Aromaticity, Optical Properties and Zero Field Splitting of Homo- and

Article pubs.acs.org/JPCA

Aromaticity, Optical Properties and Zero Field Splitting of Homoand Hetero-bimetallic (C8H8)M(μ2−,η8C8H8)M(C8H8) where M = Ti, Zr, Th Complexes Dayán Páez-Hernández* and Ramiro Arratia-Pérez Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andrés Bello, República 275, Santiago 8370146, Chile S Supporting Information *

ABSTRACT: This work presents a relativistic calculation of electron delocalization, optical properties, and zero field splitting in a group of molecules with the structure (C8H8)M(μ2−,η8C8H8)M(C8H8), where M = Ti, Zr and Th. Additionally we also studied the heterobimetallic combinations (Ti−Th and Zr−Th). The molecular properties are discussed based on their electronic structure and the influence of the electron mobility in metal−metal communication. Nucleus independent chemical shift (NICS) was determined via the gauge-including-atomic-orbital (GIAO) method with the OPBE functional. The time-dependent density functional theory (TDDFT) was employed to calculate excitation energies, and the electronic transitions over 500 nm are presented with the objective to analyze the transition metal role as an antenna effect in the absorption band in the near-IR region. Finally the ZFS was calculated using Pederson−Khana and coupled perturbed DFT approaches implemented in the ORCA code. The contributions to spin−spin coupling (SS) and spin−orbit coupling (SOC) were analyzed, and the spindensity over the metal centers is discussed employing our scheme of metal−metal communication. Our aim is to determine the influence of the electronic structure over the optical and magnetic properties in a group of model compounds to understand the transition metals effect over these properties.

1. INTRODUCTION Molecular coordination compounds of lanthanide and actinide ions attract a growing interest in material science due to their luminescent and magnetic properties.1,2 The rather large and anisotropic magnetic moments of most of the lanthanide (III) and actinide ions make these ions appealing building blocks in the molecular approach of magnetic materials.1−5 Numerous compounds containing lanthanide or actinides ions and paramagnetic species such as transition metal ions or organic radicals have been described;1−18 however, little is known concerning the nature and magnitude of the coupling in such compounds or the evolution of the magnetic properties in them.1,9,13 One major challenge in the chemistry and physics of actinide and lanthanide (f-ion) complexes is to understand the role that f-electrons play in magnetism in general and in exchange coupling in particular.9,19 This is in marked contrast with transition-metal magnetochemistry where a straightforward spin-only Hamiltonian approach can clarify magnetic behavior and quantify the exchange coupling of d-electrons. Exchange coupling in few actinide and lanthanide complexes has been analyzed quantitatively since a spin-only Hamiltonian is not applicable to systems with unquenched orbital angular momenta. This difficulty complicates efforts to explain the interesting and fundamentally important magnetic behavior of lanthanide and actinide complexes.1,9,19,20 © 2012 American Chemical Society

One of the most important and potential applications of actinide and lanthanide complexes is in the design of new molecules with special optical and magnetic properties; particularly, near-infrared (NIR) luminescence is of technological interest in telecommunications.21−26 Optical networks based on silica fibers use NIR radiation to send information because in this region silica has a high transparency. Control of NIR emission from lanthanide and actinide is a fundamentally important topic that is key to the continued development of next-generation optical fiber technologies. Another important application of these complexes is in the area of single-molecule magnets (SMMs). Some of these molecules possess a high-spin ground state for which spin−orbit coupling results in a zerofield splitting in a manner that creates the thermal relaxation barrier and gives rise to magnetic bistability at low temperature.27 The zero-field splitting (ZFS) is typically the leading term in the spin Hamiltonian for transition metal complexes with a total ground state spin S > 1/2. Its net effect is to introduce a splitting of the 2S + 1 Ms levels (which is exactly degenerate at the level of a Born−Oppenheimer Hamiltonian), even in the absence for an external magnetic field.28−38 Thus, Received: April 24, 2012 Revised: June 20, 2012 Published: June 21, 2012 7584

