Aromaticity, Optical Properties and Zero Field Splitting of Homo-and Hetero-bimetallic (C8H8)M(μ2−,η8C8H8)M(C8H8) where M = Ti,Zr, Th ComplexesDayan Paez-Hernandez* and Ramiro Arratia-Perez

Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Republica 275, Santiago 8370146,Chile

*S Supporting Information

ABSTRACT: This work presents a relativistic calculation of electrondelocalization, optical properties, and zero field splitting in a group ofmolecules with the structure (C8H8)M(μ2−,η8C8H8)M(C8H8),where M = Ti, Zr and Th. Additionally we also studied theheterobimetallic combinations (Ti−Th and Zr−Th). The molecularproperties are discussed based on their electronic structure and theinfluence of the electron mobility in metal−metal communication.Nucleus independent chemical shift (NICS) was determined via thegauge-including-atomic-orbital (GIAO) method with the OPBEfunctional. The time-dependent density functional theory (TDDFT)was employed to calculate excitation energies, and the electronictransitions over 500 nm are presented with the objective to analyze thetransition metal role as an antenna effect in the absorption band in thenear-IR region. Finally the ZFS was calculated using Pederson−Khana and coupled perturbed DFT approaches implemented inthe ORCA code. The contributions to spin−spin coupling (SS) and spin−orbit coupling (SOC) were analyzed, and the spin-density over the metal centers is discussed employing our scheme of metal−metal communication. Our aim is to determine theinfluence of the electronic structure over the optical and magnetic properties in a group of model compounds to understand thetransition metals effect over these properties.

1. INTRODUCTIONMolecular coordination compounds of lanthanide and actinideions attract a growing interest in material science due to theirluminescent and magnetic properties.1,2 The rather large andanisotropic magnetic moments of most of the lanthanide (III)and actinide ions make these ions appealing building blocks inthe molecular approach of magnetic materials.1−5 Numerouscompounds containing lanthanide or actinides ions andparamagnetic species such as transition metal ions or organicradicals have been described;1−18 however, little is knownconcerning the nature and magnitude of the coupling in suchcompounds or the evolution of the magnetic properties inthem.1,9,13 One major challenge in the chemistry and physics ofactinide and lanthanide (f-ion) complexes is to understand therole that f-electrons play in magnetism in general and inexchange coupling in particular.9,19 This is in marked contrastwith transition-metal magnetochemistry where a straightfor-ward spin-only Hamiltonian approach can clarify magneticbehavior and quantify the exchange coupling of d-electrons.Exchange coupling in few actinide and lanthanide complexeshas been analyzed quantitatively since a spin-only Hamiltonianis not applicable to systems with unquenched orbital angularmomenta. This difficulty complicates efforts to explain theinteresting and fundamentally important magnetic behavior oflanthanide and actinide complexes.1,9,19,20

One of the most important and potential applications ofactinide and lanthanide complexes is in the design of newmolecules with special optical and magnetic properties;particularly, near-infrared (NIR) luminescence is of techno-logical interest in telecommunications.21−26 Optical networksbased on silica fibers use NIR radiation to send informationbecause in this region silica has a high transparency. Control ofNIR emission from lanthanide and actinide is a fundamentallyimportant topic that is key to the continued development ofnext-generation optical fiber technologies. Another importantapplication of these complexes is in the area of single-moleculemagnets (SMMs). Some of these molecules possess a high-spinground state for which spin−orbit coupling results in a zero-field splitting in a manner that creates the thermal relaxationbarrier and gives rise to magnetic bistability at low temper-ature.27 The zero-field splitting (ZFS) is typically the leadingterm in the spin Hamiltonian for transition metal complexeswith a total ground state spin S > 1/2. Its net effect is tointroduce a splitting of the 2S + 1 Ms levels (which is exactlydegenerate at the level of a Born−Oppenheimer Hamiltonian),even in the absence for an external magnetic field.28−38 Thus,

Received: April 24, 2012Revised: June 20, 2012Published: June 21, 2012

Article

pubs.acs.org/JPCA

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

an analysis and interpretation of the ZFS is imperative for theinformation content of the various physical methods that aresensitive to ZFS effects, such as electron paramagneticresonance (EPR), magnetic susceptibility measurements,magnetic circular dichorism (MCD) and magnetic Mossbauerspectroscopy. There is renewed interest in ZFSs due to itsimportance in the field of molecular magnetism.28−30 Theultimate goal is to design SMMs for which is it known that alarge axial ZFS together with high total ground state spin areessential to achieve the desired magnetic characteristics.30−38

