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J. Phys. Chem. B 2008, 112, 2958-2963
Perturbation of Local Solvent Structure by a Small Dication: A Theoretical Study on Structural, Vibrational, and Reactive Properties of Beryllium Ion in Water S. Gnanakaran,*,† Brian Scott,‡ T. Mark McCleskey,‡ and Angel E. Garcia§ Theoretical Biology and Biophysics Group, MPA-Materials Chemistry, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and Department of Physics, Applied Physics and Astronomy, Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180 ReceiVed: July 29, 2007; In Final Form: December 10, 2007
A molecular based understanding of beryllium chemistry in the context of biomolecules is necessary for gaining progress in prevention and treatment of chronic beryllium disease. One aspect that has hindered the theoretical progress has been the lack of a simple classical two-body potential for the aqueous beryllium ion (Be2+) to be used with biomolecular simulations. We provide new parameters for Be2+ that capture the structural and reactive properties of this small dication. Using classical molecular dynamics simulations, we show that these parameters reproduce the correct radial distribution function and coordination numbers for this cation in explicit aqueous solution when compared to published diffraction and NMR measurements. The geometrical parameters obtained using classical simulations are also in agreement with ab initio calculations. We successfully predict the vibrational modes of the tetra aqua Be2+ dication from ab initio calculations on solvated structures obtained from the simulations. The calculated vibrational modes show better agreement with experiments compared to any published work. This new potential also produces a well-established hydrogen bonding between the first and second solvation shells. More importantly, when the molecular dynamics (MD) and ab initio results are interpreted in concert, the dynamics and nature of interactions between the first and second shells capture the pivotal role they play on the reactivity of aqua-Be complexes.
Introduction Beryllium (Be) is used in industry in metal, oxide, and alloy forms for manufacturing nuclear components, electronic devices, golf clubs, aircraft brakes, X-ray tubes, high-temperature ceramics, and structural components in satellites and space shuttles. At the same time, it is also listed as a class A Environmental Protection Agency (EPA) carcinogen and causes chronic beryllium disease (CBD), a human granulomatous lung disease.1 The molecular aspects of beryllium chemistry in the context of biological systems are not well understood.2,3 Computational methodologies should prove valuable in guiding and enhancing our understanding of the interaction between Be ions (Be2+) and biomolecules. There have been some efforts on inferring binding sites of beryllium ions in proteins on the basis of ab initio studies of Be2+ binding sites in small inorganic molecule mimics4 and the electrostatic potentials of proteins.5 We believe that classical molecular dynamics (MD) simulations are essential for providing an atomistic description of Be2+ interactions and for identifying potential binding sites in relevant biological systems, such as human lung surfactant proteins and major histocompatibility complex II proteins associated with CBD. Therefore, it is imperative that we develop accurate, but simple, potential parameters for Be2+ that can be used with large-scale classical simulations of the biomolecules for elucidation of binding sites. * To whom correspondence should be addressed. Tel: (505)-6651923. Fax: (505)-665-3493. E-mail:
[email protected]. † Theoretical Biology and Biophysics Group, Los Alamos National Laboratory. ‡ MPA-Materials Chemistry, Los Alamos National Laboratory. § Rensselaer Polytechnic Institute.
Here, we describe the structural and spectroscopic properties of Be2+ ions in explicit water using a classical potential. There has been significant interest in obtaining parameters for Be2+ to be used in classical simulations, but the difficulty has been to reproduce the structural properties of aqueous Be2+ ion with the simple 6-12 Lennard-Jones (LJ) potential and Coulombic interactions. For example, when a two-body potential derived from ab initio calculations was used, it was not possible to reproduce the correct structural ordering of Be2+ in water as it led to six water coordinated complexes.6 It was necessary to augment this two-body potential with an additional three-body term to reproduce the correct hydration number of four water molecules.7 Furthermore, it was suggested that polarization of oxygens of water was necessary for the induction effects that mainly account for the nonadditivity.7 We show here that one can reproduce many structural, spectroscopic, and reactive properties of aqueous Be2+ ions with a simple two-body potential thus allowing greater applicability and extension to larger systems. This potential is consistent with the form of popular biomolecular force fields such as AMBER,8 CHARMM,9 and GROMACS10 and can easily be incorporated. Importantly, our potential for Be2+ also captures the pivotal roles of the first and second solvent shells on the reactivity of Be2+ aqua complexes. We have considered the water exchange between the first two hydration shells and their respective fluctuations to characterize the reactive process. Finally, we have subjected an arbitrary configuration, including its second solvent shell, from the classical simulation to detailed ab initio calculations to obtain vibrational mode frequencies and to quantify the involvement of the second shell on the reactivity of the aqueous [Be(H2O)4]2+complex.
