Stability of Different Zinc(II)−Diamine Complexes in Aqueous

In the context of our detailed study of the chemical behavior of aquo− and ammine−Zn(II) complexes, ab initio quantum mechanical/molecular mechani...
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J. Phys. Chem. B 2007, 111, 151-158

151

Stability of Different Zinc(II)-Diamine Complexes in Aqueous Solution with Respect to Structure and Dynamics: A QM/MM MD Study M. Qaiser Fatmi, Thomas S. Hofer, Bernhard R. Randolf, and Bernd M. Rode* Theoretical Chemistry DiVision, Institute of General, Inorganic and Theoretical Chemistry, UniVersity of Innsbruck, Innrain 52a, A-6020 Innsbruck, Austria ReceiVed: August 22, 2006; In Final Form: October 13, 2006

In the context of our detailed study of the chemical behavior of aquo- and ammine-Zn(II) complexes, ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations were performed at the Hartree-Fock (HF) level for the zinc(II)-diamine complexes in aqueous solution. The initial structures of cis and trans isomers of the tetraaquodiamminezinc(II) complex were found to transform into the triaquodiamminezinc(II) complex by releasing one water ligand after ∼6 and ∼22 ps of simulation time, respectively. The structural and dynamical properties of these three zinc complexes, i.e., cis-[Zn(NH3)2(H2O)4]2+, trans-[Zn(NH3)2(H2O)4]2+, and [Zn(NH3)2(H2O)3]2+, were analyzed in terms of radial distribution functions (RDF), coordination number distributions (CND), angular distribution functions (ADF), tilt and θ angle distributions, ligands’ mean residence times (MRTs), and ion-ligand stretching frequencies. One considerably elongated Zn-O bond of 2.43 Å was observed in the case of the cis isomer for one of the water ligands located in the trans position to an ammonia ligand. In the trans isomer the average Zn-O bond length was observed to be 2.23 Å, while in the triaquodiamminezinc(II) complex two distinct Zn-O bonds, namely 2.12 Å for the ligands in the trigonal plane and 2.26 Å for axial water molecules, were observed. As both of the octahedral isomers are transformed into the pentacoordinated structure within the picosecond range, they might be regarded as “metastable species or intermediates”, while the triaquodiamminezinc(II) complex is the most stable species of the zinc(II)-diamine complex in aqueous solution.

1. Introduction The study of model coordination complexes of transition metal ions provides precious information about the chemistry of the active sites of metalloenzymes and for designing efficient artificial metalloenzymes. In general, the major role of transition metal ions in metalloenzymes can be catalytic, cocatalytic, or structural. In catalytic processes these metal ions participate either by acting as a Lewis acid catalyst or by being involved in redox reactions. The Zn(II) ion, unlike other first-row transition metal cations contains a complete set of d electrons (d10) and, therefore, does not contribute to redox reactions but functions as a Lewis acid catalyst.1,2 For more than 300 enzymes, covering all six classes of enzymes, the Zn(II) ion is mandatory for their biological activity, and in its absence a complete loss of the activity is observed.3 Several experimental and theoretical studies have been reported3-11 modeling different complexes of Zn(II) with H2O, OH-, C2H5OH, HCOO-, NH3, H2NCH2CH2NH2, CH2dNH, alanine, glycine, H2S, CH3SH, CH3S-, and CH3SCH3. However, their major concerns were the evaluation of thermodynamic, spectroscopic, and structural properties of the system. Vallet et al.9 have evaluated thermodynamical properties (i.e., electronic energy calculated at HF/MP2 level and entropy, enthalpy and Gibbs energy calculated at the gas-phase geometry) of different complexes of zinc(II) with NH3, H2O, and H2NCH2CH2NH2, which revealed that the differences in electronic energy and entropy for both cis and trans isomers of the isolated tetraaquodiamminezinc(II) complex are * Address correspondence to this author. E-mail: bernd.m.rode@ uibk.ac.at. Phone: +43-512-507-5160. Fax: +43-512-507-2714.

negligible (i.e., less than 2 kJ/mol and 2 J/(K‚mol), respectively). To our knowledge, no experimental/theoretical data for the zinc(II)-diamine complex in aqueous solution are available discussing the structure and, in particular, the dynamics of the system. According to common models the preferred arrangement of ligands in ions with filled d shells is mostly due to electrostatic and steric ligand-ligand interactions.12,13 Kinetic instability of the cis isomer might be attributed to the “trans-effect” and the steric NH3-NH3 interactions. A similar kinetic trans effect has been observed in methanol exchange of the Co(CH3OH)5Py2+ complex studied by NMR,14 influence of the imidazole group on the Co-S bond length in the [Co(C2N2H8)2(C3N2H4)(SO3)]ClO4·2H2O complex15 recorded by X-ray diffraction, and the trans effect of triphenylstibine and triphenylphosphine in Pt(II) complexes studied by stopped-flow spectrophotometry.16 In general, the trans effect can be observed by its influence on ground-state (metal-ligand bond length, metal-ligand stretching force constant, etc.), thermodynamic, and kinetic properties.17 In continuation of our series of investigations of structural as well as dynamical properties of model zinc(II) complexes with water and ammonia ligands, the present work describes the QM/MM MD simulations of the zinc(II)-diamine complexes in aqueous solution. The structural and dynamical properties of zinc(II)-diamine complexes (cis and trans isomers of the tetraaquodiamminezinc(II) complex and the triaquodiamminezinc(II) complex) were separately evaluated and compared. Furthermore, the results were also compared with the zinc(II)-monoamine complex18 and with Cu(II) and Ni(II) analogues reported by Schwenk et al.19,20

