond force constants,and bond orders in the hydrogen-bonded complexes involving hydrogen halides

To uncover the correlation between the bond length change and the corresponding stretching frequency shift of the proton donor D–H upon hydrogen bond formation, a series of hydrogen-bonded complexes involving HF and HCl which exhibit the characteristics of red-shifted hydrogen bond were investigated at the MP2/aug-cc-pVTZ, M062X/aug-cc-pVTZ, and B3LYP/aug-cc-pVTZ(GD3) levels of theory with CP optimizations. A statistical analysis of these complexes leads to the quantitative illustrations of the relations between bond length and stretching vibrational frequency, between bond length and bond force constant, between stretching vibrational frequency and bond force constant, between bond length and bond order for hydrohalides in a mathematical way, which would provide valuable insights into the explanation of the geometrical and spectroscopic behaviors during hydrogen bond formation.     

Proton Transfer Influence on Geometry and Electron Density in Benzoic Acid–Pyridine Complexes

The influence of the proton transfer on the geometry of donor and acceptor molecule in benzoic acid–pyridine complexes is investigated by theoretical calculations at the B3LYP/6‐311++G** level of theory. Systematic shifts of the H‐atom in the H‐bond are reflected in the geometry of the COOH group and the lengths of aromatic ring bond lengths of the proton acceptor. Changes in electron densities have been studied by atoms in molecules analysis. A systematic natural bond orbital analysis has been performed to study the proton transfer mechanism. Two donor orbitals are engaged in the proton transfer process which is accompanied by a change in orbital delocalization of H‐atom that can switch between two donor orbitals so the path of proton transfer in intermolecular H‐bond is not determined by the orbital shape. Theoretical results have been confirmed by experimental results published previously.     

Hydrogen bonding in substituted formic acid dimers

The hydrogen-bonded dimers of formic acid derivatives XCOOH (X = H, F, Cl, and CH3) have been investigated using density functional theory (B3LYP) and second-order M?ller-Plesset perturbation (MP2) methods, with the geometry optimization carried out using 6-311++G(2d,2p) basis set. The dimerization energies calculated using aug-cc-pVXZ (with X = D and T) basis have been extrapolated to infinite basis set limit using the standard methodology. The results indicate that the fluorine-substituted formic acid dimer is the most stable one in comparison to the others. Topological analysis carried out using Bader's atoms in molecules (AIM) theory shows good correlation of the values of electron density and its Laplacian at the bond critical points (BCP) with the hydrogen bond length in the dimers. Natural bond orbital (NBO) analysis carried out to study the charge transfer from the proton acceptor to the antibonding orbital of the X-H bond in the complexes reveals that most of the dimers are associated with conventional H-bonding except a few, where improper blue-shifting hydrogen bonds are found to be present.     

On the physical origin of blue-shifted hydrogen bonds

For blue-shifted hydrogen-bonded systems, the hydrogen stretching frequency increases rather than decreases on complexation. In computations at various levels of theory, the blue-shift in the archetypical system, F(3)C-H.FH, is reproduced at the Hartree-Fock level, indicating that electron correlation is not the primary cause. Calculations also demonstrate that a blue-shift does not require either a carbon center or the absence of a lone pair on the proton donor, because F(3)Si-H.OH(2), F(2)NH.FH, F(2)PH.NH(3), and F(2)PH.OH(2) have substantial blue-shifts. Orbital interactions are shown to lengthen the X-H bond and lower its vibrational frequency, and thus cannot be the source of the blue-shift. In the F(3)CH.FH system, the charge redistribution in F(3)CH can be reproduced very well by replacing the FH with a simple dipole, which suggests that the interactions are predominantly electrostatic. When modeled with a point charge for the proton acceptor, attractive electrostatic interactions elongate the F(3)C-H, while repulsive interactions shorten it. At the equilibrium geometry of a hydrogen-bonded complex, the electrostatic attraction between the dipole moments of the proton donor and proton acceptor must be balanced by the Pauli repulsion between the two fragments. In the absence of orbital interactions that cause bond elongation, this repulsive interaction leads to compression of the X-H bond and a blue-shift in its vibrational frequency.     