The ZFS tensor contains essential information on spin states aswell as on molecular and electronic structure of a system. Itlargely determines the tunneling barrier and thus the criticaltemperature of molecular magnetism and is therefore a centralquantity in the field.27 Various models for the interpretation ofthe SO contributions to ZFS tensors are available.28−38

However, in the field of transition metal complexes, theserely largely on ligand-field theory, whereas the treatment of ZFSfor organic triplet states or biradicals typically employssemiempirical molecular orbital models.28 The ZFS is acomplicated quantity, and its quantitative treatment byquantum chemical methods is considered a true challenge.The calculation of ZFSs from first principles is still in itsinfancy, and the first ab initio results for molecular systems withstate-of-the-art quantum chemical theory are only emerging.38

Our aim in the present work is to obtain electronic, optical, andmagnetic properties in a systematic group of molecules thatinvolves Ti and Zr transition metal with and actinide element inan analogue electronic state, d1. This kind of molecule when theinteraction between two metals is supported by an aromaticbridge ligand has been intensely studied because it representsand is an important cornerstone in the design of new systemswith special magnetic and optical properties.

2. COMPUTATIONAL DETAILSIn this work we report a series of calculations that describe thestructure and magnetic properties of sandwich compounds withgeneral structure (C8H8)M(μ2−,η8C8H8)M(C8H8) where M= Ti, Zr and Th, and C8H8

−2COT (Figure 1) and with totalspin values S = 1 (triplet state). Additionally, we propose thepossibility of heterobimetallic complexes when in the samestructure appear the Th and one of two another elements (Tior Zr). In all models presented here, we assumed that the threerings are planar, and only in the heterobimetallic did weconsider the deformation in the central ring. All structures were

optimized using the Amsterdam Density Functional (ADF)code,39 where the relativistic scalar and spin−orbit effects areincorporated by the zeroth-order relativistic approximation(ZORA Hamiltonian). The Perdew−Burke−Ernzerhof (PBE)generalized gradient approximation exchange-correlation func-tional was used with standard Slater type orbital basis set TZ2Pfor all atoms.40−42 Nucleus independent chemical shift (NICS)was obtained by calculating NMR shielding values with thegauge-including-atomic-orbital (GIAO) method using thegeneralized gradient approximation (GGA) OPBE functional,which was specially designed for the calculation of chemicalshifts.43−46 Time-dependent density functional theory(TDDFT) was employed to calculate excitation energies. Wealso used the GGA SAOP (statistical average of orbitalsexchange correlation potential) functional that was speciallydesigned for the calculation of optical properties.47−49

All ZFS calculations presented were carried out with theORCA code package.50 The def2-TZVPP basis set of Schafer etal. was used throughout.51 Tight convergence criteria was usedin order to ensure that the results are well converged withrespect to technical parameters, and the DFT calculations wererealized with GGA PBE42 and hybrid B3LYP52,53 functionals.The spin orbit interaction was evaluated in two ways: first weonly 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-fieldapproximation. In this case, the calculation includes exchangevia one-center exact integrals including the spin−other orbitinteraction (SOMF).55 ZFS parameters were calculated intotwo approximations implemented in the ORCA code. Theseare coupled perturbed DFT33 and Pederson Khana ap-proaches.37 The principal differences between these methodsare the use of different coefficients in second-order perturbationequations.33 All the calculations with the ORCA codeadditionally used the ZORA Hamiltonian to include the scalarrelativistic effects (a brief theoretical reference is presented inthe Supporting Information).

