Theoretical study on the hydration of hydrogen peroxide in terms of ab initio method and atom-bond electronegativity equalization method fused into molecular mechanics

Abstract

In this paper, the interaction between hydrogen peroxide (HP) and water were systemically studied by atom-bond electronegativity equalization method fused into molecular mechanics (ABEEM/MM) and ab initio method. The results show that the optimized geometries, interaction energies and dipole moments of hydrated HP clusters HP(H₂O)_n (n = 1–6) calculated by ABEEM/MM model are fairly consistent with the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ results. The ABEEM/MM results indicate that n = 4 is the transition state structure from 2D planar structure to 3D network structure. The variations of the average hydrogen bond length with the increasing number of water molecules given by ABEEM/MM model agree well with those of ab initio studies. Moreover, the radial distribution functions (RDFs) of water molecule around HP in HP aqueous solution have been analyzed in detail. It can be confirmed that HP is a good proton donor and poor proton acceptor in aqueous solution by analysis of the RDFs.

Keywords

ABEEM/MM model / ab initio calculation / hydrogen peroxide / water

Introduction

Hydrogen peroxide (HP) is a substance that plays an important role in atmospheric chemistry, biology, biochemistry, environmental chemistry and medicine [1-11]. It is a dominant oxidant in clouds, fog, and rain, affecting the aqueous oxidation of SO₂ [10]. It is a byproduct of several metabolic pathways, giving significant quantities of HP detectable in the human blood [11]. It is also used medicinally, in the form of a 3% aqueous solution, as an antiseptic and throat wash. On the other hand, it is interesting as one of the simplest molecules for which internal rotation can take place.

In recent years, a number of theoretical work has been devoted to the study of small H₂O₂(H₂O)_n complexes [12-19]. The rotational barrier of hydrogen peroxide in hydrogen bonded structure of H₂O₂–H₂O complexes in gas and solution phase have been studied by Du et al. [13]. Ab initio studies due to Dobado and Molina [17] reported three minima and two transition state structures for H₂O₂–H₂O complexes. They estimated the binding energy of this heterocluster to be (6.4±0.2) kcal/mol, typical of hydrogen bonded complexes. Mo et al. [19] carried out investigations on structures, vibrational frequencies and thermodynamic properties of the H₂O₂–H₂O complex. According to those work the global minimum of H₂O₂–H₂O at both the restricted Hartree-Fock (RHF) and MP2 levels is a five-membered ring, comprising both covalent and hydrogen bonds. The structures as well as thermodynamic properties of H₂O₂(H₂O)_n (n = 1-3) have been studied by Ju et al. [16]. Those results indicated that the polarity of the solvent has played an important role on the structures, relative stabilities and rotational barriers of different isomers. Kulkarni et al. have performed extensive quantum chemical studies on H₂O₂(H₂O)_n (n = 1-6) [14] and (H₂O₂)₂(H₂O)_n (n = 1-2) [15] at HF and MP2 levels of theory. The structures of these complexes once again show a close structural resemblance with the corresponding (H₂O₂)_n as well as (H₂O)_n clusters. Comparison of the electronic excitation and ionization of H₂O₂(H₂O)_n (n = 1-6) with (H₂O)_n (n = 1-7) clusters has been investigated by Ferreira et al. [20]. Their studies provided useful data to assess how a reactive oxidative species presents in water clusters from an electronic point of view. Furthermore, computational studies in the condensed phase have been reported, including a quantum chemical investigation on the interaction with ice surface model [21], as well as classical simulations of HP dissociation in supercritical water [22] or adsorption at the air/water interface [23]. Recently, Martins-Costa and Ruiz-López [24] have investigated hydrogen peroxide in aqueous solution using combined quantum/classical force field.

