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J. Phys. Chem. B 2008, 112, 5788-5794
Exploring Structure and Dynamics of the Diaquotriamminezinc(II) Complex by QM/MM MD Simulation M. Qaiser Fatmi,† Thomas S. Hofer,‡ Bernhard R. Randolf,‡ and Bernd M. Rode*,‡ HEJ Research Institute of Chemistry, International Center for Chemical and Biological Sciences, UniVersity of Karachi, Karachi-75270, Pakistan, and Theoretical Chemistry DiVision, Institute of General, Inorganic and Theoretical Chemistry, UniVersity of Innsbruck, Innrain 52a, A-6020 Innsbruck, Austria ReceiVed: October 24, 2007; In Final Form: January 7, 2008
The structural and dynamical properties of the cis-(O-Zn-O angle ≈ 90°) and trans-(O-Zn-O angle ≈ 180°) isomers of the model diaquotriamminezinc(II) complex in aqueous solution have been evaluated using the hybrid quantum mechanical/molecular mechanical molecular dynamics simulation approach at ab initio Hartree-Fock level. In both complexes, the first hydration shell contains five ligands (two water and three ammonia molecules) arranged in a trigonal bipyramidal geometry. In the metastable cis-isomer two different bond lengths of 2.34 and 2.13 Å are observed for the Zn-Oax and Zn-Oeq bonds, respectively. The transisomer shows the maximum of the Zn-O distance at 2.26 Å. The Zn-N bond distances in both cases are ∼2.12 Å. A geometrical transformation of the cis-isomer into the trans-isomer was observed after 11.5 ps of simulation, and the trans-isomer then remained stable throughout the whole simulation time of 30 ps. A comparative study for both isomers has been performed in terms of radial distribution functions, coordination number distributions, angular distribution functions, tilt and θ angle distributions, ligands’ mean residence time, ion-ligand stretching frequencies, and the vibrational and librational motions of water ligands. The results are compared with the data for the previously studied zinc-monoamine and -diamine complexes.
Introduction The study of structure and dynamics of biologically relevant ligands, coordinated to various transition metal ions is one of the prominent topics in bioinorganic chemistry. Transition metal cations comprise the active sites of several enzymes, specifically known as metalloenzymes, providing good binding sites for substrates and thereby enhancing the rate of the biochemical reactions. Among these transition metal ions, zinc(II) is the second most abundant metal following iron in the human body and exhibits versatile roles in more than 300 enzymes covering all 6 enzyme classes.1,2 Although a tetrahedral geometry is common for zinc complexes in biological systems, fivecoordinated structures of trigonal-bipyramidal or squarepyramidal arrangement are also known, and the trigonalbipyramidal geometry seems to be essential for the catalytic action of metalloenzymes. In particular, the pentacoordinate trigonal-bipyramidal structures based on Zn-X (X ) O and N) bonding play a key role in the stereochemistry and dynamics of biochemical reactions:3 Several zinc-containing metalloproteins such as adenosine deaminase,4 meprin R,5 B nerve growth factor,6 and enolase7 are reported to have this trigonalbipyramidal geometry. Furthermore, it has also been suggested that in carbonic anhydrase (CA), carboxypeptidase, thermolysin, and alcohol dehydrogenase a pentacoordinate transition state of zinc(II) is formed.8-15 Despite of the importance of the pentacoordinated zinc complexes in biological systems, only few experimental3,16-19 * To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: +43-512-507-5160. Fax: +43-512507-2714. † University of Karachi. ‡ University of Innsbruck.
Figure 1. Zn-O and Zn-N RDFs and their running integration numbers for cis- (a and b) and trans-isomers (c and d) of the [Zn(NH3)3(H2O)2]2+ complex in aqueous solution obtained from the QM/ MM MD simulation. The Zn-Oax and Zn-Oeq RDF for the cis-isomer is also shown in the inset of (a).
and theoretical8,20,21 works have been reported in the literature. The experimental data are mainly based on NMR studies, X-ray crystallography, circular dichroism spectroscopy, and IR spectroscopy, primarily focusing on structures, activities, biochemical reaction mechanisms, kinetics, thermodynamics, and catalysis of highly complicated systems. The theoretical works mainly deal with energetics, thermodynamics, and structures of different zinc-triamine complexes, mostly with bulky ligands. The geometry optimization of the cis-diaquotriamminezinc(II) complex carried out by Krauss et al.20 suggested a larger axial Zn-O bond length (2.44 Å) compared to the equatorial Zn-O bond (2.13 Å). The binding energy for the Zn-H2Oax was calculated
10.1021/jp710270z CCC: $40.75 © 2008 American Chemical Society Published on Web 05/01/2008
Structure and Dynamics of Diaquotriamminezinc(II)
Figure 2. Coordination number distributions of the first and the second hydration shells for (a) cis- and (b) trans-isomers of the [Zn(NH3)3(H2O)2]2+ complex in aqueous solution obtained from the QM/MM MD simulation.
