M = Mn, Fe, Co, Ni, Cu, Zn - American Chemical Society

ARTICLE pubs.acs.org/JPCA

DFT-B3LYP, NPA-, and QTAIM-Based Study of the Physical Properties of [M(II)(H2O)2(15-crown-5)] (M = Mn, Fe, Co, Ni, Cu, Zn) Complexes Pradeep R. Varadwaj,*,† Arpita Varadwaj,† and Helder M. Marques*,‡ †

Centre for Research in Molecular Modeling and Department of Chemistry and Biochemistry, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec, Canada, H4B 1R6 ‡ Molecular Sciences Institute, School of Chemistry, University of the Witwatersrand, P.O. Wits, Johannesburg 2050, South Africa

bS Supporting Information ABSTRACT: A density functional theory study of the structure of the title compounds with the divalent metal ions in their high-spin ground state, obtained using B3LYP/ 6-311þþG(d,p) in vacuo and in aqueous solution simulated using a polarized continuum medium, is reported for the first time. The modeling reproduces the pseudo pentagonal bipyramidal crystallographic structures very well, including some asymmetry in the equatorial bonds lengths to the crown ether O donors. The very marked asymmetry in the Ni2þ structure due to a JahnTeller distortion of a d8 system in a D5h ligand field is also well reproduced. The gas phase binding energies of the complexes follow the order Mn2þ < Fe2þ < Co2þ < Ni2þ < Cu2þ > Zn2þ, in precise agreement with the IrvingWilliam series. Both the NPA and Bader charges show there is ligand-to-metal charge transfer; however, the values obtained from the NPA procedure, unlike those obtained from Bader’s quantum theory of molecules approach, do not correlate with the electronegativity of the metal ions, the stabilization energies of the solvated complexes or the ionic radii of the metal ions, and so appear to be less reliable. The nature of the bonding between the ligands and the metal ions has been explored using the topological properties of the electron charge density. The metalligand bond distances were found to be exponentially correlated with the electron charge density, its Laplacian, and with its curvature in the direction of the bond path at MO bond critical points. While the bonding with coordinated H2O is predominantly ionic, that to the crown ether donor atoms has some covalent character the extent of which increases across the first transition series. The delocalization indices of MO bonds in these complexes correlate reasonably well with the electron density and its Laplacian at the bond critical points; this therefore provides a rapid and computationally very efficient way of determining these properties, from which insight into the nature of the bonding can be obtained, obviating the need for time-consuming integration over atomic basins.

1. INTRODUCTION The formation of complexes between the later transition metals of the first row in their þ2 oxidation state and many ligands, and the structure, electronic, and magnetic properties of the resultant complexes, studied both experimentally and using computational chemistry methods, has been the subject of many reports (for example, see refs 18). Ligands with neutral oxygen donors are important because the presence of such a donor in a five-membered chelating ring assists in the selectivity of larger metal ions relative to smaller metal ions.9 The crown ethers, first reported by Pedersen,10,11 are cyclic oligomers of dioxane with ethyleneoxy, CH2CH2O, repeating units.12 Thus, 18-crown6 (18C6) has six such repeating units, and other common examples include 15C5 and 12C4. We are interested in complexes formed between 15C5 and the later 2þ cations of the first transition series. Steed et al.,13 Hao et al.,14,15 and, subsequently, Siegler et al.1618 reported the synthesis and the structural analysis of the family of complexes [M(H2O)2(15C5)]2þ (M = Mg, Mn, Fe, Co, Ni, Cu, Zn) in their divalent oxidation states in the presence of a variety of counterions (NO3, HSO4, Br, Cl, and ClO4, for example) using r 2011 American Chemical Society

X-ray diffraction methods. The coordination geometry around the high-spin metal ion is pseudo pentagonal bipyramidal with the two H2O ligands trans to each other along the principal axis with the macrocycle occupying the equatorial coordination sites. It is expected that the metal ions in these complexes will be high-spin because their hexa-aqua complexes are high-spin and replacement of the equatorial H2O ligands by 15C5, which forms longer and weaker bonds to the metal than H2O, will not change the spin state of the metal.17 This view is supported by experimental evidence including the electronic spectrum of [Mn(H2O)2(15C5)]2þ,23 and magnetic moment measurements.26 A noteworthy feature of these complexes is the asymmetry in the NiO bond lengths to 15C5. It has been argued that this is not a consequence of a JahnTeller effect because there are paired electrons in the eg orbitals of d8 Ni2þ;17 in fact, in a D5h field the metal d orbitals transform as a10 (z2), e20 (xy, x2-y2), and e100 (xz, yz), and the electronic structure is (e100 )4(e20 )3(a10 )1.19,20 Received: January 5, 2011 Revised: May 4, 2011 Published: May 13, 2011 5592