Theoretical analysis based on X-H bonding strength and electronic properties in red- and blue-shifting hydrogen-bonded X-H···π complexes

A theoretical study based on the X-H bond strength of the proton donor fragment and its concomitant classical red-shifting or improper blue-shifting of the pure stretching frequency, in weakly hydrogen-bonded X-H···π complexes, is presented. In this sense, the dissociation energy differences, defined as, ΔD(e) = D(e)(X-H)[complex] - D(e)(X-H) [isolated], showed to be linearly connected with the change in stretching frequencies, Δν = ν(X-H)[complex] - ν(X-H)[isolated], of red- and blue-shifting H-bonds. This relationship allows us to define a threshold for the type of the stretching shift of the X-H bond: ΔD(e)(X-H) > 50.3 kcal mol(-1) leads to blue-shifting whereas ΔD(e)(X-H) < 50.3 kcal mol(-1) leads to red-shifting behavior. Complementarily, natural bond orbital analysis along the X-H stretching coordinate and electric dipole polarizability was performed to investigate the factors involved in red- or blue-shifting hydrogen-bonded complexes. It has been found that a high tendency to deplete the electronic population on the H atom upon X-H stretching is exhibited in blue-shifting H-bonded complexes. On the other hand, these types of complexes present a compact electronic redistribution in agreement with polarizability values. This study has been carried out taking as models the following systems: chloroform-benzene (Cl(3)C-H···C(6)H(6)), fluoroform-benzene (F(3)C-H···C(6)H(6)), chloroform-fluorobenzene, as blue-shifting hydrogen-bonded complexes and cyanide acid-benzene (NC-H···C(6)H(6)), bromide and chloride acids-benzene ((Br)Cl-H···C(6)H(6)) and acetylene-benzene (C(2)H(2)···C(6)H(6)) as red-shifting complexes.     

Cooperativity and proton transfer in hydrogen-bonded triads.

Ab initio MP2/6-311+G(3df,2pd) and MP2/aug-cc-pVTZ calculations have been carried out to investigate the structures and properties of AHXHYH(3) (A=F, Cl; X=F, Cl; Y=N, P) hydrogen-bonded complexes. Significant cooperative effects are observed in the XHYH3 dyads in the triads due to the presence of the polar near-neighbor AH. These effects are greater when the polar partner is HF, which is a better proton donor than HCl. Structural changes, red shifts of proton-donor stretching frequencies, nonadditive interaction energies, and electron density redistributions unambiguously demonstrate that the X--HY hydrogen bond (HB) is stronger in the triads than in the corresponding dyads, while the X--H bond of the proton donor becomes weaker. Even more pronounced cooperative effects are observed in the AHXH dyads due to the presence of the YH3 partner. These effects are weaker in complexes having PH3 rather than NH3 as the proton acceptor, since NH3 is a stronger base. Cooperativity also enhances the proton-donating ability of the YH3 moiety, with the result that all complexes except FHFHPH3 are cyclic. Cooperativity, together with the ease of breaking the Cl--H bond in ClHClHNH3 and FHClHNH3, leads to proton transfer (PT), so that these two complexes are better described as approaching hydrogen-bonded ClHCl- x +HNH3 and FHCl- x +HNH3 ion pairs.     

精氨酸侧链和核酸碱基间离子氢键作用强度分析

采用MP2/6-31+G(d,p)方法优化得到了22个由精氨酸侧链与碱基尿嘧啶、 胸腺嘧啶、 胞嘧啶、 鸟嘌呤及腺嘌呤形成的氢键复合物的气相稳定结构, 使用包含BSSE校正的MP2/aug-cc-pVTZ方法计算得到了复合物的气相结合能, 通过MP2/6-31+G(d,p)方法和PCM模型优化得到了复合物的水相稳定结构, 采用MP2/aug-cc-pVTZ方法和PCM模型计算得到了复合物的水相结合能. 研究发现, 精氨酸侧链与碱基间的离子氢键作用强度与单体间电荷转移量、 氢键临界点电子密度及二阶作用稳定化能密切相关. 与中性氢键相比, 离子氢键作用具有更显著的共价作用成分. 研究还发现, 精氨酸侧链和碱基间形成的氢键复合物的稳定性次序可以通过氢键受体碱基分子上氧原子和氮原子的质子化反应焓变进行预测, 质子化反应焓变越负, 形成的氢键复合物越稳定.     