3. RESULTS AND DISCUSSION3.1. Geometry and Electronic Structure. The principal

objective here is to calculate the optical and magneticproperties in molecules containing the group IV of elementsM = Ti, Zr, and actinide Th. For that reason we construct aseries of model compounds (Figure 1) and optimize itsgeometries in a D2h (M2COT3) and C2v (MThCOT3)symmetries; these geometries are idealized compared with thecrystallographic data available for some triple-decker sandwichstructures (see, for instance, refs 56−64). The results ofgeometries optimization are presented in Table 1. In general,the metal−metal distance increases in the group, and the sameresult is obtained with other geometric parameters. In the caseof mixing systems in C2v symmetry, the central ring is slightlydeformed with a direct influence over metal−ring distances.These deformations are more important in TiThCOT3, and itsvalues are presented in Table 1.To analyze the bonding in this kind of complexes and its

influence over metal−metal communications and ZFS results, aseries of calculations about electronic structure were done. Thecentral ring has a crucial importance in the metal−metalinteraction, and for that reason it was necessary to explore theelectronic density in the region between the metal atoms tounderstand the electron delocalization in their structure. Withthis aim, the NICS values in the position shown in Figure 1

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

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp3039576 | J. Phys. Chem. A 2012, 116, 7584−75927585

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 theSupporting Information, Table S1).The NICS values show an important electron mobility in the

region between two metals in all cases, particularly around the zaxis, which indicate the presence of diatropic currents andtherefore and delocalized structure. Figure 2 represents theNICS values tendency along a main axis of the Th2COT3. Ascan be seen in the region between the metal and the centralring, the NICSzz reduces its values in the direction to the metal,but the NICSxx and NICSyy values increase in the direction tothe metal. This behavior indicates an important anisotropy inthe electron mobility in this complex. These differences can beunderstood based on the molecular orbital structure for this

system. In Th2COT3 and generally in actinocene compounds,the principal interaction that stabilizes the system involves a δorbital configuration between the metal f ( f xyz and fz(x2−y2)) andd (dx2−y2 and dxy) orbitals with the π (pz symmetry adaptedcombinations) 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 thepresence of magnetic field, induce an electronic circulationaround the z axis, and the diatropic currents appear. On theother hand, in the perpendicular direction, the contribution ofthe orbitals with a possibility of electronic circulation is low,and the result is paratropic circulation. In general, the isotropicvalue 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

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 3.465 1.733 1.617 2.534 2.451Zr2COT3 3.971 1.985 1.715 2.727 2.533Th2COT3 4.054 2.027 2.023 2.772 2.747TiThCOT3 4.079 2.205, 1.875 2.037, 1.507 2.719, 2.755 2.792

2.710, 2.564 2.421ZrThCOT3 4.731 2.835, 1.895 1.974, 1.782 2.736, 3,315 2.742

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

Table 2. NICS Values for M2COT3 Complexesa

point z NICSxx NICSyy NICSzz NICSiso

Ti2COT3

1 0.0 −26.1 (−25.9) −26.4 (−26.2) −69.3 (−69.1) −40.6 (−40.4)2 0.5 −33.6 (−33.4) −34.0 (−33.9) −78.7 (−78.4) −48.8 (−48.6)3 1.0 −37.3 (−36.8) −37.7 (−37.1) −116.2 (−115.5) −63.7 (−63.1)

Zr2COT3

1 0.0 −7.3 (−7.2) −7.4 (−7.4) −70.3 (−70.2) −28.35 (−28.2)2 0.5 −7.3 (−7.3) −7.4 (−7.4) −79.8 (−79.6) −31.5 (−31.4)3 1.0 1.0 (0.7) 0.9 (0.6) −116.2 (−115.6) −38.1 (−38.1)

Th2COT3

1 0.0 −25.4 (−25.0) −27.2 (−27.2) −86.3 (−85.0) −46.3 (−45.7)2 0.5 −18.9 (−19.5) −22.5 (−23.9) −100.0 (−98.2) −47.1 (−47.2)3 1.0 40.4 (30.4) 26.8 (15.9) −156.6 (−155.6) −29.8 (−36.4)

aSpin−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 pointsrepresented in Figure 1. (A) NICS values between central ring and metal center. (B) NICS values between metal and external ring.

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp3039576 | J. Phys. Chem. A 2012, 116, 7584−75927586

where it is possible to see the principal differences betweenmetal and rings orbital interactions. In both cases, the d orbitalcontributions are similar, but in the actinide case, the possibilityof f orbitals participation modifies the interaction with rings inthe valence region of molecule and modifies other properties ofthese systems, in particular their optical properties. This is thereason for which the heterobimetallic systems were modeled.The electronic structure of M2COT3 complexes has the neededcharacteristic to design bimetallic molecules in which theelectronic transition and magnetic properties can be modulated.Table 3 shows the NICS values calculated in the regionbetween 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 notproduce an important change in the electron delocalization andcorroborates the idea about spatial aromaticity in this kind ofmolecules.56 It is important to note that in the position near thetransition metal center (0, 0, −1.5), the NICS value is positive,which indicates a displacement of the electronic density in thedirection toward the central ring and the Th atom. For

TiThCOT3, the NICS value near to Th atoms is positive too,indicating a particular concentration of electronic density in thecentral ring and its migration to external rings. In Figure 4 wedepict the qualitative molecular orbital diagram in the valenceregion of this molecule.