On the basis of the electronegativity equalization method (ABEEM), the fluctuating charge models in combination with molecular mechanics have been widely developed in the past few years [25-44]. Rick and Berne [28] have developed dynamical fluctuating charge (FQ) force field to study the liquid water; Patel et al. [37] have developed CHARMM FQ force field, which is applied to the protein simulations. Based on the atom-bond electronegativity equalization method [45-47] fused into molecular mechanics (MM), Yang et al. [48-59] have developed a new polarizable force field, i.e., ABEEM/MM fluctuating charge model. It has been applied successfully to the water system [48,49], ion-water system [50-52], organic molecules [53], peptides [54], nucleic acid system [55-57] and proteins [58]. Recently, we have constructed a new ABEEM/MM potential for HP system [59], and successfully applied it to gas-phase HP clusters and liquid-state HP.

The primary of this paper is to carry out a systemic study on the hydration of HP in terms of a high-level ab initio methods and ABEEM/MM polarizable force field. The essence of this model is to employ the ABEEM charges of all atoms, bonds, and lone-pairs electrons of the system into the calculation of electrostatic interaction term. First, conformations associated with the H₂O₂(H₂O)_n (n = 1-6) are searched by the ab initio method. Then, we will construct an ABEEM/MM interaction potential for the HP-water system, and reliability of this potential will be confirmed in view of the comparison of the hydrated HP clusters with QM calculations. Furthermore, the structural properties of HP aqueous solution will be investigated by classical molecular dynamics simulation. The remainder of this article is arranged as follows. In section 2, the theoretical methods are briefly introduced. In section 3, we will present the results and discussions of the static properties for H₂O₂(H₂O)_n (n = 1-6) clusters and the structural properties of HP aqueous solution. Finally, a brief conclusion will be given.

Methodology

Quantum mechanical calculations

The quantum mechanical calculations were performed on an SGI Altix 3700 server by using the Gaussian 03 [60] program package. Geometries were optimized at the MP2/aug-mL-pVDZ level with and without counterpoise correction [61](using OPT= tight and SCF= tight keywords), respectively. Energies were determined on the MP2/aug-mL-pVTZ level with basis set superposition error (BSSE) correction.

The ABEEM/MM potential model for H₂O₂–H₂O system

Based on the previous researchers of our group [49,59] the ABEEM/MM potential energy, E_{\mathrm{A}\mathrm{B}\mathrm{E}\mathrm{E}\mathrm{M}/\mathrm{M}\mathrm{M}}, of H₂O₂–H₂O system is expressed as a sum of terms (Eq. (1)), each describing the energy required for distorting a molecule in a specific fashion (Eqs. (2)–(6)).

(1)E_{\mathrm{A}\mathrm{B}\mathrm{E}\mathrm{E}\mathrm{M}/\mathrm{M}\mathrm{M}}=E_{\mathrm{s}\mathrm{t}\mathrm{r}}+E_{\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{d}}+E_{\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}}+E_{\mathrm{v}\mathrm{d}\mathrm{w}}+E_{\mathrm{e}\mathrm{l}\mathrm{e}}

(2)E_{\mathrm{s}\mathrm{t}\mathrm{r}}={\sum _{\mathrm{b}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{s}}{k}_r(r-r_{eq})}^{\mathrm{2}}

(3)E_{\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{d}}={\sum _{\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}\mathrm{s}}{k}_{\theta }(\theta -{\theta }_{eq})}^{\mathrm{2}}

(4)E_{\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\displaystyle \sum _{\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}[{\nu }_{\mathrm{1}}(\mathrm{1}+\cos \phi )+{\nu }_{\mathrm{2}}(\mathrm{1}-\cos \mathrm{2}\phi )+{\nu }_{\mathrm{3}}(\mathrm{1}+\cos \mathrm{3}\phi )]}

(5)E_{\mathrm{v}\mathrm{d}\mathrm{w}}={\displaystyle \sum _{i,j}\left[\mathrm{4}{f}_{ij}{ϵ}_{ij}\left({\displaystyle \frac{{\sigma }_{ij}^{\mathrm{12}}}{R_{ij}^{\mathrm{12}}}}-{\displaystyle \frac{{\sigma }_{ij}^{\mathrm{6}}}{R_{ij}^{\mathrm{6}}}}\right)\right]}