Proton affinity correlations between hydrogen and dihydrogen bond acceptors

Several series of hydrogen- and dihydrogen-bonded complexes with HCN, C2H2, HF, H2O, CH3CONH2, and CH3COOH as donors and H2O, MeOH, EtOH, MeOMe, NH3, NH2Me, NHMe2, NMe3, NEtMe2, and BH3-NMe3 as acceptors were investigated using the MP2/6-311++G(d,p) level of theory. The total lowering of the X-H stretching frequencies in the hydrogen-bonded complexes were linearly correlated with the proton affinities of the accepting bases. From comparison of hydrogen- and dihydrogen-bonded complexes, a scaling factor to estimate the exact proton affinity of a dihydrogen bond acceptor was developed. Further, the scaling factor involving linear donors (1.204) is marginally higher than that involving nonlinear donor molecules (1.162). Finally, it was found that, given identical conditions, a hydrogen bond will be about 16-20% stronger than a corresponding dihydrogen bond.     

One-bond spin-spin coupling constants of X-1H proton donors in complexes with X-H-Y hydrogen bonds, for X = 13C, 15N, 17O, and 19F: predictions, comparisons, and relationships among 1J X-H, 1K X-H, and X-H distances

Ab initio calculations at the equation-of-motion coupled cluster (EOM-CCSD) level of theory have been carried out to investigate one-bond (13)C-(1)H, (15)N-(1)H, (17)O-(1)H, and (19)F-(1)H coupling constants in a systematic study of monomers and hydrogen-bonded complexes. Computed coupling constants ((1)J(X-H)) for monomers are in good agreement with available experimental data. All reduced Fermi-contact terms and reduced coupling constants ((1)K(X-H)) for monomers and complexes are positive. Plots of (1)K(X-H) versus the X-H distance for the 16 monomers and the 64 complexes in which these monomers are proton donors exhibit significant scatter. However, a linear relationship has been demonstrated for the first time between coupling constants and X-H distances for different X atoms by plotting the ratios of the coupling constants for complexes and corresponding monomers versus the ratios of distances for complexes and corresponding monomers times the square of the Pauling electronegativity. Since the ratio removes the dependence of coupling constants on the magnetogyric ratios of X, this relationship holds for both (1)K(X-H) and (1)J(X-H). The decrease in reduced coupling constants ((1)K(X-H)) as the X-H distance increases is due primarily to the increased proton-shared character of the hydrogen bond.     

Chemical origin of blue- and redshifted hydrogen bonds: intramolecular hyperconjugation and its coupling with intermolecular hyperconjugation

Upon formation of a H bond Y...H-XZ, intramolecular hyperconjugation n(Z)-->sigma*(X-H) of the proton donor plays a key role in red- and blueshift characters of H bonds and must be introduced in the concepts of hyperconjugation and rehybridization. Intermolecular hyperconjugation transfers electron density from Y to sigma*(X-H) and causes elongation and stretch frequency redshift of the X-H bond; intramolecular hyperconjugation couples with intermolecular hyperconjugation and can adjust electron density in sigma*(X-H); rehybridization causes contraction and stretch frequency blueshift of the X-H bond on complexation. The three factors--intra- and intermolecular hyperconjugations and rehybridization--determine commonly red- or blueshift of the formed H bond. A proton donor that has strong intramolecular hyperconjugation often forms blueshifted H bonds.     

HCN(HNC)与NH3, H2O和HF分子间相互作用的理论研究

在MP2/aug-cc-pVTZ水平上, 对HCN(HNC)与NH3, H2O和HF分子间可能存在的氢键型复合物进行了全自由度能量梯度优化, 通过在相同水平上的频率验证分析发现了稳定的分子间相互作用形式是HCN(HNC)作为质子供体或作为质子受体形成的复合物. 基组重叠误差对总相互作用能的影响均小于3.34 kJ/mol. 通过自然键轨道(NBO)分析, 研究了单体和复合物中的原子电荷和电荷转移对分子间相互作用的影响. 对称性匹配微扰理论(SAPT, Symmetry Adapted Perturbation Theory)能量分解结果表明, 在分子间相互作用中, 静电作用与诱导作用占主导地位, 而诱导作用与复合物的电荷转移之间具有良好的正相关性.     