as 23.7 kcal/mol. Garmer et al.21 have performed a geometry optimization of the cis-diaquotriamminezinc(II) complex at unrestricted Hartree-Fock level and evaluated the energetics for adding a water molecule to the four-coordinated carboxypeptidase model (CA) at HF/MP2 level (57.3 kcal/mol). Sola` et al.8 have performed gas-phase, ab initio, all-electron restricted Hartree-Fock (RHF) calculations to evaluate the structural, electronic and energetic changes occurring in different pentacoordinated zinc complexes such as [Zn(NH3)3(H2O)(CH3OH)]2+, [Zn(NH3)3(H2O)(OCH3)]+, [Zn(NH3)3(OH)(CH3OH)]+, and [Zn(NH3)3(OH)(OCH3)], employing 3-21G basis sets for all atoms except for the hydrogens of the NH3 and CH3 groups, for which STO-3G basis sets were employed. In all complexes, larger axial Zn-N and Zn-O bonds compared to the equatorial ones were observed and it was concluded that the Zn-ligand bond lengths depend on the number of attached ligands, the location of the ligands, and the total charge of the complex. The current work is a continuation of our detailed study on understanding the chemical behavior of aquo- and ammineZn(II) complexes in aqueous solution. The results are compared with the previous ab initio hybrid quantum mechanical/ molecular mechanical molecular dynamics (QM/MM MD) simulations of zinc-monoamine and -diamine complexes, and the effects of ammonia substitution on structural and dynamical behavior and stability of cis-(O-Zn-O angle ≈ 90°) and trans-(O-Zn-O angle ≈ 180°) isomers are discussed. Methodology Construction of Potential Functions. In the hybrid QM/ MM MD simulation, the accurate description of the system depends on the proper choice of a basis set and the level of theory applied in the QM region. Recent investigations and
J. Phys. Chem. B, Vol. 112, No. 18, 2008 5789 previous simulations have shown that Dunning double-ζ plus polarization function basis sets for oxygen, nitrogen, and hydrogen can be successfully applied,22-25 and thus, these basis sets were chosen for this investigation as well. The LANL2DZ ECP basis set, which also includes a relativistically corrected ECP was chosen for Zn(II),26 with a minor modification (s and p basis functions with lowest exponent have been removed from uncontracted basis functions, leaving a double-ζ basis set to make it more compatible with the Zn(II) ion rather than the zinc atom). To be consistent with previous simulations, we chose the ab initio Hartree-Fock formalism, which has shown to be reliable to obtain good structural and dynamical data, also compared to correlated methods.25,27 The hybrid QM/MM MD approach further requires the construction of sufficiently accurate potential functions for Zn-H2O and Zn-NH3. The two- and three-body potentials for Zn-H2O were taken from the previous simulation of the Zn(II)-water complex,25 while the two-body potential for Zn-NH3 and three-body potentials for H2O-Zn-NH3 and H3N-Zn-NH3 were same as in the recently published study of the zinc-monoamine complex28 and the zincdiamine complex.27 The details of the construction of Zn-H2O and Zn-NH3 two-body interactions and H2O-Zn-H2O, H2O-Zn-NH3, and H3N-Zn-NH3 three-body interactions have been given in these papers.25,27,28 In all cases, the energy points were calculated at RHF level employing the TURBOMOLE 5.5 program.29-32 Simulation Protocol. For the MD simulation, a cubic box with a side length of 24.71 Å corresponding to the experimental density33 (0.997 g/cm3) of pure water at 298 K was employed, containing 1 Zn(II), 3 ammonia, and 496 water molecules. The temperature of the NVT ensembles was controlled via the Berendsen algorithm34,35 with a relaxation time of 0.1 ps. The cutoff distances for the non-Coulombic interactions were set to 6.0 Å for N-H, 5.0 Å for both HN-HN and O-H and 3.0° Å for HO-HO. For all other pair interactions, the cutoff was 12.0 Å. Periodic boundary conditions were applied; long-range interactions were treated by the reaction field method.36 The flexible BJH-CF2 water model37,38 and a flexible four-site ammonia model39 were used, including intramolecular potentials enabling explicit hydrogen movements. Therefore, the time step for the simulation was set to 0.2 fs. The Newtonian equations of motion were integrated by a predictor-corrector algorithm. After 5 ps of the equilibration of the initial box by the QM/ MM MD method, the system was sampled for further 30 ps. To ensure the full inclusion of the first shell into the QM zone, the radius of the QM sphere was set to 3.6 Å in accordance with the Zn-O radial distribution functions (RDFs). Water and ammonia molecules whose center of mass is located within the QM sphere are treated quantum mechanically; otherwise forces
TABLE 1: Characteristic Values of Radial Distribution Functions gZn-O(r), gZn-N(r), and gZn-H(r) for the Cis- and Trans-Isomers of the [Zn(NH3)3(H2O)2]2+ Complex in Aqueous Solution Obtained from the QM/MM MD Simulationa complex 2+
cis-[Zn(NH3)3(H2O)2]
trans-[Zn(NH3)3(H2O)2]2+
a
Zn-Oav Zn-Oax Zn-Oeq Zn-HO Zn-N Zn-HN Zn-O Zn-HO Zn-N Zn-HN
rM1 (Å)
rm1 (Å)
CNav,1
rM2 (Å)
rm2 (Å)
CNav,2
2.15 2.34 2.12 2.76 2.13 2.72 2.26 2.90 2.12 2.69
3.38 3.38 2.38 3.84 2.54 3.25 3.26 3.83 2.43 3.14
2 1 1 4 3 9 2 4 3 9
4.75/5.22
6.56
35
5.32
6.79
50
4.80 5.33 -
6.50 6.64 -
35 47 -
rM denotes maximums and rm minimums observed in the RDFs, CNav represents the average coordination number.