(6)E_{\mathrm{e}\mathrm{l}\mathrm{e}}={\displaystyle \sum _i{\displaystyle \sum _{j\ne i}}}\left\{\underset{(H,lp\mathrm{i}\mathrm{n}\mathrm{H}\mathrm{B}\mathrm{I}\mathrm{R})}{\sum _{H\in i}{\displaystyle \sum _{lp\in j}}}{k}_{lp,H}(R_{iH,j(lp)}){\displaystyle \frac{q_{iH}{q}_{j(lp)}}{R_{iH,j(lp)}}}+k\left[{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\displaystyle \sum _a{\displaystyle \sum _b{\displaystyle \frac{q_{ia}{q}_{jb}}{R_{ia,jb}}}}}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\displaystyle \sum _{a-b}{\displaystyle \sum _{g-h}{\displaystyle \frac{q_{i(a-b)}{q}_{j(g-h)}}{R_{i(a-b),j(g-h)}}}}}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\displaystyle \sum _{lp}{\displaystyle \sum _{l{p}^{\prime }}{\displaystyle \frac{q_{i(lp)}{q}_{j(l{p}^{\prime })}}{R_{i(lp),j(l{p}^{\prime })}}}}}+{\displaystyle \sum _{g-h}{\displaystyle \sum _a{\displaystyle \frac{q_{ia}{q}_{j(g-h)}}{R_{ia,j(g-h)}}}}}+\underset{(a\ne H,H\mathrm{i}\mathrm{n}\mathrm{H}\mathrm{B}\mathrm{I}\mathrm{R}\mathrm{a}\mathrm{n}\mathrm{d}lp\mathrm{n}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{H}\mathrm{B}\mathrm{I}\mathrm{R})}{\sum _a{\displaystyle \sum _{lp}}}{\displaystyle \frac{q_{ia}{q}_{j(lp)}}{R_{ia,j(lp)}}}+{\displaystyle \sum _{lp}{\displaystyle \sum _{a-b}{\displaystyle \frac{q_{i(a-b)}{q}_{j(lp)}}{R_{i(a-b),j(lp)}}}}}\right]\right\}

In Eqs. (1) –(6), E_{\mathrm{s}\mathrm{t}\mathrm{r}} is the energy function for stretching O–O bond or O–H bond in H₂O₂ molecule or H₂O molecule, E_{\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{d}} represents the energy required for bending an angle, E_{\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}} is the torsional energy for rotation around O–O bond in H₂O₂ molecule. E_{\mathrm{v}\mathrm{d}\mathrm{w}} and E_{\mathrm{e}\mathrm{l}\mathrm{e}} describe the non-bonded atom-atom interactions. k_r, k_{\theta }, v_{\mathrm{1}}, v_{\mathrm{2}} and v_{\mathrm{3}} represent the force constants of the bond stretching, angle bending, and dihedral angle torsion, respectively. r_{\mathrm{e}\mathrm{q}} and {\theta }_{\mathrm{e}\mathrm{q}} are used to denote the equilibrium values of the bond lengths and angles, respectively. r, \theta, and \phi stand for the real bond lengths, bond angles, and dihedral angles, respectively. We use Lennard-Jones function to describe the van der Waals energy. The combining rules for the Lennard-Jones coefficients are employed: {\sigma }_{ij}={({\sigma }_{ii}{\sigma }_{jj})}^{\mathrm{1}/\mathrm{2}} and {ϵ}_{ij}={({ϵ}_{ii}{ϵ}_{jj})}^{\mathrm{1}/\mathrm{2}}. Furthermore, if i and j are intramolecular atoms, the coefficient f_{ij}=\mathrm{0.0} for any i–j pair connected by a valence bond (1-2 pairs) or a valence bond angle (1-3 pairs), f_{ij}=\mathrm{0.5} for 1, 4 interactions (atoms separated by three bonds), and f_{ij}=\mathrm{1.0} for intermolecular cases. For the Coulomb term, q_i and q_j denote the site charges of atoms, bonds, and lone-pairs, which are obtained by the ABEEM method. R_{ij} is the distance between the site points i and j, and k_{ij} is equal to 0.57 [62], which is an overall optimized correction coefficient in ABEEM. As is known, there are two types of hydrogen bonds between HP and water molecules: The first is that formed between the lone-pair electron on HP oxygen and the water hydrogen (lpO(HP)…H–O(water)); the second is formed between the lone-pair electron on water oxygen and HP hydrogen (lpO(water)…H–O(HP)). To well depict the nature of the two types of hydrogen bonds, we take special treatment by introducing the parameters k_{lo\mathrm{O},\mathrm{H}\mathrm{w}}(R_{ij}) and k_{lp\mathrm{O}\mathrm{w},\mathrm{H}}(R_{ij}) to describe the electrostatic interaction of the two types of hydrogen bonds. The fitted expressions of k_{lp\mathrm{O},\mathrm{H}\mathrm{w}}(R_{ij}) and k_{lp\mathrm{O}\mathrm{w},\mathrm{H}}(R_{ij}) are expressed as follows:

(7)k_{lp\mathrm{O},\mathrm{H}\mathrm{w}}(R_{ij})=\mathrm{0.660}-{\displaystyle \frac{\mathrm{0.140}}{\mathrm{1}+{\mathrm{e}}^{[(R_{ij}-\mathrm{1.288})/\mathrm{0.022}]}}},

(8)k_{lp\mathrm{O}\mathrm{w},\mathrm{H}}(R_{ij})=\mathrm{0.600}-{\displaystyle \frac{\mathrm{0.126}}{\mathrm{1}+{\mathrm{e}}^{[(R_{ij}-\mathrm{1.112})/\mathrm{0.097}]}}}.

The corresponding plots of k_{lp\mathrm{O},\mathrm{H}\mathrm{w}}(R_{ij}) and k_{lp\mathrm{O},\mathrm{H}\mathrm{w}}(R_{ij}) are shown in Fig. 1. The parameters of HP and water employed here are all taken from Refs. [49,59].

Molecular dynamics simulations for H₂O₂ aqueous solution

A classical molecular dynamics (MD) simulation was performed in terms of the ABEEM/MM, starting with 70 HP molecules in a cubic box of length 24.662 Å containing 311 H₂O molecules (the mass fraction of HP is about 30%). The system was optimized first, and then the MD simulation was carried out in the isothermal-isobaric (constant pressure and temperature, NPT) ensemble with Anderson thermostats and velocity Verlet integrator. Furthermore, cubic periodic boundary conditions and a time step of 1fs were used, with all bonds to hydrogen constrained using the rattle algorithm. Minimum image conditions were used and no dielectric constant was needed because the explicitly solvent molecules were presented. For molecular dynamics simulation, 0.5 ns of a MD run for equilibration was performed, followed by 1.5 ns of simulations for the calculation of various properties. We recomputed the partial charges of all sites using the ABEEM method every step. Charges are allowed to transfer just between charged sites on the same molecule, not between different molecules. The cutoff radius of 9.0 Å with the nearest image convention is used for the nonbonded interactions in the simulations. The nonbonded interactions are truncated, using force shifting [63], where the calculated forces and energies are smoothly shifted to zero at the cutoff distance.

