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J. Phys. Chem. B 2008, 112, 12032–12037
Structural and Dynamical Properties of Hydrogen Fluoride in Aqueous Solution: An ab Initio Quantum Mechanical Charge Field Molecular Dynamics Simulation Chinapong Kritayakornupong,*,† Viwat Vchirawongkwin,‡ Thomas S. Hofer,§ and Bernd M. Rode§ Department of Chemistry, Faculty of Science, King Mongkut’s UniVersity of Technology Thonburi, Bangkok, 10140 Thailand, Department of Chemistry, Faculty of Science, Chulalongkorn UniVersity, Bangkok, 10330 Thailand, and Theoretical Chemistry DiVision, Institute of General, Inorganic and Theoretical Chemistry, UniVersity of Innsbruck, Innrain 52a, A-6020 Innsbruck, Austria ReceiVed: June 17, 2008; ReVised Manuscript ReceiVed: July 3, 2008
The novel ab initio quantum mechanical charge field (QMCF) molecular dynamics simulation at the Hartree-Fock level has been employed to investigate hydration structure and dynamics of hydrogen fluoride in aqueous solution. The average H-F bond length of 0.93 Å obtained from the QMCF MD simulation is in good agreement with the experimental data. The HHF · · · Ow distance of 1.62 Å was evaluated for the first hydration shell, and 2.00 Å was observed for the FHF · · · Hw distance. The stability of hydrogen bonding is more pronounced in the hydrogen site of hydrogen fluoride, with a single water molecule in this part of the first hydration shell. A wide range of coordination numbers between 3 and 9 with an average value of 5.6 was obtained for the fluorine site. The force constants of 819.1 and 5.9 N/m were obtained for the HHF-FHF and HHF · · · Ow interactions, respectively, proving the stability of the nondissociated form of hydrogen fluoride in aqueous solution. The mean residence times of 2.1 and 2.5 ps were determined for ligand exchange processes in the neighborhood of fluorine and hydrogen atoms of hydrogen fluoride, respectively, indicating a weak structure-making effect of hydrogen fluoride in water. The corresponding H-bond lifetimes attribute this effect to the H atom site of HF. 1. Introduction In most chemical and biological reactions, hydrogen bond formation and proton activity have been a subject of great interest because of the complexity of acid-water interaction via hydrogen bonds in aqueous solution.1 For the series of the hydrohalic acids HF, HCl, HBr, and HI, HF is well-known to be the smallest natural model for the study of acidity in aqueous solution. Hydrogen fluoride is a weak acid in dilute solution with a small dissociation constant (K25 °C ) 7.2 × 10-5), whereas hydrogen chloride, bromide, and iodide completely dissociate in aqueous solution. Hydrogen bonding between hydrogen fluoride and water molecule is very strong,2,3 opposite to the three other heavier hydrogen halides. In concentrated solution, hydrogen fluoride behaves as a strong acid.4,5 To our knowledge, no structural properties have been obtained from X-ray or neutron scattering techniques; only theoretical investigations have been performed to evaluate characteristics of hydrogen fluoride in aqueous solution.6-15 The ionic dissociation of hydrogen fluoride has been extensively investigated by using ab initio quantum mechanical methods.6-8,10,13-15 Most of these calculations were performed with small clusters consisting of hydrogen fluoride and some water molecules. The mono- and dihydrated HF complexes were studied by using the MP2/6-31+G** method in the continuum model of solvation, showing that there is no proton transfer in the dihydrated HF complex.6 According to the older work with the DFT, HF, and * Corresponding author. Fax: +66(2)470-8962. E-mail:chinapong.kri@ kmutt.ac.th. † King Mongkut’s University of Technology Thonburi. ‡ Chulalongkorn University. § University of Innsbruck.
