Characteristics of the Multi-Hydrogen Bonded Systems: DFT Description on the Solvated Electrons

Abstract

The multi-hydrogen bonded systems with the solvated electrons are investigated at the B3LYP/6-311++$G^{**}$ basis set level. The symmetrical linear geometrical characteristic is common for the dimer systems, while for the tetramer system, the tetrahedron configuration is generated. The NBO charge analyses demonstrate that the multi-hydrogen-multi-electron (mH-ne) coupling exist in these anion systems, as is supported by the electrostatic potential and the molecular orbital analyses. The positive chemical shift value of the central hydrogen ($H_c$) and the negative chemical shift value of the terminal hydrogen ($H_t$) indicate that the $H_c$ is electronegative while the $H_t$ is electropositive, respectively. Strong coupling between two central hydrogen atoms is demonstrated by the large spin-spin coupling constants. The solvated electron donates significant contributions for the stability of these systems.

Introduction

The hydrogen, which is abundant and exists in various configurations, can generate the covalent bond with electronegative atoms or make the metal hydride with the electropositive metal atoms. The hydrogen plays vital roles in the fields of biology, chemistry, and materials. The typical hydrogen bond has been extended with the observation of dihydrogen bond,1-7 which consists of Hδ+⋯Hδ- and Hδ+⋯e⋯Hδ+ two forms. The significance of the solvated electron in such systems has been emphasized specifically.89 A comprehensive ab initio study was performed on the wet electron − an electron interacting with a small cluster of water molecules − in the water hexamer system, providing the nature of a wet electron.10 The monoelectron dihydrogen bond H⋯e⋯H in the anionic (FH)n⋯e⋯(HF)n clusters has been described.11 The application of solvated electron in the enhancement of hydrogen storage ability of metal hydride has been addressed.12 Along with the development of the science, the knowledge about the nature of hydrogen is deepen and comprehensive gradually. H3+ is taken as the cornerstone of interstellar chemistry because it initiates the reactions responsible for the production of many larger molecules observed in the interstellar medium.1314 The time evolution of electron density descriptors in H3+ and LiF is defined by the quantum theory of atoms in molecules.15 The structure and energy of the ion induced dipole Hn− clusters are investigated with the density functional theory (DFT) method. Recent DFT calculations have predicted unexpected molecular structures for the ion induced dipole Hn− clusters with the trihydrogen bond.1617 The nature of this trihydrogen bond is characterized as H−⋯δ+H-Hδ−. Thus, the number of hydrogen atom involved in the hydrogen bond is expanded from one to two, and then to multihydrogen.

Is it possible for the system involving heavy atoms to generate the multihydrogen bond (MHB)? Which kind of environment is suitable for the formation of MHB? How about the nature of the MHB? With the intention to resolve the above questions, this work is carried out with the DFT approach. The following section describes the detailed calculation method. Then, the results and corresponding discussions are represented in the results and discussion part. Main conclusions are collected in the last section.

 

Calculation Details

The hybrid density functional methods have been pro-sperously employed in the electronic structure optimizations and the energy determinations. They are uniquely successful in describing large free radicals and intermolecular com-plexes. The reliability of the B3LYP/6-311++G** basis set level for the MHB system has also been verified by Metta et al.17 Therefore, the whole calculations were all carried out employing the B3LYP approach with the 6-311++G** basis set. Vibrational frequency analysis was performed for each complex at the same level to verify whether the optimized structures correspond to genuine local minima on the global potential energy surface or not. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) analyses, as well as the natural bond orbital (NBO) charge population were carried out to explore the nature of the complexes. The orbital interactions between the donor (Lewis type) orbitals and the acceptor (non-Lewis type) orbitals are estimated according to the second-order perturbation theory. For each donor NBO orbital (i) and acceptor NBO orbital ( j), the interaction energy E(2) associated with delocalization i → j is given by the formula

where qi is the donor orbital occupancy and F(i, j) is the off-di-agonal NBO Fock matrix element. εi and εj are diagonal ele-ments (orbital energies).

The proton chemical shift is determined according to value of TMS. The nuclear magnetic resonance (NMR) spin-spin coupling constant, J, is calculated as a sum of the Fermi-contact (FC), spin dipolar (SD), paramagnetic spin-orbital (PSO), and diamagnetic spin-orbit (DSO) contributions.