Results and discussion

Properties of H₂O₂–H₂O dimer

Optimized geometries and interaction energies

Figure 2 depicts the two stable structures of H₂O₂–H₂O dimer, denoted as W1-A and W1-B, respectively. The ABEEM/MM optimized H-bond lengths (Å) are shown first followed by the MP2/aug-mL-pVDZ normal and counterpoise corrections (CP) optimized results. It can be seen from Fig. 2 that the optimized H-bond lengths of MP2 method with CP corrections are obviously longer than those of the MP2 normal optimized results. However, the MP2 CP optimized angles are consistent with those of the MP2 normal optimized results. W1-A has a H-bond structure of five-membered ring, in which the H-bond length of H-Ow is 0.294 Å shorter than that of O-Hw by ABEEM/MM model (both of the MP2 values are 0.274 Å). W1-B is of a single hydrogen-bonded structure, with one hydrogen atom of H₂O as the proton donor and one oxygen atom of HP as the proton acceptor. And the H-bond length calculated by ABEEM/MM model is 2.013 Å, which is close to the MP2 results of 2.004 Å. In addition, the related angles from ABEEM/MM shown in Fig. 2 agree well with those of MP2 calculations.

The interaction energies of H₂O₂–H₂O dimer calculated by ABEEM/MM model and ab initio methods are listed in Table 1. We have taken into account that the correction of the BSSE for the interaction energy should be performed at the BSSE corrected equilibrium geometry. We can see that the interaction energies for the CP and normal optimized geometries are similar. The results have shown that the five-membered ring H-bonded structure (W1-A) is more stable than the single H-bonded structure (W1-B) by 3.26 kcal/mol from ABEEM/MM model, which is close to those of the MP2 calculations (2.92/2.88 kcal/mol). Compared with the MP2 results of this work, the average absolute deviations (AAD) of the ABEEM/MM interaction energies for H₂O₂–H₂O dimer are only 0.17/0.19 kcal/mol.

The ABEEM charge distributions

The ABEEM charge distributions of isolated H₂O₂, H₂O, and H₂O₂–H₂O dimer are listed in Table 2. It is shown that the charge distribution of H₂O₂–H₂O dimer is quite different from those of isolated H₂O and H₂O₂. Two points should be mentioned here: (1) The significant variation of charges takes place at the position where the H-bond forms. There are two types of hydrogen bond formed in W1-A. One is formed between H2 of H₂O₂ and lpO5 of H₂O, where q_H2 increases by 0.0300 while q_lpOw5 decreases by 0.0581 compared with the isolated H₂O₂ and H₂O. The other is formed between H7 of H₂O and lpO3 of H₂O₂, where q_Hw7 increases by 0.065 while q_lpO3 decreases by 0.0163 compared with the isolated H₂O and H₂O₂. For W1-B, the obvious charge variations take place at H6 and lpO1’, where q_Hw6 increases by 0.0617 and q_lpO1’ decreases by 0.0047 compared with the isolated H₂O and H₂O₂. (2) As revealed by experimental gas phase data [64] and molecular dynamic simulations of H₂O₂ in aqueous solution [24,64], H₂O₂ is a better proton donor but a poor proton acceptor than H₂O. This can also be confirmed by the analysis of the charge distribution in H₂O₂. From the two parts of H₂O₂ formed H-bond with H₂O, we can easily find that the variation of the lone-pair electronic charges are relatively smaller compared with the charge changes of hydrogen atom. To summarize, the fluctuating charges ABEEM/MM model can reasonably reflect the variations of charge distribution caused by the changing environment.

Properties of H₂O₂(H₂O)_n (n = 2-6) clusters

Optimized geometries and interaction energies

The ABEEM/MM optimized geometries of hydrated clusters of H₂O₂(H₂O)_n (n = 2-6) are presented in Fig. 3 and Fig. 4, along with the corresponding H-bond lengths (Å). The corresponding interaction energies of these structures determined by ABEEM/MM model and several ab initio methods are listed in Table 3. For n = 2, three cyclic H-bond structures are obtained by ABEEM/MM model. The seven-membered ring structure, named W2-cyclic-A, which can be viewed as a combination of water dimer with an HP molecule linked by hydrogen bonds, and this is more energy favorable than the other two six-membered ring hydrogen bond structures (W2-cyclic-B and W2-cyclic-C). The interaction energies calculated by ABEEM/MM model for 1∶2 complexes are -16.91, -15.81 and -15.49 kcal/mol, respectively, which agree well with those of MP2/aug-mL-pVTZ//MP2/aug-mL-pVDZ results.