10.1021/jp0654213 CCC: $37.00 © 2007 American Chemical Society Published on Web 12/10/2006

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TABLE 1: Average Binding Energies (E) for the [Zn-H2O]2+ and the [Zn-NH3]2+ Clusters, Zn-O and Zn-N Bond Distances (r), and Basis Set Superposition Error (BSSE) for the Zn-NH3 and the Zn-H2O Complexes Obtained from HF, BLYP, and MP2 Calculations system

[Zn(NH3)2(H2O)3]2+

[Zn(NH3)2(H2O)4]2+ Zn-NH3 Zn-H2O

EZn-H2O (kcal/mol) EZn-NH3 (kcal/mol) rZn-Oax (Å) rZn-Oeq (Å) rZn-Neq (Å) EZn-H2O (kcal/mol) EZn-NH3 (kcal/mol) rZn-O (Å) rZn-N (Å) BSSE (kcal/mol) BSSE (kcal/mol)

2. Methodology 2.1. Construction of Potential Functions. The choice of a proper basis set and the level of theory applied in the QM region is the first step of a hybrid QM/MM MD simulation. Recent investigations have shown that Dunning double-ζ plus polarization function (DZP) basis sets for oxygen, nitrogen, and hydrogen can be successfully applied,21-24 so these basis sets were chosen for this investigation as well. The LANL2DZ ECP basis set with a minor modification (s and p basis functions with the lowest exponent have been removed to make the basis set more compatible with the Zn(II) ion rather than the zinc atom) was chosen for Zn(II),25 including the relativistically corrected ECP. Concerning the level of theory for the QM region, either Hartree-Fock (HF) self-consistent field (SCF) or density functional (DFT) methods are manageable, considering the amount of necessary computational effort. To be consistent with previous simulations,18,24 we chose the ab initio Hartree-Fock formalism, which has proven to be somewhat more reliable than DFT in obtaining good structural data, also compared to correlated methods in Zn-water complexes.24 To estimate whether our method of choice is also reliable for the Zn-amine systems, geometry optimizations of the [Zn(NH3)2(H2O)3]2+ and [Zn(NH3)2(H2O)4]2+ complexes were performed employing the HF, BLYP, and MP2 level of theory. Table 1 lists the average binding energies and Zn-O and Zn-N bond distances calculated for both ([Zn(NH3)2(H2O)3]2+ and [Zn(NH3)2(H2O)4]2+) complexes, including basis set superposition errors (BSSE) for Zn-monohydrate and -monoamine at HF, BLYP, and MP2 levels of theory. The results indicate that the deviation of the values of the Zn-O bond distances obtained from HF and BLYP are negligible compared to those of the MP2 method (the latter could have slightly overestimated correlation effects as well). The deviations of the Zn-H2O and Zn-NH3 average binding energies in HF (-0.6 and -1.0 kcal/mol for triaquodiamminezinc(II) and -0.4 and -0.7 kcal/mol for tetraaquodiamminezinc(II)) and in BLYP (+1.0 and +2.3 kcal/mol for triaquodiamminezinc(II) and +1.1 and +1.7 kcal/mol for tetraaquodiamminezinc(II)) compared to the MP2 level clearly suggest the superiority of the HF method over BLYP for the QM region in QM/MM simulation. The higher value of BSSE in BLYP compared to the HF method further supports the HF method as a proper choice for the QM region. The hybrid QM/MM MD approach further requires the construction of sufficiently accurate potential functions for Zn-H2O and Zn-NH3 interactions for a meaningful description of the second shell and the bulk. The two- and three-body potential interactions for Zn-H2O were taken from a previous simulation of the Zn(II)-water complex,24 while the Zn-NH3 two-body potential was the same as in a recently published study

HF

BLYP

MP2

-41.8 -59.3 2.23 2.08 2.12 -35.6 -44.6 2.23 2.16 1.2 1.7

-43.4 -62.6 2.22 2.08 2.12 -37.1 -47.0 2.23 2.16 1.6 2.9

-42.4 -60.3 2.22 2.06 2.09 -36.0 -45.3 2.21 2.13 3.3 1.7

TABLE 2: Corrected Three-Body Potentials for the O-Zn-N and N-Zn-N Interactions parameters, kcal/mol O-Zn-N N-Zn-N