MP2 methods, hydrogen fluoride with four water molecules shows a preference for the dissociated form.7 A calculation employing a 6-31++G** basis set with electron correlation effects treated at the MP2 level also indicated that ionization of HF readily occurs in larger clusters such as HF(H2O)7.10 A dissociated structure of HF(H2O)n was obtained at MP2/augcc-pVDZ+(2s2p/2s) level for n g 4. Furthermore, calculations of HF(H2O)n clusters with systematic extension to cluster size up to n ) 7 were performed by using the B3LYP/D95++(d,p) method, and it was found that the most stable structure should be the nondissociated form.11 The MP2 method in conjunction with TZVP basis set confirmed nondissociation in clusters HF(H2O)n, with n ) 1-5.13 Larger-size HF(H2O)n (n e 10) clusters were investigated by using the MP2/aug-cc-pVDZ+(2s2p/ 2s) method, exhibiting that the dissociated form of hydrogen fluoride in HF(H2O)n clusters is less stable at 0 K than the undissociated form until n ) 10.15 A combination of electronic structure and Monte Carlo methodology was utilized to study the acid dissociation of hydrogen fluoride in aqueous solution.8 The hydration structure of HF in water was also evaluated by RISM-SCF/MCSCF approach.9 The solvation of a deuterium floride (DF) molecule in heavy water (31 D2O molecules) was investigated by using the Car-Parrinello simulation scheme, showing that DF forms a strongly bound complex dynamically fluctuating between F-D · · · D2O and F · · · D3O structures.16 In view of the small number of D2O molecules and the functional used, this result had to be re-examined by an ab initio simulation method with a number of solvent molecules sufficient to reproduce hydration and bulk. An equimolar mixture of water-hydrogen fluoride was also studied by the CP MD technique.17 The results revealed that hydrogen bonding plays an important role to enhance the stability of nondissociated HF
10.1021/jp805321c CCC: $40.75 2008 American Chemical Society Published on Web 08/27/2008
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Figure 1. Definition of the quantum mechanical (QM) and molecular mechanical (MM) regions in the QMCF approach.
in aqueous solution. In general, the characteristics and stability of dissociated and nondissociated forms of hydrogen fluoride in aqueous solution appear to depend strongly on the cluster size and the accuracy of theoretical approaches employed, but the majority of data point to the dominance of nondissociated HF in aqueous solution. In the present study, an ab initio quantum mechanical charge field (QMCF) molecular dynamics simulation was performed to evaluate the structural and dynamical properties of hydrogen fluoride in dilute aqueous solution. Structural parameters of solvated hydrogen fluoride were described in terms of radial distribution functions (RDF), coordination numbers, angular distributions, θ-angle, and tilt-angle distributions. For description of dynamics, mean ligand residence times were estimated for ligand exchange processes between the hydration shell of hydrogen fluoride and bulk. 2. QMCF MD Simulation The novel ab initio QMCF molecular dynamics formalism has been developed18 and applied to examine structural and dynamical data for composite chemical species in solution.18-21 This formalism allows to study the solute without construction of ab initio generated pair and three-body potential functions, which are required in conventional quantum mechanical/ molecular mechanical (QM/MM) molecular dynamics simulations. The QMCF MD, similar to conventional QM/MM MD approaches,22-24 separates the system into QM and MM regions. However, the QM region in the QMCF method consists of two subregions, namely, the core region (inner QM subregion) and the solvation layer (outer QM subregion). The QMCF MD scheme is displayed in Figure 1. The main difference between the conventional QM/MM MD and the QMCF MD simulation is the evaluation of the forces between the core region and the MM region. The forces acting on each particle in the different subregions are defined as
Fjcore ) FjQM
(1)
M
Fjlayer ) FjQM +
∑ FijBJHnC
(2)
i)1
M
QM N1+N2 q i
FjMM ) Σ FijBJH + Σ i)1 i*j
i)1
· qjMM rij2
N2
+ Σ FijBJHnC i)1
(3)
where Fcore represents the quantum mechanical force acting on j the particle j in the core region, Flayer represents the forces acting j