For n = 3, all four structures are energetically close to each other, and W3-cyclic-A is the most stable structure indicated by ABEEM/MM model and MP2 methods. The energy order of these conformations is W3-cyclic-A<W3-cyclic-B<W3-cyclic-D<W3-cyclic-C, and the interaction energies from the ABEEM/MM model are close to those from the MP2 calculation. W3-cyclic-A has the smallest ABEEM/MM interaction energy of -27.69 kcal/mol (MP2 value is -26.78/-26.72 kcal/mol), and W3-cyclic-C has the greatest ABEEM/MM interaction energy of -26.14 kcal/mol (W3-cyclic-C and W3-cyclic-D have the same interaction energies of -26.09 kcal/mol at MP2 level, and MP2(CP) values are -26.07 and -26.02 kcal/mol, respectively).

For n = 4, the four stable structures are portrayed in Fig. 3, from which the obvious transformation from 2D planar structure to 3D hydrogen bonding network structure can be seen. The cyclic structures (W4-cyclic-A and W4-cyclic-B) are relatively more stable than the open structure (W4-open-C) and the prism structure (W4-prism-D) both from ABEEM/MM model and MP2 methods. The interaction energies calculated by ABEEM/MM model for n = 4 are -36.02, -36.04, -35.21 and -33.41 kcal/mol, respectively, which is in accordance with the MP2 calculations of -35.59/-35.48, -35.59/-35.48, -35.48/-35.35 and -34.60/-34.49 kcal/mol.

For n = 5, three prism-like structures are shown in Fig. 4. The interaction energies calculated by ABEEM/MM model are -50.99, -46.61 and -46.43 kcal/mol, respectively. Although ABEEM/MM model overestimates the interaction energy of W5-prism-A, it is acceptable as the deviations of the interaction energies for the other two structures relative to MP2 results are all within 2 kcal/mol, and the energy order is consistent with those from MP2 method. For n = 6, five of the most favorable clusters, namely, W6-cage-A, W6-cage-B, W6-cage-C, W6-cage-D, and W6-cage-E, are shown in Fig. 4, where the increased number of H-bonds is evident. The interaction energy of the most possible structure, W6-cage-A is -55.86 kcal/mol, which is also in accordance with the MP2 results (-56.48/-56.29 kcal/mol). For the other four complexes, the maximum deviation with respect to MP2 results is within 6%.

The changing tendencies of the average H-bond lengths for O-Hw and H-Ow in the hydrated clusters of HP(H₂O)_n (n = 1-6) are depicted in Fig. 5. From the viewpoint of geometrical structure, three points must be mentioned: (1) From n = 1 to 4, in the wake of the augmentation of the cyclic structure, all the H-bond lengths are shortened obviously. This trend can be clearly seen in Fig. 5. (2) n = 4 is the transition state structure from 2D planar structure to 3D network structure. From the cyclic structure to open structure, the H-bond length of O-Hw is elongated by about 0.171 Å by ABEEM/MM model, close to the MP2 results of 0.198/0.194 Å. But from open structure to prism structure, the H-bond length of O-Hw changes inconspicuously. However, the H-bond length of H-Ow remains steady along with the transformation from cyclic structure to prism structure for n = 4. (3) From n = 5 to 6, the ABEEM/MM H-bond lengths of O-Hw decreases about 0.078 Å, which is consistent with the MP2/aug-mL-pVDZ results (0.083 Å). However, the ABEEM/MM H-bond length of H-Ow decreases 0.010 Å from n = 5 to n = 6, while the MP2 results increases by 0.014/0.029 Å.

