A Systemic Investigation of Hydrogen Peroxide Clusters (H2O2)n (n

ARTICLE pubs.acs.org/JPCA

A Systemic Investigation of Hydrogen Peroxide Clusters (H2O2)n (n = 1-6) and Liquid-State Hydrogen Peroxide: Based on Atom-Bond Electronegativity Equalization Method Fused into Molecular Mechanics and Molecular Dynamics Chun-Yang Yu and Zhong-Zhi Yang* Chemistry and Chemical Engineering Faculty, Liaoning Normal University, Dalian 116029, China

bS Supporting Information ABSTRACT: Hydrogen peroxide (HP) clusters (H2O2)n (n = 1-6) and liquid-state HP have been systemically investigated by the newly constructed ABEEM/MM fluctuating charge model. Because of the explicit description of charge distribution and special treatment of the hydrogen-bond interaction region, the ABEEM/MM potential model gives reasonable properties of HP clusters, including geometries, interaction energies, and dipole moments, when comparing with the present ab initio results. Meanwhile, the average dipole moment, static dielectric constant, heats of vaporization, radial distribution function, and diffusion constant for the dynamic properties of liquid HP at 273 K and 1 atm are fairly consistent with the available experimental data. To the best of our knowledge, this is the first theoretical investigation of condensed HP. The properties of HP monomer are studied in detail involving the structure, torsion potentials, molecular orbital analysis, charge distribution, dipole moment, and vibrational frequency.

1. INTRODUCTION Hydrogen peroxide (HP) has recently received considerable attention due to its importance in atmospheric chemistry, biochemistry, and medicine. It is a dominant oxidant in clouds, fog, and rain, effecting the aqueous oxidation of SO2;1 it is a byproduct of several metabolic pathways, giving significant quantities of H2O2 detectable in the human blood;2 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. HP has been the subject of many experimental3-14 and theoretical studies.11,15-36 Early in 1965, Hunt and co-worker3 investigated the torsional oscillation between the two OH groups of the HP molecule through a study of the far-infrared absorption spectrum of the molecule. Likewise, a few groups have studied HP in low-temperature matrices.11-14 Along with the fast progress for theoretical and computational chemistry in the last quarter of the 20th century, high-level ab initio methods were applied to investigate the properties of HP monomer and HP clusters. A notable theoretical study due to Gonzalez et al.20 compared MP2 and DFT calculations for the H2O2 dimer and H2O2-H2O complex for investigation of interaction energies and O-H frequency shifts in these multiple hydrogen-bonded systems. They observed that in the H2O2-H2O complex, each unit can behave as either a hydrogen-bond donor or an acceptor forming cyclic structures, which generally involve nonidentical hydrogen r 2011 American Chemical Society

bonds. Their study also demonstrated that popular DFTbased models yielded energies and vibrational shifts sizably overestimated than those at the MP2 level. Koput et al.23 presented the potential energy surface of HP from large-scale ab initio calculations using the CCSD(T)/cc-pVQZ method. The calculated molecular properties are found to be in good agreement with experimental data. Engdahl et al.11,25 performed a low temperature Ar-matrix isolation as well as an ab initio study of the H2O2 dimer and its deuterated analogues and proposed that the dimer at the MP2 level should exhibit a “cyclic” structure with two hydrogen bonds. This proposition was experimentally confirmed through IR spectroscopy. Kulkarni et al.27 have explored HP clusters (H2 O2)n (n = 2-4), using ab initio techniques. Their study at the MP2 level shows the ability of HP to form a three-dimensional network remarkably similar to that of the corresponding water clusters. Subramanian and Sathyamurthy33 reported by using HF, DFT, and MP2 calculations that HP clusters tended to form hydrogen-bonded cyclic and cage structures along the lines expected of a molecule that can act as a proton donor as well as an acceptor. In addition, the HF calculations suggest the formation of stable helical structures for larger clusters, provided the neighbors form an open book structure. Received: November 27, 2010 Revised: January 16, 2011 Published: March 09, 2011 2615

dx.doi.org/10.1021/jp111284t | J. Phys. Chem. A 2011, 115, 2615–2626

The Journal of Physical Chemistry A

ARTICLE

2.2. ABEEM/MM Potential for HP. 2.2.1. ABEEM Fluctuating Charge Model for HP. The ABEEM model has been developed

Figure 1. The structure of monomer hydrogen peroxide (HP) by ABEEM model.

However, up to now, only few researchers have focused on pure HP due to its difficulty to handle,10,25,37 which is probably the reason why its liquid-state properties have been much less studied than those of water. Classical molecular dynamics using predefined potentials, force fields, based either on empirical data or on independent electronic structure calculations, is well established as a powerful tool serving to investigate manybody condensed matter systems, including biomolecular assemblies. In a force field, the electrostatic energy is determined by the Coulombic interaction between the partial charges. Thus, the inclusion of polarization effects or not directly influences the accurate description of intermolecular interactions. Because the polarizable force field can reflect the response of the electron density to an electrostatic field of condense phase environment, it has been developed quickly and used widely since the 1970s. On the basis of the atom-bond electronegativity equalization method (ABEEM)38-42 fused into molecular mechanics (MM), Yang et al.43-53 have developed a new polarization force field, that is, the ABEEM/MM fluctuating charge model. It has been applied successfully to the water system,43,44 ion-water system, 45-47 organic molecules,48 peptides,49 and nucleic acid systems.50-52 Recently, the ABEEM/MM model has been used to perform dynamics simulation for proteins.53 In this Article, we carry out a systemic analysis of HP clusters in terms of ab initio methods and the newly constructed ABEEM/MM fluctuating charge model. Furthermore, the model is used to investigate the dynamic properties of the pure liquid-state HP. The remainder of this Article is arranged as follows. In section 2, we describe the new ABEEM/MM potential model for HP system. In section 3, we give the results and discussions of the static properties for HP clusters and the dynamic properties for liquid-state HP, respectively. Finally, conclusion and outlook for the ABEEM/MM/MD model are given.