10.1021/jp076001w CCC: $40.75 © 2008 American Chemical Society Published on Web 02/19/2008
Local Solvent Structure Perturbation by Dication
J. Phys. Chem. B, Vol. 112, No. 10, 2008 2959
Materials and Methods Details of Be Ion Potential. Under the context of existing biomolecular force fields, the nonbonded interaction between Be2+ and solvent (and protein) atoms is assumed to be a sum of LJ interactions and electrostatic interactions between point charges. The interaction potential between Be2+ and water is given as
VBe-W )
qBeqj
∑j r
Be-j
+
∑ O
ABeAO rBe-O12
-
BBeBO rBe-O6
where qBe and qj are partial charges assigned to Be2+ and water atoms, respectively. A and B are the LJ parameters for repulsive and attractive interactions, respectively. The subscript O refers to the oxygen of water. The TIP3P water model11 is utilized for consistency with biomolecular force fields. The parameters derived for LJ term for Be2+ ion are ABe ) 2.38 × 10-3 kcal Å6/mol and BBe ) 6.326 × 10-4 kcalÅ12/mol. The attractive LJ term for Be2+ is obtained from the London dispersion energy that primarily arises from the induced dipoleinduced dipole interactions. Calculations of Ca2+ and Mg2+ potentials suggest that London dispersion constants can be reasonably incorporated into an LJ like force field to describe a nonparametrized attractive potential.12 We have obtained these dispersion constants from the calculations of Bartolotti et al.12 They utilized the hydrodynamic formulation of quantum mechanics to calculate accurate London dispersion energies for various charged atoms. In brief, they employed the hydrodynamic formulation of time-dependent Kohn-Sham theory to calculate the dipole Cauchy moments of the ions of interest and then used the method of Pade approximants to generate a set of dipole oscillator strengths and the transition frequencies in the two-body dispersion terms. We find that the covalent radius of Be2+ ion is sufficient enough to define the repulsive contribution. A full charge of +2 (qBe ) 2) is considered for electrostatic interactions. Simulation Details. For the MD simulations, the Be2+ ion was solvated with 293 water molecules in a cubic box with periodic boundary conditions. No counterions were included. Initially, this system was equilibrated at constant temperature (300 K) and pressure (1 atm) for 200 ps to obtain a cubic box of 24.6 Å in length, corresponding to the density of water at room temperature. Then, the system was simulated under canonical (NVT) conditions. A time step of 2 fs was used. The internal degrees of freedom of TIP3P waters were constrained by using SHAKE with a tolerance of 0.0005 Å.13 The system was coupled to an external heat bath with relaxation time of 0.1 ps.14 The particle mesh Ewald was used for electrostatic interactions with a cutoff of 8 Å. AMBER 613 was employed for these simulations. The simulation was carried out for 6 ns, and the last 3 ns were considered for production and analysis. The error analysis was done with block averages of 1 ns. Ab Initio Calculations. A snapshot of one of the MD trajectories was used as the starting point for the optimization of the Be2+ dication and 18 water molecules. The structure was optimized using Gaussian03,15 with an HF/3-21G* model chemistry, in vacuum. The Raman and IR vibrational frequencies were calculated after the optimization and did not show any negative frequencies. The Hartree-Fork (HF) frequencies were scaled using the typical, empirically derived value of 0.89. Results and Discussion First, structural characteristics of the hydrated beryllium complex, [Be(H2O)4]2+, from MD simulations are examined.