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Figure 3. Transformation of the cis-isomer (a) into the trans-isomer (b) of the [Zn(NH3)3(H2O)2]2+ complex in aqueous solution via a fourcoordinated geometry (a*). (snapshots taken by MOLVISION.)
of the diaquotriamminezinc(II) complex in aqueous solution. The evalution of metal-ligand stretching frequency was carried out using velocity autocorrelation functions (VACFs), C(t), defined as Nt N
C(t) )
∑i ∑j Vbj (ti)Vbj (ti + t) Nt N
NtN
Figure 4. Distribution of the (a) O-Zn-O, (b) O-Zn-N, and (c) N-Zn-N angle in degree obtained from the QM/MM simulation for cis- (dashed line) and trans-isomers (solid line) of the [Zn(NH3)3(H2O)2]2+ complex in aqueous solution. The dotted line shows the normalization according to the cosine law.
are evaluated by means of empirical force field.24,40-43 The total force acting on a particle is calculated according to the following expression: QM MM Ftot ) Fsys MM + (FQM - FQM ) S(r)
(1)
sys Ftot is the total force acting on a particle, FMM is the MM force QM MM of the entire system, and FQM and FQM are QM and MM forces in the QM region. A smoothing function S(r) is applied in a region of 0.2 Å to ensure smooth transitions of water molecules44,45 between QM and MM regions,
S(r) ) 1, S(r) )
for
re r1
(r02 - r2)2(r02 + 2r2 - 3r12) , (r02 - r12)3 S(r) ) 0,
for
for
(2) r1 < r e r0
r > r0
where r1 and r0 are the distances characterizing the QM region, where smoothing applies. Radial and angular distribution functions were evaluated to characterize the structural properties
(3)
Vj (ti) ∑i ∑j Vbj (ti)b
where N is the number of particles, Nt is the number of time origins ti, and b Vj denotes the given velocity components of the particle j. The power spectrum of the VACF was calculated by Fourier transformation, using a correlation length of 2.0 ps with 2000 averaged time origins. The ion-oxygen and ion-nitrogen stretching frequencies were computed using the approximative normal coordinate analysis.46 Ligand mean residence times (MRTs, τ) in the second hydration shell were calculated using the standard direct method.41 The parameter t*, determining the minimum time span to account a ligand displacement from its original shell, was set to 0 and 0.5 ps, respectively. The sustainability of exchange processes can then be defined as 0 Sex ) N0.5 ex /Nex
(4)
where Sex is the sustainability coefficient, N0ex is the number of all transitions through a shell boundary (t* ) 0), and N0.5 ex denotes the number of exchanges persisting longer than 0.5 ps. Its inverse (1/Sex) accounts how many attempts are needed to produce one lasting exchange between the hydration shell and bulk. Reorientational time correlation function (RTCFs) of water molecules were calculated as
bi(0)u bi(t))〉 Cli(t) ) 〈Pl(u
(5)
where Pl is the Legendre polynomial of lth order and b ui is a unit vector along the three principal axes i defined in a fixed coordinate frame. The RTCFs were fitted to the following simple form,
Cl(t) ) a exp(-t/τ1)
(6)
where a and τ1 are the fitting parameters and τ1 corresponds to the relaxation time.