A

B

C

0.5878696 7.0081247

0.1264529 0.3311281

0.5025078 0.8651834

of the zinc-monoamine complex.18 The details of the construction of Zn-H2O and Zn-NH3 two-body interactions have been given in the corresponding literature.18,24 To take three-body interactions including NH3 into account, two additional threebody potential functions were constructed for H2O-Zn-NH3 and H3N-Zn-NH3 interactions, respectively, from around 10 000 ab initio generated energy points each, calculated at the Restricted Hartree-Fock (RHF) level with the TURBOMOLE 5.526-29 program. The three-body ab initio energies were computed as follows: ab ab ab ab ∆E3bd cor r ) EL1ML2 - (EM + EL1 + EL2) 2bd 2bd + EML + EL2bd ) (1) (EML 1 2 1L2

where ELab1ML2 is the SCF energy of the H2O-Zn-NH3 or ab ab H3N-Zn-NH3 clusters. Eab M , EL1, and EL2 represent the ab initio energy of the Zn(II) ion, ligand-I (H2O or NH3; in the case of H2O-Zn-NH3 or H3N-Zn-NH3, respectively), and 2bd 2bd ligand-II (NH3). EML and EML account for the Zn-ligand-I 1 2 and Zn-ligand-II interaction energies, respectively, obtained from the pair potential18,24 and EL2bd denotes the 1L 2 ligand-I-ligand-II interactions (i.e., water-ammonia or ammonia-ammonia interactions, calculated by the flexible four site ammonia model30 and the flexible BJH-CF2 water model31,32). The analytical three-body fitting function was set up as -B(r1+r2) exp-Cr3(CL - r1)2(CL - r2)2 (2) E3bd Fit ) A exp

where A, B, and C are adjustable parameters (Table 2), r1 and r2 are the distances Zn-L1 and Zn-L2, respectively, r3 is the distance between L1 and L2, and CL is a cutoff limit set to 6.0 Å, where three-body terms become negligible. 2.2. Simulation Protocol. For the molecular dynamics (MD) simulation a cubic box with a side length of 24.70 Å corresponding to the experimental density of pure water at 298 K (0.997 g/cm3)33 was employed, containing one Zn(II), two ammonia, and 497 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 H(N)-H(N) and O-H, and 3.0 Å for H(O)-H(O). For all other pair interactions the general cutoff was 12.0 Å,

Stability of Zn(II)-Diamine Complexes in Aqueous Solution i.e., half of the box length. Periodic boundary conditions were applied and long-range interactions were treated by the reaction field method.36 The flexible BJH-CF2 water model31,32 and a flexible four-site ammonia model30 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 a classical MD simulation with 2 + 3 body potentials was performed to equilibrate the initial box, the QM/MM MD simulations of cis and trans isomers of the tetraaquodiamminezinc(II) complex were started from the respective equilibrated configurations. To ensure the full inclusion of the first shell into the QM zone the diameter of the QM sphere was set to 7.2 Å in accordance with the Zn-O RDF obtained from the classical simulation. After 3 ps of re-equilibration both QM/ MM MD simulations were performed for a total simulation time of 41 ps. The cis and trans isomers of the tetraaquodiamminezinc(II) complex retained their geometry for 6 and 22 ps, respectively, before transforming into the more stable triaquodiamminezinc(II) complex. The data collected for the triaquodiamminezinc(II) complex obtained from the transformation of both cis and trans isomers of the tetraaquodiamminezinc(II) complex are almost identical, but the data obtained from the cis isomer simulation were taken to evaluate the properties for the triaquodiamminezinc(II) complex due to the longer sampling of 30 ps. Prior to the sampling for the triaquodiamminezinc(II) a period of 5 ps was discarded to ensure full re-equilibration. The total force acting on a particle is calculated according to the following expression: QM MM Ftot ) Fsys MM + (FQM - FQM )/S(r)

(3)

sys where Ftot is the total force acting on a particle, FMM is the QM MM MM force 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 molecules37,38 between QM and MM regions.

S(r) ) 1, S(r) )

for r e r1

(r02 - r2)2(r02 + 2r2 - 3r12) , (r02 - r12)3 S(r) ) 0,

for r1 < r e r0

for r > r0

(4)

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 of cis and trans isomers of the tetraaquodiamminezinc(II) complex and the triaquodiamminezinc(II) complex in aqueous solution. The evaluation of the metal-ligand stretching frequency was carried out by using velocity autocorrelation functions (VACFs), C(t), defined as:

∑i ∑j bυj(ti)υbj(ti + t) Nt N

NtN

Figure 1. Zn-O and Zn-H radial distribution functions (RDFs) and their running integration numbers for cis-[Zn(NH3)2(H2O)4]2+ (a), trans-[Zn(NH3)2(H2O)4]2+ (b), and [Zn(NH3)2(H2O)3]2+ (c) complexes in aqueous solution obtained from the QM/MM MD simulation.