on particle j located in the solvation layer, FMM j denotes the forces acting on the particle j in the MM region, and M is the number of atoms in the MM region. The forces in the core region (Fcore j ) are evaluated from the ab initio quantum mechanical calculation in each simulation step, whereas the forces in the MM region (FMM ) are derived from the BJH-CF2 water model25,26 augj mented by the Coulombic forces exerted by all atoms in the core region (N1) and the solvation layer (N2) and the nonCoulombic forces generated by the atoms in the solvation layer (N2). Consequently, the QM forces in the solvation layer (Flayer ) j are supplemented by the non-Coulombic forces of particles in the MM region evaluated from the BJH-CF2 water model.25,26 The Coulombic interactions are calculated with the point charges of the atoms in the MM region and the quantum chemically evaluated partial charges on the atoms in the QM region. The charges of the particles in the MM region are incorporated via a perturbation term into the core Hamiltonian
Vi )
M
q
∑ rijj
(4)
j)1
where qj are the partial charges of each atoms. The values of -0.65996 and +0.32983 corresponding to the BJH-CF2 charges of water model employed in the MM region25,26 were used for oxygen and hydrogen charges. For a smooth exchange of particles between the QM and MM region, a continuous transition of forces at the boundary has to be assured by applying a smoothing function27 within an interval of 0.2 Å. The forces acting on each particle in the system can be defined as
Fjsmooth ) FjMM + (Fjlayer - FjMM) · Sm(r)
(5)
where FjMM represents the force acting on the particle j in the MM region, Fjlayer is the force acting on the particle j located in the solvation layer, r is the distance of the water molecule from the fluorine atom of the solute molecule, and Sm is a smoothing function,27
Sm(r) ) 1 Sm(r) )
for r e r1
(r20 - r2)2(r20 + 2r2 - 3r21)
Sm(r) ) 0
(r20 - r21)3 for r > r0
for r1 < r e r0 (6)
where r1 and r0 are the limiting solute-water distances of the transition region. The QMCF MD simulations were performed in a canonical NVT ensemble, consisting of one hydrogen fluoride and 498 water molecules in a 24.65 Å periodic boundary cubic box. The system temperature of 298.15 K was maintained by the Berendsen temperature-scaling algorithm28 with a relaxation time of 100 fs. The density of the simulation box was fixed at 0.997 g cm-3, which is the experimental value of pure water. The diameters of the core and the layer region were chosen as 6.0 and 11.0 Å, respectively. The forces in the QM region were calculated at the restricted Hartree-Fock (RHF) level by using the TURBOMOLE 5.9 program.29-31 The Dunning double-ζ plus polarization function (DZP) basis sets32,33 were applied for fluorine, oxygen, and hydrogen atoms. The values of 5.5 and 5.7 Å were set for r1 and r0, respectively. With these values, the full first hydration shell and a part of the second hydration shell, estimated from the RDF in the equilibrated state, are included in the QM region. The flexible BJH-CF2 water model25,26 including an intramolecular potential was utilized for
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describing the interactions between pairs of water molecules in the MM region, because this model allows explicit hydrogen movements. The reaction field34 was used to correct for longrange Coulombic interactions. Cutoff distances of 5 and 3 Å were applied for non-Coulombic O-H and H-H interactions, respectively. For Coulombic interactions, the radial cutoff limit was set to half the box length. The QMCF MD simulation was equilibrated for 1 ps, and further 10 ps were performed for data sampling. The vibration mode of the hydrogen fluoride molecule (C∞ν) is both infrared- and Raman-active. The H velocity was projected onto a unit vector parallel to the F-H bond (u b1). We defined the vibration mode as ν ) U1, where the U1 denotes the projection of the H velocity onto the unit vector b u1. The vibrational frequency of the normal mode and the intermolecular vibration frequency HHF · · · Ow were evaluated by means of the velocity autocorrelation functions (VACFs) and their Fourier transformations. The normalized VACF, C(t), is defined by
C(t) )
Nt
N
i
j Nt
N
i
j
∑ ∑ Vj(ti)Vj(ti + t) NtN
(7)
∑ ∑ Vj(ti)Vj(ti)
where N is the number of particles, Nt is the number of time origins ti, and Vj represents a certain velocity component of the particle j. In order to estimate the water exchange processes in the hydration shells of hydrogen fluoride, the direct method35 was utilized to determine the mean residence times (MRTs). The MRT referring to the direct method is defined as
τ)
tsimCNav Nex
Figure 2. (a) HHF · · · Ow and (b) FHF · · · Hw RDF and their corresponding integration numbers.