Figure 1. Structural characteristics of the hydrated beryllium complex [Be(H2O)4]2+. The beryllium ion-water oxygen radial distribution function (solid) and the corresponding integration numbers (dashed) are shown.
Figure 2. Geometric values of [Be(H2O)4]2+ complex. Bond and angular values are marked.
The most common species in many aqua complexes is the [Be(H2O)4]2+ ion.16 Experimental studies also find [Be(H2O)4]2+ to be the dominant species under strong acidic conditions.17 The beryllium ion-water oxygen (Be-OH2) radial distribution function (RDF) and the corresponding integration numbers are given in Figure 1. A sharp peak in the RDF is seen with maximum at 1.63 ( 0.02 Å. The first shell has a coordination number of 4. A snapshot from the simulations with a tetracoordinated Be2+ ion is shown in Figure 2. The Be2+ ion remains as a [Be(H2O)4]2+ complex during the entire duration of simulations. There is little variation in the structural/geometrical values of this complex. Bond and angular values and their flexibilities of the Be-water complex are evaluated and are schematically shown in Figure 2. The Be-O bond distance is 1.61 Å (standard deviation (STD) ) 0.04). The O-Be-O angle is 109.36° (STD ) 4.45°). The O-Be-H angle is 127.0° (STD ) 7.1°). The results from MD simulations are in good agreement with the available experimental measurements. X-ray scattering investigations of a BeCl2 solution determined the distance of Be(OH)2 to be 1.67 Å.6 In the crystal structure of [Be(H2O)4](NO3)2, the distance is reported as 1.61 Å.18 The tetracoordination is in agreement with the coordination number of 4.1 measured from diffraction and NMR experiments.19 Geometrical values obtained in this study are on par with those obtained with quantum mechanical calculations or classical simulations
2960 J. Phys. Chem. B, Vol. 112, No. 10, 2008 using many-body potentials. A DFT/B3LYP/LANL2DZ method on Be2+ ion with water clusters found the Be-O distance in [Be(H2O)4]2+ complex to be 1.65 Å.20 With optimized geometry and MP2/6-31+G(1p,1d), the calculated distance is 1.656 Å.21 An ab initio MD with Be2+ ion in 31 water molecules found the distance to be 1.66 Å.22 Asthagiri and Pratt using a similar system with ab initio MD found the distance to be 1.64 Å.23 The ab initio calculations presented in this paper, using the HF/ 3-21G* model chemistry, yield an average Be-O distance of 1.63 Å. Next, the geometrical values of the [Be(H2O)4]2+ complex are compared to the structural data on crystal structures that are from the Inorganic Crystal Structure Database24 and the Cambridge Structural Database.25 These structures contained beryllium coordinated with four oxygen atoms (beryllium sulfate tetrahydrates and beryllium carboxylates).26 The Be-O distances lie between 1.60 and 1.63 Å. Even though the average O-Be-O angle conforms to a tetrahedron complex (109.5°), it varied between 87° and 122°. The Be-O-H angle in structures from the neutron diffraction lies between 118.2° and 126.2°.26 As mentioned above, Be-O distance is in excellent agreement with the X-ray and neutron diffraction data. The average O-Be-O angle from simulations conforms to a regular tetrahedron of 109.34° in accord with structural data. The ab initio optimization yielded O-Be-O angles ranging from 107.96° to 111.92° with an average of 109.45° and a standard deviation of 1.8°. The Be-O-H angle of 127° obtained in MD is also in reasonable agreement with the experimentally determined structures. This is at the higher end range and can be a manifestation of the rigid water model considered in the simulations that does not allow flexibility of H-O-H angle. In the ab initio calculations, the H-O-H angle of the bound water molecule is 112.7°, which is different from the angle of 104.0° found in free water. Also, other ab initio calculations show that an increase in hydrogenbonding partners results in an increase in the H-O-H angle.26 An important aspect of the solvation is to consider how the Be2+ affects the local solvent structure. The second solvation shell is well separated from the first one (Figure 1). It potentially indicates a lack of exchange between shells during the time of observation thus confirming that the [Be(H2O)4]2+ is a stable complex in water. In fact, there are only a very few anions that can replace the water in the first coordination shell of Be2+. The second shell is seen between 2.5 Å and 4.5 Å, is broad, and contains 12 water molecules. It consists of two peaks centered at 3.2 Å and 4.0 Å. A snapshot from the simulations with a tetracoordinated Be2+ ion with its second solvent shell is shown in Figure 3A. The broadness of the second shell is an indication of flexibility within this shell. The splitting that gives rise to the two peaks indicates mutual distortions in the second hydration shell because of the close proximity to the Be2+ cation.7 Similar observations have also been made in the simulations of Mg2+ and Ca2+.27,28 A critical step toward quantifying the reactivity of the Be2+ ion is the consideration of the nature of hydrogen-bonding dynamics between the first and second shells. An extensive network of hydrogen bonding (Figure 3A-C) involving first and second shells was observed in the simulations. The Be2+ ion affects the second-shell water molecules by pulling them closer. Thus, one of the most important aspects of this network is to bring the first- and second-shell water molecules much closer. In fact, previous studies have also recognized that hydration generally strengthens and tightens the complex.29-32 The average O-O distance of 2.86 Å between the first- and second-shell water molecules is shorter than the distance of 2.93 Å found
Gnanakaran et al.