3.2. Optical Properties. We have a special interest in theelectronic transitions that involve the charge transfer betweentwo metals and metal with central ring; because these kind ofelectronic transitions are responsible for metal−metal commu-nication and are important for the magnetic behavior of thesesystems. For that reason, the TDDFT study presented hereonly include the transitions above 500 nm to the near-IRregion. Also, in this study we could analyze the possible designof antenna chromophores based in transition metal complexesto sensitize the actinide center, i.e., Th in the present case. Thecalculated absorption spectra of the M2COT3 systems arepresented 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 theassociated oscillator strength). For the Ti complex, the moreintense transitions appear at 649.5 nm ( f = 5 × 10−4) with a d→ d character and a ligand−metal charge transfer (LMCT) at500 nm ( f = 4 × 10−3). In the case of Zr complex the moreintense transitions appear below 500 nm with two importanttransitions 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 electronictransition because of the participation of f orbitals and thepresence of transitions where d and f orbitals appear mixed. It ispossible to see in Figure S2 that, in this case, all transitioncharacterized over 500 nm have a metal−metal transfercharacter being the most important of the d → f transitions.Figure S1 shows the structure of the molecular orbitals involvedin these electronic transitions. Another important transition inTh systems are the d( f) → f at 650.4 nm ( f = 6 × 10−7) andd( 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 interestingresults. In two cases appeared important transitions in the near-IR region of spectrum with important contribution to metal−metal electron transfer in the direction M → Th. ForTiThCOT3 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). Thesecond type of transition have a d(Ti) → f(Th) and appear at1584.6 nm ( f = 9 × 10−3) and 678.5 nm ( f = 3 × 10−2). Alsoother kind of transition between two metals appears, forinstance, transition with d(Ti) → s(Th) character. In thesecond complex in the IR region appear three importanttransitions, the first is a charge transfer at 1356.7 nm fromd(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 thetransition at 1021.9 nm is more complicated because it alsoinvolve a little d(Ti) orbital character. Two other transitionsappear 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 thepossibility of the latter molecules to form absorption bandsbetween the transition metal and the actinide element. These

Figure 3. δ molecular orbitals for Th2COT3 and MThCOT3complexes responsible for the stabilization in these systems. Theatomic orbital contributions are presented, and the z axis contains thetwo metal centers.

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp3039576 | J. Phys. Chem. A 2012, 116, 7584−75927587

kind of electronic transitions are important for understandingthe mechanism to sensitize the emission in actinide systemswith a transition metal acting as the antenna. All the moleculesstudied here display an important transition band in the visibleregion of the electromagnetic spectrum, and this is the oneuseful for designing molecules with desired absorption andemission properties.3.3. ZFS Results. With all the electronic parameters

described before, it is possible to complete our study with anevaluation of the performance of DFT for the calculation ofZFS in this kind of organometallic compound. With thispurpose, we used two methodologies to determine ZFSimplemented in the ORCA code.50 Unfortunately, theexperimental values for these types of molecules are notavailable yet; here we carried out a systematic evaluation ofelectronic effects over ZFS parameters to test the availablemethodologies. All calculations presented here were done

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 systematicbehavior is the reduction of the SS and the increase of the SOcontributions. This is due to the unpaired electrons that arelocalized in the centers physically separated in the molecule(Table 5), and therefore the dipolar interaction responsible forSS reduces its value.31 On the other side, the SOC increasesbecause in these systems the atomic number of the metal centerincreases and the relativistic effects begin to be more important.In this point, it is necessary to call attention to the fact that inthis work all calculations of the SOC contribution were done atthe second-order perturbation level (eqs 8−10 in theSupporting Information), and therefore the real picture inwhich the spin−orbit effect needed to be treated at the four-