dx.doi.org/10.1021/jp2001157 | J. Phys. Chem. A 2011, 115, 5592–5601

The Journal of Physical Chemistry A The stability constants of six-coordinate complexes of the later metals of the first transition series usually follow the IrvingWilliams series21 order Mn2þ < Fe2þ < Co2þ < Ni2þ < Cu2þ > Zn2þ irrespective of the nature of the ligands (whether monodentate, bidentate, chelating, or macrocyclic) or of the number of ligands involved. A polarographic determination of stability constants of 15C5 with Co2þ (log KML = 3.62) > Ni2þ (2.59) > Zn2þ (2.29) ≈ Cu2þ (2.20) in methanol showed there is little dependence on the metal ion radius.22 In 90% (v/v) DMSO/ H2O, the trend found was Cu2þ (2.25) > Mn2þ (2.11) > Ni2þ (2.02) > Co2þ (1.98) > Zn2þ (1.94);23 a similar trend, but with marginally smaller log KML values, was found in 40% (v/v) ethanol/H2O.24 Hence, the stability constant for Mn2þ is unusually high, leading to suggestions that the match between the cavity size of the macrocycle and the ionic radius of the metal is an important factor of controlling stability, a crucial issue we have addressed here. Our focus was to analyze the structure and relative stability of the isolated high-spin complexes [M(H2O)2(15C5)]2þ (M = Mn, Fe, Co, Ni, Cu, Zn) computationally both in the gas phase and, to account for the effect of solvation, in a polarized continuum medium because medium effects appear to play an important role in the stability of crown-ether complexes.2733 We wished to determine whether the 7-coordinate geometry of these complexes was reproduced in the calculations, whether the asymmetry we noted in the solid state structures (vide infra) was evidenced in the computed structures, and also whether we could find a correlation between the stability of the computed structures and the experimentally determined stability constants, a subject of enduring interest to coordination chemists. We have recently demonstrated that the ligand-tometal charge transfer (ΔQ) correlates with the stability of a metal complex.68 Since ΔQ is related to the electronegativity of the metal ion,8 this too may correlate with complex stability. To the best of our knowledge, we report here the first systematic study of the complexes of the metals from the latter half of the first transition series in their high-spin ground states with 15C5 and H2O. We have used the B3LYP functional2528 in conjunction with a triple-ζ valence quality basis set, 6-311þþ G(d,p), because this functional is known to produce reliable structures and electronic properties2933 although, as in many DFT methods, its handling of the electron correlation energy is deficient.34 First, we compare our calculated geometries with the solidstate geometries of these complexes to determine the ability of B3LYP/6-311þþG(d,p) to reproduce the available crystal structures. Second, the charge distribution is evaluated using both Natural Population Analysis (NPA)35 and Bader’s quantum theory of atoms in molecules (QTAIM) analysis36 from which the ligand-to-metal charge transfer in these complexes in the gas phase, as well as in solvent simulated by incorporating the polarized continuum medium (PCM) of Tomassi and coworkers,37,38 is assessed. We examine whether the NPA or the Bader atomic charges are reliable for a better understanding of the ligand-to-metal charge transfer in these systems. Third, based on the topology of the electron density and a number of bond descriptors at bond critical points (bcps), we characterize the nature of interactions in the isolated ligands and that between the ligands and the metal ions in these systems. The relationship between electron density and bond length has been explored for the metalligand bonds as well as for other bonds in these complexes. Finally, we explore the dependence between the delocalization indices δ(A, B), the number of electron pairs

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Figure 1. Comparison of the solid-state (red) and the energy-minimized gas-phase (blue) structures of [Ni(H2O)2(15C5)]2þ.

delocalized between the basins of atoms A and B in a bond, and the topological properties of the electron charge density at MO bcps.

2. COMPUTATIONAL DETAILS The geometry of each of the metal complexes was obtained using Gaussian 03,39 and visualization was done with the help of the Gaussview 04 suite of programs.40 All the complexes were energy-minimized with the B3LYP functional together with a 6-311þþG(d,p) basis set without any symmetry constraints utilizing unrestricted high-spin states for Mn2þ (S = 5/2), Fe2þ (2), Co2þ (3/2), Ni2þ (1), and Cu2þ (1/2) and restricted spin for Zn2þ (0). The isolated ligands 15C5 and H2O were energyminimized at the same level of theory with the restricted spin formalism. Normal mode frequency calculations were performed analytically using the second derivatives of each B3LYP potential energy surface with respect to the atom-fixed nuclear coordinates to examine the nature of the stationary points; the absence of negative frequencies confirmed that the structures were local minimum-energy structures. The convergence criterion with SCF = Fermi together with an ultrafine integration grid was used in calculations to avoid SCF convergence failures because of near-degenerate Fermi level ground terms in transition metal complexes.4143 All the structures (both the isolated ligands and the metal complexes) were then reoptimized using a self-consistent reaction field (SCRF) approach coupled with the polarized continuum model (PCM) of Tomassi and co-workers37,38 to simulated water (ε = 78.39), a cavity consisting of tesserae of average area (TSARE) 0.3 Å2, and UAKS atomic radii for all atoms constituting the ligands or complexes. We used TSNUM = 100 as the number of surface elements for each sphere instead of the default value 60 to avoid oscillatory behavior during geometry optimizations. The atom-centered partial charges were calculated on the B3LYP-optimized structures within the framework of NPA35 and Bader charges using the space partitioning approach of QTAIM.36 The ligand-to-metal charge transfer (ΔQ) was calculated as the difference between the formal þ2 charge on the metal ion and the charge on the metal in the complex. The topological properties of the electron density in these complexes were calculated with QTAIM using AIMALL44 and AIM2000.45 The charge density (Fb), Hessain eigenvalues (λ1,2,3), its Laplacian (r2Fb), the ellipticity (εb), the kinetic (Gb), the potential (Vb), and the total energy (Hb) densities, the localization (λ), and the delocalization (δ) indices were used to 5593

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The Journal of Physical Chemistry A

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Table 1. Comparison of Modeled (B3LYP/6-311þþG(d,p)) and Crystallographically Observed MO Bond Lengths in [M(H2O)2(15C5)]2þ Complexesa gas phase

crystallographicb

solvated

MO(H2O) MO(15C5) mean MO MO(H2O) MO(15C5) mean MO

a

MO(H2O)

MO(15C5)

mean MO

2.25(7) 2.1292.337

2.15(17)

Cu2þ

1.994(0)

2.26(5)

2.19(14)

1.972(1)

2.27(7)

2.15(18)

1.909(8) 1.8921.925

Ni2þ

2.082(7)

2.26(23)

2.21(20)

2.056(1)

2.26(23)

2.20(21)

1.984(12) 1.9712.002 2.23(14) 2.0252.548

2.16(16)

Zn2þ Co2þ

2.151(0) 2.152(1)

2.23(4) 2.23(4)

2.21(5) 2.21(5)

2.091(0) 2.112(2)

2.24(4) 2.23(4)

2.19(8) 2.20(7)

2.001(18) 1.9502.051 2.22(5) 2.1312.304 2.066(14) 2.0492.096 2.21(3) 2.1372.259

2.16(11) 2.17(7)

Fe2þ

2.208(0)

2.23(5)

2.22(4)

2.157(1)

2.24(6)

2.21(6)

2.066(13) 2.0272.090 2.23(3) 2.1712.278

2.18(8)

Mn2þ

2.277(1)

2.25(3)

2.26(3)

2.214(1)

2.25(4)

2.24(4)

2.135(14) 2.1132.161 2.25(4) 2.1622.299

2.22(6)

Bond lengths in Å. b A second line entry lists the range of values. See Table ST1 of the Supporting Information for further details.

characterize the nature of a bond at a bond critical point (bcp) and of a ring surface at a ring critical point (rcp).