Structure and Dynamics of Diaquotriamminezinc(II)
J. Phys. Chem. B, Vol. 112, No. 18, 2008 5791
Results and Discussion Structural Features. Figure 1 displays the Zn-O and the Zn-N RDFs obtained from the QM/MM MD simulation of cisand trans-isomers of the [Zn(NH3)3(H2O)2]2+ complex in aqueous solution; the distinctive features of the Zn-H2O and the Zn-NH3 RDFs are summarized in Table 1. Two wellseparated peaks in the Zn-O RDF of both isomers (Figure 1a and c) represent distinct first and second hydration shells. A third shell is not recognizable. In the case of the cis-isomer (Figure 1a), the Zn-Oax and Zn-Oeq RDFs have two distinctly different peak maximums appearing at 2.34 and 2.13 Å, respectively (see the inset of Figure 1a). Krauss et al.20 have performed the ab initio calculations on a pentacoordinated cluster model for the active site of the carbonic anhydrase and reported the Zn-Oax and Zn-Oeq distances to be 2.44 and 2.13 Å, respectively. Differences between the Zn-O (axial and equitorial) distances have also been reported in more complex and constrained systems, where the cis-isomer is predominant, making the Zn-H2Oax bond highly flexible. Kimura et al.10 have reported the X-ray crystal structure of a pentacoordinated Zn(II) complex with phenol-pendant macrocyclic triamine 2-(2-hydroxyphenyl)1,5,9-triazacyclododecane, indicating a difference of ∼0.29 Å between Zn-Oax and Zn-Oeq bond length. The unusually long Zn-Oax distance is related to the instability of the cisconformation (vide infra). The peak maximum of the first shell in the Zn-O RDF of the trans-isomer (Figure 1c) appeared at a distance of 2.26 Å, which is further elongated compared to the average Zn-O bonds in zinc-monoamine28 (2.19 Å) and -diamine complexes27 (2.22 and 2.23 Å for cis- and trans-isomers of the tetraaquodiamminezine(II) complex, respectively, and 2.15 Å for the triaquodiamminezinc(II) complex). In the Zn-N RDFs of both isomers (Figure 1b and 1d), a single peak with an integration number of 3 refers to the first shell ammonia ligands, which appeared at distances of 2.13 and 2.12 Å for cis- and trans-isomers, respectively. A similar Zn-N bond length (2.12 Å) was observed in the [Zn(NH3)2(H2O)3]2+ complex and seems to be a typical, therefore, for the trigonalbipyramidal structure. Some shoulders are, however, recognized at the top of the peak, indicating slightly different Zn-N bond lengths to exist. Figure 2 plots the coordination number distributions of water and ammonia ligands around the zinc(II) ion obtained from the QM/MM MD simulation of cis- and trans-isomers of the diaquotriamminezinc(II) complex. In the first hydration shell of both isomers, the coordination numbers of 2 + 3 for water + ammonia ligands are observed with 100% occurrence proving that no water exchange processes took place within the simulation time, except for the process related to the cis-trans isomerization (vide infra) via a four-coordinated geometry (Figure 3). It should also be noticed that no hexacoordinated structures are observed throughout the whole simulation period. Kleifeld et al.47 have also observed the variation in the zinc coordination during the Thermoanaerobacter brockii alcohol dehydrogenase catalysis of the oxidation of secondary alcohols, studied by means of time-resolved X-ray absorption spectroscopy, where the tetrahedral coordination of the Zn(II) ion converts into a pentacoordinate structure upon addition of a water ligand. Both isomers showed a large variation in the second shell coordination number varying from 30 to 39 with a maximum probability of 35, which is considerable higher than the second shell coordination number of zinc-monoamine (19) and
Figure 5. Tilt (a) and θ (b) angle distributions of the Zn-water geometry of cis- (dashed line) and trans-isomers (solid line) of the [Zn(NH3)3(H2O)2]2+ complex in aqueous solution.