 

Results and Discussion

Geometry. The optimized geometry structures of selected MHB systems are all collected in Figure 1. The primary parameters showing the characteristic of these complexes are also represented. For the dimer of hydrogenated HF, F22−, the system is in D2h symmetry. There are two excess electrons to enhance the stabilization of the system. The distance between two central hydrogen atoms is 0.828 Å, longer as compared with that of the neutral dihydrogen gas (0.744 Å), the dihydrogen anion (0.772 Å), as well as the dihydrogen with two excess electrons (0.780 Å). The F-H covalent bond distance is 0.937 Å, a little longer than that of the HF monomer, 0.922 Å, indicating the coupling between the central and the terminal hydrogen atoms. The length of central hydrogen and the terminal one is 2.037 Å, which is shorter significantly than the H⋯e⋯H distance of anionic (HF)2− (2.942 Å).7 A rhombus structure is generated with four hydrogen atoms. There is only one excess electron is solvated in the hydrogenated HCl dimer system, Cl2− which is also in D2h point group. As compared with the distance of two central hydrogen atoms in F22−, the distance of the central hydrogen atoms in Cl2- system is condensed slightly (0.807 Å). While, the distance between the central hydrogen and the terminal one is extended a little (2.087 Å). The variation of the rhombus structure is slight for these two systems. The length of Cl-H covalent bond is 1.300 Å, longer by 0.013 Å as compared to that of free HCl in the gas phase. There is a four-hydrogen-atom-ring for each of these two systems.

Two imidazole rings populate symmetrically upon the central hydrogen atom in ImH2− system. These two rings are almost perpendicular to each other and the system is in C2 point group. Similarly, the NH bond length is a little longer as compared with that of the free imidazole monomer. The distance between the Hc and the Ht is only 1.379 Å, shorter distinctly than the typical value of nonbonding H⋯H contacts (2.4 Å). The reported H⋯e⋯H distance in anionic imidazole dimer is more than 3.7 Å.7 One excess electron is solvated in the center of the system. From a geometrical point of view, this is a three-hydrogen-bonded system. For the more complicated system, ImH4−, the central hydride is solvated by four imidazole rings. The system is in tetrahedron geometry. The NH covalent bonds are shorter in length by 0.05 Å as compared with those in the ImH2− system. While, the distance between the central hydrogen and the terminal one is 1.622 Å, longer than that in the ImH2− system by 0.24 Å. It is clear that this is a five-hydrogen-bonded system.

Figure 1.Optimized geometry structures. The bond is represented in Å.

NBO Charge Analysis. The natural bond orbital (NBO) analysis is carried out for all these systems. The calculated NBO charges of the central hydrogen (Qc) and the terminal ones (Qt) are collected in Table 1. In the F22− system, the Qc is −0.909 and the Qt is −0.592. This indicates that the character of the MHB should be Hδ+⋯H22−⋯Hδ+. Thus, the feature of this system is the four-hydrogen-four-electron (4H-4e) coupling. The negative charges populate mainly on two central hydrogen atoms, while the terminal hydrogen atom carry distinct positive charge and the F atom is electro-negative strongly. The electrostatic interaction between the central hydrogen atoms and the terminal hydrogen/the electronegative F decreases the strength of F-H covalent bond and extends its distance. It is similar for the other systems. The Qc and Qt in the Cl2− system is −0.381 and 0.305, respectively, demonstrating the feature of this MHB system should be Hδ+⋯H2−⋯Hδ+. The characteristic of this anionic dimer is the four-hydrogen-three-electron (4H-3e) coupling. The NBO charges on the central hydrogen and the terminal ones in the ImH2− system is −0.583 and 0.409, respectively. This MHB system is typical for its Hδ+⋯H−⋯Hδ+ structure and the three-hydrogen-two-electron (3H-2e) coupling. In the complicated ImH4− system, the Qc and Qt are −0.658 and 0.447, respectively. Although more negative electron populated on the central hydrogen, it is shared by four imidazole rings, instead of two rings in the ImH2− system. The characteristic of the ImH4− system can be assigned as 5H-2e coupling. Therefore, the coupling between the central and the terminal hydrogen atoms should be weaker, as is reflected by their H⋯H distances in these two MHB systems. Table 1 illustrates that the Hc is electronegative while the Ht is electropositive for all these four systems.