Table 3. NICS Values for MThCOT3 Complexesa

point z NICSxx NICSyy NICSzz NICSiso

TiThCOT3

1 −1.5 199.0 (168.6) 172.5 (143.6) −350.1 (−356.0) 7.1 (−14.6)2 −1.0 1.427 (−8.6) −15.5 (−21.6) −138.2 (−138.9) −50.8 (−56.3)3 −0.5 −19.7 (−21.7) −40.7 (−40.8) −86.3 (−86.3) −48.9 (−49.6)4 0.0 −26.5 (−26.9) −54.0 (−53.5) −68.9 (−68.9) −49.8 (−49.8)5 0.5 −44.9 (−45.1) −70.4 (−69.8) −81.1 (−80.9) −65.5 (−65.2)6 1.0 −85.5 (−84.5) −88.8 (−87.0) −132.1 (−132.4) −102.1 (−101.3)7 1.5 262.7 (264.6) 173.4 (190.4) −151.3 (−145.0) 94.9 (103.3)

ZrThCOT3

1 −1.5 163.9 (163.6) 161.1 (160.9) −243.5 (−243.5) 27.2 (27.0)2 −1.0 −10.7 (−10.7) −10.7 (−10.8) −120.2 (−121.2) −47.2 (−47.2)3 −0.5 −21.1 (−21.2) −21.3 (−21.3) −83.7 (−84.0) −42.2 (−42.1)4 0.0 −18.9 (−18.7) −19.0 (−18.8) −73.0 (−73.1) −36.9 (−36.9)5 0.5 −17.4 (−17.6) −17.5 (−17.5) −82.0 (−82.2) −39.0 (−39.1)6 1.0 −8.1 (−8.0) −8.2 (−8.0) −117.5 (−116.9) −44.6 (−44.3)7 1.5 107.6 (108.0) 107.7 (108.0) −252.0 (−251.8) −12.2 (−11.9)

aSpin−orbit calculations appear between parentheses, and z indicates the position of the point. The 4 point is located on (0, 0, 0) coordinates in thecentral 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.

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp3039576 | J. Phys. Chem. A 2012, 116, 7584−75927588

component Dirac theory is not considered here. For thatreason, in an attempt to describe the spin−orbit effects, werecalculated all values at the SOMF level where the spin−otherorbit 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 arein all calculations around to 2.00 cm−1 with an SS and SOCcontribution in the same order. The results for Zr2COT3 arevery different; here two methods give different values, and eventhe CP method produces a negative ZFS; the PK method givesa value below that of a similar calculation in a Ti complex. Inthe Th system, all methods produced negative values with avery small SS contribution. If we compare the PK results inthree cases, the tendency is a reduction to ZFS producedbasically by a negative contribution to SOC from spin−fliptransitions (α → β) in the Zr case and α → α transitions in Thcomplex. In order to complete the calculation, we repeat theCP method for the Ti and Zr complexes using the B3LYPfunctional (Table 6). The inclusion of exchange contributionproduces a reduction of the Ti ZFS value from 2.05 (PBE) to0.95 (B3LYP), and the SS contribution in this case is moreimportant than the D result. In a heavier Zr atom, the SOCcontribution is bigger than the SS part and is positive withrespect to the PBE calculation, which results in a positive ZFS.These modifications in the SOC contribution were the result ofcompensation between transition contributions with respect toPBE calculations; in the Ti case, the α→ α transitions continue

being more important, and for the Zr complex, now the mostimportant contributions come from α → α and β → βtransitions.The ZFS parameters are so related to the electronic

structure, in particular with ligand-field models; but in generalthe best procedure for the connection between them is notevident.32 Here an attempt was made to obtain some insightinto the relation between spin−density and metal−metalcommunications and its influence over ZFS. In Tables 5 and6, the spin density over metal center and atomic orbitalscontribution are presented; as can be seen for M2COT3systems, the spin density values over metal reduce in theorder Ti > Zr > Th, and in the three cases the unpairedelectrons are localized in d orbitals, while for Th case they arealso in f orbitals. In Figure 6 we show the spin density maps ofthese molecules; in the first column only a positive spin densityis presented. Here is possible to see that when the metalchanges, the spin density becomes more diffuse in the seriesand therefore the electron delocalization and interaction withthe central ring increases significantly. In the case of Thsystems, the participation of f orbitals produces an importantcommunication between metal−ring−metal. This delocaliza-tion allows us to say that the exchange stabilization of the