triaquodiamminezinc(II) (30) complexes, thus showing an increase of the second shell coordination number with increasing number of ammonia ligands. This increase in the second shell coordination number is associated with an elongation of the mean distance of the second shell and can be seen as a consequence of the considerable loss of charge of the Zn(II) ion upon binding of additional ammonia ligands. However, it still remains cationic with an average charge of ∼1.43. The O-Zn-O, O-Zn-N, and N-Zn-N angular distribution functions obtained for the first shell of the QM/MM MD simulation for both isomers of the triaquodiamminezinc(II) complex are plotted in Figure 4a-c. A single peak is observed for the O-Zn-O angle in both cis- and trans-isomers located at ∼81° and ∼170°, respectively, clearly indicating the cis and trans arrangements of water ligands around the Zn(II) ion. The O-Zn-N angle distribution is shown in Figure 4b. The cis-isomer showed two peak maximums at 87° (with a broad tailing toward higher angles) and 170°. However, for the transisomer a single peak was observed at ∼90° representing the ligand(ax)-Zn-ligand(eq) angles in the trigonal-bipyramidal geometry. The distortion of the cis-isomer is well demonstrated by the N-Zn-N angle (depicted in Figure 4c), peaking at 97° and 109°, while the trans-isomer showed only a single peak located at 120°, clearly demonstrating the arrangement of the three ammonia ligands in a plane. For a deeper insight into the orientation of the water molecules relative to the ion, two angles were defined: θ as the angle between the Zn-O vector and the dipole vector, and “tilt” as the angle between the Zn-O connection vector and the plane formed by the O-H vector (see sketch in Figure 5). The tilt and θ angle distributions of the first shell obtained from the QM/MM simulation are displayed in Figure 5. The tilt angle distributions for both isomers range from -45° to +43° and -45° to +52° with half-widths of ∼32° and ∼33° for cis- and trans-isomers, respectively, reflecting a substantial flexibility of water ligands in the first shell. The maximums of the θ angle distributions are observed at ∼170° for both isomers, which is almost the same as found in the θ angle distributions of zinc-monoamine (∼170°) and -diamine (∼171°) complexes.
5792 J. Phys. Chem. B, Vol. 112, No. 18, 2008
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Figure 6. Fluctuation of the Zn-O and the Zn-N bond distances for (a) cis- and (b) trans-isomers of the [Zn(NH3)3(H2O)2]2+ complex in aqueous solution.
Dynamical Properties. Sections a and b in Figure 6 show the fluctuation of the Zn-O and the Zn-N bond distances for both cis- and trans-isomers, respectively, which give a clear picture of the varying length of individual Zn-O and the Zn-N bonds. The distance plot of the cis-isomer (Figure 6a) distinctly shows two different Zn-O and Zn-N bond lengths for axial and equatorial ligands. The mean Zn-Oeq bond distance is observed at 2.11 Å, which is comparable to that observed in the triaquodiamminezinc(II) complex27 (∼2.13 Å). A considerably elongated Zn-Oax bond distance is observed, namely, 2.50 Å, with increasingly strong fluctuations in the bond length, ultimately forcing this water to leave the first hydration shell and producing a four-coordinated intermediate behind. The mean Zn-Nax and Zn-Neq bonds in the cis-complex are observed at 2.18 and 2.14 Å, respectively. This difference in the Zn-N bond length is only reflected by small shoulders on the RDF peak. On the other hand, in the trans-isomer, the mean Zn-Oax and Zn-Neq bond distances are ∼2.33 and ∼2.14 Å, respectively. Although fluctuations are also observed in the Zn-Oax bonds, but the trans-isomer appears to be a stable structure in aqueous solution. Figure 7a further demonstrates the kinetic instability of the cis-isomer in aqueous solution: after 11.5 ps of simulation time, the H2Oax ligand is ejected from the first coordination sphere and the four-coordinated intermediate prevails for ∼5 ps, until another water molecule enters the first hydration shell from the opposite side thus producing a trans-isomer. This transisomer remained stable throughout the whole simulation time of 30 ps. These observations allow a classification of the cis-[Zn(NH3)3(H2O)2]2+ and the [Zn(NH3)3(H2O)]2+ complex as metastable conformation and intermediate, respectively. In the second shell, numerous exchange events are observed. The characteristic values of these water exchange reactions are summarized in Table 2. The second shell ligands’ MRT value for the stable trans-isomer is ∼6.9 ps, which is insignificantly higher than the MRT value of the triaquodiamminezinc(II) complex27 (∼6.5 ps). The number of attempts necessary for one successful exchange process (1/Sex) in the trans-diaquotriamminezinc(II) complex of 11 is also almost equal to the value of the triaquodiamminezinc(II) complex (11.5) showing an almost negligible influence of a third ammonia substitution on the second hydration shell.
Figure 7. Ion-ligand distance plot for (a) cis- and (b) trans-isomers of the diaquotriamminezinc(II) complex in aqueous solution. The water exchange processes in (a) indicate the cis-trans isomerization. Ammonia molecules are represented as orange, cyan, and green colors. Blue, red, and black are the color code for water molecules. The second shell ligands and bulk are shown in gray.
Figure 8. Power spectra of the Zn-O (solid line) and Zn-N (dashed line) stretching frequencies for the trans-[Zn(NH3)3(H2O)2]2+ complex in aqueous solution.