3. RESULTS AND DISCUSSION 3.1. Structural Properties. As the only complexes of [M(H2O)2(15C5)]2þ found in the Cambridge Structural Database (CSD)46 have the two coordinated H2O ligands trans to each other, we have confined our calculations to these isomers. Figure 1 shows the structure of the Ni2þ complex optimized at the UB3LYP/6-311þþG(d,p) level in the gas phase overlaid on the solid state structure. Table 1 shows a comparison of the mean DFT and crystallographic bond lengths for the MO(H2O) and MO(15C5) bonds (see Table ST1 for further details). It is not uncommon for DFT calculations to overestimate bond lengths, and this is indeed seen in the present results. The most noticeable effect of solvation (as we found in a recent study on [M(H2O)4(NO3)2] complexes8) is that it shortens the MO(H2O) bonds while the bonds to the ethereal O donors of the macrocycle are marginally lengthened. There is a reasonable agreement between the computed and the solid-state — OMO (15C5) valence bond angles, and the values are all within the range of the experimental standard deviations (Table ST2). In the gas phase structure of Ni2þ ion, we found an interaction between a ethereal O on the macrocycle and an axial H2O molecule, (15C5)O2 3 3 3 HO7(H), 2.24 Å, which disappeared in calculations incorporating a simulation of solvent. Very noticeable in Table 1, in both the solid state and the modeled structures, is the high standard deviations in the MO(15C5) bond lengths, and particularly so for the Ni2þ complex. An examination of the solid state structures shows that there is some asymmetry in the MO(15C5) bond lengths of the crystallographic structures of [M(H2O)2(15C5)]2þ (Table 1 and detailed in Table ST1). Thus, for example, the average MnO bond length in the 17 independent observations of the [Mn(H2O)2(15C5)]2þ in eight separate structures (in several of the structures there is more than one cation in the unit cell) is 2.247 ( 0.038 Å. However, in each structure, one MnO bond length is somewhat shorter than the other four; grouping the MnO bond lengths into two clusters, containing 1 and 4 MnO bond length values in each, respectively, gives clustered values of 2.185 ( 0.021 and 2.263 ( 0.021 Å, respectively (Δd, the difference between the means of the two clusters = 0.08 ( 0.04 Å). In the case of Co2þ complexes, the bond lengths seem to fall into two clusters containing 2 and 3 bond length values, respectively, although the difference in the mean values of the

two clusters is probably not statistically significant (Δd = 0.04 ( 0.05 Å). In the case of Cu2þ, there appear to be three distinct clustered values with means of 2.137 ( 0.005, 2.236 ( 0.015, and 2.325 ( 0.006 Å, respectively. The Zn complexes also show a small difference between one longer (2.242 ( 0.016 Å) and four shorter (2.150 ( 0.016 Å, Δd = 0.09 ( 0.09 Å) bonds. But by far the most significant asymmetry is seen in the Ni2þ complexes where one bond (2.536 ( 0.012 Å) to a donor of the macrocycle is very much larger than the other four (2.173 ( 0.084 Å, Δd = 0.36 ( 0.09 Å). Thus, the distortion in the Ni(II) complexes is probably a consequence of a JahnTeller distortion of a highspin (e100 4(e20 )3(a10 )1 ground-state, which would lift the degeneracy of the e20 orbitals. Generally, the modeling preserves the clustering, both in the gas phase and the solvent models (Table ST1); thus, the Mn2þ, Fe2þ, Co2þ, and Zn2þ complexes do indeed have one shorter and four longer bonds; and the Cu2þ and Ni2þ complexes have 2 shorter, 2 longer, and 1 long bond, with that bond being especially long in [Ni(H2O)2(15C5)]2þ. This strongly suggests that the asymmetry is not merely a consequence of packing forces. We suggest that it arises from steric effects consequent on accommodating seven donor atoms into the inner coordination sphere of these relatively small metal ions, whose coordination chemistry is dominated by 4- and 6-coordinate complexes. The extent of distortion, Δd, increases with the ionic radius of the metal for the four smallest metal ions in the series (Ni2þ , Cu2þ < Zn2þ < Co2þ), but it is difficult to separate a steric and an electronic effect in the case of Ni2þ; the effect seems to saturate (the extent of distortion among Co2þ, Fe2þ and Mn2þ is similar). There are four major structural changes that occur when the computed structure of the free 15C5 ligand is compared to that in a metal complex. (1) Shrinkage in the cavity size as the ligand complexes the metal ion (Figure S1 of the Supporting Information); the minimum and maximum diagonal OO distances (i.e., distances between O atoms in a 1,7 relationship) in free, solvated 15C5 is 4.110 and 5.110 Å, respectively, while these distances are 4.435 and 4.192 Å in the Cu2þ, 4.451 and 4.190 Å in the Ni2þ, 4.297 and 4.182 Å in the Zn2þ, 4.307 and 4.171 in the Co2þ, 4.343 and 4.158 Å in the Fe2þ, and 4.332 and 4.219 Å in the Mn2þ complex (Figure S1 of the Supporting Information). (2) Consequent on formation of metalO bonds to the 15C5 ligand, an elongation of the CO bond length. The mean value of CO bond lengths in the free 15C5 ligand is 1.424(3) Å, while it is 1.442(1) Å in the Mn2þ, 1.441(2) Å in the Fe2þ, 1.441(2) Å in the Co2þ, 1.438(2) Å in the Cu2þ, 1.442(7) in the Ni2þ Å, and 1.439(1) Å in the Zn2þ complex. (3) A shortening of the adjacent (i.e., 1,4) OO nonbonded distances (Figure S1) on formation 5594



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Table 2. B3LYP/6-311þþG(d,p) Computed Stabilization Energies of [M(H2O)2(15C5)]2þ Complexes in Gas Phase (Eb) and in a Simulated Solvent Environment (ΔE)a M2þ

Eb

BSSE

Ebcorr.