(8)
where tsim represents the simulation time, CNav denotes the average coordination number, and Nex is the number of registered exchange events. Further, the sustainability of water exchange processes was elucidated by comparing the number of all transitions through a shell boundary (N0ex) to the number of the exchange processes lasting at least 0.5 ps (N0.5 ex ). Thus, a sustainability coefficient has been defined as35
Sex )
N0.5 ex N0ex
(9)
The average number of attempts leading to a successful exchange process is given by 1/Sex. 3. Results and Discussion 3.1. Structural Properties. The QMCF MD simulation predicts the average H-F distance of 0.93 Å, which is not much different from the experimental gas-phase value of 0.917 Å.36 The structural parameters such as RDF, coordination numbers, and angular distributions were determined to describe the hydration structure of hydrogen fluoride in aqueous solution. The RDF for each atom of hydrogen fluoride and its neighboring water molecules together with their corresponding integration numbers obtained from the QMCF MD simulation are displayed in Figure 2. The first sharp peak in the HHF · · · Ow RDF, corresponding to the first hydration shell, is located at 1.62 Å. The integration of this HHF · · · Ow peak predicts a single water molecule bound to H. The second peak is centered at 3.49 Å, referring to the water molecules near the fluorine site in the
Figure 3. First shell coordination number distribution of F atoms in hydrated hydrogen fluoride.
first hydration shell. In Figure 2b, the first FHF · · · Hw peak is situated between 1.7 and 2.5 Å. A relatively clear second peak is observed in this RDF with a maximum around 3.2 Å. These two peaks indicate the distance between the fluorine atom and both hydrogen atoms of the water molecules in the first hydration shell. Figure 3 presents the first shell coordination number distributions evaluated from the FHF · · · Ow interactions of the hydrated hydrogen fluoride. The coordination number of 1 is the absolutely dominating one (99%) in the HHF · · · Ow distribution. The coordination number distribution of water ligands near the
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Figure 4. Distributions of (a) Ow · · · H-F angles and (b) H-F · · · Hw angles, obtained from the QMCF MD simulation.
fluorine atom is illustrated in Figure 3, covering a wide range of 3-9, 5 representing the most probable configuration (37%), followed by the coordination numbers of 6, 4, and 7 with the probabilities of 22, 17, and 16%, respectively. These data prove that mostly one water molecule is bound to the H atom of hydrogen fluoride, whereas frequent exchanges occur at the F atom. To describe the hydrogen bond angle between hydrogen fluoride and water molecule, the angular distribution functions of the Ow · · · HHF-FHF and HHF-FHF · · · Hw angles in the first hydration shell are depicted in Figure 4. The maximum of the Ow · · · HHF-FHF angular distribution presented in Figure 4a is centered at -0.98 (170°) with tailing until -0.17 (100°), indicating a dominantly linear hydrogen bond between water and HHF. The HHF-FHF · · · Hw angular distribution illustrated in Figure 4b is very broad with an almost insignificant peak between -0.17 and -0.57 (100 and 125°), indicating nonlinear, weak, and flexible hydrogen bonding between water and the fluorine site of HF. The orientation and flexibility of the water ligands around HF can be further determined in terms of angle θ and tilt angle. The angle θ is the angle between the vector pointing along Cg-Ow (Cg is the center of mass of the HF molecule) and the dipole vector of water molecule. The tilt angle is the angle between the HHF-FHF axis and the plane defined by the Ow-Hw vectors. The θ and tilt angular distributions in the first hydration shell of hydrogen fluoride are shown in Figure 5, presenting a broad peak of the angle θ distribution for the first hydration shell ranging from 0 to 180°, having its maximum at 136°. This demonstrates two different dipole-oriented arrangements of the ligands around hydrogen and fluorine sites of the HF molecule. The distribution of the tilt angle for the first-shell ligand obtained from the QMCF MD simulation reaches zero at (90° with its maximum at 5°, showing a high degree of flexibility of the ligand orientation in the first hydration shell. 3.2. Dynamical Properties. The spectra of the HHF · · · Ow and HHF-FHF vibrational modes in the first hydration shell obtained from the QMCF MD simulation are depicted in Figure 6. The peak of the HHF · · · Ow vibrational mode in the first hydration shell shown in Figure 6a is centered at 326 cm-1. The force constant evaluated for this frequency is 5.9 N/m, which is higher than that of 1.6 N/m determined for the experimental Ow-H · · · Ow stretching frequency (170 cm-1),37 reflecting a more stable H bond for HHF · · · Ow. The maximum value of the HHF-FHF stretching mode is located at 3811 cm-1
Figure 5. θ and tilt angular distributions of water ligands near the hydrogen fluoride molecule.