The power spectra of the Zn-O and Zn-N stretching vibrations obtained for the first shell of the trans-[Zn(NH3)3(H2O)2]2+ complex are displayed in Figure 8. The frequencies
Structure and Dynamics of Diaquotriamminezinc(II)
J. Phys. Chem. B, Vol. 112, No. 18, 2008 5793
TABLE 2: Mean Ligand Residence Time (τ) for t* Values of 0 and 0.5 psa second shell complex 2+
[Zn(NH3)3(H2O)2] (trans) [Zn(NH3)2(H2O)3]2+ [Zn(NH3)(H2O)5]2+ [Zn(H2O)6]2+
N0.0 ex /10 ps
τ0.0 d
N0.5 ex /10 ps
τ0.5 d
Sex
1/Sex
ref
558 515 465 306
0.61 0.56 0.4 0.4
49.6 44.8 26.6 14.0
6.92 6.52 7.2 10.5
0.089 0.08 0.05 0.04
11 11.5 20 21.8
this work 27 28 25
a Number of accounted ligand exchange events N, sustainability of migration processes to/from the second hydration shell Sex, and number of attempts necessary for one successful exchange process (1/Sex) obtained from the QM/MM MD simulation.
TABLE 3: Reorientational Times (τ) of First and Second Order of Water Molecules in the First and Second Shells and the Bulk for the trans-[Zn(NH3)3(H2O)2]2+ Complex and the Previously Studied Zinc-Water, - Monoamine, and -Diamine Complexes in Aqueous Solution Obtained from the QM/MM MD Simulationa
reorientational time (in ps) complex 2+ b
trans-[Zn(NH3)3(H2O)2] [Zn(NH3)2(H2O)3]2+ c [Zn(NH3)(H2O)5]2+ d [Zn(H2O)6]2+ e
phase
τ1x
τ1y
τ1z
τ2x
τ2y
τ2z
first shell second shell bulk first shell second shell bulk first shell second shell bulk first shell second shell bulk
12.9 6.1 6.8 16.0 8.4 7.8 7.8 6.4 7.3 54.8 10.6 6.6
35.5 7.2 7.0 39.3 9.7 8.2 28.8 8.0 7.7 100.2 10.8 6.8 7.5
11.4 4.7 4.7 14.5 6.2 5.3 6.9 4.9 5.0 47.0 8.0 4.4
4.9 2.2 3.1 6.3 3.8 3.6 3.1 3.1 3.3 19.1 4.3 3.0
12.3 2.7 2.7 19.7 3.5 3.0 11.3 3.0 3.0 33.3 4.0 2.6 2.5
4.6 2.1 2.2 5.8 2.6 2.4 2.6 2.4 2.3 16.0 3.0 2.0
H2O(exp)f a
The x, y, and z Axes of the water molecule have also been shown. b This work. c Values taken from the QM/MM MD simulations of the most stable pentacoordinated zinc-diamine complex.27 d QM/MM MD simulations of hexacoordinated zinc-monoamine complex.28 e QM/MM MD simulations of hexaaquozinc(II) complex at room temperature.25 f Experimental reorientational correlation time of water.51
have been multiplied with the standard scaling factor for Hartree-Fock calculations of 0.8948,49 to make them comparable with experimental values. The Zn-O stretching vibrations for the trans-diaquotriamminezinc(II) complex appeared at 237 cm-1 (force constant 42.5 N m-1) along with a second peak at 91 cm-1 (force constant 6.3 N m-1), indicating different kinds of Zn-O bonds. This splitting of the Zn-O stretching peak has also been observed in previously studied zinc complexes (e.g., zinc-water,25 zinc-monoamine,28 and zinc-diamine27 complexes). However, the splitting becomes more pronounced upon introduction of each additional ammonia ligand, indicating a gradually increasing distinction between axial and eqatorial Zn-O bonds, which is also reflected in other structural data, such as the RDFs obtained by the simulations. At higher temperature, this splitting vanishes in favor of a broader and less intense peak with a noticeable tailing toward lower frequencies,50 apparently as a consequence of the accelerated dynamics of the complex. These values of the Zn-O stretching frequencies are considerably lower compared to the pentacoordinated trigonalbipymidal triaquodiamminezinc(II) complex,27 where the Zn-O stretching vibration peak appeared at 279 (force constant 59 N m-1) and 115 cm-1 (force constant 10 N m-1), thus clearly demonstrating the influence of an additional ammonia ligand on the Zn-O bond strength.