2. METHODOLOGY 2.1. Quantum Mechanical Calculations. The quantum mechanical calculations were performed on an SGI Altix 3700 server by using the Gaussian 0354 program package. Geometries were optimized at the MP2 level with the 6-311þþG(d,p) basis set. Energies were determined on the same level with the 6-311þþG(2d,2p) basis set, and the counterpoise procedure of Boys and Bernardi55 was applied to correct for the basis set superposition error (BSSE).

in the framework of the principle of electronegativity equalization and density functional theory. Here, the ABEEM model gives the explicit sites of all molecular regions, such as atoms, bonds, and lone-pair electrons. There are totally 11 sites in a HP molecule including 4 atoms, 3 (O-O and 2 O-H) bonds, and 4 lone-pairs (Figure 1). The centers of bond regions are located on the points that partition the bond lengths according to the ratio of covalent atomic radii of two bonded atoms, and the centers of the lone-pairs are 0.74 Å far from the oxygen nucleus and with an intervening angle, θLOL, of 109.46. The partial positive charges on the O and H atoms are balanced by an appropriate negative charge located at the O-O and O-H bonds, and the lone-pair electrons. The detailed formulas concerning charge calculation are shown in the following. In this model, the total electronic energy Emol of a molecule at the ground state can be expressed as follows: Emol ¼

∑a ½Ea - μa qa þ ηa q2a þ þ

∑ ½Ea - b - μa - b qa - b þ ηa - b q2a - b

a-b

∑lp ½Elp - μlp qlp þ ηlp q2lp þ g ∑- h að¼g∑, hÞ ka, g R- h qa qg - h a, g - h

"

þ

∑a lpð∈aÞ ∑ ka,Rlpqa qlp þ k 12 ∑a bð∑6¼aÞ qRa qb

a, lp a, b qa - b qg - h 1 qlp qlp0 1 þ þ 0 2 a - b g - hð6¼a - bÞ Ra - b, g - h 2 lp lp ð6¼lpÞ Rlp, lp0

∑

∑

∑∑

∑ ∑

qa qg - h þ þ g - h að6¼g , hÞ Ra, g - h

∑a ∑

qa qlp þ lpð6¼aÞ Ra, lp

∑lp ∑

qa - b qlp a - b Ra - b, lp

#

ð1Þ where μa*, μa-b*, and μlp* are the valence-state chemical potential of atom a, bond a-b, and lone-pair electron lp in the molecule, respectively; ηa*, ηa-b*, and ηlp* are the valence-state hardness of atom a, bond a-b, and lone-pair electron lp, respectively; qa, qa-b, and qlp are the partial charges of atom a, bond a-b, and lone-pair electron lp in the molecule, respectively. R is the distance between charge sites; for example, Ra,b is the distance between atom a and atom b. ka,g-h and ka,lp are regarded as adjustable parameters; k is an overall correction coefficient in this model. The effective electronegativity of an atom or a chemical bond or a lone-pair electron is identified as the negative of the corresponding effective chemical potential, that is, the partial derivative of total energy E with respect to the corresponding electron number or partial charge: μi = (∂E/∂Ni)R,Nj = -(∂E/ ∂qi)R,qj = -χi. Thus, based on eq 1, we obtain eqs 2-4 for the effective electronegativities of atom a, bond a-b, and lone-pair electron lp in molecule, respectively.

χa ¼ χa þ 2ηa qa þ Ca ð

∑

qb þk þ bð6¼aÞ Ra, b 2616

∑

a-b

qa - b þ

∑

∑

lpð∈aÞ

qlp Þ

qg - h þ g - hð6¼a - bÞ Ra, g - h

∑

qlp lpð6¼aÞ Ra, lp

! ð2Þ

dx.doi.org/10.1021/jp111284t |J. Phys. Chem. A 2011, 115, 2615–2626


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Table 1. ABEEM Parameters for HPa

Table 2. Force Field Parameters for HP

χ* HP

2η*

χ0

bond stretching

kr

req (Å)

H-

2.003

8.550

2.200

O-H

523.0

0.964

O-

3.660

29.600

3.550

O-O

290.0

1.460

H-O

4.436

64.336

O-O

4.516

16.767

lpO-

7.608

25.850

χ* and η* are the valence-state electronegativity and valence-state hardness parameters for atom H, atom O, bond H-O, bond O-O, and lone pair electrons of oxygen, respectively. χ0 is the Pauling electronegativity scale.

bond bending

kθ

θeq (deg)

O-O-H

60.0

98.5

a

χa - b ¼ χa - b þ 2ηa - b qa - b þ Ca - b, a qa þ Da - b, b qb þk

∑

qg

gð6¼a, bÞ Ra - b, g

þ

∑

qg - h

g - hð6¼a - bÞ Ra - b, g - h

þ

∑lp R

!

qlp

þ

∑

qg - h

g - h Rlp, g - h

þ

∑

qlp

lpð6¼lpÞ Rlp0 , lp

χa ¼ χb ¼ ::: ¼ χa - b ¼ χg - h ¼ ::: ¼ χlp ¼ χ

ð4Þ

ð5Þ

This yields n þ m þ l simultaneous equation for an arbitrary molecule containing m atoms, n bonds, and l lone-pair electrons. These equations, along with the constraint equation on its net charge, can be solved to give the charges on each atom, each bond, and each lone-pair electron in the molecule if all parameters in eqs 2-4 are known. The parameters for ABEEM are explicitly described in Table 1. The ABEEM model is to treat partial charges on atom, bond, and lone pair as fluctuating variables, which respond to their environments. The partial charges are propagated in time and will be redistributed on a molecule due to the equal electronegativity of each site. 2.2.2. Combination of ABEEM Model and MM for Describing the HP System. Based on the combination of ABEEM and MM, the potential energy EABEEM/MM of HP system is expressed as a sum of terms, each describing the energy required for distorting a molecule in a specific fashion. EABEEM=MM ¼ Estr þ Ebend þ Etors þ Evdw þ Eele

Ebend ¼ Etors ¼

kr ðr - req Þ2

ð7Þ

∑

kθ ðθ - θeq Þ2

ð8Þ

angles

H-O-O-H

3.350

-3.270

0.000

van der Waals

σ (Å)

ε (kcal/mol)

O H

2.332 2.100

0.054 0.012

∑

1 ½ν1 ð1 þ cos jÞ þ ν2 ð1 - cos 2jÞ 2 torsions þ ν3 ð1 þ cos 3jÞ

∑i, j

"

ð9Þ

4fij εij

∑i, j

"