ΔE

log KML2þ, b

Mn2þ

314.3

7.11

307.2

163.5

2.11

Fe2þ

336.8

7.52

329.3

164.3

Co2þ

348.5

7.53

341.0

165.4

1.98

Ni2þ

362.2

7.75

354.4

166.5

2.02

Cu2þ Zn2þ

366.3 353.9

7.81 7.67

358.5 346.2

168.8 165.0

2.25 1.94

a

Included are also the BSSE and BSSE-corrected energies (Ebcorr) in the gas phase. Energies in kcal mol1. b Stability constants from ref 23.

of the five-membered chelating rings with the metal. (4) A decrease in the — OCCO dihedral angles. In the free solvated ligand two of these torsions measure 61.6, while three measure 72.1. Coordination to the metal and confinement of the equatorial plane decreases these angles to between 14.2 and 16.5, and the 15C5 ligand is significantly flattened. There is no simple relationship between any of these changes and the ionic radius of the metal ion. These structural metrics are clearly inter-related, and change in a complex and crosscorrelated manner as the ligand adjusts to variation in the ionic radius of the metal at the center of the macrocyclic cavity. 3.2. Stabilization Energies and the BSSE. The uncorrected binding energy, Eb, of each complex was calculated using the supramolecular model (eq 1) proposed by Pople.47 Eb ¼ E½MðH2 OÞ2 ð15C5Þ2þ fEðM2þ Þ þ Eð15C5Þ þ 2EðH2 OÞ2 g

ð1Þ All calculations were carried out in the gas phase; E represents the total energy of a complex or a fragment at 0 K with appropriate charge and multiplicity, and the energy of the isolated divalent metal cations, M2þ, were calculated in the high-spin ground states using single point energy calculations with tight convergence and ultrafine integration grid criteria.7,8 It is not a simple matter to thoroughly explore the conformational space of the free ligand because of its skeletal flexibility, as has been pointed out for a related system.48 Our point of departure for modeling the free 15C5 ligand was to remove the metal ion and the axial ligands from the computed low-energy structure and to energy-minimize at the same level of theory used for modeling the metal complex. Of the complexes studied, [Cu(H2O)2(15C5)]2þ is found to be the most stable, while [Mn(H2O)2(15C5)]2þ is the least stable (Table 2). The binding affinity increases in the order Mn2þ < Fe2þ < Co2þ < Ni2þ < Cu2þ > Zn2þ, in precise agreement with the Irving-Williams series. The effect of basis set superposition error (BSSE) on the binding energy of the gas phase complexes (but not for the solvated structures as the SCRF is not implemented with counterpoise) was calculated as described previously,8 using the counterpoise procedure of Boys and Bernardi.49 The BSSE varied between 7.81 kcal mol1 for Cu2þ complex and 7.11 kcal mol1 for the Mn2þ complex (ca. 2%). The size of a macrocycle cavity and its match to the ionic radius of an ion is often used to rationalize the observed dependence of stability constants on ionic radius and is one of the parameters taken into consideration when designing novel ligand systems.50 While this may be appropriate for relatively

Figure 2. Correlation between the stabilization energy ΔE and the formation constant (log KML2þ) in [M(H2O)2(15C5)]2þ(M = Co, Ni, Cu, Zn) complexes, r2 = 0.963 (value for Mn2þ excluded; no data for Fe2þ).

rigid systems such as phthalocyanines and porphyrins, ligand flexibility may make this of secondary importance. The cavity radius of 15C5 is between 0.86 and 0.92 Å,50 yet this ligand binds more strongly to Cu2þ (r = 0.73 Å51) than does high-spin Mn2þ ion (r = 0.83 Å; see Figure S1), strongly suggesting that the holesize concept is not of primary importance in these systems. This is in agreement with the results of Islam et al.4 who have shown by calculation that 18C6 binds Naþ more tightly than does 15C5 even though the cavity size in 15C5 matches the size of Naþ. In the PCM model, the total energy is calculated as the sum of the energies of the solute, the solvent, and the cavity. The stabilization energy, ΔE, is then calculated by subtracting the total energies of the gas phase and the solvated structures (ΔE = Esol Egas); values are listed in Table 2. Solvation causes a significant increase in the calculated stabilization energies of the complexes, but the stability constants still follow the Irving-Williams series with an alternation of the relative stabilities of the Zn2þ and Co2þ complexes, similar to the experimental formation constants (Table 2). As the bond energy is expected to vary with the bond length for an ion-induced dipole electrostatic interaction, there is, as expected, a direct correlation between ΔE and 1/R2 (where R was taken as the mean value of all MO bond lengths) in these complexes (Figure S2 of the Supporting Information). With the exception of the value for Mn2þ (log K = 2.11), there is a good correlation between ΔE and experimental23 log K values (Figure 2). The reason for the discrepancy with Mn2þ is unclear. 3.3. Ligand-to-Metal Charge Transfer. The partial charges (Q) on the metal in [M(H2O)2(15C5)]2þ complexes obtained from a natural population analysis both in the gas phase and in solvent are summarized in Table 3. In all cases, the values of ΔQ shows that there is significant charge transfer from the ligands to the metal ion. One might have expected the extent of charge transfer to parallel complex stability (Mn2þ < Fe2þ < Co2þ < Ni2þ < Cu2þ > Zn2þ), but this is not the case, and instead, the NPA results, for both the gas phase and the solvated structures, unexpectedly gave (Table 3) Mn2þ > Fe2þ > Co2þ < Ni2þ > Cu2þ > Zn2þ. Recently, Jeanvoine and Spezia52 reported an investigation of dichalcogen-bridged complexes of the same divalent metals using B3LYP and MP2 in the gas phase. Their result shows a consistently smaller charge on the metal cations (hence, a larger ΔQ) when using B3LYP than when using MP2. In that study there was also no direct correlation between the 5595