dx.doi.org/10.1021/jp3039576 | J. Phys. Chem. A 2012, 116, 7584−7592

The Journal of Physical Chemistry A

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optimized using the Amsterdam Density Functional (ADF) code,39 where the relativistic scalar and spin−orbit effects are incorporated by the zeroth-order relativistic approximation (ZORA Hamiltonian). The Perdew−Burke−Ernzerhof (PBE) generalized gradient approximation exchange-correlation functional was used with standard Slater type orbital basis set TZ2P for all atoms.40−42 Nucleus independent chemical shift (NICS) was obtained by calculating NMR shielding values with the gauge-including-atomic-orbital (GIAO) method using the generalized gradient approximation (GGA) OPBE functional, which was specially designed for the calculation of chemical shifts. 43−46 Time-dependent density functional theory (TDDFT) was employed to calculate excitation energies. We also used the GGA SAOP (statistical average of orbitals exchange correlation potential) functional that was specially designed for the calculation of optical properties.47−49 All ZFS calculations presented were carried out with the ORCA code package.50 The def2-TZVPP basis set of Schäfer et al. was used throughout.51 Tight convergence criteria was used in order to ensure that the results are well converged with respect to technical parameters, and the DFT calculations were realized with GGA PBE42 and hybrid B3LYP52,53 functionals. The spin orbit interaction was evaluated in two ways: first we only consider one-electron and Coulomb terms in a DFT-Veff (Veff).54 This is a very approximate method, and for that reason, in a second step, we employed the complete mean-field approximation. In this case, the calculation includes exchange via one-center exact integrals including the spin−other orbit interaction (SOMF).55 ZFS parameters were calculated into two approximations implemented in the ORCA code. These are coupled perturbed DFT33 and Pederson Khana approaches.37 The principal differences between these methods are the use of different coefficients in second-order perturbation equations.33 All the calculations with the ORCA code additionally used the ZORA Hamiltonian to include the scalar relativistic effects (a brief theoretical reference is presented in the Supporting Information).

an analysis and interpretation of the ZFS is imperative for the information content of the various physical methods that are sensitive to ZFS effects, such as electron paramagnetic resonance (EPR), magnetic susceptibility measurements, magnetic circular dichorism (MCD) and magnetic Mössbauer spectroscopy. There is renewed interest in ZFSs due to its importance in the field of molecular magnetism.28−30 The ultimate goal is to design SMMs for which is it known that a large axial ZFS together with high total ground state spin are essential to achieve the desired magnetic characteristics.30−38 The ZFS tensor contains essential information on spin states as well as on molecular and electronic structure of a system. It largely determines the tunneling barrier and thus the critical temperature of molecular magnetism and is therefore a central quantity in the field.27 Various models for the interpretation of the SO contributions to ZFS tensors are available.28−38 However, in the field of transition metal complexes, these rely largely on ligand-field theory, whereas the treatment of ZFS for organic triplet states or biradicals typically employs semiempirical molecular orbital models.28 The ZFS is a complicated quantity, and its quantitative treatment by quantum chemical methods is considered a true challenge. The calculation of ZFSs from first principles is still in its infancy, and the first ab initio results for molecular systems with state-of-the-art quantum chemical theory are only emerging.38 Our aim in the present work is to obtain electronic, optical, and magnetic properties in a systematic group of molecules that involves Ti and Zr transition metal with and actinide element in an analogue electronic state, d1. This kind of molecule when the interaction between two metals is supported by an aromatic bridge ligand has been intensely studied because it represents and is an important cornerstone in the design of new systems with special magnetic and optical properties.

2. COMPUTATIONAL DETAILS In this work we report a series of calculations that describe the structure and magnetic properties of sandwich compounds with general structure (C8H8)M(μ2−,η8C8H8)M(C8H8) where M = Ti, Zr and Th, and C8H8−2COT (Figure 1) and with total spin values S = 1 (triplet state). Additionally, we propose the possibility of heterobimetallic complexes when in the same structure appear the Th and one of two another elements (Ti or Zr). In all models presented here, we assumed that the three rings are planar, and only in the heterobimetallic did we consider the deformation in the central ring. All structures were