σ 12 σ6 R 12 R 6

q qj e2 kij i Rij

!# ð10Þ

# ð11Þ

In eqs 6-11, Estr is the energy function for stretching O-O or O-H bonds in HP molecule, Ebend represents the energy required for bending O-O-H angle, Etors is the torsional energy for rotation around O-O bond, and Evdw and Eele describe the nonbonded atom-atom interactions. kr and kθ represent the force constants of the bond stretching and angle bending, respectively. req and θeq are used to denote the equilibrium values of the bond lengths and angles. v1, v2, and v3 are the force constants of the dihedral angle torsions. r, θ, and j stand for the bond lengths, the bond angles, and the dihedral angles. Geometric combining rules for the Lennard-Jones coefficients are employed: σij = (σiiσjj)1/2 and εij = (εiiεjj)1/2. Furthermore, if i and j are intramolecular, the coefficient fij = 0.0 for any i-j pair connected by a valence bond (1-2 pairs) or a valence bond angle (1-3 pairs), fij = 0.5 for 1,4 interactions (atoms separated by three bonds), and fij = 1.0 for intermolecular cases. For the Coulomb term, qi and qj denote the site charges of atoms, bonds, and lone-pairs, which are obtained by the ABEEM method. Rij is the distance between the site points i and j, and kij is equal to 0.57,39 which is an overall optimized correction coefficient in ABEEM. In the hydrogen-bond interaction region (HBIR), kij is replaced by kH-bond(Rij) to describe the electrostatic interaction between the hydrogen atom and the lone-pair electron. For the HP system, the best-fitted function kH-bond(Rij) is expressed as follows:

ð6Þ

∑

bonds

v3

Eele ¼

lp, g

Here, Ca-b,a = ka,a-b/Ra,a-b, Da-b,b = kb,a-b/Rb,a-b, Ca, and Clp are regarded as adjustable parameters. The electronegativity equalization principle demands that eq 5 apply for all atoms, all bonds, and all lone-pair electrons in the molecule:

Estr ¼

v2

Evdw ¼

qg ∑ gðˇlpÞ R

!

v1

a - b, lp

ð3Þ χlp ¼ χlp þ 2ηlp qlp þ Clp qað6¼lpÞ þ k

bond torsion

klp, H ðRÞ ¼ 0:686 -

0:091 1 þ exp½ðR - 1:185Þ=0:261

For the force field parameters, the bond stretching and the angle bending are regarded as “hard” degrees of freedom parameters, which means the variation of the bond length and bond angle required much larger energy than the torsional angle variation; therefore, the discrepancy of the value of bond length and angle in different HP clusters is relatively smaller. So the equilibrium values of bond length and angle (Table 1) were extracted directly from the experimental values4,56 of monomer HP, but the necessary modification was made because we take 2617



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Figure 3. Different conformers of HP, along with the point group classification. Large spheres represent the oxygen atoms, and small spheres represent the hydrogen atoms.

Figure 2. Variation of conformation energy with H-O-O-H angle of the HP monomer.

the values of bond length and angle of large HP clusters into account. Torsion terms are often regarded as “soft” degrees of freedom, in which most of the variation in structure and relative energies is due to the complex interplay between the torsional and nonbonded contributions. In this work, we fit the torsion parameters through the least-squares optimization procedure to make the variation of conformation energy with H-O-O-H angle of HP monomer be in good agreement with those from our ab initio calculations, and make the energy difference of isolated conformers be in agreement with the experimental data.3,4,6,56 In addition, the Lennard-Jones parameters are very necessary to be adjusted to reproduce clusters interaction energies for small HP clusters. These parameters are all summarized in Table 2. 2.3. Molecular Dynamic Simulations (MDS). The dynamic simulations are performed using the modified Tinker program in the canonical (constant temperature and volume, NVT) ensemble with Berendsen thermostats and velocity Verlet integrator. Furthermore, cubic periodic boundary conditions and a time step of 1 fs were employed. The box length is set to 23 Å with 216 HP molecules, which correspond to the experimental density of liquid HP (1.44 g/cm3) at a temperature of 273 K. The Minimum image conditions are also used, and no dielectric constant is employed because the explicit solvent molecules are presented. For MDS, 0.5 ns of a MD run for equilibration was performed, followed by 4.5 ns of simulations for the calculation of various properties. We recomputed the partial charges of all sites using the ABEEM method at every 0.1 ps.

3. RESULTS AND DISCUSSION 3.1. Properties of HP Monomer. The HP molecule contains a dihedral angle for which the barriers associated with its motion are low and through them links all lower energy conformers. We performed calculations for a HP molecule to change the dihedral angle from 180 to -180 using the CCSD(T) method, MP2 method, and ABEEM/MM model (Figure 2). As compared to the CCSD(T) and MP2 methods, the rotation potential energy curve along the dihedral angle presented by ABEEM/MM model is depicted very well. In this potential energy surface, three typical structures were found: one is the nonplanar structure named open book (112.0), and the other includes two planar structures named trans (180.0) and cis (0.0), respectively. The optimized structures of these three conformers are provided in Figure 3.

Figure 4. The nO and σOO molecular orbitals of three hydrogen peroxide (HP) conformers. The geometrical structures were determined at the MP2/6-311þþG(d,p) level.

From the viewpoint of molecular orbital theory, the open book structure is stabilized by hyperconjugative interactions between the lone pair orbitals (nO) with the vicinal OH antibond orbitals (σOH*), which means the charge transfer occurred from nO into σOH*. However, the nOfσOH* overlap diminishes when the dihedral angle increases to 180 (trans), thereby losing the hyperconjugative stabilization and resulting in the trans barrier. The cis barrier has been associated with electronic strain. Carpenter and Weinhold35 found that the eclipsing interaction of the O-H bonds in the cis conformation results in a slightly bent O-O bond, the bonding hybrids directed by ∼4 off the line of centers. Meanwhile, the electrostatic repulsion of OH dipoles in cis structure leads to opening of the OOH angle to 104.3 as compared to the open book structure of 99.6 (calculated at the MP2/6-311þþG(d,p) level). To clearly see the molecular orbital interaction, the nO and σOO orbitals of three HP conformers were shown in Figure 4. It is indicated that the lone pair (perpendicular to the HOO plane) overlaps with the OH antibond orbitals significantly for the open book structure, and there is no overlap for trans and cis structures. In addition, that the hybrid directions differ from the line of center in the cis conformer is also shown obviously in Figure 4. Electronic strain is weaker in open book and trans conformers as the hybrids are more nearly directed along the line of centers. As the most stable structure in the HP monomer, the open book structure was investigated by various quantum mechanical methods and ABEEM/MM model to provide the basis for further study in the present work. The calculated H-O and O-O bond lengths, H-O-O bond angle, and H-O-O-H 2618



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Table 3. Calculated and Experimental Geometrical Parameters and Relative Stabilities of Various Conformers of HP relative stabilitya(kcal/mol) theoretical method 33

I

II

geometries of open book structure III

O-H (Å)

O-O (Å)

O-O-H (deg)

H-O-O-H (deg)