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Table 3. B3LYP/6-311þþG(d,p) Computed Partial Charges (units e) on the Metal Ions and the Ligand-to-Metal Charge Transfer in [M(H2O)2(15C5)]2þ Complexes Obtained from a NPA (Q and ΔQ) and Bader’s (QBader and ΔQBader) Population Analysesa gas phase structures M

Q

ΔQ

Mn2þ Fe2þ Co2þ Ni2þ Cu2þ Zn2þ

1.446 1.495 1.512 1.502 1.506 1.685

0.554 0.505 0.488 0.498 0.494 0.315

Q

Bader

1.569 1.502 1.430 1.361 1.331 1.439

solvated structures ΔQ

Bader

0.431 0.498 0.570 0.639 0.669 0.561

Q

ΔQ

1.434 1.488 1.510 1.498 1.500 1.688

0.566 0.512 0.490 0.502 0.500 0.312

Q

Bader

1.572 1.491 1.420 1.350 1.319 1.433

MP2 (gas) ΔQ

Bader

0.428 0.509 0.580 0.650 0.681 0.567

Q

ΔQ

χb

1.485 1.581 1.604 1.595 1.598 1.685

0.515 0.419 0.396 0.405 0.402 0.315

1.263 1.292 1.321 1.367 1.372 1.336

a

Included are also the MP2/6-311þþG(d,p) computed gas phase charges on the metal ions obtained using the B3LYP/6-311þþG (d,p) optimized geometries of the [M(H2O)2(15C5)]2þ complexes. b The electronegativity of high-spin divalent metal ions.61

binding energy and ΔQ. At the MP2 level, while not perfect, there was a better correlation. For example, their B3LYP ΔQ values follow the order Cu2þ > Ni2þ > Co2þ > Fe2þ > Zn2þ > Mn2þ when they are coordinated by either H2O2, H2S2, or to H2Se2; at the MP2 level, the order is Cu2þ > Ni2þ > Co2þ > Fe2þ > Zn2þ > Mn2þ when the metal is coordinated by H2O2, but is Cu2þ > Ni2þ > Zn2þ > Co2þ > Fe2þ > Mn2þ when coordinated by H2S2 or H2Se2. It appears that the B3LYP functional is inadequate for describing the ligand-to-metal charge transfer for their systems, which is, only to some extent, better described at the MP2 level. Accepting that there is a problem with NPA charges obtained using B3LYP,52 we recalculated these at the MP2/6-311þþG(d,p) level (single point calculations on the B3LYP- optimized gas phase geometries) even though we recently demonstrated the discrepancy between ΔQ values obtained using the MP2 method and several DFT functionals together with a full core triple-ζ valence quality basis set for all atoms in those complexes, as well as centering effective core potential basis sets on the metal cations and a triple-ζ valence quality basis set on the main group elements.8 We found (Table 3) that MP2 gave smaller values of ΔQ in our complexes although the order is identical to that obtained from the B3LYP functional. A referee has pointed out that NPA is usually not overly method sensitive (although there are reports to the contrary53,54); we have therefore tested several other DFT functionals (X3LYP,33 M05,55 BP8656,57) in the gas phase, and the results are given in Table ST3 of the Supporting Information. A comparison of NPA ΔQ values given both in Table 3 and Table ST3 shows the trend Mn2þ > Fe2þ > Ni2þ > Cu2þ > Co2þ > Zn2þ at the B3LYP and MP2 levels, whereas M05 and X3LYP gave the order Ni2þ > Cu2þ > Fe2þ > Co2þ > Zn2þ and BP86 gave the order Ni2þ > Cu2þ > Mn2þ > Co2þ > Fe2þ > Zn2þ. This suggests that NPA charges are indeed functional-sensitive, confirming the observations of others.53,54 Listed in Table 3 are the Bader charges evaluated using the checkpoint file generated during NPA calculations at each level. In this case, the trend in ΔQBader is in precise agreement with the trends in ΔE, namely, Mn2þ < Fe2þ < Co2þ < Ni2þ < Cu2þ > Zn2þ, except at the BP86 level, which inverts the position of Ni2þ and Cu2þ (Table ST3). The Bader charges are thus more systematic and less sensitive to the correlated method used. We have found the same effect in our recent studies, which we shall report elsewhere, on a series of oxalato complexes with deprotonated oxalate dianions and water and on complexes of the same metal ions with 18C6 and H2O as coordinating ligands.

Figure 3. Correlation between the metal-to-ligand charge transfer, as determined using Bader’s QTAIM model, and the empirical electronegativity for high-spin divalent cations proposed by Keyan and Xue for [M(H2O)2(15C5)]2þ complexes (r2 = 0.964).

Our results suggest that the NPA procedure is not very reliable for exploring charge transfer between ligands and metals in Werner-type complexes. The discrepancy between the two methods might be because QTAIM accounts for atomic polarization contributions such as dipolar, quadupolar, and higher moments, while such contributions are typically ignored by other wave function based methods and point-charge models as well;58 a further possible reason could be the ambiguously suppressing contributions from the NPA-based near-valent AO orbitals (e.g., 4p and 4d Rydberg orbitals) in a manner that causes a pronounced change in fundamental properties (such as atomic charge) that might alter the qualitative trends of the systems studied.59,60 A further indication of the reliability of ΔQBader is the good correlation with the empirical electronegativity, χ, for high-spin 2þ cations (but in six-coordinate environments) proposed by Keyan and Xue (Figure 3).61 The size of metal ions is often invoked to explain trends in coordination chemistry. However, this is sometimes inappropriately used. For example, crystal radii are sometimes used as effective ionic radii62 and sometimes the low-spin radii are assigned to the high-spin states16 to interpret observed experimental data. In a study of [Ni(H2O)2(15C5)]2þ and related complexes, Siegler et al.16 used an ionic radius 0.67 Å reported in Greenwood and Earnshaw63 for six-coordinate high-spin Mn2þ (which is actually the low-spin value51) instead of 0.9 Å (the appropriate value for a seven-coordinate high-spin Mn2þ ion51). Their rationalization, that d5 high-spin Mn2þ imposes no geometrical 5596