As in zinc-monoamine and -diamine complexes,27,28 the Zn-N stretching frequency in the trans-diaquotriamminezinc(II) complex is also found at a considerably higher value than the Zn-O frequency, namely, at 333 cm-1 (force constant 75 N m-1), indicating the higher affinity of Zn2+ to ammonia than to water. Reorientational time correlation functions are another important dynamical parameter as they allow us to study the rotational properties of water molecules around the principal axes under the influence of a cation. The correlation functions for l ) 1 are related to IR line shapes and l ) 2 to Raman line shapes and NMR relaxation times.35,51 The reorientational time correlation functions are consistent with librational motions. Table 3 lists the first- and second-order reorientational times for water molecules around x, y, and z axes in the first and second shells and in the bulk, obtained from the QM/MM MD simulations of the trans-diaquotriamminezinc(II) complex. For comparison, the values of previously studied zinc complexes25,27,28 have also been listed in Table 3. The first shell of the trans-diaquotriamminezinc(II) complex shows the highest relaxation time for rotations around the y-axis, and consequently, this seems to be the most hindered rotation. This observation is similar to those observed for other zinc complexes.25,27,28 The irregularity in the values of reorientational times going from the zinc-water complex to its mono-, di-, and trisubstituted
5794 J. Phys. Chem. B, Vol. 112, No. 18, 2008 zinc-amine complexes (i.e., zinc-monoamine, -diamine, and -triamine complexes) is associated with the first shell coordination number, which determines the geometry of the complex and the Zn-O bond lengths. For example, the hexacoordinated zinc-water complex displays a shorter Zn-O distance (2.11 Å) than the hexa-coordinated zinc-monoamine complex (Zn-O ) 2.19 Å) due to the ammonia substitution. This leads to a stronger hindrance of the water rotation, which is reflected in the reorientational time of water molecules in the unsubstituted zinc-water complex by a higher value. Introduction of one more ammonia ligand into the zinc-monoamine complex, reduces the coordination number from 6 to 5, which reduces the Zn-O bond length to 2.15 Å in the zinc-diamine complex, and thus leads to a higher reorientational time of water ligands compared to the monosubstituted complex. Further substitution of the pentacoordinated zinc-diamine complex by an additional ammonia ligand elongates the Zn-O bond again to 2.26 Å, and consequently, the water ligands’ reorientational time decreases. Conclusion The present QM/MM MD simulation study performed to evaluate the structural and dynamical properties of the diaquotriamminezinc(II) complex reveals that the stable isomer of the diaquotriamminezinc(II) complex in aqueous solution is the trans-species. The cis-conformation issat bestsmetastable and isomerizes via a four-coordinated intermediate to the transisomer. This relative instability of the cis-conformation can play a role for the zinc coordination occurring in biologoical catalysis, as active sites of several zinc(II)-containing enzymes are present in a constrained/distorted trigonal-bipyramidal configuration with a cis-conformation. A further study of the kinetics and the thermodynamics of such complexes may thus provide further insight into the reaction mechanisms of such compounds. Furthermore, the comparison of the results obtained for the diaquotriamminezinc(II) complex with those of the zincmonoamine and -diamine complexes leads to the conclusion that the influence of additional ammonia ligands in the first shell is only observed in terms of Zn-ligand bond lengths, stretching frequencies, reorientational times, and in the second shell coordination number distributions. The other properties of the trans-diaquotriamminezinc(II) complex in comparison to the zinc-diamine complex such as tilt and angle distributions, MRT values, number of exchange processes (Nex), and number of attempts necessary for one successful exchange process (1/Sex) seem to remain almost unaffected. On the other hand, the large differences in the MRT, Nex, and 1/Sex values between pentacoordinated zinc-triamine/zinc-diamine and hexacoordinated zinc-monoamine species can be explained as a combined effect of ammonia introduction and associated changes in the coordination geometry of the complexes. Acknowledgment. Financial support for this work by Austrian Science Foundation (FWF) and an Austrian Technology Grant (BMBWK/RFTE) are gratefully acknowledged. References and Notes (1) (2) (3) (4)
Gaither, L. A.; David, J. E. BioMetals 2001, 14, 251. Maret, W. BioMetals 2001, 14, 187. Kirchner, C.; Krebs, B. Inorg. Chem. 1987, 26, 3569. Wilson, D.; Quiocho, F. Biochemistry 1993, 32, 1689.
