ARTICLE pubs.acs.org/JPCA
Bonding and Magnetic Response Properties of Several Toroid Structures. Insights of the Role of Ni2S2 as a Building Block from Relativistic Density Functional Theory Calculations Alvaro Mu~noz-Castro* Doctorado en Fisico-Quimica Molecular, Relativistic Molecular Physics (ReMoPh) group, Universidad Andres Bello, Republica 275, Santiago, Chile
bS Supporting Information ABSTRACT: Relativistic density functional calculations were carried out on several nickel toroid mercaptides of the general formula [Ni(μ-SR)2]n, with the aim to characterize and analyze their stability and magnetic response properties, in order to gain more insights into their stabilization and size-dependent behavior. The Niligand interaction has been studied by means projected density of states and energy decomposition analysis, which denotes its stabilizing character. The graphical representation of the response to an external magnetic field is applied for the very first time taking into account the spinorbit term. This map allows one to clearly characterize the magnetic behavior inside and in the closeness of the toroid structure showing the prescence of paratropic ring currents inside the Nin ring, and by contrast, diatropic currents confined in each Ni2S2 motif denoting an aromatic behavior (in terms of magnetic criteria). The calculated data suggests that the Ni2S2 moiety can be regarded as a stable constructing block, which can afford several toroid structures of different nuclearities in agreement with that reported in the experimental literature. In addition, the effects of the relativistic treatment over the magnetic response properties on these lighter compounds are denoted by comparing nonrelativistic, scalar relativistic, and scalar plus spinorbit relativistic treatments, showing their acting, although nonpronunced, role.
’ INTRODUCTION Crown ethers have received much attention since their discovery in 1967,1 prompted by their particular structures and properties giving rise to a rapid development of the hostguest chemistry. Their ability to selectively bind metal atoms or ions2 is of importance in several fields such as supramolecular chemistry, catalysis, material science,3 or as simple model systems for understanding noncovalent interactions.4 In this context, their inorganic counterparts have become an area of increasing interest driven by the versatility of a discrete number of redox centers into a molecular macrocyclic array with properties related to the organic crown ethers moieties, leading to the development of some inorganic cages5 and metallocrowns,6 toward the design of multimetallic catalysts7 and enzyme mimics,8 among other applications in materials science.9 Nickel mercaptides (Ni(SR)2) are a fundamental issue in the development of metallocrowns, since the pioneering work by Woodward10a in the middle of the 1960s. Initially considered as insoluble high polymers,11 their definitive structural characterization was achieved following efforts to include more soluble ligands, revealing their molecular toroid structure10 through the discrete hexanuclear [Ni(μ-SCH2CH3)2]6 complex,10a anticipating the characterization of related systems with different nuclearities and including other redox centers from the same group.1215 r 2011 American Chemical Society
The resulting robust structure allows one to include in a cyclic arrangement several redox centers in a molecular unit of four-,12 five-13 and six-10,14 nickel vertices, among others,15 where the NiNi intermetallic distance remains longer than the mean separation in nickel metal (2.49 Å),16 with values ranging from 2.65 to 3.05 Å,1014 suggesting the potential ability to selectively determinate a desired size of host domains by varying the number of vertices, which could give rise to materials with sizedependent properties leading to exceptional novelty and intriguing behavior.17 In this article we focus on the four-, five-, and six-membered nickel mercaptides, with the aim to characterize the energetic and electronic variations due to the increase in nuclearity, which in turn determine the diameter and bonding of the host, which ensure the stability of the toroid structure. In addition, we explore the magnetic behavior of these closed-shell systems by mapping the shielded and deshielded areas18 in an applied external field, via the nucleus-independent chemical shifts (NICS) procedure,1921 in order to clarify zones that exhibits diatropic (aromaticity) and paratropic (antiaromaticity) induced currents. Finally, we will compare nonrelativistic and relativistic calculations in order to Received: March 27, 2011 Revised: July 16, 2011 Published: September 01, 2011 10789
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characterize the dependence of the magnetic response to the scalar and spinorbit terms in the first-row transition metal systems as part of our current research.22,23
’ COMPUTATIONAL DETAILS Relativistic density functional theory calculations24 were done by using the ADF 2010.02 code,25 incorporating both scalar and spinorbit corrections via the two-component ZORA Hamiltonian.26,27 Triple-ξ Slater basis set plus polarization function (STO-TZP) were employed within the generalized gradient
Figure 1. Schematic representation of 1, 2, and 3.