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. Ion-oxygen and Ion-nitrogen stretching frequencies were computed by using the approximative normal coordinate analysis.39 Mean ligand residence times (MRT, τ) in the second hydration shell were calculated by using the standard direct method.40 The parameter t*, determining the minimum time span to account for a ligand displacement from its original shell, was set to 0 and 0.5 ps, respectively. The sustainability of exchange processes can be defined as:

Sex )

N0.5 ex N0ex

(6)

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) measures how many attempts are needed to produce one lasting exchange between the hydration shells and/or bulk. Reorientational time correlation functions (RTCFs) of water molecules were calculated as:

bi(0)u bi(t))〉 Cli(t) ) 〈Pl(u

(7)

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)

(8)

where a and τ1 are the fitting parameters and τ1 corresponds to the relaxation time.

Nt N

C(t) )

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(5)

∑i ∑j bυj(ti)υbj(ti)

where N is the number of particles, Nt is the number of time origins ti, and b υj denotes a given velocity component of the

3. Results and Discussion 3.1. Structural Properties. Figures 1 and 2 display the Zn-H2O and the Zn-NH3 radial distribution functions (RDFs) obtained from the QM/MM MD simulation of cis and trans isomers of [Zn(NH3)2(H2O)4]2+ and the [Zn(NH3)2(H2O)3]2+ complex in aqueous solution and their characteristic data are sum-

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Figure 2. Zn-N (a) and Zn-H (b) radial distribution functions (RDFs) and their running integration numbers for cis-[Zn(NH3)2(H2O)4]2+ (dotted line), trans-[Zn(NH3)2(H2O)4]2+ (dashed line), and [Zn(NH3)2(H2O)3]2+ (solid line) complexes in aqueous solution obtained from the QM/MM MD simulation.

Figure 3. Water coordination number distributions of the first and the second hydration shell for (a) cis-[Zn(NH3)2(H2O)4]2, (b) trans-[Zn(NH3)2(H2O)4]2+, and (c) triaquodiamminezinc(II) complexes in aqueous solution obtained from the QM/MM MD simulation.

marized in Table 3. Two well-discerned peaks in Zn-O and Zn-HO RDFs of all three complexes represent distinct first and second hydration shells. A third shell is not recognizable. The peak maxima of the first and second shell in the Zn-O RDF appeared at distances of 2.22 and 4.71/5.35 Å (split peak) for the cis isomer, 2.23 and 4.70/5.40 Å (split peak) for the trans isomer and 2.15 and 4.60 Å for the triaquodiamminezinc(II) complex, respectively. In all three complexes a shorter distance was observed for the Zn-N bond in the first shell, namely 2.17 Å for the cis isomer, 2.16 Å for the trans isomer, and 2.12 Å for the triaquodiamminezinc(II) complex, due to the higher affinity of nitrogen to coordinate to the metal ion compared to oxygen (cf. Figure 7). Gas-phase geometry optimizations of several Zn(II) complexes at the HF level performed by Vallet et al.9 also yielded shorter Zn-N bonds compared to Zn-O in cis-[Zn(NH3)2(H2O)4]2+ (2.14 Å for Zn-N and 2.23 Å for Zn-O), [Zn(CH3NH2)2(H2O)4]2+ (2.125 Å for Zn-N and 2.25 Å for Zn-O), and [Zn(H2NCH2CH2NH2)(H2O)4]2+ (2.15 Å for Zn-N and 2.20 Å for Zn-O). A shorter Zn-N bond length (Zn-N(His-196) ) 2.17 Å, Zn-N(His-69) ) 2.03 Å) compared to the Zn-O distance (Zn-O(H2O) ) 2.19 Å, Zn-O(Glu-72) ) 2.19 Å, Zn-O(Glu-72) ) 2.30 Å) has also been observed in the crystal structure of the pentacoordinated active site of carboxypeptidase (CPA).41-43 X-ray crystallography of the (alanine)2Zn(II) complex further proved

a shorter Zn-N distance (2.04 Å) compared to Zn-O (2.11 Å).11 A shorter metal-N bond compared to the metal-O bond was also observed by Schwenk et al. in the QM/MM MD simulation of the tetraaquo-Ni(II)-diamine complex19 (trans, 2.15 Å for Ni-N and 2.18 Å for Ni-O) and the tetraaquo-Cu(II)diamine complex20 (cis, 2.08 Å for Cu-N and 2.13 Å for CuO; trans, 2.17 Å for Cu-N and 2.28 Å for Cu-O). The Zn-O and Zn-N bond distances in the triaquodiamminezinc(II) complex (2.15 and 2.12 Å, respectively) are considerably shorter compared to the distances in cis- and transtetraaquodiamminezinc(II) complexes indicating compactness and stability of this complex. The average binding energies of the Zn-O (octahedral: -35.6 kcal/mol, pentagonal: -41.8 kcal/mol) and the Zn-N (octahedral: -44.6 kcal/mol; pentagonal: -59.3 kcal/mol) bonds obtained from the geometry optimization of both octahedral and pentagonal complexes at the HF level of theory further confirm the stability of the triaquodiamminezinc(II) complex. This could also be seen as a first indication that both octahedral complexes could be regarded rather as “intermediates” than as stable species. Figure 3 displays the coordination number distribution of water ligands around the zinc(II) ion obtained from the QM/MM MD simulation of cis and trans isomers of the tetraaquodiamminezinc(II) complex and the triaquodiamminezinc(II) complex. In the first hydration shell, exclusive coordina-