Figure 6. Power spectra of (a) HHF · · · Ow and (b) HHF-FHF stretching modes in the first hydration shell.
with shoulder peak at 4104 cm-1, which corresponds to the force constants of 819.1 and 949.8 N/m. This HHF-FHF stretching frequency is in reasonable agreement with the experimental observation of the free HF molecule (3959 cm-1).38,39 The split peak of the HHF-FHF stretching mode can be explained by ligand exchange processes in the hydrogen site of hydrogen fluoride. The calculated force constant of the HHF-FHF interaction is much higher than that obtained for the H · · · Ow interaction, thus explaining the stability of the nondissociated form of hydrogen fluoride in aqueous solution. The MRTs of water molecules in the hydration shell classify the water exchange processes between hydration shells and bulk. The direct method,35 for both t* ) 0 and t* ) 0.5, was employed to evaluate these MRT values. The number of ligand exchange processes, the MRTs, and the sustainability of migration processes from the first hydration shell are summarized in Table 1. Figure 7 shows the HHF · · · Ow and the FHF · · · Ow distance plots at t* value of 0.5 ps in the first hydration shell. Two water
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TABLE 1: Mean Ligand Residence Times and Sustainability of Migration Processes to and from the First Hydration Shell of F and H atoms of the HF molecule t* ) 0 ps
a
t* ) 0.5 ps
solute
tsim
0 Nex
τH0 2O
0.5 Nex
τH0.52O
Sex
1/Sex
FHF HHF bulka
10.0 10.0 10.0
203 12 269
0.3 0.8 0.3
27 4 24
2.1 2.5 1.7
0.13 0.06 0.09
7.7 16.7 11.2
Values obtained from a QM/MM MD simulation of pure water.35
with the experimental values. The coordination number of (5 + 1) is the most preferred one for the first hydration shell. A mostly linear and strong hydrogen bond between water and the hydrogen site of HF was observed, whereas nonlinear and weak hydrogen bonding dominates at the fluorine site. Several first shell ligand exchange processes occurred during the simulation, most of these in the neighborhood of F. Acknowledgment. Financial support for this work by the Austrian Science Foundation is gratefully acknowledged. References and Notes
Figure 7. Distributions of (a) the HHF · · · Ow and (b) the FHF · · · Ow distances in the first hydration shell obtained from the QMCF MD simulation.
exchange processes occurred at the hydrogen site of hydrogen fluoride as shown in Figure 7a, the first one taking place at ∼1 ps and the second one in the range of 6-7 ps, while numerous ligand exchange processes were observed at F atom (Figure 7b). The MRT value for the first hydration shell located around the fluorine atom is 2.1 ps, which is slightly shorter than that of 2.5 ps evaluated for the hydrogen site. However, the hydrogen bond life times of 2.5 and 0.36 ps resulting for the FHF-HHF · · · Ow and HHF-FHF · · · Hw hydrogen bonds, respectively, clearly demonstrate the differences in stability. The values of 0.13 and 0.06 were determined for sustainability coefficients of F and H atom sites of hydrogen fluoride, respectively. The corresponding 1/Sex values are 7.7 and 16.7, indicating that 8-17 attempts to leave or enter the first hydration shell are required to achieve one lasting exchange process in the neighborhood of F and H, respectively. The average lifetime of the FHF-H · · · Ow hydrogen bond is much higher than the values of 0.55 and 0.33 ps evaluated for pure water by experiment40 and a QM/MM MD simulation,41 stressing once more the stability of this H bond. The value of 0.36 ps obtained for the H-F · · · Hw hydrogen bond is within methodical limits of both experiment and simulation identical to that of water itself. The MRT values and the hydrogen bond lifetime obtained from the QMCF MD simulation indicate that HF in aqueous solution is a weak structure-making species and that the hydrogen atom of HF is responsible for this effect. 4. Conclusion The novel ab initio QMCF molecular dynamics simulation has proven its ability to investigate structural and dynamical properties of hydrogen fluoride in aqueous solution. It proved the stability of nondissociated HF structure and revealed weak hydrogen bonding in the first hydration shell. Data for the H-F bond length and its vibrational frequency are in good agreement
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