3. RESULTS AND DISCUSSION 3.1. Geometry and Electronic Structure. The principal objective here is to calculate the optical and magnetic properties in molecules containing the group IV of elements M = Ti, Zr, and actinide Th. For that reason we construct a series of model compounds (Figure 1) and optimize its geometries in a D2h (M2COT3) and C2v (MThCOT3) symmetries; these geometries are idealized compared with the crystallographic data available for some triple-decker sandwich structures (see, for instance, refs 56−64). The results of geometries optimization are presented in Table 1. In general, the metal−metal distance increases in the group, and the same result is obtained with other geometric parameters. In the case of mixing systems in C2v symmetry, the central ring is slightly deformed with a direct influence over metal−ring distances. These deformations are more important in TiThCOT3, and its values are presented in Table 1. To analyze the bonding in this kind of complexes and its influence over metal−metal communications and ZFS results, a series of calculations about electronic structure were done. The central ring has a crucial importance in the metal−metal interaction, and for that reason it was necessary to explore the electronic density in the region between the metal atoms to understand the electron delocalization in their structure. With this aim, the NICS values in the position shown in Figure 1

Figure 1. Model complexes. Ghost atoms indicate the position where the NICS values were calculated. 7585



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Table 1. Calculated Bond Lengths (Å) molecule

d(M−M)

d(M−COTint)a

d(M−COText)a

d(M-C(COTint))b

d(M-C(COText))b

Ti2COT3 Zr2COT3 Th2COT3 TiThCOT3

3.465 3.971 4.054 4.079

1.733 1.985 2.027 2.205, 1.875

1.617 1.715 2.023 2.037, 1.507

ZrThCOT3

4.731

2.835, 1.895

1.974, 1.782

2.534 2.727 2.772 2.719, 2.755 2.710, 2.564 2.736, 3,315

2.451 2.533 2.747 2.792 2.421 2.742

a

These values represent the distance between metal and ring centroid. bThese values represent the distance between metal and carbon atoms to central (int) and external rings (ext), respectively.

Table 2. NICS Values for M2COT3 Complexesa

a

point

z

NICSxx

1 2 3

0.0 0.5 1.0

−26.1 (−25.9) −33.6 (−33.4) −37.3 (−36.8)

1 2 3

0.0 0.5 1.0

−7.3 (−7.2) −7.3 (−7.3) 1.0 (0.7)

1 2 3

0.0 0.5 1.0

−25.4 (−25.0) −18.9 (−19.5) 40.4 (30.4)

NICSyy Ti2COT3 −26.4 (−26.2) −34.0 (−33.9) −37.7 (−37.1) Zr2COT3 −7.4 (−7.4) −7.4 (−7.4) 0.9 (0.6) Th2COT3 −27.2 (−27.2) −22.5 (−23.9) 26.8 (15.9)

NICSzz

NICSiso

−69.3 (−69.1) −78.7 (−78.4) −116.2 (−115.5)

−40.6 (−40.4) −48.8 (−48.6) −63.7 (−63.1)

−70.3 (−70.2) −79.8 (−79.6) −116.2 (−115.6)

−28.35 (−28.2) −31.5 (−31.4) −38.1 (−38.1)

−86.3 (−85.0) −100.0 (−98.2) −156.6 (−155.6)

−46.3 (−45.7) −47.1 (−47.2) −29.8 (−36.4)

Spin−orbit calculations appear between parentheses; z indicates the position of the point.

Figure 2. Tendency of NICS values related with the distance in Th2COT3. All values were determined over the principal axis (z) in points represented in Figure 1. (A) NICS values between central ring and metal center. (B) NICS values between metal and external ring.

system. In Th2COT3 and generally in actinocene compounds, the principal interaction that stabilizes the system involves a δ orbital configuration between the metal f ( f xyz and fz(x2−y2)) and d (dx2−y2 and dxy) orbitals with the π (pz symmetry adapted combinations) orbitals in the ring,65 as can be seen in Figure 3. These molecular orbitals have an axial symmetry, and, together with ring symmetry-adapted combinations in the presence of magnetic field, induce an electronic circulation around the z axis, and the diatropic currents appear. On the other hand, in the perpendicular direction, the contribution of the orbitals with a possibility of electronic circulation is low, and the result is paratropic circulation. In general, the isotropic value in all cases was negative, indicating a net diatropic current. Figure S1 in the Supporting Information section shows qualitative molecular orbital diagrams for Ti and Th complexes