TABLE 3: Characteristic Values of Radial Distribution Functions gZn-O(r), gZn-N(r), and gZn-H(r) for cis- and trans-[Zn(NH3)2(H2O)4]2+ and [Zn(NH3)2(H2O)3]2+ Complexes in Aqueous Solution Obtained from the QM/MM MD Simulationa complex cis-[Zn(NH3)2(H2O)4]2+

trans-[Zn(NH3)2(H2O)4]2+

[Zn(NH3)2(H2O)3]2+ a

Zn-O Zn-HO Zn-N Zn-HN Zn-O 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

2.22 2.90 2.17 2.74 2.23 2.91 2.16 2.70 2.15 2.80 2.12 2.69

3.11 3.80 2.57 3.26 3.24 3.96 2.48 3.24 3.22 3.62 2.43 3.18

4 8 2 6 4 8 2 6 3 6 2 6

4.71/5.35 5.25

6.01 6.26

28 58

4.70/5.40 5.17

6.41 6.42

33 61

4.60 5.23

6.25 6.09

29 50

rM denotes maxima and rm minima observed in the RDFs, CNav represents the average coordination number.

Stability of Zn(II)-Diamine Complexes in Aqueous Solution

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Figure 5. Tilt (a) and θ (b) angle distributions of the Zn(II)-water geometry obtained from the QM/MM MD simulation of cis-[Zn(NH3)2(H2O)4]2+ (I), trans-[Zn(NH3)2(H2O)4]2+ (II), and [Zn(NH3)2(H2O)3]2+ (III) complexes. Figure 4. Angular distributions of O-Zn(II)-O (a), O-Zn(II)-N (b), and N-Zn(II)-N (c) (in degree) obtained from the QM/MM simulation of cis-[Zn(NH3)2(H2O)4]2+ (dotted line), trans-[Zn(NH3)2(H2O)4]2+ (dashed line), and [Zn(NH3)2(H2O)3]2+ (solid line) complexes in aqueous solution.

tion numbers of 4 for cis and trans isomers of the tetraaquodiamminezinc(II) complex and 3 for the triaquodiamminezinc(II) complex are observed. The second shell shows a large variation in the coordination number varying from 22 to 32 with a maximum probability of 28 for the cis isomer, 27 to 38 with a maximum of 33 for the trans isomer, and 24 to 34 for the triaquodiamminezinc(II) complex, 30 being the most probable coordination number. The extraordinary large second shells are highly flexible and labile compared to the zinc-monoamine complex, where it ranges from 15 to 24 with a maximum intensity at 19. This remarkable increase in the second shell coordination number as compared to the zincmonoamine complex associated with an elongation of the mean distance of the second shell is obviously a consequence of the considerable loss of charge of the Zn(II) ion upon binding of two ammonia ligands. (The partial charge on the Zn(II) ion dropped from 1.61 to 1.51 as obtained from the geometry optimizations of hexaquozinc(II) and tetraquodiamminezinc(II) complexes at the HF level employing the same basis set as used in the QM/MM MD simulations.) O-Zn-O, O-Zn-N, and N-Zn-N angular distribution functions (ADFs) obtained from the first shell of the QM/MM MD simulations of cis- and trans-[Zn(NH3)2(H2O)4]2+ and [Zn(NH3)2(H2O)3]2+ complexes are plotted in Figure 4, and characteristic values are given in Table 4. Two peaks are distinctly visible for all three complexes in the O-Zn-O angle distributions (Figure 4a), located at 85°/169° for the cis isomer, 87°/173° for the trans isomer, and 87°/172° for the triaquodiamminezinc(II) complex. A stronger deviation from the octahedral geometry is observed for the cis isomer compared to the trans isomer indicating the cis isomer to be the least stable species. TABLE 4: Characteristic Values of Ligand-Ion-Ligand Angle Distributions for Zn(II)-Diamine Complexes in Aqueous Solution Obtained from the QM/MM MD Simulation. angle (deg) complex 2+

cis-[Zn(NH3)2(H2O)4] trans-[Zn(NH3)2(H2O)4]2+ [Zn(NH3)2(H2O)3]2+

O-Zn-O

O-Zn-N

N-Zn-N

85/169 87/173 87/172

91/167 89 91/121

99 170 120

Figure 6. Power spectra of the Zn-O (a) and Zn-N (b) stretching frequency (in cm-1) obtained from the QM/MM simulation of cis-[Zn(NH3)2(H2O)4]2+ (dotted line) and trans-[Zn(NH3)2(H2O)4]2+ (dashed line) isomers and [Zn(NH3)2(H2O)3]2+ (solid line) complexes.