In summary, from n = 1 to 6, the overall trends of the interaction energy of HP(H₂O)_n (n = 1-6) is that it increases about 10 kcal/mol, which is about twice as the interaction energy of water dimer when a water molecule is added. The MP2 CP optimized H-bond lengths are obviously longer than those of the normal MP2 optimized and ABEEM/MM results, and the average value is about 0.070 Å. However, the interaction energies between the CP and normal optimized geometries are negligible. Compared with MP2/aug-mL-pVTZ//MP2/aug-mL-pVDZ method, ABEEM fluctuating charge potential model can give correct description of the geometries and interaction energies of H₂O₂(H₂O)_n (n = 1-6). The AAD for interaction energies is 1.00 kcal/mol, and the AAD of H-bond lengths and angles associated with the HP molecule (shown in Fig. 4, but not shown in Fig. 5 for clarity) are 0.024 Å and 1.8°, respectively.

Dipole moments

The charge distribution of H₂O₂(H₂O)_n (n = 2-6) complexes are listed in supplementary materials. Similar to the H₂O₂–H₂O dimer, the variation of charge in the H₂O₂(H₂O)_n (n = 2-6) clusters are mainly at the positions where H-bonds form. Dipole moment is an important quality for representing charge distributions, which can be the criterion of reasonable charge distribution. In addition, it can provide the total information of structural properties. Correlation of the dipoles for H₂O₂(H₂O)_n (n = 1-6) evaluated with ab initio calculations at MP2/aug-mL-pVTZ level and the ABEEM/MM model is shown in Fig. 6., and the linear correlation coefficient is 0.9498. This further validates the reliability of the newly constructed ABEEM/MM interaction potential for H₂O₂–H₂O systems.

Structural properties of H₂O₂ in aqueous solution

The detailed structure of H₂O₂ in aqueous solution is characterized by the radial distribution functions (RDFs), which describes how the density of surrounding atoms varies as a function of the distance from a particular atom. Here, the structure feature of the water molecules surrounding the HP is described by the RDFs of the hydrogen atoms of water molecules around the oxygen atom of HP (Fig. 7(a)) and the oxygen atoms of water molecules around the hydrogen atom on the HP (Fig. 7(b)). The g_O-Hw shows a sharp and low first peak located at 2.019 Å, followed by a higher second peak centered at about 3.250 Å, and the third peak is very weak located at about 6.0 Å. The g_H-Ow has a high and sharp first peak located at 1.749 Å corresponding to the first hydration shell, followed by a lower and boarder second peak centered at about 3.675 Å. The g_H-Ow has well-defined first peaks, indicating strong hydrogen bond interaction between the hydrogen on the HP and water oxygen. Meanwhile, the first peak of g_H-Ow is about 0.270 Å shorter than that of g_O-Hw, and this also shows that the HP is a good proton donor and poor proton acceptor in aqueous solution.

Conclusion and outlook

In this work, we have systematically investigated the hydrogen bond interaction of complexes between HP and water (with up to six water molecules) by high-level ab initio method and a newly constructed ABEEM/MM fluctuating charge model. This potential gives reasonable properties of H₂O₂–H₂O clusters through comparision with the ab initio calculations. The AAD for interaction energies, H-bond lengths and angles associated with HP are 1.00 kcal/mol, 0.024 Å and 1.8°, respectively. The linear correlation coefficient of dipole moments between ABEEM/MM model and MP2/aug-mL-pVDZ method reaches 0.9498. The ABEEM/MM results also indicate that n = 4 is the transition state structure from 2D planar structure to 3D network structure. The variation of the average H-bond length with the increasing number of water molecules given by ABEEM/MM model agree well with those given by the ab initio studies. Molecular dynamics simulation HP aqueous solution has been carried out by ABEEM/MM model, and the results confirms that HP is a good proton donor and poor proton acceptor in aqueous solution through the analysis of the RDFs and the charge distributions.

Overall, the newly constructed ABEEM potential model can reproduce rather accurate structural and energetic properties of H₂O₂(H₂O)_n (n = 1-6) clusters and H₂O₂ aqueous solution. Based on this potential, studies of H₂O₂ interaction with nucleic acid base in aqueous solution has been undertaking.

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