were determined. It is possible to see these results in Table 2, where we report relativistic scalar ZORA and spin−orbit ZORA (a more complete Table with NICS values is given in the Supporting Information, Table S1). The NICS values show an important electron mobility in the region between two metals in all cases, particularly around the z axis, which indicate the presence of diatropic currents and therefore and delocalized structure. Figure 2 represents the NICS values tendency along a main axis of the Th2COT3. As can be seen in the region between the metal and the central ring, the NICSzz reduces its values in the direction to the metal, but the NICSxx and NICSyy values increase in the direction to the metal. This behavior indicates an important anisotropy in the electron mobility in this complex. These differences can be understood based on the molecular orbital structure for this 7586



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TiThCOT3, the NICS value near to Th atoms is positive too, indicating a particular concentration of electronic density in the central ring and its migration to external rings. In Figure 4 we depict the qualitative molecular orbital diagram in the valence region of this molecule. 3.2. Optical Properties. We have a special interest in the electronic transitions that involve the charge transfer between two metals and metal with central ring; because these kind of electronic transitions are responsible for metal−metal communication and are important for the magnetic behavior of these systems. For that reason, the TDDFT study presented here only include the transitions above 500 nm to the near-IR region. Also, in this study we could analyze the possible design of antenna chromophores based in transition metal complexes to sensitize the actinide center, i.e., Th in the present case. The calculated absorption spectra of the M2COT3 systems are presented in Figure S2 in the Supporting Information section. As can be seen, the longest wavelengths are 696.5 nm ( f = 2 × 10−9), 698.0 nm (f = 1.2 × 10−10) and 779.3 nm (f = 1.4 × 10−1) for Ti, Zr, and Th complexes, respectively (where f is the associated oscillator strength). For the Ti complex, the more intense transitions appear at 649.5 nm ( f = 5 × 10−4) with a d → d character and a ligand−metal charge transfer (LMCT) at 500 nm ( f = 4 × 10−3). In the case of Zr complex the more intense transitions appear below 500 nm with two important transitions over this value, the first at 512.1 nm (f = 3.1 * 10−3) with d → d character and the second at 641.8 nm (f = 4.6 * 10−3). The Th complex has the most interesting electronic transition because of the participation of f orbitals and the presence of transitions where d and f orbitals appear mixed. It is possible to see in Figure S2 that, in this case, all transition characterized over 500 nm have a metal−metal transfer character being the most important of the d → f transitions. Figure S1 shows the structure of the molecular orbitals involved in these electronic transitions. Another important transition in Th systems are the d(f) → f at 650.4 nm (f = 6 × 10−7) and d( f) → f transitions at 601.2 nm (f = 1.2 × 10−2) and 615.3 nm ( f = 1 × 10−2), respectively. The results in the case of MThCOT3 systems are presented in Figure 5. In these calculations we obtained very interesting results. In two cases appeared important transitions in the nearIR region of spectrum with important contribution to metal− metal electron transfer in the direction M → Th. For TiThCOT3 the principal transitions have a d(Ti) → d(Th) character and appear at 1649. Six nanometer ( f = 6 × 10−5), 1584.6 nm (f = 9 × 10−3) and 1028.2 nm (f = 4 × 10−2). The second type of transition have a d(Ti) → f(Th) and appear at 1584.6 nm (f = 9 × 10−3) and 678.5 nm (f = 3 × 10−2). Also other kind of transition between two metals appears, for instance, transition with d(Ti) → s(Th) character. In the second complex in the IR region appear three important transitions, the first is a charge transfer at 1356.7 nm from d(Th) orbitals to π orbitals in the central ring (f = 2.3 × 10−3); the remaining two transitions appear at 1109.8 and 1021.9 nm, respectively, and both have a d(Th) → d(Th) character but the transition at 1021.9 nm is more complicated because it also involve a little d(Ti) orbital character. Two other transitions appear at 708.3 nm (f = 1.3 × 10−3) and 546.7 nm (f = 3.6 × 10−3); in these cases both transition have MLCT character. As can be shown, substantial differences exist between the M2COT3 and MThCOT3 spectra, and the reason is the possibility of the latter molecules to form absorption bands between the transition metal and the actinide element. These