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Figure 4. Dependence of the ligand-to-metal charge transfer (ΔQBader) in [M(H2O)2(15C5)]2þ complexes on (a) Shannon’s and (b) Brewer et al.’s ionic radii of the divalent metal cations (the value for Cu2þ in (a) and Zn2þ in (b) is excluded from the correlation).

preference on its environment and can therefore reside in a “compromise” position near the center of the 15C5 equatorial ligand and hence have long Mn2þO bonds, we believe to be misleading; in our view, the long bonds are a direct consequence of the relatively large ionic radius of seven-coordinate high-spin Mn2þ. The reasonable correlation between the ionic radius of the metal ions with ΔQBader (Figure 4), and with ΔE (Figure S3 of Supporting Information) clearly demonstrates that ΔQBader is a useful measure of bond stability (also see Figure S4). For this we have used the values (for high-spin six-coordinate ions because data for seven-coordinate ions are not available) of Shannon51 and of Brewer et al.64 While not perfect (the value for Cu2þ is out in the correlation with the Shannon radii while that for Zn2þ is out in the correlation with the Brewer radii), the correlation show that ΔQBader increases as the size of the metal ion decreases. This is intuitively reasonable because the charge density of the metal and, hence, its ionic potential and polarizing power will increase with a decrease in the ionic radius. 3.4. Characterization of the Bonding Based on a QTAIM Study. We have already demonstrated the usefulness of Bader’s quantum theory of atoms in molecules (QTAIM)36 for characterizing the bonding in the complexes of the first transition series.68,65 Based on the topological properties of the electron density, F(r), QTAIM stipulates that for two atoms in a molecule to be bonded to each other requires the presence of a bond path, the unique line of maximum electron density that connects the nuclei of the two atoms in an equilibrium configuration and where the potential energy density is maximally stabilizing, as well as the presence of a bond critical point (bcp) along the bond path where the gradient of F(r) vanishes (rF(r) = 0). The value of F at the bcp, Fb, is a measure of the bond strength as has been adequately demonstrated (for example, in neutral66,67 and in charged systems6,7,68). Whether structures obtained by computational methods in a field that simulates a solvent are representative of solid state structures is a moot point; in anticipation that the solvated structures will take into account at least some of the effects of a condensed phase, we shall focus our attention on only these in the discussion that follows. In Table ST4 of the Supporting Information we have highlighted the important topological properties at the bcps of MO bonds; those at the ring critical points are given in Table ST5 and that of the isolated ligands are given in Table ST6.

Figure 5. Metalligand bond distances plotted against (a) the electron charge density at the bcp (r2 = 0.989) and (b) the eigenvalue λ3 of Fb (r2 = 0.933) in [M(H2O)2(15C5)]2þ (M = Mn, Fe, Co, Ni, Cu, and Zn) complexes. The data are fitted to a first order exponential function.

All CO, CC, CH, and OH bonds in the free ligands have topological characteristics of the electron density consistent with a shared (covalent) interaction where the potential energy density dominates over the kinetic energy density. In the free 15C5 ligand, the Fb values are in the range 1.6801.715 eÅ3 for CO bonds and 1.7341.740 eÅ3 for CC bonds (see Table ST6), indicating that the latter bonds are stronger than the former, even though the CC bond distances (in the range 1.5141.519 Å with a mean value of 1.515(1) Å) are larger than the CO bond distances (in the range 1.4201.429 Å with a mean value of 1.424(3) Å). The electron density at the bcp for a CC single bond is around 1.71.9 eÅ3,6971 and that for a CO single bond is 1.68(2) eÅ3;72 the present results are in agreement with those values. The values of r2Fb are more negative at the CC bond bcps (15.23 to 15.39 eÅ5) than at the CO bond bcps (10.65 to 10.93 eÅ5), while |λ1/λ3| is close to 1.01 for CO bonds and around 1.37 for the CC bonds. This is consistent with the CC bonds being more covalent than the CO bonds36,73 because of the greater electronegativity of O. The coordination of 15C5 and the two H2O ligands to metal ions causes redistribution of the electron density at various critical points in the ligands as a consequence of the polarizing effect of the metal ions. There is an elongation of the CO bond with a concomitant decrease in the bcp electron density; r2Fb values are similar to those in the free ligand, albeit smaller in magnitude. There is a correlation between the CC bond length and the electron density at the bcp (see Table ST6 and Figure S5 of the Supporting Information). Correlations are also observed between the electron charge density Fb and its Laplacian, r2Fb, 5597