HF/6-311þþG(d,p)

0.0

8.6

0.9

0.943

1.385

102.9

117.6

B3LYP/6-31G*33

0.0

8.9

0.7

0.973

1.455

99.7

118.7

B3LYP/6-31þþG(d,p)b

0.0

9.6

0.8

0.967

1.454

100.5

121.1

MP2/6-311þþG(d,p)33

0.0

9.0

1.0

0.965

1.450

99.6

121.5

MP2/6-311þþG(2d,2p)b

0.0

7.83

1.2

0.964

1.460

99.4

115.2

MP2/aug-cc-pVTZb

0.0

8.5

1.2

0.967

1.454

99.6

112.5

CCSD(T)/cc-pVTZb CCSD(T)/aug-cc-pVQZ57

0.0 0.0

8.4 7.19

1.2 1.09

0.964 0.964

1.458 1.453

99.6 100.05

113.9 112.40

OUDQMC30

0.0

7.22

1.10

0.9642

1.4521

100.12

112.34

ABEEM/MM

0.0

7.31

1.14

0.968

1.463

99.3

112.0

expt.3,4,6,56

0.0

7.03

1.104

0.9654

4

6

7.11

1.11

0.967

56

1.4644

99.44 56

1.4556

102.32

111.84 56

113.7056

6

7.32 a

Refer to Figure 3 for the definition of I, II, and III. b This work.

Table 4. Gas-Phase Atom Charge q, Dipole Moment μ (D), and Frequencies ω (cm-1) of Open Book HP Monomer from the ABEEM Model and ab Initio Methods ABEEMa

ABEEMb

qO1/ qO3

0.0247

-0.3187

-0.2696

-0.2582

qH2/ qH4

0.3395

0.3187

0.2696

0.2582

1.816

1.895

qO1-O3

-0.0361

qO1-H2/qO3-H4

-0.0416

qlpO1/qlpO3

-0.1548

qlpO10 /qlpO30 μ (D)

-0.1498 2.21

-1

ω (cm )

a

MP2/6-311þþG(d,p)

MP2/aug-cc-pVDZ

expt.

2.2058

443.9, 879.5

394.2, 920.6

393.9, 880.7

1306.9, 1366.4

1300.1, 1456.6

1309.6, 1413.8

371, 877 1266, 1402

3606.0, 3609.3

3848.0, 3849.0

3767.6, 3769.0

3599, 360817

b

The geometries are shown in Figure 3. The charge distributions include atoms, bonds, and lone pairs. The charges regressed to atoms.

torsion angle along with those of different ab initio results and the experimental values are listed in Table 3. As compared to experimental values, the majority of ab initio methods overestimate the conformational energy of conformer II (trans) about 1 kcal/mol. Likewise, HF and DFT33 underestimate the conformational energy of conformer III (cis) about several tenths of a kilocalorie per mole. Yet the results from OUDQMC,30 MP2/6-311þþG(2d,2p), and CCSD(T)/aug-cc-pVQZ 57 methods are in accord with the experimental data. It can be seen from Table 3 that the ABEEM/MM results are in better agreement with experimental and high-level ab initio results. The results of the ABEEM/MM model show that the planar cis and trans conformations are less stable than the most stable nonplanar open book structure by 7.31 and 1.14 kcal/mol, which agree well with the experimental values of 7.32/7.11/7.0 and 1.11/1.10 kcal/mol. The detailed charge distributions of the open book structure are shown in Table 4. The positive charges are located on the atoms, and the negative charges are located at the bonds and lone-pair regions. To show the reasonability of the ABEEM charge distribution, we compared the ABEEM atomic charges to those from Mulliken charge distributions (at MP2/6-311þþG(d,p) and MP2/aug-ccpVDZ level). The ABEEM atomic charges are obtained by regressing

Figure 5. Structures for two conformers of HP dimer.

the charges of the bond and lone-pair to the conjoint atoms. Results show that ABEEM gives bigger negative charges for oxygen atoms, and bigger positive charges for hydrogen atoms. It is reasonable due to the suitable charge sites of ABEEM method. As a good measure to evaluate molecular charge distribution, the dipole moment of open book structure has been calculated. The dipole moment of HP monomer is 2.21 D by the ABEEM/ MM model, which is very close to the experimental value of 2.2 D, as compared to the MP2/aug-cc-pVDZ (1.90 D) and MP2/6311þþG(d,p) (1.82 D) calculations. The harmonic vibration frequencies for isolated HP are also listed in Table 4. We can see not only in the high frequency part, but also in the low frequency part, the ABEEM/MM model gives reasonable results, as compared to the experimental and ab initio results. 2619



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Table 5. Gas-Phase H-Bond Lengths, H-Bond Angles, Net Dipole Moment, Interaction Energies, and Partial Frequencies ω (cm-1) of the Two Conformers of HP Dimer 2-UD

2-UU MP2a

ABEEM/MM rO 3 3 3 H (Å)

a

exp11

MP2a

ABEEM/MM

1.934

1.935

1.929

1.930

θO-H 3 3 3 O (deg) ΔE (kcal/mol)

147.0 -7.97

154.5 -7.37

153.1 -7.60

153.6 -7.15

μ (D)

0.0

0.0

3.54

3.41

ω (cm-1)

3624.9, 3618.9

3842.2, 3842.1

3581.6, 3576.9

3627.8, 3622.0

3842.9, 3842.8

3609.5, 1368.3

3725.4, 1495.4

3471.3, 1417.9

3609.4, 1364.2

3726.5, 1487.1

1312.9, 879.9

1381.8, 919.8

1293.5, 866.6

1310.7, 880.3

1339.2, 925.0

This work: calculated at the MP2/6-311þþG(d,p) level.