The O-Zn-N angle distribution plotted in Figure 4b shows two well-separated peaks for the cis isomer peaking at 91° and 167°. In the trans isomer only one peak is observed for the O-Zn-N angle at 89°. In the triaquodiamminezinc(II) complex one peak is located at 91° with a broad tailing toward higher angles. In the N-Zn-N ADF depicted in Figure 4c, a single peak is observed for all three complexes appearing at 99°, 170°, and 120° for cis, trans, and triaquodiamminezinc(II) complexes, respectively. The distortion of the cis isomer is well demonstrated by the large N-Zn-N angle. Orientational flexibility of water molecules relative to the ion is another important structural parameter describing the stability of the complex. Two angles were defined for this purpose: 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 (for further details see the sketch in Figure 5). The tilt and θ angle distributions of the first shell obtained from the QM/MM simulation of all three complexes are displayed in Figure 5. The cis isomer of the tetraaquodiamminezinc(II) complex shows an unsymmetrical tilt angle distribution ranging from ca. -52° to ca. 52° with a half width of ca. 42° and the center of the half width located at lower

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Fatmi et al. TABLE 6: Reorientational Times (τ) of First and Second Order of Water Molecules in the First and Second Shell and the Bulk for cis- and trans-[Zn(NH3)2(H2O)4]2+ and [Zn(NH3)2(H2O)3]2+ Complexes in Aqueous Solution Obtained from the QM/MM MD Simulation with the x, y, and z Axes Shown Here

reorientational time (ps) complex cis-[Zn(NH3)2(H2O)4]2+

Figure 7. Geometry conversion of cis-[Zn(NH3)2(H2O)4]2+ (a) and trans-[Zn(NH3)2(H2O)4]2+ (c) isomers of the complex into the [Zn(NH3)2(H2O)3]2+ complex (b) via structures (a*) and (c*), respectively (snapshots taken by MOLVISION) and ligand exchange processes showing the transformation of cis (I) and trans (II) isomers into the [Zn(NH3)2(H2O)3]2+ complex.

trans-[Zn(NH3)2(H2O)4]2+ [Zn(NH3)2(H2O)3]2+ [Zn(NH3)(H2O)5]2+

angles (∆ ca. -3.6°). A symmetrical tilt angle distribution is observed for the trans isomer and the triaquodiamminezinc(II) complex varying from ca. -50° to ca. 50° (half width ) ca. 45°) and ca. -48° to ca. 59° (half width ) ca. 44.8°), respectively. The maxima of the θ angle distribution for all three complexes are observed at ∼171°, which is comparable to the θ angle distribution in the zinc(II)-monoamine complex (∼170°), indicating a minor influence of ligand substitution on the θ angle distributions. 3.2. Dynamical Properties. 3.2.1. Vibrational Spectra. The power spectra of Zn(II)-O and Zn(II)-N stretching vibrations obtained from the first shell of the QM/MM MD simulation of cis- and trans-[Zn(NH3)2(H2O)4]2+ and [Zn(NH3)2(H2O)3]2+ complexes are displayed in Figure 6, and distinctive features along with the corresponding force constants are listed in Table 5. The frequencies have been multiplied with the standard scaling factor for Hartree-Fock calculations of 0.8944,45 to make them comparable with experimental values. The Zn-N stretching frequencies in all three complexes are found at considerably higher values (cis, 292 cm-1; trans , 320 cm-1; and triaquodiamminezinc(II), 335 cm-1) than the Zn-O frequencies, TABLE 5: Characteristic Values of Ion-Ligand Stretching Motions in Terms of Frequency (υ) and Corresponding Force Constants (k) for cis- and trans-[Zn(NH3)2(H2O)4]2+ and [Zn(NH3)2(H2O)3]2+ Complexes in Aqueous Solution Obtained from the QM/MM MD Simulationa υ (cm-1)

complex 2+

cis-[Zn(NH3)2(H2O)4]

trans-[Zn(NH3)2(H2O)4]2+ [Zn(NH3)2(H2O)3]2+ [Zn(NH3)(H2O)5]2+ a

Zn-O Zn-N Zn-O Zn-N Zn-O Zn-N Zn-O Zn-N

274/120(s) 292 243/112(s) 320 279b/115(s) 335 264 363

k (N/m) 57/11 58 45/10 70 59/10 76 53 90

ref this work this work this work this work this work this work (18) (18)

(s) denotes shoulder observed in the peak. b Average of a broader peak (258 and 299 cm-1).