Benchmark of density functional theory methods on the prediction of bond energies and bond distances of noble-gas containing molecules

We have tested three pure density functional theory (DFT) functionals, BLYP, MPWPW91, MPWB95, and ten hybrid DFT functionals, B3LYP, B3P86, B98, MPW1B95, MPW1PW91, BMK, M05-2X, M06-2X, B2GP-PLYP, and DSD-BLYP with a series of commonly used basis sets on the performance of predicting the bond energies and bond distances of 31 small neutral noble-gas containing molecules. The reference structures were obtained using the CCSD(T)∕aug-cc-pVTZ theory and the reference energies were based on the calculation at the CCSD(T)∕CBS level. While in general the hybrid functionals performed significantly better than the pure functionals, our tests showed a range of performance by these hybrid functionals. For the bond energies, the MPW1B95∕6-311+G(2df,2pd), BMK∕aug-cc-pVTZ, B2GP-PLYP∕aug-cc-pVTZ, and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 2.0-2.3 kcal∕mol per molecule. For the bond distances, the MPW1B95∕6-311+G(2df,2pd), MPW1PW91∕6-311+G(2df,2pd), and B3P86∕6-311+G(2df,2pd), DSD-BLYP∕6-311+G(2df,2pd), and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 0.008-0.013 A? per bond. The current study showed that a careful selection of DFT functionals is very important in the study of noble-gas chemistry, and the most recommended methods are MPW1B95∕6-311+G(2df,2pd) and DSD-BLYP∕aug-cc-pVTZ.     

NCBBH…HNa(H2O)n和CNBBH…HNa(H2O)n(n=1~5)结构与性质的理论研究

为了探索缺电子B-H键作为质子供体形成双氢键复合物的溶剂化效应,分别采用DFT-B3LYP/6-311++G**和CCSD(T)/6-311++G**方法对NCBBH…HNa和CNBBH…HNa及其水合物NCBBH…HNa(H2O)n和CNBBH…HNa(H2O)n(n=1~5)进行了结构优化和相互作用能计算,并利用AIM(atom in molecule)方法分析了H…H键特征,借助前线分子轨道理论探讨了水合物中双氢键形成H-H共价键的本质。结果表明:随着H2O分子数的增加,B-H键拉长,H…H距离缩短,双氢键由离子型向共价型过渡;当H2O分子数达到4时,双氢键相互作用能和NCBBH…HNa与水分子间的相互作用能分别达到-374.21和-306.50 kJ.mol-1,形成了H-H共价键;缺电子B-H键作为质子供体形成双氢键复合物的水合物析出H2的能力比FH…HLi(H2O)n弱。     

On the question of hydrogen bond proton transfer

A simple relation is found that connects the proton displacement value along the line of an H-bond X-H…Y at its formation with the proton transfer barrier to the acceptor Y. The fulfillment of the relation is verified by quantum-chemical calculations at the B3LYP/6-31+G(d, p) level of a series of H-bonded molecular complexes at different interatomic distances X…Y. With the aim to analyze the accuracy of this relation, calculations of model complexes were also performed with different basis sets. The effects of the basis set extension and electron correlation on the calculated values of the proton transfer barrier and the length of the X-H covalent bond in the molecular complex are considered. Using the suggested formalism for problems of proton transfer in H-bonded systems is discussed. A criterion of the barrierless transfer is introduced.     

Interpreting geometric preferences in π‐stacking interactions through molecular orbital analysis

The preference of π‐stacking interactions for parallel‐displaced (PD) and twisted (TW) conformations over the fully eclipsed sandwich (S) in small π‐stacked dimers of benzene, pyridine, pyrimidine, 1,3,5‐trifluorobenzene, and hexafluorobenzene are examined in terms of enhancement of the inter‐ring density through mixing of the monomer orbitals (MOs). PD and/or TW conformations are consistent with a non‐zero “stack bond order” (SBO), defined in analogy to the bond order of conventional MO theory, as the difference in the occupation of bonding and antibonding π‐type dimer MOs. In the S conformation, the equal number of bonding and antibonding MOs cancel overall stack bonding character between the monomers for an SBO of zero and an overall repulsive interaction. PD from the S shifts the character of at least one antibonding combination of monomer π‐type MOs with nodes perpendicular to the coordinate for PD to bonding, leading to an attractive nonzero SBO. The inter‐ring density measured through the Wiberg bond index analysis shows an enhancement at the PD conformations consistent with greater interpenetration of the monomer densities. This intuitive bonding model for π‐stacking interactions is complementary to highly accurate calculations of π‐stacking energies and allows a predictive understanding of relative stability using cheaper quantum chemical methods.     