Figure 3. δ molecular orbitals for Th2COT3 and MThCOT3 complexes responsible for the stabilization in these systems. The atomic orbital contributions are presented, and the z axis contains the two metal centers.

where it is possible to see the principal differences between metal and rings orbital interactions. In both cases, the d orbital contributions are similar, but in the actinide case, the possibility of f orbitals participation modifies the interaction with rings in the valence region of molecule and modifies other properties of these systems, in particular their optical properties. This is the reason for which the heterobimetallic systems were modeled. The electronic structure of M2COT3 complexes has the needed characteristic to design bimetallic molecules in which the electronic transition and magnetic properties can be modulated. Table 3 shows the NICS values calculated in the region between the Th atom and the transition metal. The values in the coordinate’s origin are negative; this indicates that the deformation in the central ring does not produce an important change in the electron delocalization and corroborates the idea about spatial aromaticity in this kind of molecules.56 It is important to note that in the position near the transition metal center (0, 0, −1.5), the NICS value is positive, which indicates a displacement of the electronic density in the direction toward the central ring and the Th atom. For 7587



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Table 3. NICS Values for MThCOT3 Complexesa point

z

NICSxx

1 2 3 4 5 6 7

−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

199.0 (168.6) 1.427 (−8.6) −19.7 (−21.7) −26.5 (−26.9) −44.9 (−45.1) −85.5 (−84.5) 262.7 (264.6)

1 2 3 4 5 6 7

−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

163.9 −10.7 −21.1 −18.9 −17.4 −8.1 107.6

(163.6) (−10.7) (−21.2) (−18.7) (−17.6) (−8.0) (108.0)

NICSyy

NICSzz

TiThCOT3 172.5 (143.6) −15.5 (−21.6) −40.7 (−40.8) −54.0 (−53.5) −70.4 (−69.8) −88.8 (−87.0) 173.4 (190.4) ZrThCOT3 161.1 (160.9) −10.7 (−10.8) −21.3 (−21.3) −19.0 (−18.8) −17.5 (−17.5) −8.2 (−8.0) 107.7 (108.0)

−350.1 −138.2 −86.3 −68.9 −81.1 −132.1 −151.3

(−356.0) (−138.9) (−86.3) (−68.9) (−80.9) (−132.4) (−145.0)

−243.5 −120.2 −83.7 −73.0 −82.0 −117.5 −252.0

(−243.5) (−121.2) (−84.0) (−73.1) (−82.2) (−116.9) (−251.8)

NICSiso 7.1 (−14.6) −50.8 (−56.3) −48.9 (−49.6) −49.8 (−49.8) −65.5 (−65.2) −102.1 (−101.3) 94.9 (103.3) 27.2 −47.2 −42.2 −36.9 −39.0 −44.6 −12.2

(27.0) (−47.2) (−42.1) (−36.9) (−39.1) (−44.3) (−11.9)

a

Spin−orbit calculations appear between parentheses, and z indicates the position of the point. The 4 point is located on (0, 0, 0) coordinates in the central ring; negative values are in the direction toward the transition metal, and positive values are in the direction toward the Th atom.

Figure 4. Qualitative molecular orbital diagram for MThCOT3 systems. Only valence region and metal atomic orbital contributions are presented.

following the published work of Neese et al.28−36 In Table 4, we list the ZFS results of M2COT3 molecules. For the three systems shown in Table 4, we present also the D and D/E values, the SS contributions, spin−orbit coupling (SOC), and all transition contributions. The first systematic behavior is the reduction of the SS and the increase of the SO contributions. This is due to the unpaired electrons that are localized in the centers physically separated in the molecule (Table 5), and therefore the dipolar interaction responsible for SS reduces its value.31 On the other side, the SOC increases because in these systems the atomic number of the metal center increases and the relativistic effects begin to be more important. In this point, it is necessary to call attention to the fact that in this work all calculations of the SOC contribution were done at the second-order perturbation level (eqs 8−10 in the Supporting Information), and therefore the real picture in which the spin−orbit effect needed to be treated at the four-

kind of electronic transitions are important for understanding the mechanism to sensitize the emission in actinide systems with a transition metal acting as the antenna. All the molecules studied here display an important transition band in the visible region of the electromagnetic spectrum, and this is the one useful for designing molecules with desired absorption and emission properties. 3.3. ZFS Results. With all the electronic parameters described before, it is possible to complete our study with an evaluation of the performance of DFT for the calculation of ZFS in this kind of organometallic compound. With this purpose, we used two methodologies to determine ZFS implemented in the ORCA code.50 Unfortunately, the experimental values for these types of molecules are not available yet; here we carried out a systematic evaluation of electronic effects over ZFS parameters to test the available methodologies. All calculations presented here were done 7588