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

Table 4. ZFS Parameters (in cm−1) Calculated for M2COT3with Two Different Methodologies (CP = CoupledPerturbed, PK= Pederson−Khanna) in the DFT Approach

Ti2COT3

Veff SOMF

CP PK CP PK

D 2.050 2.030 1.080 1.370E/D 0.000 0.000 0.000 0.000SS 0.719 0.719 0.622 0.622SOC 1.33 1.584 0.455 0.749αα 1.923 1.922 1.231 1.231ββ 0.073 0.073 0.271 0.271αβ −0.634 −0.317 −0.955 −0.477βα −0.032 −0.095 −0.092 −0.276

Zr2COT3

Veff SOMF

CP PK CP PK

D −11.280 0.866 −10.650 0.620E/D 0.000 0.000 0.000 0.000SS −0.044 −0.044 −0.041 −0.041SOC −11.236 0.904 −10.611 0.665αα 21.091 21.091 23.942 23.944ββ 12.063 12.063 16.791 16.793αβ −40.368 −20.184 −45.586 −22.795βα −4.022 −12.066 −5.758 −17.277

Th2COT3

Veff SOMF

CP PK CP PK

D −36.018 −87.811 −52.160 −64.590E/D 0.206 0.026 0.032 0.005SS 5.0 × 10−5 5.0 × 10−5 5.8 × 10−5 5.8 × 10−5

SOC −36.018 −87.81 −52.161 −64.588αα −236.966 −236.967 −152.734 −153.262ββ 10.909 10.909 39.201 39.677αβ 172.748 86.375 54.868 36.959βα 17.291 51.872 7.504 22.038

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp3039576 | J. Phys. Chem. A 2012, 116, 7584−75927589

occupied spin-up orbitals is so large that they fall energeticallyin the region of the central ring orbitals and mix strongly withthem. An analysis in terms of metal orbitals contribution isimpossible, but of course the metal character is still containedin the occupied space (see above), and it is possible todetermine its contribution to a global property. It is well-knownthat, to second-order in perturbation theory, the spin−orbitintroduces some angular momentum into the ground state(assumed orbitally nondegenerate), and this mix between metalorbitals with degenerate or quasidegenerate local orbitals in thecentral ring affects directly the SOC and its influence over ZFSas seen above. On the other hand, this electronic delocalizationwas explained above based on the NICS calculations, and thisspin density analysis corroborates our previous results.

2. CONCLUSIONSThis work demonstrates the importance of electron delocaliza-tion over optical and magnetic properties in inverted-sandwichcomplexes and the capability of relativistic density functionalapproach for the calculation of different contributions to ZFS

and the absorption spectrum in homometallic and hetero-bimetallic molecules. NICS calculations show an importantelectron mobility in the region between the metals and thecentral ring, which is more important in the order Th > Zr > Ti.Also, it is possible to obtain this conclusion by analyzing thespin density over the metals in all cases. This electrondelocalization allows the strong mix between metal and ringorbitals with a consequent effect over the SOC term in the ZFScalculation. We think that these kinds of model systems areimportant to understand the electronic structure and itsinfluence over other properties in molecules with potentialapplications as molecular magnets or NIR sensitizers in opticalapplications.

Table 5. Spin Density over Metals and Atomic Orbital Contribution

Spin density over metal and orbital contribution

Veff SOMF

Ti2COT3

Mulliken 1.91 d = 1.84 1.78 d = 1.73Loedwin 1.88 d = 1.84 1.89 d = 1.77

Zr2COT3

Mulliken 1.19 d = 1.07 1.19 d = 1.10Loedwin 1.00 d = 0.99 1.00 d = 0.99

Th2COT3

Mulliken 0.74 d = 0.33 f = 0.39 0.83 d = 0.38 f = 0.35Loedwin 0.81 d = 0.41 f = 0.35 0.64 d = 0.27 f = 0.35