Hydrogen bond and halogen bond inside the carbon nanotube

The hydrogen bond and halogen bond inside the open-ended single-walled carbon nanotubes have been investigated theoretically employing the newly developed density functional M06 with the suitable basis set and the natural bond orbital analysis. Comparing with the hydrogen or halogen bond in the gas phase, we find that the strength of the hydrogen or halogen bond inside the carbon nanotube will become weaker if there is a larger intramolecular electron-density transfer from the electron-rich region of the hydrogen or halogen atom donor to the antibonding orbital of the X-H or X-Hal bond involved in the formation of the hydrogen or halogen bond and will become stronger if there is a larger intermolecular electron-density transfer from the electron-rich region of the hydrogen or halogen atom acceptor to the antibonding orbital of the X-H or X-Hal bond. According to the analysis of the molecular electrostatic potential of the carbon nanotube, the driving force for the electron-density transfer is found to be the negative electric field formed in the carbon nanotube inner phase. Our results also show that the X-H bond involved in the formation of the hydrogen bond and the X-Hal bond involved in the formation of the halogen bond are all elongated when encapsulating the hydrogen bond and halogen bond within the carbon nanotube, so the carbon nanotube confinement may change the blue-shifting hydrogen bond and the blue-shifting halogen bond into the red-shifting hydrogen bond and the red-shifting halogen bond. The possibility to replace the all electron nanotube-confined calculation by the simple polarizable continuum model is also evaluated.     

Characteristics of X-H···π interactions: ab initio and QTAIM studies

The MP2/6-311++G(d,p) calculations were performed on several hydrogen-bonded systems. Different complexes were taken into account to analyze various types of hydrogen bonds, possessing different types of proton donors and proton acceptors as well as characterized by the broad range of the interaction energy. The Quantum Theory of Atoms in Molecules is applied. The results of the hybrid variational-perturbational approach are discussed. The unique properties of hydrogen bonds, where π-electrons act as the proton acceptor (X-H···π), are analyzed, and these interactions are compared with the other types of hydrogen bonds, mainly with C-H···Y interactions. It is shown that for X-H···π systems the ellipticity at the bond critical point of the proton···acceptor interaction is much greater than for the other types of hydrogen bonds. However, both X-H···π and C-H···Y interactions are characterized by the dominance of the dispersive energy.     

How to determine whether intramolecular H...H interactions can be classified as dihydrogen bonds

Different types of intramolecular H...H interactions have been analyzed using the MP2/6-311++G(d,p) level of approximation. These are C-H...H-B, C-H...H-Al, C-H...H-C, C-H...H-O, O-H...H-Al and O-H...H-B contacts. Quantum theory of atoms in molecules and natural bond orbitals methods were applied to better understand the nature of these interactions. It was found that some of the species analyzed possess the characteristics of typical hydrogen bonds, such as the O-H...O ones. The electron charge transfer from the Lewis base to the antibonding X-H (for example O-H) orbital of the Lewis acid is one such characteristic. The NBO method may be considered decisive to classify any system as dihydrogen bonded.     

取代基对1-甲基尿嘧啶与N-甲基乙酰胺氢键复合物中氢键强度的影响

使用密度泛函理论B3LYP方法和二阶微扰理论MP2方法对由1-甲基尿嘧啶与N-甲基乙酰胺所形成的氢键复合物中的氢键强度进行了理论研究, 探讨了不同取代基取代氢键受体分子1-甲基尿嘧啶中的氢原子对氢键强度的影响和氢键的协同性. 研究表明: 供电子取代基使N－H…O＝C氢键键长r(H…O)缩短, 氢键强度增强; 吸电子取代基使N－H…O＝C氢键键长r(H…O)伸长, 氢键强度减弱. 自然键轨道(NBO)分析表明: 供电子基团使参与形成氢键的氢原子的正电荷增加, 使氧原子的负电荷增加, 使质子供体和受体分子间的电荷转移量增多; 吸电子基团则相反. 供电子基团使N－H…O＝C氢键中氧原子的孤对电子轨道n(O)对N－H的反键轨道σ^*(N－H)的二阶相互作用稳定化能增强, 吸电子基团使这种二阶相互作用稳定化能减弱. 取代基对与其相近的N－H…O＝C氢键影响更大.