H2O(exptl)a a

phase

τ1x

τ1y

τ1z

τ2x

τ2y

τ2z

1st shell 24.8 86.1 21.9 10.3 25.0 8.4 2nd shell 6.1 8.2 4.7 3.4 3.1 2.3 bulk 8.1 8.1 5.3 3.5 3.1 2.4 1st shell 5.8 29.5 5.6 3.4 11.7 3.2 2nd shell 6.2 6.2 4.3 2.9 2.5 1.9 bulk 7.0 7.3 4.9 3.2 2.8 2.2 1st shell 16.0 39.3 14.5 6.3 19.7 5.8 2nd shell 8.4 9.7 6.2 3.8 3.5 2.6 bulk 7.8 8.2 5.3 3.6 3.0 2.4 1st shell 7.8 28.8 6.9 3.1 11.3 2.6 2nd shell 6.4 8.0 4.9 3.1 3.0 2.4 bulk 7.3 7.7 5.0 3.3 3.0 2.3 7.5 2.5

Experimental reorientational correlation time of water.46

affirming the stronger Zn-N coordination. However, these values are lower than the Zn-N stretching frequency in the zinc(II)-monoamine complex18 (363 cm-1; force constant 90 N m-1). All three complexes exhibit a much broader peak for the Zn-O stretching vibrations along with clear shoulders at lower frequencies indicating different types of Zn-O bonds. These shoulders are more pronounced in the cis isomer (120 cm-1, corresponding to the H2O located at longest distance) and triaquodiamminezinc(II) (115 cm-1), apparently due to the lower symmetry of these complexes. The relative strengths of ion-O and ion-N force constants for the cis isomer in comparison to Cu(II) and Ni(II) analogues are

Ni(II)-N (79 N/m) > Cu(II)-N (72 N/m) > Zn(II)-N (58 N/m) Zn(II)-O (57 N/m) > Cu(II)-O (55 N/m) > Ni(II)-O (52 N/m) The comparison of metal-N and metal-O stretching frequencies of trans-[M(NH3)2(H2O)4]2+ complexes produces a quite different result mainly because of the pronounced Jahn-Teller distortion of the [Cu(NH3)2(H2O)4]2+ complex. The relative strengths of ion-O and ion-N force constants for the trans isomers are

Cu(II)-N (90 N/m) > Ni(II)-N (78 N/m) > Zn(II)-N (70 N/m) Ni(II)-O (59 N/m) > Zn(II)-O (45 N/m) > Cu(II)-O (32 N/m)

Stability of Zn(II)-Diamine Complexes in Aqueous Solution

J. Phys. Chem. B, Vol. 111, No. 1, 2007 157

TABLE 7: Mean Ligand Residence Time (τ) for t* Values of 0 and 0.5 ps, Number of Ligand Exchange Events (N), and Sustainability of Migration Processes to/from the Second Hydration Shell (Sex) Obtained from the QM/MM MD Simulation second shell complex 2+

cis-[Zn(NH3)2(H2O)4] trans-[Zn(NH3)2(H2O)4]2+ [Zn(NH3)2(H2O)3]2+ [Zn(NH3)(H2O)5]2+ [Zn(H2O)6]2+

Nex0.0/10 ps

τd0.0

Nex0.5/10 ps

τd0.5

Sex

1/Sex

ref

565 487 515 465 306

0.49 0.68 0.56 0.4 0.4

38.3 47.6 44.8 26.6 14.0

7.19 6.93 6.52 7.2 10.5

0.06 0.09 0.08 0.05 0.04

15 10 11 20 22

this work this work this work 18 24

3.2.2. Reorientational Time. Reorientational time correlation functions are another important dynamical parameter, which allow the study of 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.35,46 The reorientational time correlation functions are consistent with librational motions. Table 6 lists the first- and second-order reorientational times for water molecules around x, y, and z axes in the first and second shell and in the bulk, obtained from the QM/MM MD simulations of cis and trans isomers of the tetraaquodiamminezinc(II) complex and the triaquodiamminezinc(II) complex. Strongly increased relaxation times were only observed for the first hydration shell, outside of which the ions’ influence is rather weak. The first shell shows the highest relaxation time for rotations around the y axis in all three complexes as found for many aquo- and ammine-metal complexes,18,22,24 and consequently this is the most hindered rotation. Moreover, the first- and second-order reorientational times in the first shell of the cis isomer and the triaquodiamminezinc(II) complex are considerably higher compared to values of the zinc(II)-monoamine complex, whereas the trans isomer displays values similar to it.

Figure 8. Fluctuation of Zn-O distances in Å for cis-[Zn(NH3)2(H2O)4]2+ (a), trans-[Zn(NH3)2(H2O)4]2+ (b), and [Zn(NH3)2(H2O)3]2+ (c) complexes in aqueous solution obtained from the QM/MM MD simulations. In panels a and b the transformation into the complex (panel c) after 6 and 22.5 ps can be seen from the elimination of one ligand.