TiThCOT3

Mulliken 1.42 (Ti) d = 1.190.41 (Th) d = 0.10 f = 0.41

Loedwin 1.24 (Ti) d = 1.210.39 (Th) d = 0.04 f = 0.34

ZrThCOT3

Mulliken 0.88 (Zr) d = 0.740.39 (Th) d = 0.15 f = 0.18

Loedwin 0.71 (Zr) d = 0.650.37 (Th) d = 0.14 f = 0.19

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

B3LYP

CP Ti2COT3 Zr2COT3

D 0.95 1.40E/D 0.00 0.00SS 0.97 −0.04SOC −0.02 1.43αα −1.54 79.41ββ 0.82 71.99αβ 0.56 −140.67βα 0.14 −9.30Mulliken 2.02 1.05

d = 1.94 d = 0.98Loewdin 1.93 0.88

d = 1.88 d = 0.87aSpin density over metal and atomic orbitals contribution are included.

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

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp3039576 | J. Phys. Chem. A 2012, 116, 7584−75927590

■ ASSOCIATED CONTENT

*S Supporting InformationInformation about energy levels diagram of the M2COT3complexes and its calculated absorption spectrum, NIC valuesin all positions shown in Figure 1 and a brief discussion aboutZFS theory implemented in Orca code is presented. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: d.paezhernandez@yahoo.es.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The authors acknowledge funding from Grants FONDECYT1110758, UNAB-DI-05-11/I, and UNAB-DI-17-11/R and anMECESUP fellowship.

■ REFERENCES(1) Kahn, M. L.; Sutter, J. P; Golhen, S.; Guionneau, P.; Ouahab, L.;Kahn, O.; Chasseau, D. J. Am. Chem. Soc. 2000, 122, 3413−3421.(2) Archer, R. D.; Chen, H.; Thompson, L. C.; Ziessel, R. Inorg.Chem. 1998, 37, 2089−2095.(3) Prodi, L.; Pivari, S.; Bolletta, F.; Hissler, M.; Ziessel, R. Eur. J.Inorg. Chem. 1998, 1959−1965.(4) Sanada, T.; Suzuki, T.; Yoshida, T.; Kaiszaki, S. Inorg. Chem.1998, 37, 4712−4717.(5) Kahn, M. L.; Verelst, M.; Lecante, P.; Mathonniere, C.; Kahn, O.Eur. J. Inorg. Chem. 1999, 527−531.(6) Decurtins, S.; Gross, M.; Schmalle, H. W.; Ferlay, S. Inorg. Chem.1998, 37, 2443−2449.(7) Costes, J. P.; Dahan, F.; Dupuis, A.; Laurent, L. P. Inorg. Chem.1997, 36, 3429−3433.(8) Ramade, I.; Kahn, O.; Jeannin, Y.; Robert, F. Inorg. Chem. 1997,36, 930−936.(9) Ishikawa, N.; Iino, T.; Kaizu, Y J. Am. Chem. Soc. 2002, 124,11440−11447.(10) Gao, Y.; Zhao, L.; Xu, X.; Xu, G. F.; Guo, Y. N.; Tang, J.; Liu, Z.Inorg. Chem. 2011, 50, 1304−1308.(11) Veauthier, J. M.; Schelter, E. J.; Kuehl, Ch. J.; Clark, A. E.; Scott,B. L.; Morris, D. E.; Martin, R. L.; Thompson, J. D.; Kiplinger, J. L.;John, K. D. Inorg. Chem. 2005, 44, 5911−5920.(12) Edelstein, N.; Streitweiser, A., Jr; Morrell, D. G.; Walker, R.Inorg. Chem. 1976, 15, 1397−1398.(13) Kozimor, S. A.; Bartlett, B. M.; Rinehart, J. D.; Long, J. R. J. Am.Chem. Soc. 2007, 129, 10672−10674.(14) Rinehart, J. D.; Harris, T. D.; Kozimor, S. A.; Bartlett, B. M.;Long, J. R. Inorg. Chem. 2009, 48, 3382−3395.(15) Schelter, E. J.; Morris, D. E.; Scott, B. L.; Thompson, J. D.;Kiplinger, J. L. Inorg. Chem. 2007, 46, 5528−2236.(16) Schelter, E. J.; Veauthier, J. M.; Thompson, J. D.; Scott, B. L.;John, K. D.; Morris, D. E.; Kiplinger, J. L. J. Am. Chem. Soc. 2006, 128,2198−2199.(17) Schultz, M.; Boncella, J. M.; Berg, D. J.; Tilley, T. d.; Anderson,R. A. Organometallics 2002, 21, 460−472.(18) Berg, D. J.; Boncella, J. M.; Anderson, R. A. Organometallic2002, 21, 4622−4631.(19) Chabach, D.; Lachkar, M.; De Cian, A.; Fischer, J.; Weiss, R.New J. Chem. Spectrom. 1997, 8, 161.(20) Schelter, E. J.; Wu, R.; Veauthier, J. H.; Bauer, E. D.; Booth, C.H.; Thompson, R. K.; Graves, Ch. R.; John, K. D.; Scott, B. L.;Thompson, J. D.; et al. Inorg. Chem. 2010, 49, 1995−2007.