Table 6. Charge Distributions for the Two Conformers of HP Dimer dimer:

2-ud

2-uu

dimer:

2-ud

2-uu

sym.:

Ci

C2

sym.:

Ci

C2

qO1

0.0243

0.0243

qO5-H6

-0.0419

-0.0417

qH2

0.3693

0.3710

qO5-O7

-0.0379

-0.0384

qO3

0.0224

0.0224

qO7-H8

-0.0433

-0.0436

qH4

0.3365

0.3347

qlpO1

-0.1504

-0.1496

qO5 qH6

0.0224 0.3365

0.0224 0.3347

qlp0 O1 qlpO3

-0.1546 -0.1711

-0.1548 -0.1717

qO7

0.0243

0.0243

qlp0 O3

-0.1532

-0.1526

qH8

0.3693

0.3710

qlpO5

-0.1711

-0.1717

qO1-H2

-0.0433

-0.0436

qlp0 O5

-0.1532

-0.1526

qO1-O3

-0.0379

-0.0384

qlpO7

-0.1504

-0.1548

qO3-H4

-0.0419

-0.0417

qlp0 O7

-0.1546

-0.1496

3.2. Properties of HP Dimer. The HP dimer is the basic component for hydrogen bonding in pure HP solution. Hence, a correct description of HP dimer is essential for small HP clusters and HP solution. As reported by Kulkarni27 and Elango et al.,33 the HP dimer has two energetically closely cyclic conformers, which we denoted as 2-UD and 2-UU (Figure 5). The calculated equilibrium geometries (H-bond lengths and angles) from ab initio calculations and ABEEM/MM model are presented in Table 5. Results show that the ABEEM/MM results are in satisfactory agreement with those of ab initio method. The most obvious discrepancy occurs in the H-bond angle of 2-UD; the ABEEM/MM value is 147.0 versus the value of 154.5 for ab initio calculations. The ABEEM/MM model overestimates the interaction energy 0.60 and 0.45 kcal/mol for these two conformers. It is interesting to calculate the harmonic vibrational frequencies for HP dimer, which are also listed in Table 5 with experimental measurements based on analysis of different isotopomers of hydrogen peroxide in argon matrices and high level ab initio calculation by MP2/6-311þþG(d,p) basis set. The ABEEM model gives normal modes with relatively larger components in magnitude at all frequency parts as compared to the experimental value. This is due to the fact that the expression of potential energy function of molecular mechanics is too simple and adds some additional terms, which will improve the frequencies computation to some extent. The ABEEM charge distributions of these two conformers are listed in Table 6, which are different from the isolated HP (see Table 4). For the isolated HP molecule, there is no other atom or

Figure 6. Structures of HP clusters (H2O2)n (n = 3-6).

molecule to affect its electron cloud, but for HP dimer, the electron clouds will redistribute due to the formation of intermolecular hydrogen bond. The significant changes of the charge distribution for HP dimer take place at the H atom and lone-pair electron of O atom, which form a hydrogen bond in HBIR. The two HP molecules play a dual role of a proton donor as well as acceptor in these two HP conformers, because they are all a cyclic hydrogen-bonded structure. Therefore, the variations for the H atom are not large, only 0.0298 and 0.0315 in these two conformers, respectively, while the variations for the lone-pair electron of the O atom are only 0.0163 and 0.0169, respectively. We can further validate the reasonableness of ABEEM charge distributions from the dipole moments. The calculated dipole moments of the two conformers of HP dimer by ABEEM/MM model are 0.0 and 3.54 D, respectively, which are in quantitative agreement with the ab initio results (0.0 and 3.41 D, respectively). 2620



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Table 7. Average Bond Length, Angle, and Dihedral Angle of (H2O2)n (n = 2-6) MP2/6-311þþG(d,p)

ABEEM/MM

rO-H/rO-O (Å)

θO-O-H (deg)

jH-O-O-H (deg)

rO-H/rO-H (Å)

θO-O-H (deg)

jH-O-O-H (deg)

2-UD

0.969/1.451

99.5

117.8

0.969/1.467

100.5

112.3

2-UU

0.969/1.449

99.8

116.0

0.968/1.466

99.7

116.7

3-linear-a

0.971/1.449

99.9

113.1

0.967/1.467

99.8

115.1

3-linear-b

0.972/1.452

99.4

118.8

0.967/1.467

99.8

117.8

3-linear-c

0.971/1.451

99.7

114.5

0.968/1.466

100.2

115.8

3-cyclic

0.970/1.447

100.2

120.7

0.968/1.467

99.6

120.4

3-prism 4-helix

0.971/1.467 0.965/1.449

100.1 100.7

123.1 110.5

0.969/1.467 0.966/1.469

100.2 98.8

123.1 113.7

4-cyclic

0.975/1.457

99.1

121.6

0.969/1.466

100.1

133.8

5-helix

0.977/1.449

100.0

108.2

0.968/1.471

100.2

112.9

5-cyclic

0.977/1.457

99.1

125.5

0.972/1.469

100.2

135.1

6-helix

0.974/1.449

100.0

108.0

0.967/1.471

100.0

113.1

6-cage-1

0.977/1.452

100.3

124.0

0.967/1.465

100.0

138.7

6-cage-2

0.976/1.454

99.9

124.3

0.968/1.466

100.0

139.3

Table 8. Structures of H-Bonds in (H2O2)n (n = 2-6) MP2/6-311þþG(d,p)

ABEEM/MM

n(H-bond)

RO 3 3 3 O (Å)

θO-H 3 3 3 O (deg)

RO 3 3 3 O (Å)

θO-H 3 3 3 O (deg)

2-ud

2

2.843

154.5

2.800

147.0

2-uu

2

2.834

153.6

2.826

153.1

3-linear-a

4

2.800

153.2

2.795

153.0

3-linear-b

4

2.807

155.0

2.808

154.5

3-linear-c

4

2.806

154.4

2.804

152.8

3-cyclic 3-prism

3 6

2.787 2.942

167.2 137.0

2.782 2.891

166.2 133.2

4-helix

6

2.785

152.6

2.778

152.5

4-cyclic

8

2.835

150.6

2.775

143.4

5-helix

8

2.777

152.5

2.767

152.2

5-cyclic

10

2.792

155.2

2.787

151.1

6-helix

10

2.772

152.8

2.761

152.4

6-cage-1

12

2.818

155.6

2.772

145.0

6-cage-2

12

2.816

153.8

2.764

144.2

3.3. Properties of (H2O2)n (n = 3-6) Clusters. 3.3.1. Optimal Structures. Figure 6 depicts the graphical representation of small