The Journal of Physical Chemistry A with the total energy density Hb (Figures S6 and S7), indicating that both Fb and r2Fb can be used as a measure of bond strength. In the case of CO bonds, the data are more scattered (Figure S8). The bond paths between the metal and the 15C5 and H2O ligands are well-developed, with very little curvature (Figure S9 of the Supporting Information). The values of Fb at MO bcps are small compared to those of the covalent bonds in the complexes (as discussed above; see Table ST4); the mean values (in eÅ3) are 0.354 for Cu2þ; 0.341 for Ni2þ; 0.330 for Zn2þ; 0.318 for Co2þ; 0.315 for Fe2þ; and 0.307 for Mn2þ. The average value of Fb at MOH2 bcps is always larger than the average value at ethereal MO bcps; hence the aqua ligands form stronger bonds with the metal ions than do the ethereal O donors. The values of Fb are in the range observed experimentally74 for metaloxygen bonds (0.2940.428 eÅ3 for MnO bonds, 0.2920.501 eÅ3 for FeO bonds, and 0.3380.445 eÅ3 for CoO bonds in tephroite, fayalite and Co2SiO4, respectively). There is an exponential relationship between the electron density at MO bcp and the MO bond length (Figure 5a). The value of r2Fb is always positive at the MOH2 and MO bcps (Table ST4) and invariably larger for the former than for the latter. The experimental r2Fb values74 for MnO (4.106.36 eÅ5), FeO (3.977.84 eÅ5), and CoO (4.677.58 eÅ5) bonds match reasonably well with our calculated values. We observe an exponential dependence of MO bond distance on r2Fb values at the bcp (Figure S9 of the Supporting Information), and that with the curvature in the direction of the bond path λ3 at the bcp (Figure 5b). The relationship established here for metalligand interactions holds for the noncovalent interacting systems.75,76 As we noted above, there is significant asymmetry in the equatorial NiO bond lengths because of a JahnTeller distortion of the high-spin ground state electronic configuration. One of the bonds (NiO2, Figure 1) is much longer than the other four (Table ST1); associated with this is a smaller value of Fb and r2Fb (Table ST4), consistent with a significantly weaker bond. The bonds between the metal ions and the ligands result in five five-membered ring surfaces characterized by (3,þ1) ring critical points (rcps; see Figure S10 of the Supporting Information); their distance from the bcps is indicative of a structurally stable system. The ellipticity, εb = |λ1|/|λ2| 1, is a function of the ratio of the rate of electron density decrease in the two directions perpendicular to the bond path at the bond critical point.36 Its value is always positive because λ1, λ2 < 0 (see Table ST4), and a large value of ellipticity at a bcp is known to reflect structural instability.77 The values of εb for the two MOH2 bonds within each complex are very similar (percentage relative standard deviation, %rsd 0.80 As seen in Table ST4, the MO bonds are indeed characterized by r2F > 0 and Hb values very close to zero; in the complexes with the less electronegative ions (Figure 3), these are all, or predominantly, positive (Mn2þ, Fe2þ), while in other complexes (the more electronegative ions Co2þ, Ni2þ, Cu2þ, and Zn2þ), they are all, or predominantly, negative. Thus, the metalO bonds are best described as ionic with some covalent character, the covalency being particularly evident with the more electronegative metal ions. Another metric used for determining the nature of a bonding interaction is the ratio |Vb|/Gb.81 Interactions with |Vb|/Gb < 1 are characteristic of ionic interactions; those with |Vb|/Gb > 2 are typically covalent interactions; while interactions with 1 < |Vb|/ Gb < 2 have intermediate character. On this basis, the bonding in CC and CO bonds is predominantly covalent. The metalligand bonds in the Mn2þ and Fe2þ complexes all have |Vb|/ Gb < 1 and could be considered purely ionic; the majority of the bonds in the Co2þ and Ni2þ complexes have 1 < |Vb|/Gb < 2, as do those in the Cu2þ and Zn2þ complexes. Thus, the degree of covalency in the metaloxygen bonds in these complexes increases across the first transition period. An important development in QTAIM theory73,82 is the introduction of the localization (λ(A,B)) and the delocalization (δ(A,B)) indices. The latter is a measure of the average number of electron pairs shared or delocalized between two atomic basins A and B, and is a measure of the bond order of a chemical bond.73 We have already discussed the usefulness of δ(A,B) in our recent report on aqua-ammine complexes of Co2þ,7 so we have not repeated the details here. The average number of electrons N(M), on an atom is given by N(M) = λ(M) þ ∑M6¼O δ(M, O)/2 > λ(M).83 The quantity Z-N(M), where Z is the atomic number, then gives the charge on atom M. As shown in Table ST7, this follows the order Mn2þ > Fe2þ > Zn2þ ≈ Co2þ > Ni2þ > Cu2þ, in agreement with the order of the electronegativity of the metal ions (Figure 3), that is, the least electronegative ion carries the greatest charge (Mn2þ, 1.57 e, Table ST7), while the 5598



Figure 7. Dependence of delocalization index of each bond δ(M,O) on the Laplacian of electron charge density at the MO bcps in [M(H2O)2(15C5)]2þ complexes (r2 = 0.961).

Figure 8. Dependence of delocalization index of each bond δ(M,O) on the MO bond distances in [M(H2O)2(15C5)]2þ complexes (r2 = 0.930).

most electronegative ion (Cu2þ, 1.32 e) carries the smallest charge, consistent with the polarizing power of the ion. All O atoms have N(O) values >9, with that on O of H2O larger than that of ethereal O of 15C5. The atomic localization index increases from 22.57 for Mn2þ to 27.72 for Zn2þ. The difference between N(M) and λ(M) for each metal complex (which is close to 1e) is the number of electrons delocalized between basins of the metal and the coordinated O-donors. This follows the order Mn2þ < Fe2þ < Zn2þ < Co2þ < Cu2þ < Ni2þ. Interestingly, the localization index correlates precisely with the electrostatic potential, V, of the metals in these complexes (Figure S11 of the Supporting Information). The delocalization index of the coordinate bonds, δ(M,O), increase with the value of the electron density at the bcp (Figure 6). This sort of relationship has been demonstrated by Matta and co-workers in a topological analysis of the bonding in polycyclic aromatic hydrocarbons.84 The magnitude of r2Fb at MO bcps increases with an increase in δ(M,O) (Figure 7) similar to an observation of Bader and Matta80 for CC bonds in the hydrocarbon framework of a Ti complex. There is a clear relationship between the delocalization indices and the kinetic and potential energy densities (Figure S12); however, there is no such simple relationship between the indices and the total energy density at the MO bcps. Interestingly, there is an exponential dependence of the MO bond distances on the delocalization of the same bonds (Figure 8).