’ RESULTS AND DISCUSSION
Table 1. Selected Distances (Å) and Angles (deg) of the Systems 1, 2, and 3 1 calc. (D2)
a
2 exp.a
calc. (Cs)
3 exp.a
calc. (D3)
exp.a
diam. Ni
3.883
4.876
5.848
5.848
diam. S
5.246
5.550
6.639
6.635
NiNi
2.737
2.924
2.928
NiNi BOb
0.22
NiS
2.253
NiS BOb
0.76
NiNiNi
90
89
110
108
120
120
NiSNi
75
74
80
80
83
84
SNiS
98
98
98
98
98
97
2.665
2.892
2.835
0.18 2.208
2.243
0.15 2.207
0.77
approximation (GGA) according to the PerdewBurkeErnzerhof (PBE)28a,b in order to account for the exchange-correlation (xc) effects due to its improved performance on long-range interactions and relative low computational cost for larger molecules.28c,d,e Geometry optimizations were done without any symmetry restrain, via the analytical energy gradient method implemented by Verluis and Ziegler.29 Bond order calculations were carried out according to Mayer as it is implemented in the ADF package, due to its valuable results in analyzing inorganic molecules and clusters.3032 The map of induced magnetic fields18 were calculated according to the NICS19,20 procedure of the Schleyer group, employing the GGA exchange expression proposed by Handy and Cohen28f and the correlation expression proposed by Perdew, Burke, and Ernzerhof28 (OPBE), incorporating the scalar relativistic (OPBE/ ZORA) and both scalar and spinorbit effects (OPBE/ZORA +SO) through the ZORA Hamiltonian and STO-TZP as the basis set. For comparison, nonrelativistic (NR) calculations were done at a similar level of theory.
2.205
2.210
0.77
holding anglec
110°
117°
122°
123°
twist angled
13°
10°
7°
6°
Averaged experimental values from refs 12a, 13b, and 14e for [Ni(μSC5H9N(CH3)2)2]4, [Ni(μ-SCH2SiCH3)2]5, and [Ni(μ-SCH2CH2OH)2]6, respectively. b Bond order calculations via Mayer analyses.3032 c Folding angle of the Ni2S2 moiety. d Twist angle of the NiS4 moiety.
Molecular Structures. Toroid structures are already obtained by using several bridging mercaptide ligands, such as NaSR and NaSeR,1015 and a nickel salt, resulting in cyclic arrays of different nuclearity. In order to obtain an overall picture of the four-, five-, and six- membered cyclic nickel mercaptides ([Ni(μSR)2]n), we consider methyl-mercaptide (R = CH3)-based compounds, namely, [Ni(μ-SCH3)2]4 (1), [Ni(μ-SCH3)2]5 (2), and [Ni(μ-SCH3)2]6 (3) (Figure 1). The optimized structures are close to the highest point symmetry possible, resulting in almost D2 structure for 1, Cs for 2, and D3 for 3. These structures exhibit only a few imaginary frequencies due to the free rotation of the methyl groups in the range of 120i cm1 to 140i cm1. Calculated geometrical parameters for these slightly simplified models are summarized in Table 1, denoting its reasonable agreement with the available experimental data for [Ni(μSC5H9N(CH3)2)2]4,12a [Ni(μ-SCH2SiCH3)2]5,13b and [Ni(μSCH2CH2OH)2]6.14e The closest NiNi distances vary from 2.737 Å for 1, to 2.924 Å for 3, leading to metallocrowns of diameter 3.883 Å, 4.876 Å, and 5.848 Å, depicted by the Nin ring, embeded between two Sn rings of 5.246 Å, 5.550 Å, and 6.639 Å diameter, respectively, for 1, 2 and 3. The NiS distance remain similar in the series. Moreover, the NiNiNi angle increases in relation to the circumference size, in contrast with the NiSNi angle of each Ni2S2 rhomboid varying to a lesser degree,15a suggesting that in the toroid structure, the Ni2S2 moiety is a
Figure 2. DOS, projected DOS for 3p of S and 3d of Ni atoms, and Mulliken orbital overlap population (MOOP) between both atomic shells of 1, 2, and 3. Red dashed line denotes the EF. 10790