3.2.3. Ligand Exchange Processes. In the QM/MM MD simulation no first shell water exchange reaction was observed, as in Cu-diamine complexes,20 but a transformation of both the cis and the trans isomers of the tetraaquodiamminezinc(II) complex into the triaquodiamminezinc(II) complex occurred after 6 and 22 ps of simulation time, respectively (see Figure 7). The faster transformation of the cis isomer into the triaquodiamminezinc(II) complex compared to the trans isomer agrees well with all previous conclusions on the lesser stability of the cis isomer based on RDF and ADF data and on ion-ligand stretching frequencies. In the Cu(II) analogues, the cis isomer is kinetically more stable than the trans isomer, demonstrating the strong influence of the Jahn-Teller effect.20 Although the existence of the cis isomer in our simulation was rather short, it was long enough to characterize structure and dynamics of this isomer, which can be regarded as a possible intermediate for water exchange in the triaquodiamminezinc(II) complex. The life span of the trans isomer is even much longer, and both of them thus have a lifetime considerably above that of a usual transition state, allowing them to be classified as “metastable compounds”. To prove the existence of these metastable species and their continuous formation/decomposition a very long trajectory would be required which, due to the computational demand required for the quantum mechanical

Figure 9. Fluctuation of Zn-N distances (in Å) for cis-[Zn(NH3)2(H2O)4]2+ (a), trans-[Zn(NH3)2(H2O)4]2+ (b), and [Zn(NH3)2(H2O)3]2+ (c) complexes in aqueous solution obtained from the QM/MM MD simulations.

158 J. Phys. Chem. B, Vol. 111, No. 1, 2007 treatment, is still far beyond today’s fastest available parallelizing computers. Figures 8 and 9 show Zn-O and Zn-N distance plots, respectively, providing a detailed picture of the varying length of the individual Zn-O and Zn-N bonds in all three complexes. For the cis isomer a considerably elongated Zn-O bond, namely 2.43 Å, is observed representing the H2O ligand located trans to the ammonia ligand compared to the other three Zn-O bonds (average 2.23 Å) as a consequence of the strong influence of the trans ligand and NH3-NH3 steric effect. The trans isomer exhibits a smaller Zn-O bond variation, i.e., from 2.27 to 2.31 Å with an average of ∼2.28 Å apparently due to the higher symmetry in the geometry. However, the Zn-O bond variation produces a shoulder at the lower frequencies (Figure 6), though less pronounced than that of the triaquodiamminezinc(II) complex. The triaquodiamminezinc(II) complex shows two distinct Zn-O bond lengths, ∼2.26 Å for the water molecules perpendicular to the trigonal plane (axial H2O) and a considerably shorter Zn-O bond, namely 2.12 Å, for the water in the trigonal plane. The differing Zn-O bond lengths are reflected in the Zn-O stretching frequencies observed for this complex (Figure 6), where a broader peak is accompanied by distinct shoulders. Unlike in the Zn-O distance, the Zn-N distance shows a consistency in the mean distance for all three complexes, namely 2.19 and 2.20 Å for the cis isomer, 2.16 and 2.17 Å for the trans isomer, and 2.13 and 2.14 Å for the triaquodiamminezinc(II) complex, which is directly related to the Zn-N stretching frequencies, where a single peak appeared for each complex at 292, 320, and 363 cm-1, respectively, for the cis-, trans-, and triaquodiamminezinc(II) complexes. The strongest Zn-N bond is observed in the case of the triaquodiamminezinc(II) complex. The characteristic values of ligand exchange reactions in the second shell obtained from the QM/MM MD simulations of all three complexes are summarized in Table 7. The second shell ligands’ mean residence time (MRT) values for cis and trans isomers of the tetraaquodiamminezinc(II) complex and the triaquodiamminezinc(II) complex have been evaluated to be 7.2, 6.9, and 6.5 ps, respectively, and are similar to the MRT value of the zinc(II)-monoamine complex18 (7.2 ps) and cis and trans isomers of the tetraaquo-Ni(II)-diamine complex19 (7.0 and 7.8 ps, respectively). The number of attempts needed for one successful exchange process in the zinc(II)-monoamine complex20 is remarkably higher as compared to that of cis15 and trans10 isomers of the tetraaquodiamminezinc(II) complex and the triaquodiamminezinc(II) complex.11 4. Conclusion The present QM/MM MD simulations provide some interesting pictures of the stability of the zinc(II)-diamine complexes in aqueous solution. The only stable species of the zinc(II)-diamine complex in aqueous solution is obviously the trigonal bipyramidal triaquodiamminezinc(II) complex while octahedral species may be regarded as intermediates or metastable species. This is in contrast to the stable octahedral species of Cu(II)- and Ni(II)-diamine complexes and points at other differences in the complex chemistry of Zn(II) compared to its neighbors in the periodic system. These results encourage further investigations with more ammonia ligands, in order to see whether further differences, e.g., in water exchange reactions occurring in Cu(II)- and Ni(II)-triamine complexes, could be found. Acknowledgment. Financial support for this work by the Austrian Science Foundation (FWF) (project P18429) and an

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