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Table 4. ZFS Parameters (in cm−1) Calculated for M2COT3 with Two Different Methodologies (CP = Coupled Perturbed, PK= Pederson−Khanna) in the DFT Approach Ti2COT3 Veff D E/D SS SOC αα ββ αβ βα

SOMF

CP

PK

CP

PK

2.050 0.000 0.719 1.33 1.923 0.073 −0.634 −0.032

2.030 0.000 0.719 1.584 1.922 0.073 −0.317 −0.095 Zr2COT3

1.080 0.000 0.622 0.455 1.231 0.271 −0.955 −0.092

1.370 0.000 0.622 0.749 1.231 0.271 −0.477 −0.276

Veff CP D E/D SS SOC αα ββ αβ βα

−11.280 0.000 −0.044 −11.236 21.091 12.063 −40.368 −4.022

SOMF PK 0.866 0.000 −0.044 0.904 21.091 12.063 −20.184 −12.066 Th2COT3

CP

PK

−10.650 0.000 −0.041 −10.611 23.942 16.791 −45.586 −5.758

0.620 0.000 −0.041 0.665 23.944 16.793 −22.795 −17.277

Veff D E/D SS SOC αα ββ αβ βα

Figure 5. Absorption spectra calculated for MThCOT3 systems. The principal transitions over 500 nm to the near-IR region are presented.

component Dirac theory is not considered here. For that reason, in an attempt to describe the spin−orbit effects, we recalculated all values at the SOMF level where the spin−other orbit term is taken into account. In all cases, the D/E value was zero or near zero in the Th2COT3 with an exception to CP result in this last molecule, when the value increase to 0.23. For Ti2COT3, the D values are in all calculations around to 2.00 cm−1 with an SS and SOC contribution in the same order. The results for Zr2COT3 are very different; here two methods give different values, and even the CP method produces a negative ZFS; the PK method gives a value below that of a similar calculation in a Ti complex. In the Th system, all methods produced negative values with a very small SS contribution. If we compare the PK results in three cases, the tendency is a reduction to ZFS produced basically by a negative contribution to SOC from spin−flip transitions (α → β) in the Zr case and α → α transitions in Th complex. In order to complete the calculation, we repeat the CP method for the Ti and Zr complexes using the B3LYP functional (Table 6). The inclusion of exchange contribution produces a reduction of the Ti ZFS value from 2.05 (PBE) to 0.95 (B3LYP), and the SS contribution in this case is more important than the D result. In a heavier Zr atom, the SOC contribution is bigger than the SS part and is positive with respect to the PBE calculation, which results in a positive ZFS. These modifications in the SOC contribution were the result of compensation between transition contributions with respect to PBE calculations; in the Ti case, the α → α transitions continue

SOMF

CP

PK

CP

PK

−36.018 0.206 5.0 × 10−5 −36.018 −236.966 10.909 172.748 17.291

−87.811 0.026 5.0 × 10−5 −87.81 −236.967 10.909 86.375 51.872

−52.160 0.032 5.8 × 10−5 −52.161 −152.734 39.201 54.868 7.504

−64.590 0.005 5.8 × 10−5 −64.588 −153.262 39.677 36.959 22.038

being more important, and for the Zr complex, now the most important contributions come from α → α and β → β transitions. The ZFS parameters are so related to the electronic structure, in particular with ligand-field models; but in general the best procedure for the connection between them is not evident.32 Here an attempt was made to obtain some insight into the relation between spin−density and metal−metal communications and its influence over ZFS. In Tables 5 and 6, the spin density over metal center and atomic orbitals contribution are presented; as can be seen for M2COT3 systems, the spin density values over metal reduce in the order Ti > Zr > Th, and in the three cases the unpaired electrons are localized in d orbitals, while for Th case they are also in f orbitals. In Figure 6 we show the spin density maps of these molecules; in the first column only a positive spin density is presented. Here is possible to see that when the metal changes, the spin density becomes more diffuse in the series and therefore the electron delocalization and interaction with the central ring increases significantly. In the case of Th systems, the participation of f orbitals produces an important communication between metal−ring−metal. This delocalization allows us to say that the exchange stabilization of the 7589