Figure 3. Interplay between first and second solvent shells. (A) Hydrogen-bonding network between first- and second-shell water molecules. (B) One of the continuously connected hydrogen-bonding networks from A. (C) Water molecules from second solvent shell that are at close proximity to the cation. The Be dication is in red. The color gradient from green to blue is used to mark the distance from the cation (green, close; blue, far).
for water molecules in the bulk. The hydrogen-bonding angle, H-O-H, is 152.8° compared to 153.4° found for the bulk. The Be2+ ion distorts the solvent structure to the extent that the structure and dynamics of hydrogen bonding between the first and second shells is different from the bulk. This kind of perturbation of local solvent shells is expected for Be2+ because of its large charge/radius ratio. NMR measurements indicated that the lifetime of the first-shell water molecule at room temperature is approximately 3 × 10-4 seconds.33 This time is longer than most of the known first-shell water residence times of most of the cations. One exception is Al3+ (0.78 s), which has a slightly higher charge/radius ratio.34 In our classical simulations, the calculated lifetime for the hydrogen bonding between the first- and second-shell water molecules (1.1 ps) is longer than that of bulk solvent (0.8 ps). Even though these time scales are shorter than the residence times reported in ref 32, the trend is consistent. One would expect the residence time to be determined by some sort of hydrogen-bonding network. However, no simple correlation between hydrogen-bonding lifetime and residence time is found.35 As observed here, water molecules tend to remain in proximity to positive charges irrespective of whether they form a hydrogen bond or not and give rise to longer residence times.36 The effect of Be2+ ion on its second shell is further characterized by considering the radial distribution function. The oxygen-oxygen radial distribution functions for first-shell and bulk water are plotted in Figure 4. Radial distribution functions were calculated for water molecules from bulk that had the most
Local Solvent Structure Perturbation by Dication
Figure 4. Radial distribution function and coordination numbers (insert) for water molecules from first shell and bulk. The O-O radial distribution function is plotted for water molecules from first shell (blue) and from bulk (green and red). In the inserted ball-and-stick picture (balls: green, Be ion; red, oxygen; white, hydrogen), double arrows indicate the distinction in O-O radial distribution functions. Bulk radial distribution is calculated for a water molecule that has the most (dash: red) and the least (solid: green) contact with the first shell. The green and red plots mostly overlay on top of each other.