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robust elementary building block to obtain toroid structures with different numbers of vertices, which vary slightly from 1 to 3. The nonplanarity of this rhomboid is denoted by the folding angle (Table 1),14a which indicates that, going from the four- to the sixmembered systems, the structure comes more relaxed from 110° to 122° toward a planar structure (180°). Accordingly, the twist angle of NiS4 denotes a more planar square for 3. It is important to note that the geometrical parameters of the Nin core of the metallocrowns 1, 2, and 3 are well reproduced by using methyl mercaptide ligands. This fact suggests that the robust toroid structure depicted by the NiS core remains similar despite the use of different ligands.1014 Electronic Structures. The resulting molecular electronic structure of the studied systems remains similar, as can be seen from the density of states (DOS) depicted in Figure 2, where the Fermi level (EF) is denoted by a dashed line. The energy gap between the highest occupied (HOMO) and lowest unoccupied Table 2. Energy Decomposition Analysis of the Interaction of a Ni Atom and the Rest of the Structure (kcal/mol), Charge Analysis (a.u.) via the Hirshfeld and Voronoi Deformation Density (VDD) Schemes, and HOMOLUMO gap (HL) 1
a
2
3
ΔEorb
435.64
42%
437.18
43%
464.29
45%
ΔEelstat
595.66
58%
582.72
57%
559.73
55%
ΔEpauli
+219.58
+211.27
+218.42
ΔEint Nia
811.72
808.63
805.6
Hirshfeld
+0.128
+0.131
+0.135
VDD
+0.092
+0.097
+0.110
HL
1.304
1.110
0.808
Charge analysis of each Ni nucleus.
Table 3. Values of δ(r) at Different Levels of Theory, Neglecting and Including Scalar and Spin-Orbit Terms, for 1, 2, and 3 at the Center of the Nin and Ni2S2 Rings, Respectively 1
a
2
3
Ni4b
Ni2S2c
Ni5b
Ni2S2c
Ni6b
Ni2S2c
NRa
+8.41
13.54
+7.89
13.71
+5.95
13.71
SRa
+8.70
13.24
+8.18
13.49
+6.19
13.59
SOa
+8.99
12.65
+8.29
12.85
+6.24
12.94
NR: Nonrelativistic; SR: scalar relativistic; SO: scalar + spinorbit calculations. b Center of Nin ring. c Center of Ni2S2 ring.
molecular orbital (LUMO) decreases with the increase of the toroid size (Table 2), where in all the studied systems the HOMO is mainly of Ni 3d antibonding character, and the LUMO is mainly of S 3p character (Supporting Information). To gain more insight into the bonding nature between the Ni center and the mercaptide ligand of the NiS4 moiety, we analyze the projected density of states (pDOS) of the 3d-Ni and 3p-S valence atomic levels for 1, 2, and 3. Figure 1 shows that the occupied molecular energy levels near the EF are mainly derived from the 3d-Ni shell, indicating that the Ni centers are largely involved in the chemical reactivity of these toroid systems.33 The bonding, nonbonding, and antibonding regions concerning the electronic structure are determined via the Mulliken orbital overlap population (MOOP) between the 3d-Ni shell and mercaptide ligands, where positive and negative values denote the bonding and antibonding regions, respectively, while the almost zero values denote the nonbonding regions (or almost nonbonding). The bonding block is located between 10.0 and 5.5 eV, in a region with mainly ligand character, while the antibonding region is located mainly at the LUMO. Thus, most of the antibonding combination of the NiS4 moiety remains unoccupied, ensuring the stability of the Niligand interaction, which in turn leads to a robust toroid structure. The mainly Ni 3d molecular levels (∼ 5.5 to 4.0 eV) are designated as nonbonding regions with a small antibonding character in the NiS4 fragment. Moreover, the increase of the amount of energy levels in the frontier band with orbitals of nonbonding character accounts for the