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Table 5. Spin Density over Metals and Atomic Orbital Contribution Spin density over metal and orbital contribution Veff

SOMF Ti2COT3

Mulliken Löedwin

1.91 1.88

d = 1.84 d = 1.84

Mulliken Löedwin

1.19 1.00

d = 1.07 d = 0.99

Mulliken Löedwin

0.74 0.81

d = 0.33 d = 0.41

1.78 1.89

d = 1.73 d = 1.77

1.19 1.00

d = 1.10 d = 0.99

0.83 0.64

d = 0.38 d = 0.27

1.42 (Ti) 0.41 (Th) 1.24 (Ti) 0.39 (Th)

d = 1.19 d = 0.10 f = 0.41 d = 1.21 d = 0.04 f = 0.34

0.88 (Zr) 0.39 (Th) 0.71 (Zr) 0.37 (Th)

d = 0.74 d = 0.15 f = 0.18 d = 0.65 d = 0.14 f = 0.19

Zr2COT3

Th2COT3 f = 0.39 f = 0.35

f = 0.35 f = 0.35

TiThCOT3 Mulliken Löedwin ZrThCOT3 Mulliken Löedwin

Table 6. ZFS (in cm−1) Results Employing the B3LYP and CP Methodsa B3LYP CP

Ti2COT3

Zr2COT3

D E/D SS SOC αα ββ αβ βα Mulliken

0.95 0.00 0.97 −0.02 −1.54 0.82 0.56 0.14 2.02 d = 1.94 1.93 d = 1.88

1.40 0.00 −0.04 1.43 79.41 71.99 −140.67 −9.30 1.05 d = 0.98 0.88 d = 0.87

Löewdin a

Spin density over metal and atomic orbitals contribution are included.

occupied spin-up orbitals is so large that they fall energetically in the region of the central ring orbitals and mix strongly with them. An analysis in terms of metal orbitals contribution is impossible, but of course the metal character is still contained in the occupied space (see above), and it is possible to determine its contribution to a global property. It is well-known that, to second-order in perturbation theory, the spin−orbit introduces some angular momentum into the ground state (assumed orbitally nondegenerate), and this mix between metal orbitals with degenerate or quasidegenerate local orbitals in the central ring affects directly the SOC and its influence over ZFS as seen above. On the other hand, this electronic delocalization was explained above based on the NICS calculations, and this spin density analysis corroborates our previous results.

Figure 6. Spin density maps in M2COT3 complexes. The first column presents only positive density (due to unpaired electrons), and the second column presents both sign maps.

and the absorption spectrum in homometallic and heterobimetallic molecules. NICS calculations show an important electron mobility in the region between the metals and the central ring, which is more important in the order Th > Zr > Ti. Also, it is possible to obtain this conclusion by analyzing the spin density over the metals in all cases. This electron delocalization allows the strong mix between metal and ring orbitals with a consequent effect over the SOC term in the ZFS calculation. We think that these kinds of model systems are important to understand the electronic structure and its influence over other properties in molecules with potential applications as molecular magnets or NIR sensitizers in optical applications.

2. CONCLUSIONS This work demonstrates the importance of electron delocalization over optical and magnetic properties in inverted-sandwich complexes and the capability of relativistic density functional approach for the calculation of different contributions to ZFS 7590



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ASSOCIATED CONTENT

S Supporting Information *

Information about energy levels diagram of the M2COT3 complexes and its calculated absorption spectrum, NIC values in all positions shown in Figure 1 and a brief discussion about ZFS theory implemented in Orca code is presented. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

The authors acknowledge funding from Grants FONDECYT 1110758, UNAB-DI-05-11/I, and UNAB-DI-17-11/R and an MECESUP fellowship.

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