Fatmi et al. (5) Stocker, W.; Gomis-Ruth, F.; Bode, W.; Zwilling, R. Eur. J. Biochem. 1993, 214, 215. (6) Holland, D.; Cousens, L.; Meng, W.; Matthews, B. J. Mol. Liq. 1994, 239, 385. (7) Lebioda, L.; Stec, B.; Brewer, J.; Tykarska, E. Biochemistry 1991, 30, 2823. (8) Sola`, M.; Lledo`s, A.; Duran, M.; Bertra`n, J. Inorg. Chem. 1991, 30, 2523. (9) Monzingo, A. F.; Matthews, B. W. Biochemistry 1984, 23, 5724. (10) Kimura, E.; Koike, T.; Toriumi, K. Inorg. Chem. 1988, 27, 3687. (11) Pocker, Y.; Deits, T. L. J. Am. Chem. Soc. 1982, 104, 2424. (12) Kuo, C. L.; Makinen, M. W. J. Biol. Chem. 1982, 257, 24. (13) Holmes, M. A.; Matthews, B. W. Biochemistry 1981, 20, 6912. (14) Yachandra, V.; Powers, L.; Spiro, T. G. J. Am. Chem. Soc. 1983, 105, 6596. (15) Pocker, Y.; Deits, T. L. J. Am. Chem. Soc. 1981, 103, 3949. (16) Niklas, N.; Walter, O.; Alsfasser, R. Eur. J. Inorg. Chem. 2000, 1723. (17) Nakacho, Y.; Misawa, T.; Fujiwara, T.; Wakahara, A.; Tomita, K. Bull. Chem. Soc. Jpn. 1976, 49, 595. (18) Dolla, B. A.; Villa, J. P.; Ishmael, F. T.; Bond, J. S. Biol. Chem. 2002, 383, 1167. (19) Sideraki, V.; Wilson, D. K.; Kurz, L. C.; Quiocho, F. A.; Rudolph, F. B. Biochemistry 1996, 35, 15019. (20) Krauss, M.; Garmer, D. R. J. Am. Chem. Soc. 1991, 113, 6426. (21) Garmer, D. R.; Krauss, M. J. Am. Chem. Soc. 1992, 114, 6487. (22) Dunning, T. H., Jr. J. Chem. Phys. 1970, 53, 2823. (23) Hofer, T. S.; Rode, B. M. Chem. Phys. 2005, 312, 81. (24) Hofer, T. S.; Randolf, B. R.; Rode, B. M. Phys. Chem. Chem. Phys. 2005, 7, 1382. (25) Fatmi, M. Q.; Hofer, T. S.; Randolf, B. R.; Rode, B. M. J. Chem. Phys. 2005, 123, 54514. (26) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270. (27) Fatmi, M. Q.; Hofer, T. S.; Randolf, B. R.; Rode, B. M. J. Phys. Chem. B 2006, 111, 151. (28) Fatmi, M. Q.; Hofer, T. S.; Randolf, B. R.; Rode, B. M. Phys. Chem. Chem. Phys. 2006, 8, 1675. (29) Brode, S.; Horn, H.; Ehrig, M.; Moldrup, D.; Rice, J. E.; Ahlrichs, R. J. Comput. Chem. 1993, 14, 1142. (30) Ahlrichs, R.; Ba¨r, M.; Ha¨ser, M.; Horn, H.; Ko¨lmel, C. Chem. Phys. Lett. 1989, 162, 165. (31) Ahlrichs, R.; Arnim, M. V. Methods and Techniques in Computational Chemistry, METECC-95; STEF: Cagliari, 1995. (32) Arnim, M. V.; Ahlrichs, R. J. Comput. Chem. 1998, 19, 1746. (33) Remsungnen, T.; Rode, B. M. J. Phys. Chem. A 2003, 107, 2324. (34) Berendsen, H. J.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. (35) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford Science Publications: New York, 2003. (36) Adams, D. J.; Adams, E. M.; Hills, G. J. Mol. Phys. 1979, 38, 387. (37) Stillinger, F. H.; Rahman, A. J. Chem. Phys. 1978, 68, 666. (38) Bopp, P.; Jansco, G.; Heinzinger, K. Chem. Phys. Lett. 1983, 98, 129. (39) Hannonngbua, S. V.; Ishida, T.; Spohr, E.; Heinzinger, K. Z. Naturforsch. 1988, 43, 572. (40) Rode, B. M.; Schwenk, C. F.; Tongraar, A. J. Mol. Liq. 2004, 110, 105. (41) Hofer, T. S.; Tran, H. T.; Schwenk, C. F.; Rode, B. M. J. Comput. Chem. 2004, 125, 211. (42) Kritayakornupong, C.; Plankensteiner, K.; Rode, B. M. Chem. Phys. Lett. 2003, 371, 438. (43) Loeffler, H. H.; Yagu¨e, J. I.; Rode, B. M. J. Phys. Chem. A 2002, 106, 9529. (44) Kerdcharoen, T.; Liedl, K. R.; Rode, B. M. Chem. Phys. 1996, 211, 313. (45) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4, 187. (46) Bopp, P. Chem. Phys. 1986, 106, 205. (47) Kleifeld, O.; Frenkel, A.; Martin, J. M. L.; Sagi, I. Nat. Struct. Biol. 2003, 10, 98. (48) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502. (49) DeFrees, D. J.; McLean, A. D. J. Chem. Phys. 1985, 82, 333. (50) Fatmi, M. Q.; Hofer, T. S.; Randolf, B. R.; Rode, B. M. J. Phys. Chem. B 2006, 110, 616. (51) Ohtaki, H.; Radnai, T. Chem. ReV. 1993, 93, 1157.