decrease in the HOMOLUMO gap, making systems of higher nuclearities (n > 6) attractive targets for molecular electronics applications.34,35 The interaction between the nNi vertex was analyzed based on the overlap population between the 3d atomic shells of each redox center, and by using the Meyer bond-order procedure3032 at the scalar relativistic level. A decreasing NiNi interaction is concluded because of the small overlap between the basis functions going from 1 to 3, and by the Meyer bond orders values of 0.753 for 1, 0.172 for 2, and 0.143 for 3, suggesting that the stabilization of the toroid structure involves in part a NiNi bonding in 1, which decreases as a function of the NiNi bond length. Hence, the main stabilizing factor in 2 and 3 is the Ni2S2 building block, which is reinforced by the NiNi bond in 1. It is expected that these conclusions can be extended to other related systems with higher nuclearities. Binding Energy Analysis. Energy decomposition analysis (EDA) according to the MorokumaZiegler scheme36 was employed with the aim of obtaining a deeper description of the Niligand interaction, and how it varies with the number of Ni vertices. The interaction (binding energy) is calculated
Figure 3. Maps of δ(r) denoting shielded (negative values) and deshielded (positive values) areas in ppm, for 1, 2, and 3, in an xy contour-plane representation. 10791
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The Journal of Physical Chemistry A to be largely favorable by about 811.72 kcal/mol for 1, 808.63 kcal/mol for 2, and 805.60 kcal/mol for 3, as can be expected by the bonding metalligand interaction discussed in the Electronic Structures section (see above). Within this scheme, the interaction energy (ΔEint) can be further partitioned into three main components: ΔEint = ΔEpauli + ΔEelstat + ΔEorb. Here, the two first terms are computed by considering unperturbed fragments, and the latter is obtained when the densities are allowed to relax into the final molecular orbitals. The ΔEelstat term accounts for the stabilizing electrostatic interaction, and ΔEorb stands for the stabilizing covalent character of the fragmentfragment interaction, while the ΔEpauli term accounts for the Pauli (steric) repulsion. In this sense, the ΔEelstat represents more than the 55% of the total stabilizing energy (calculated as ΔEelstat /(ΔEelstat +ΔEorb) %) in the studied compounds. Hence, these results suggest that the electrostatic interaction plays the most important role, compared to the orbital interaction (∼45%), in the stabilization of the toroid complex. The variation of the stabilizing terms from 1 to 3 suggest that that a more strained structure leads to an interaction of more electrostatic character (58% for 1, with a NiNiNi angle of 90°, and 55% for 3, with a NiNiNi angle of 120°). In order to assign a total valence population to the Ni atoms (Table 2), we employed the Hirshfeld37a and Voronoi deformation density (VDD)37b partition schemes (Table 2). The Hirshfeld and VDD analyses show similar results, which suggests that the initially formal Ni2+ receives charge from the ligand, which decreases upon going to a more relaxed structure (3). Magnetic Response. The evaluation of the magnetic response of the studied toroid structures was carried out on the basis of NICS by Schleyer,19 mapping the induced magnetic field (Bind, in ppm units) over the space by application of an external magnetic field (Bext) of 1.0 T. These two quantities are related
Figure 4. Maps of δ(r) denoting shielded (negative values) and deshielded (positive values) areas in ppm, for 3, in an xz contour-plane.