HP clusters (H2O2)n (n = 3-6). The HP trimer has five different possible conformations, including three energetically closely linear structures, one cyclic, and one prism structure. For HP tetramer and pentamer, cyclic and new reported helical structures are considered. Moreover, three conformations for HP hexamer, one helical and two cage structures, are investigated in the present study. The calculated intramolecular geometries, such as average bond lengths, bond angles, and dihedral angles of (H2O2)n (n = 2-6), are presented in Table 7. From the dimer to the hexamer, the average bond lengths and bond angles calculated by ABEEM/MM model do not vary very much, which are consistent with the ab initio results. However, as the “soft free degree” parameter, the dihedral angle is easy to be varied with surrounding environment. The dihedral angle changes from 112 to 139 by the ABEEM/MM model, a bit wider than the ab initio results from 108 to 124. As compared to the ab initio calculations, the

main differences for dihedral angles occurred to the cyclic structures of the tetramer, pentamer, and the cage structures of hexamer. The overall average absolute deviations (AAD) of intramolecular bond lengths, bond angles, and torsional angles are 0.005/0.015 Å, 0.5, and 5.4, respectively. The calculated intermolecular geometries, such as average H-bond lengths and angles of (H2O2)n (n = 2-6), are given in Table 8. For the majority of the structures, the average H-bond lengths and angles calculated by ABEEM/MM are close to those of the MP2 results, and the AAD are only 0.022 Å and 3.4, respectively. The relatively bigger deviations occurred to the conformations 2-UD (0.043 Å and 7.6), 3-cyclic (0.051 Å and 3.8), 4-cyclic (0.060 Å and 7.2), 6-cage-1 (0.046 Å and 10.7), and 6-cage-2 (0.052 Å and 9.6). Through the analysis of the H-bond geometries, it is obvious that the ABEEM/MM model can correctly obtain structural information for these HP clusters. 3.3.2. Interaction Energies. The interaction energies of HP clusters (H2O2)n (n = 3-6) calculated by the ABEEM/MM model and several QM methods are listed in Table 9. As can be 2621



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Table 9. Interaction Energies of HP Clusters (H2O2)n (n = 2-6) (kcal/mol) ABEEM/MM

MP2a

MP2b

B3LYPc

HFd

-7.97

-7.37

-6.8

-7.12

-5.94

2-UU 3-linear-A

-7.60 -15.30

-7.15 -15.13

-6.6 -14.0

-6.87 -14.71

-5.80 -12.09

3-linear-B

-15.57

-15.43

-14.3

-15.06

-12.12

3-linear-C

-15.71

-15.55

-14.4

-15.17

-12.27

3-cyclic

-12.67

-13.53

-13.5

-13.03

-12.24

3-prism

-12.96

-13.88

-11.7

-13.43

-8.15

4-helix

-23.04

-23.23

-22.66

-18.45

-24.0

-26.68

-16.82

-34.2

-30.79 -37.28

-28.40 -29.36

2-UD

4-cyclic

-27.43

-27.12

5-helix 5-cyclic

-30.88 -35.61

-31.48 -37.90

6-helix

-38.69

-39.76

-38.94

-35.51

6-cage-1

-41.66

-41.71

-37.1

-41.09

-31.64

6-cage-2

-41.47

-41.64

-35.7

-40.91

-32.15

0.57

0.00

0.51

5.00

AADe

2.19

Table 11. Properties of the ABEEM Model for Liquid HP, Including the Average Bond Length (rOH and rOO), Average Bond Angle (θOOH), Average Dihedral Angle (uHOOH), Energy (Uliquid), Heat of Vaporization (ΔHvap), Average Dipole Moment (μ), Static Dielectric Constant (ε0), and the Translational Diffusion Constant (D) at 273 Ka ABEEM/MM/MD rOH (Å)

0.970

rOO (Å)

1.466

θOOH (deg)

100.0

jHOOH (deg) Uliquid (kcal/mol)

105.4 -12.23 ( 0.09 (11.74b)

ΔHvap (kcal/mol)

12.82 ( 0.09 (12.33c)

μ (D)

2.53

ε0

80 (74.6d/79.3b)

D (10-9 m2/s)

1.62

a

The available experimental values58 are listed in parentheses. b Estimate from ref 58. c From ref 58. d From ref 58 (at 290.2 K).

a

MP2/6-311þþG(2d,2p)//MP2/6-311þþG(d,p) level with counterpoise correction in this work. b MP2/6-311þþG(d,p)//MP2/631þG(d) level after counterpoise correction from ref 33. c B3LYP/6311þþG(d,p)//B3LYP/6-311þþG(d,p) level with counterpoise correction in this work. d HF/6-311þþG(d,p)//HF/6-311þþG(d,p) level with counterpoise correction in this work. e Average absolute deviation (AAD) of the ABEEM/MM and various ab initio methods with respect to the MP2/6-311þþG(2d,2p)//MP2/6-311þþG(d,p) calculations.

Table 10. Dipole Moment of HP Clusters of (H2O2)n (n = 26) (D) MP2/6-311þþG(d,p)

ABEEM/MM

2-ud

0.00

0.00

2-uu

3.41

3.54

3-linear-a 3-linear-b

4.21 2.20

4.26 2.18

3-linear-c

2.09

1.96

3-cyclic

4.20

4.24

3-prism

0.10

0.53

4-helix

3.88

3.81

4-cyclic

0.14

0.07

5-helix

2.19

2.06

5-cyclic 6-helix

0.02 0.00

0.01 0.04

6-cage-1

0.05

0.13

6-cage-2

0.00

0.00

seen from Table 9, the results of ABEEM/MM model are in excellent agreement with these several high-level QM calculations. The AAD of the interaction energy for ABEEM/MM model is only 0.57 kcal/mol, and the linear correlation coefficient reaches 0.998, as compared to the results of the MP2/6311þþG(2d,2p)//MP2/6-311þþG(d,p) method. As compared to the MP2 and DFT method, the HF method underestimates the interaction energy due to the lack of accurate consideration of the electron correlation. For the HP trimer, the linear structure is predicted to be more stable than the cyclic and prism structures by 2.63 and 2.34 kcal/mol by ABEEM/MM calculations. This is consistent with the MP2 results (1.60 and