and the least contact with the first shell. The peak position of 2.9 Å and the overall profile for the bulk water are consistent with that of TIP3P water model. The water structure around the first-shell water molecules, however, is significantly different from that of bulk. The first-shell water has a well-defined structure as indicated by a high and narrow peak. It also shows a well-defined second peak. The shift in first-shell peak toward shorter distance compared to the bulk is a consequence of Be2+ ion pulling the second-shell water molecules closer. Additionally, the first-shell water molecules are coordinated to more water molecules than the bulk waters are (Figure 4 insert). The first-shell and bulk waters are coordinated to seven and five waters, respectively. The coordination number of 5 is typical of TIP3P water model. Thus, the Be2+ ion recruits additional water molecules to its neighborhood. Interestingly, the distortion to the tetrahedral symmetry of the [Be(H2O)4]2+ complex is caused predominantly by the second shell. In the ab initio calculations, the distortion of the tetrahedral symmetry of [Be(H2O)4]2+ is evidenced by the differences in Be-O distances and O-Be-O angles; the Be-O distances range from 1.61 to 1.64 Å, and the O-Be-O angles range from 108.0 to 111.9°. This distortion from ideal tetrahedral geometry seen for [Be(H2O)4]2+ is caused by the nonuniform second solvent shell water organization. The similarity of the [Be(H2O)4]2+ structure obtained with classical and quantum calculations suggests that incorporating the second shell is adequate to reproduce the fluctuations within the [Be(H2O)4]2+ complex. The ab initio results show an average O-O distance between first- and second-shell water molecules of 2.619 Å. This value is consistent with a published crystal structure of [o-benzenedisulfonimide]2[Be(H2O)4]‚3H2O, which has solvent water molecules coordinated to three of the first-shell water molecules at an average distance of 2.674 Å.37 The subsequent O-O distances among the second-sphere water molecules are slightly longer, showing an average of 2.636 Å. Even though the [Be(H2O)4]2+ species dominates at low pH (pKa ) 3.6), hydrolysis and cluster formation take place at higher
J. Phys. Chem. B, Vol. 112, No. 10, 2008 2961 pH. NMR measurements of a BeCl2 solution revealed at least three different beryllium species in a tetrahedrally coordinated oxygen environment. Some of the known species, corresponding to hydrolysis products, are [Be2(OH)3]+, [Be3(OH)3]3+, [Be(OH)]+, Be(OH)2, [Be5(OH)6]4+, and [Be6(OH)8]4+. The influence of the second shell on the fluctuations of the first shell enables formation of these hydrolysis products. The first step in the reactivity of the [Be(H2O)4]2+ ion involves transfer of a proton from a first-shell water molecule. The water molecules in the second shell probably act as the proton acceptors in the reaction. Once the [Be(H2O)3(OH)]+ species is formed, it then reacts with additional [Be(H2O)4]2+ species to form the beryllium cluster species listed above. Classical mechanical MD simulations can provide evidence of such interplay between the first and second shell required for the reactivity. We previously characterized the differences in the structural and dynamical differences in the interactions between first- and second-shell water molecules compared to the interactions seen between water molecules from the bulk. A more relevant property to the reactivity can be inferred from the nature of observed fluctuations of these interactions. In fact, the fluctuations observed for the hydrogen-bonding interactions between the first- and second-shell water molecules are much larger compared to those of the bulk. The hydrogen-bonding distance and the angle of first-shell water molecules show variances of 4.5 × 10-3 Å and 4.8°, respectively. For the same interactions, the O-O distance can be as short as 2.74 Å and as long as 3.01 Å. For the interactions in bulk water, the variances in H-bond distance and angle are 8.3 × 10-4 Å and 3.5°, respectively. Thus, the variance of hydrogen-bonding distance of first-shell water is an order of magnitude higher than that of bulk. The propensity for beryllium to form hydroxo and oxo bridged species in water (vide supra) is consistent with the ab initio electronic structure (Figure 5). The ab initio calculated Electrostatic Potential (ESP) charges show that the oxygen atoms of the second coordination sphere are more positive than those of the first coordination sphere as shown in Figure 5. This electronic structure view is consistent with the weakening of the hydrogen bonding observed in the second shell versus the first shell in the MD calculations. This distribution of charge is in part what drives the first-shell water molecules to donate their protons to the second-shell water molecules. In addition, this intershell proton transfer is facilitated by the ability of the highly polarizing beryllium dication to make the first-shell water protons more acidic. It appears that incorporation of the second solvent shell is adequate to determine the reactive process of the [Be(H2O)4]2+ complex. The surrounding water molecules can be considered as a polarizing buffer that strengthens the bonding between beryllium dication and weak donor H2O.31 Ab initio calculations reveal that the longer O-H bonds of the firstshell water molecules make the strongest hydrogen bonds to the second-shell water molecules, presenting a potential mechanism for proton abstraction, which would then produce the reactive [Be(H2O)3(OH)]+ that could bridge to an adjacent [Be(H2O)4]2+ species in solution. The apparent dichotomy of beryllium, possessing both the ability to polarize and break bonds and to also form oligomeric structures, is the source of its interesting chemistry in aqueous solution. Finally, we have evaluated the vibrational spectroscopic properties of the hydrated beryllium complex [Be(H2O)4]2+ including the second shell. The primary modes of interest are the vibrational frequency of the Be-OH2 symmetrical mode
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Figure 5. Influence of second solvent shell on the geometry and charge distribution of the [Be(H2O)4]2+ complex. The figure provides results from ab initio calculations. The numbers in the brackets are O-O distances and the numbers in parenthesis correspond to distances from a configuration obtained from MD.