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through the shielding tensor (σ), as is given elsewhere:18 ext Bind ðrÞ ¼ σ ðrÞ B
where the isotropic shielding value (δ(r)) can be determined by the negative of the trace of the second rank tensor σ(r)19 (δ(r) = NICS = (1/3)Trσ(r)) in units of ppm. It is noteworthy that in this type of system, deshielded areas (Table 3) alternate with a highly shielded region at the Ni2S2 ring (ca. 12 ppm at the center of Ni2S2), as can be seen from Figure 3. The diatropic currents are isolated in each Ni2S2 ring and decrease precipitously toward the center of the toroid (short-range induced field18b). In Figure 4, the xz cut-plane denotes the shape of the deshielded area through the center of the macrocyclic ring, which illustrates that the paratropic currents are retained inside the toroid structure until the Sn rings, where the values of δ(r) are close to 0.0 ppm. From 1 to 3, the value of δ(r) decreases in accordance with the increase of the diameter of the Nin ring, which decreases the interaction between the deshielded areas. From Figure 3, the isotropic magnetic response denotes the similar magnetic behavior of the studied systems. In order to gain more insight into the electronic delocalization inside the toroid structure, we focus on the magnetic criteria of induced electronic delocalization (aromaticity),38 where an applied external magnetic field through the z-axis in an aromatic ring system leads to diamagnetic ring currents characterized by shielded response in the z-axis (negative values of the zz component of δ(r)). On the contrary, deshielded areas denote paramagnetic rings currents usually characterized in antiaromatic ring systems,18,19 by the map representation of the zz component of δ(r) (δzz(r)) in Figure 5. At the center of each Nin ring, the positive values indicate deshielded areas, which in turn denote paratropic currents, as has been noted recently;21 however, by the map of δzz (r), it is possible to observe that the d aromaticity inside of the Nin ring leads to diatropic ring currents (aromaticity) at the closeness of the toroid structure, which in turn induce a paratropic response at the center of the toroid structure with values of δzz (r) of 1.56 ppm for 1, 3.87 ppm for 2, and 6.33 ppm for 3, at the spinorbit relatisvitic level. This behavior contrasts with the aromatic properties of organic molecules,18b which show pure shielded response inside the ring. This aromatic behavior suggests an enhanced stabilization,39 which is more pronounced in 1. In Table 3, the isotropic δ(r) value indicates that the Ni2S2 ring exhibits diatropic ring currents indepently of the external magnetic field (Bext) axis and the size of the system, supporting its size-independent stability and its consideration and use as a constructing block.
Figure 5. Maps of δzz (r) denoting shielding zones (negative values) close to the nNi ring and a deshielding zone (positive values) at the center. 10792
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The Journal of Physical Chemistry A In addition, the relativistic effects in these nonrelativistic molecules have been revisited by comparison of the magnetic response to an external magnetic field via nonrelativistic, scalar relativistic, and scalar + spinorbit calculations.24 It is quite important to note this variation, in the sense that the nickel is termed as a nonrelativistic atom; however, the titled effects vary in their magnetic behavior, as can be seen from Table 3. The different levels of theory vary the value of the induced magnetic field, increasing the unshielded areas (center of Nin) and decreasing the shielded areas (center of Ni2S2), which can be understood in terms of the relativistic valence atomic spinorbit shells 3d3/2 and 3d5/2 for Ni, and 3p1/2 and 3p3/2 for S,2224 which in fact take part in the magnetic and related properties.24
4. CONCLUSIONS Analysis of the electronic structure and induced magnetic fields have been achieved via the relativistic two-component ZORA Hamiltonian including scalar and spinorbit coupling. The calculated data suggest that the stability arises mainly from the bonding interaction between the mercaptide ligand and the metallic center in the Ni2S2 fragment, and the intermetallic interaction is almost negligible in the multimetallic toroid structures with n > 5. By calculating the induced magnetic fields by an applied external field, we achieve an understanding of the reason for the paratropic current behavior in terms of n paratropic sites (Ni vertex), which, in conjunction, leads to a paratropic current at the center. The zz-component of the shielding tensor suggests an aromatic behavior confined to the closeness of the Nin ring, which leads to deshielded zones at the center of structure. The Ni2S2 moiety exhibits aromatic character, a property that, in addition to the high stabilization of the NiS4 interaction, allows one to conclude that the rhomboid building block ensures the stability of the robust toroid structure. In addition, the relativistic effects vary the behavior of the induced magnetic fields, even in the systems termed as “nonrelativistic compounds” (Ni: Z = 28; S: Z = 16; C: Z = 12; H: Z = 1, where Z it is the atomic number). Which, denotes that the relativistic terms influence several molecular properties. ’ ASSOCIATED CONTENT
bS
Supporting Information. Isosurfaces of the HOMO and LUMO. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The author ackowledges the financial support of FONDECYT Grant 11100027 and PROJECT MILLENNIUM No. P07-006F. The author thanks the reviewers for their helpful comments. ’ REFERENCES (1) (a) Pedersen, C. J. J. Am. Chem. Soc. 1967, 89, 2495. (b) Pedersen, C. J. Angew. Chem., Int. Ed. Engl. 1988, 27, 1021. (2) (a) Slone, R. V.; Benkstein, K. D.; Belanger, S.; Hupp, J. T.; Guzei, I. A.; Rheingold, A. L. Coord. Chem. Rev. 1998, 171, 221.(b) Lehn, J.-M. Supramolecular Chemistry. Concepts and Perspectives; VCH: Weinhein,
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