1.25 kcal/mol). However, the linear H-bond structures are less stable than the cyclic H-bond structures along with the increment of HP molecules (from tetramer to hexamer). The interaction energy of cyclic structures is larger than the helical structures in the tetramer and the pentamer by 4.39 and 4.73 kcal/mol (3.89 and 6.42 kcal/mol at MP2 level) calculated by the ABEEM/MM model. The cage structures are more stable than the helical structure in the hexamer by 2.97 and 2.78 kcal/mol (1.95 and 1.88 kcal/mol at MP2 level). The above results show that the more H-bonds form, the more stable is the conformation in the homology of the same size of HP clusters. 3.3.3. ABEEM Charge Distributions and Dipole Moments. The charge distributions and dipole moments of HP clusters (H2O2)n (n = 3-6) are computed by the ABEEM/MM model and are shown in Tables S1-S4 and Table 10. Similar to the HP dimer, the variation of the charge in (H2O2)n (n = 3-6) clusters is mainly at the positions where H-bonds formed. Dipole moment is an important quality for representing charge distributions, which can be the criterion of reasonable charge distributions. From Table 10, we can conclude that the dipole moments computed by ABEEM/MM model are in good agreement with those of MP2 calculation, as the maximum deviation is 0.43 D for structure 3-prism, and the overall AAD is 0.09 D. To summarize, the ABEEM/MM fluctuating charges model can correctly reflect the variations of the charge distribution caused by the changing environment. 3.4. Dynamic Properties of Liquid-State HP. Pure liquidstate HP is very pale blue, slightly more viscous than water that appears colorless in dilute solution. It is a weak acid, has strong oxidizing properties, and is a powerful bleaching agent. It is used as a disinfectant, antiseptic, oxidizer, and in rocketry as a propellant. The oxidizing capacity of HP is so strong that it is considered a highly reactive oxygen species. To the best of our knowledge, there has been no other report on pure liquid-state HP. Therefore, it is very interesting to perform a systematic investigation of liquid-state HP by MDS. Here, the ABEEM/MM is employed to investigate the various dynamic properties of liquid-state HP at 273 K and 1 atm. 3.4.1. Bond Length, Bond Angle, and Dihedral Angle. Table 11 summarizes the liquid-state properties computed by the ABEEM/MM/MD. The distributions of the bond length, bond angle, and dihedral angle by ABEEM model are shown in 2622



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Figure 7. Distribution of (a) O-O bond length, (b) O-H bond length, (c) O-O-H bond angle, and (d) H-O-O-H dihedral angle for liquid HP at 273 K, as determined by the ABEEM/MM/MD model.

Figure 8. Distribution of charge of (a) O atoms, (b) H atoms, (c) O-O bonds, (d) O-H bonds, and (e) lone-pair electrons for liquid-state HP at 273 K, as determined by the ABEEM/MM/MD model.

Figure 7. The computed average O-H bond length, O-O bond length, and O-O-H bond angle in the liquid phase are 0.970 Å, 1.466 Å, and 100.0, respectively. These values are bigger than

the gas-phase HP monomer values due to the formation of the intermolecular hydrogen bond, but consistent with the gas-phase small HP clusters. The computed average dihedral angle is 2623


The Journal of Physical Chemistry A 105.4, which is smaller than the corresponding values in gasphase HP monomer (111.8) and small HP clusters (112.3139.3). 3.4.2. Charge Distribution. The charge distributions of atoms, bonds, and lone-pair electrons in the liquid HP by the ABEEM model are shown in Figure 8. The maximum, minimum, and average charge for O atoms via ABEEM in liquid HP is ∼0.0279, 0.0054, and 0.0209, respectively; for the H atoms, the corresponding values are 0.4742, 0.3177, and 0.3732, respectively; for the O-O bonds, the corresponding values are -0.0357, -0.0551, and -0.0447, respectively; for the O-H bonds, the corresponding values are -0.0312, -0.0854, and -0.0441, respectively; for the lone-pair electrons, the corresponding values are -0.1505, -0.1813, and -0.1639, respectively. As compared to the charges of gas-phase small HP clusters (H2O2)n (n = 2-6), two points should be mentioned: (1) The charges of O atoms and O-O/O-H bonds in liquid HP do not vary obviously. For example, the average charges of the O atoms in linear HP clusters (H2O2)n (n = 2-6) are 0.0234, 0.0228, 0.0225, 0.0224, and 0.0222, respectively, and in liquid HP at 273 K it is 0.0209. However, the charges of H atoms and lone-pair electrons have changed due to more H atoms participated in the formation of hydrogen bond. The average charges of the H atoms in linear HP clusters (H2O2)n (n = 2-6) are 0.3529, 0.3578, 0.3604, 0.3609, and 0.3633, respectively, whereas in liquid HP at 273 K it is 0.3732. The average charges of the lone-pair electrons in linear HP clusters (H2O2)n (n = 2-6) are -0.1573, -0.1590, -0.1599, -0.1605, and -0.1609, respectively, whereas, in liquid HP at 273 K, the average charge of the lone-pair electrons is -0.1639. (2) We may differentiate the H-bonded or free H atoms, as well as the H-bonded or free lone-pair electrons only from the charge distribution. For example, the charges of H atoms in one HP molecule are 0.4020 and 0.4111, and it is undoubted that both H atoms are participating in the formation of a hydrogen bond. However, the charges of H atoms in another HP molecule are 0.3819 and 0.3468, so we can obtain that one H atom (0.3819) is H-bonded H atom and the other H atom (0.3468) is free. Figure 8 shows that the charge distributions of O atoms, H atoms, O-O bonds, and O-H bonds have only one peak, but lone-pair electrons have two obvious peaks. We can conclude that the bulk of the H atoms participate in the formation of the hydrogen bond in liquid HP. Meanwhile, the charge of the O atoms does not change obviously, because of the O atoms in liquid HP acting as the proton donor and proton acceptor simultaneously, and so the charge compensates mutually. Furthermore, there are two types of lone-pair electrons: one is participating in the formation of the hydrogen bond and the other does not, which can be clearly seen from Figure 8e. 3.4.3. Dipole Moment. As compared to the HP monomer, the geometry and charge distribution in liquid-state HP change obviously. All the variations of geometry and charge distribution (mainly about H atoms and lone-pair electrons, which participate in the formation of the hydrogen bond) contribute to enhance the average dipole moment of liquid HP by as much as 0.3 D. The distribution of the dipole moment at 273 K is shown in Figure 9. The ABEEM/MM/MD estimates the dipole moments of liquid HP in the range of 1.80-3.19 D, and the average dipole moment

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Figure 9. Distribution of the dipole moment of liquid HP at 273 K.