and the bending modes of BeO4 tetrahedron of the complex. These two primary vibrational modes of the BeO4 tetrahedron are calculated to be 516 cm-1 [ν1(A1);Td] and 334 [ν4(T2);Td] cm-1. These numbers compare favorably with previously reported experimental values of 526 cm-1 and 337 cm-1.31,38-40 Past ab initio studies on [Be(H2O)4]2+ have provided symmetric stretching frequencies between 484.3 and 471.1 depending on the level of theory.29 Interestingly, the calculated symmetrical ν1 mode at 516 cm-1 also has contributions from second-shell water-wagging modes. Recent studies have also shown the effect of surrounding hydration on the beryllium-oxygen stretching vibration.29-31 These studies found that inclusion of second-shell waters increases the frequency by 16% (from 484 cm-1 for the first shell to 561 for the second shell including up to 30 water molecules).31 This can be traced to Be-O stretching mode interactions with surrounding water molecules. The second-shell waters promote electron density to the Be-O bond thereby restricting the bond motion and increasing the frequency.31 In the current study, we are able to achieve better agreement with the experimental measurements of the Be-O stretching modes compared to the above studies that also incorporated the waters from the second shell. This can be attributed to several factors including a reasonable starting structure for the second hydration shell from MD simulations using the new parameters for the beryllium ion. We have also found that the HF/3-21G* model chemistry outperforms higher levels of theory, including density functional theory (DFT), when calculating geometries, 9Be NMR spectra, and IR and Raman vibrational modes.41 The success of this relatively low level of theory in predicting structure and physical properties of beryllium is fortuitous and opens the door
to performing ab initio calculations on moderately large bioinorganic systems containing beryllium that may be pertinent to CBD. Conclusions Because of its small size and the divalent character, the Be2+ ion presents a difficult challenge for representing its interactions classically in an aqueous solution.26 The charge transfer from water molecules to the beryllium dication in this complex and the interaction with water may exhibit substantial covalent character. Regardless, if one could obtain an effective potential that can reproduce the structural properties of aqueous Be2+ ionic complex with classical simulations, it would enable us to probe Be2+ interactions in large biological systems associated with chornic beryllium disease. As a step toward that direction, we capture several structural, reactive, and spectroscopic properties of Be2+ ion complex in water with simple two-body classical potential. When both molecular dynamics and ab initio results are analyzed together, the role of the solvent in the reactivity of the [BeAq4]2+ dication is clarified. Namely, the solvent acts to accept protons from the beryllium dication at higher pH values (>3.6). The high reactivity of the resulting [Be(H2O)3(OH)]+ species then drives the formation of beryllium hydroxo clusters, such as [Be2(OH)3]+, [Be3(OH)3]3+, [Be5(OH)6]4+, and [Be6(OH)8]4+. Next, it will be extended to the coordination chemistry of beryllium with amino acids, which is almost completely unexplored. Acknowledgment. We thank the LDRD-DR (X1V4) grant for support of this research. We are also grateful to Dr. Lawrence Pratt for many useful discussions and suggestions. A.E.G. has been supported by NSF grants MCB-0543769 and DMR0227792.
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