Table 1.athe energies are given in kcal/mol. bQt and Qc refer to the NBO charges on the hydrogen atom bonded with the heavy atom and the one populated in the center of the complex, respectively. cthe unit of σ is ppm and the unit of J is in Hz.

The NBO analyses also indicate that the couplings bet-ween two Hc atoms (68.5 kcal/mol) as well as the interactions between the Hc atoms and the terminal F (68.7 kcal/mol) donate significant contribution to the stability of the F22− system. It is the coupling between two Hc atoms (123.3 kcal/mol) stabilizing the Cl2− system. While for the ImH2− system, the couplings between Hc and two neighbouring N-H groups stabilize the system with the contribution of 183.5 kcal/mol. Four inward N-H groups couple with the Hc atom simultaneously and contribute significantly to the stability by 137.8 kcal/mol.

Electrostatic Potential. The contours of the electrostatic potential of these MHB systems are collected in Figure 2. It is obvious that the negative electrostatic potential (NEP) populates around two Hc atoms located between two HX (X = F, Cl) fragments. This indicates that the excess electrons populate on two Hc atoms, which is in consistent with the results obtained from the NBO analyses. For the ImH2− system, distinct NEP can be found around the central hydro-gen atom, furthermore, the NEP populate around two terminal imidazole nitrogen atoms. The positive electrostatic potential populates around the C-H bonds of two fragments. Similar phenomena are observed for the ImH4− system.

Frontier Molecular Orbitals. Figure 2 also collects the frontier molecular orbitals of these anion systems. The orbitals of F22− and Cl2− indicate that the multi-hydrogen-bond mole-cular orbital (MHBMO) populates on four hydrogen atoms, respectively, as demonstrates that the above mentioned 4H-4e and the 4H-3e coupling exists for F22− and Cl2−, respec-tively. The MHBMO also populates on the hydrogen atoms in the ImH2− and ImH4− systems. Furthermore, their HOMO orbitals also carry the MHBMO character with the solvated electrons locating between the imidazole ring fragments.

Figure 2.Electrostatic potential, HOMO, LUMO, and the multihydrogen bond molecular orbital (MHBMO) of the optimized geometries.

NMR Parameters. The chemical shifts (σ) and the spin-spin coupling constants (1J(H-H)) are all represented in Table 1. The chemical shift of Hc and Ht in F22− is −74.8 and −8.4 ppm, respectively. These values are shifted significantly in Cl2− system to −80.5 (low-field) and 11.4 (high-field) ppm, respectively. In the ImH2− system, the σ values of Hc and Ht are 7.2 and 18.8, respectively. The σ value of Hc/Ht increases/decreases in ImH4− as compared to that in ImH2− system. The Hc atoms of F22− and Cl22− populate in low field, while the central hydrogen atoms of ImH2− and ImH4− locate in high field, as maybe the result of strong coupling between two central hydrogen atoms. The large 1J(Hc⋯Hc) value demonstrate the strong interaction between two central hydrogen atoms in F22− and Cl2- systems. The small value of 1J(Ht⋯Hc) and 1J(Ht⋯Ht) illustrate that the weak coupling exists not only between Hc and Ht but also between the terminal hydrogen atoms.

 

Concluding Remarks

The multi-hydrogen bonded systems with the solvated electrons are investigated at the B3LYP/6-311++G** basis set level. The linear geometrical characteristic is common for the dimers (F22−, Cl2−, and ImH2−), while for the tetramer system (ImH4−), the tetrahedron configuration is generated. The NBO charge analyses demonstrate that the multi-hydro-gen-multi-electron (mH-ne) coupling exist in these anion systems. The electrostatic potential and the molecular orbital analyses also support the existence of mH-ne coupling. Our results also demonstrate that the mH-ne coupling is distinct as compared with the H⋯e⋯H interactions. The positive chemical shift value of Hc and the negative chemical shift value of Ht indicate that the Hc is electronegative while the Ht is electropositive, respectively. Strong coupling between two central hydrogen atoms is demonstrated by large chemical shifts and big spin-spin coupling constants.