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’ CONCLUSIONS We have carried out geometry optimizations on a series of trans complexes containing 15-crown-5 and two H2O molecules as coordinating ligands to the high-spin divalent metal ions Mn, Fe, Co, Ni, Cu, and Zn in their ground electronic states both in the gas phase and incorporating a polarized continuum medium to simulate H2O as a solvent to examine the local coordination environment between the ligands and the metal ions. The structures, which are in good agreement with those observed crystallographically, adopt pseudopentagonal bipyramidal geometry. The Ni2þ is distorted with one long equatorial bond to an O donor of 15C5 because of JahnTeller distortion. The other complexes have less severe distortion, that distortion attributed to the steric crowding of the inner coordination sphere of the metal ion by seven donors. The mean MOH2 bonds are shorter than the mean MO(15C5) bonds in most of the structures except in the Fe2þ and Mn2þ complexes. The most noticeable effect of solvation on the gas phase structures is that it shortens the MOH2 bonds while in compensation the equatorial bonds to 15C5 are slightly lengthened. The gas phase stabilization energies of these complexes are in line with the Irving-Williams series (Mn < Fe < Co < Ni < Cu > Zn) for divalent metal ions. While inclusion of solvation media inverts the positions of Co2þ and Zn2þ, the trend in stabilization energy agrees well with the experimentally measured formation constants of the same metal complexes (except for Mn2þ) in aqueous solution. Complex formation always results in charge transfer from the ligands to metal. While both NPA and Bader’s population analyses provide a quantitative estimate of the ligand-to-metal charge transfer it is argued that the Bader charge analysis is more reliable. We have shown that that ΔQBader correlates not only with empirical estimates of the electronegativity of the metal ions but also with both the stabilization energies and the ionic radii of the metals. This suggests that the ability of the ligands to transfer charge density to the metal is an important factor influencing complex stability. Our calculations suggest that the match between the cavity size of the crown ether and ionic radius of the metal is not of overriding importance. Thus we have shown that the Cu2þ (0.73 Å) and Ni2þ ions (0.69 Å), which have smaller ionic radii, have a higher binding affinity toward 15C5 ligand than does Mn2þ ion with a larger ionic radius close to the cavity size. Based on a QTAIM analysis we have shown that the MOH2 bonds are predominantly ionic in nature while the bonds between the metal and the O donors of 15C5 have some covalent character even though the former bonds are shorter than the latter ones. There appears to be some double bond character in the MO bonds in the Co2þ and Fe2þ complexes, presumably due to involvement of O lone pairs. We have observed an exponential dependence of MO bond distance on Fb, r2Fb, and the eigenvalue λ3 at the bcp, while the correlations between Fb and CC and Fb and CO bond lengths are linear. We have also shown that the ratio |Vb|/Gb increases with an increase in the MO bond distance for a given complex, and is accompanied by a concomitant decrease in the value of Gb/Fb and an increase in the value of Hb/Fb. Finally, we have shown that the delocalization indices δ(M,O) correlate with the electron charge density and its Laplacian at the MO bcps and with the MO bond distances in these complexes. The parameter δ can be used for the rapid evaluation of bond order of a bond from the knowledge of electron density alone without having to perform time-consuming integration over atomic basins. 5599



’ ASSOCIATED CONTENT

bS

Supporting Information. Tabulation of selected computed bond distances in the isolated 15C5 ligand and those in [M(H2O)2(15C5)]2þ complexes; the dependence of the stabilization energy (ΔE) with the inverse-square mean bond distance, with the ionic radii of the metal ions, and with the Bader charge-transferred to the metal ions; the dependence of the electron charge density Fb on the CC bond distances, and on the total energy density Hb; the total energy density Hb dependence on the Laplacian of the electron charge density, r2Fb, at the CC bond critical points; the dependence of the electron charge density Fb on the CO bond distances; an exponential dependence of the Laplacian of the electron charge density r2Fb at bcps on the MO bond distances; and the dependence of the electrostatic potential V(M) on the localization index λ(M) of the metal cations in [M(H2O)2(15C5)]2þ complexes. We also list a comparison of the crystallographic MO(15C5) bond lengths in [M(H2O)2(15C5)]2þ complexes with structures modeled at the B3LYP/6-311þþG(d,p) level; the computed partial chargesa (Q/e) on the metal ions and the ligand-to-metal charge transfer (ΔQ) in [M(H2O)2(15C5)]2þ complexes obtained from the NPA and Bader’s population analyses in the gas phase using various correlated methods; and the QTAIM properties of the ligand and those at the MO bond critical points and the ring critical points in solvated [M(H2O)2(15C5)]2þ complexes computed at the B3LYP/6-311þþG(d,p) level of theory. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: (1) 514-848-2424 (P.R.V.); (27) 11-7176737 (H.M.M.). Fax: (1) 514-848-2868 (P.R.V.); (27)11-7176749 (H.M.M.). E-mail: [email protected] (P.R.V.); helder.marques@ wits.ac.za (H.M.M.).

’ ACKNOWLEDGMENT P.R.V. acknowledges the Japan Society for the Promotion of Science (JSPS) for the award of a Postdoctoral Fellowship and financial support received for conducting research at the Department of Chemistry of Okayama University, Okayama, Japan. P.R.V. is indebted to Professor K. Kawaguchi for his rewarding support without which this work could not have been finished and thanks the Osaka University computer center for providing supercomputing facilities. We are indebted to Professor R. F. W. Bader for his valuable comments received during this work. H.M. M. gratefully acknowledges the funding provided by the Department of Science and Technology of South Africa, and the National Research Founding, through the SA Research Chairs Initiative, as well as funding provided by the University of the Witwatersrand. ’ REFERENCES (1) Gray, H. B. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 3563–3568. (2) Lippard, S. J. Nat. Chem. Biol. 2006, 504–507. (3) Hilfiger, M. G.; Chen, M.; Brinzari, T. V.; Nocera, T. M.; Shatruk, M.; Petasis, D. T.; Musfeldt, J. L.; Achim, C.; Dunbar, K. R. Angew. Chem., Int. Ed. 2010, 49, 1410–1413.

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M = Mn, Fe, Co, Ni, Cu, Zn - American Chemical Society

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