is 2.53 D, which is close to that of the HP molecule in liquid water calculated by the QM/MM59 method (2.56 D). 3.4.4. Static Dielectric Constant. The static dielectric constant or permittivity (ε0) is dependent on the magnitude of the dipole moment, the number of dipoles per unit volume, and the extent to which the directions of the dipoles are correlated, and it can be calculated from the fluctuation of the total dipole M in the central simulation box, according to ! 4πF ÆM 2 æ - ÆMæ2 ε 0 ¼ ε¥ þ 3kT Nmol where F is the density, k is Boltzmann’s constant, and Nmol is the total number of molecules. The static dielectric constant provides another estimate of the dipole moment of an HP molecule. The computed values by the ABEEM model and the available experimental results are also listed in Table 11. The static dielectric constant calculated by the ABEEM potential is 80.0, which is very close to the estimated experimental value (79.3). The above results show that the flexible ABEEM/MM fluctuating charge model has properly described the dependence of the change in dipole moment on molecular geometry. 3.4.5. Heat of Vaporization. The heat of vaporization is the energy required to transform a given quantity of a substance in liquid into gas, and it can be viewed as the energy required to overcome the intermolecular interactions in the liquid. It is calculated according to the following formula: ΔHvap ðTÞ ¼ - Uliquid ðTÞ þ PΔV ¼ - Uliquid ðTÞ þ RT where ΔHvap is the molar heat of vaporization, Uliquid is the computed intermolecular potential energy per molecule, P is the pressure, and ΔV is the molar volume change between liquid and gas. R is the gas constant, and T is the absolute temperature. The computed Uliquid and ΔHvap are also listed in Table 11, with the available experimental values. The ABEEM/MM/MD model gives reasonable predictions of Uliquid (-12.23 kcal/mol) and ΔHvap (12.82 kcal/mol), in comparison with the corresponding experimental values (-11.74 and 12.28 kcal/mol, respectively), and the absolute deviation is about 0.5 kcal/mol. There are two conceivable reasons to explain the slightly larger interaction energy. One is the parameters of the ABEEM model are fitted not by the interaction energy of liquid-state HP but by the properties of gas-phase small HP clusters, such as optimal structures, interaction energies, dipole moments, and vibrational frequencies. The other is that the increased anisotropy of the 2624



Figure 10. Radial distribution functions (RDFs) at 273 K for the ABEEM model.

polarizability may result in a slightly attractive intermolecular potential energy. 3.4.6. Radial Distribution Functions (RDFs). The detailed structure of liquid HP is characterized by the radial distribution functions, which describes how the density of surrounding matter varies as function of the distance from a particular point. The RDFs (gOO, gOH, and gHH) are shown in Figure 10. Results show that the first peak of gOO is 2.74 Å, which is slightly smaller than the values of RO 3 3 3 O in the gas-phase HP clusters (about 2.8 Å). This is because that the formation of a three-dimensional hydrogen-bonding network in liquid HP and the cooperative effects of hydrogen bond lead to shortening the distance between O and O. The hydrogen bonding is characterized by gOH, and the first peak of gOH is 2.01 Å, which is slightly larger than the value of RO 3 3 3 H in the HP dimer (about 1.93 Å). In addition, the second peak of it gives the distribution of acceptor O with the donor H’s neighbor H, and it is in a wide range from 3.0 to 4.5 Å, which is reflecting the intramolecular dihedral angle rotation along O-O bond in a wide range. The gHH has two obvious peaks: the first one split into two peaks, at 2.41 and 2.86 Å, respectively, and the second one at 4.52 Å. 3.4.7. Diffusion Constant. The diffusion constant is a very important quality, because of the fact that it is one of the few time-dependent properties that can be measured directly, both in experiments and in simulations. The diffusion constant D is determined from the Einstein relation: ÆjrFi ðtÞ - F r i ð0Þj2 æ D ¼ lim tf¥ 6t where Br i(t) corresponds to the position vector of the center of mass molecule i, and the average is taken over all molecules and simulations. Transport properties are intimately related to the short-range and long-range intermolecular potential. The diffusion constant provides a particular valuable and fundamental test for a solvent model. The diffusion constant determined by the flexible and fluctuating charge ABEEM/MM/MD model is 1.6, which is smaller than the diffusion constant of water (experimental value 2.3 and ABEEM value 1.843). The discrepancy between hydrogen peroxide and water is attributed to the stronger electrostatic interaction for HP system and the relatively harder internal flexibility for HP molecule. The above result also confirms that hydrogen peroxide is more viscous than water.

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4. CONCLUSION AND OUTLOOK In this work, the newly constructed ABEEM/MM fluctuating charge potential model investigation of the properties for the HP clusters (H2O2)n (n = 1-6) and liquid-state HP has been presented. This potential model gives reasonable properties for small HP clusters and dynamic properties for liquid-state HP when comparing with the present ab initio calculations and available experimental data. The overall AAD for intramolecular bond length, bond angle, and torsional angle of HP clusters (H2O2)n (n = 2-6) are 0.005/0.015 Å, 0.5, and 5.4, respectively. The AAD for intermolecular hydrogen bond length and angle are 0.022 Å and 3.4, respectively. Because of the explicit description of charge distribution and special treatment of HBIR, the AAD for interaction energies is only 0.57 kcal/mol, and the linear correlation coefficient reaches 0.998. As for the dynamic properties of liquid HP, the static dielectric constant calculated by the ABEEM potential is 80.0, which is very close to the estimated experimental value (79.3). Meanwhile, the intermolecular potential energy per molecule Uliquid (-12.23 kcal/mol) and the molar heat of vaporization ΔHvap (12.82 kcal/mol) predicted by ABEEM/MM/MD are reasonable in comparison with the corresponding experimental values (-11.74 and 12.28 kcal/mol, respectively). In addition, the diffusion constant calculated by the ABEEM/MM/MD model also confirmed that hydrogen peroxide is more viscous than water. Overall, the new constructed ABEEM potential model can reproduce rather accurate properties of small HP clusters and liquid-state HP solution. On the basis of this potential, together with the ABEEM-7P water potential, the properties of HP aqueous solution and HP interacting with nucleic acid base will be explored. ’ ASSOCIATED CONTENT

bS

Supporting Information. Tables S1-S4 giving the ABEEM charge distributions of (H2O2)n (n = 3-6) clusters. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Telephone: 86-411-82159607. E-mail: [email protected].

’ ACKNOWLEDGMENT We greatly thank Professor Jay William Ponder for providing the Tinker programs. This work is supported by grants from the National Natural Science Foundation of China (nos. 20633050 and 20703022) and the Foundation of Education Bureau of Liaoning Province of China (no. 2009T057). ’ REFERENCES (1) McArdle, J. V.; Hoffmann, M. R. J. Chem. Phys. 1983, 87, 5425. (2) Varma, S. D.; Devamanoharan, P. S. Free Radical Res. Commun. 1991, 14, 125. (3) Hunt, R. H.; Leacock, R. A.; Peters, C. W.; Hecht, K. T. J. Chem. Phys. 1965, 42, 1931. (4) Koput, J. J. Mol. Spectrosc. 1986, 115, 438. (5) Olson, W. B.; Hunt, R. H.; Young, B. W.; Maki, A. G.; Brault, J. W. J. Mol. Spectrosc. 1988, 127, 12. (6) Flaud, J.-M.; Camy-Peyret, C. J. Chem. Phys. 1989, 91, 1504. 2625


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