(21) Shaveleev, N .M.; Accorsi, G.; Virgili, D.; Bell, Z. R.; Lazarides,T.; Calogero, G.; Armaroli, N.; Ward, M. D. Inorg. Chem. 2005, 44,61−72.(22) Chen, F. F.; Chen, Z. Q.; Bian, Z. Q.; Huang, Ch. H. Coord.Chem. Rev. 2010, 254, 991−1010.(23) Balzani, V.; Ballardini, R. Photochem. Photobiol. 1990, 52, 409−415.(24) Ward, M. D. Coord. Chem. Rev. 2007, 251, 1663−1677.(25) Hasegawa, Y.; Wada, Y.; Yanagida, S. J. Photochem. Photobiol. C:Photochem. Rev. 2005, 5, 183−202.(26) Armelao, L.; Quici, S.; Barigelletti, F.; Accorsi, G.; Bottaro, G.;Cavazzini, M.; Tondello, E. Coord. Chem. Rev. 2010, 254, 487−505.(27) Rinehart, J. H.; Long, J. R. J. Am. Chem. Soc. 2009, 131, 12558−12559.(28) Sinnecker, S.; Neese, F. J. Phys. Chem. A 2006, 110, 12267−12275.(29) Zein, S.; Neese, F. J. Chem. Phys. A 2008, 112, 7976−7983.(30) Neese, F. J. Chem. Phys. 2007, 127, 164112.(31) Sinnecker, S.; Neese, F.; Noodleman, L.; Lubitz, W. J. Am.Chem. Soc. 2004, 126, 2613−2622.(32) Duboc, C.; Phoeung, T.; Zein, S.; Pecaut, J.; Collomb, M. N.;Neese, F. Inorg. Chem. 2007, 46, 4905−4916.(33) Zein, S.; Duboc, C.; Lubitz, W.; Neese, F. Inorg. Chem. 2008, 47,134−142.(34) Ganyushin, D.; Gilka, N.; Taylor, P. R.; Marian, Ch. M.; Neese,F. J. Chem. Phys. 2010, 132, 144111.(35) Ganyushin, D.; Neese, F. J. Chem. Phys. 2006, 125, 024103.(36) Neese, F. J. Am. Chem. Soc. 2006, 128, 10213−10222.(37) Pederson, M. R.; Khanna, S. N Phys. Rev. B 1999, 60, 9566.(38) Reviakine, R.; Arbuznikov, A. V.; Tremblay, J. Ch.; Remenyi,Ch.; Malkina, O. L.; Malkin, V. G.; Kaupp, M. J. Chem. Phys. 2006,125, 054110.(39) Amsterdam Density Functional (ADF) Code; Vrije Universiteit:Amsterdam, 2007.(40) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.;Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. Rev. B: Condens. Matter1993, 48, 4978.(41) Verluis, L.; Ziegler, T. J. J. Chem. Phys. 1988, 88, 322−329.(42) Vosko, S. H.; Kilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200.(43) Cheeseman, J. R.; Truck, G. W.; Keith, T. A.; Freisch, M. J. J.Chem. Phys. 1996, 104, 882−899.(44) Schreckenbach, G.; Ziegler, T. Int. J. Quantum Chem. 1996, 60,753−766.(45) Schreckenbach, G.; Ziegler, T. J. Phys. Chem. 1995, 99, 606−611.(46) Zhang, Y.; Wu, A.; Xu, X.; Yan, Y. Chem. Phys. Lett. 2006, 421,383.(47) Kootstra, F.; de Boeij, P. L.; Snijders, J. G. J. Chem. Phys. 2000,112, 6517−6532.(48) Romaniello, P.; de Boeij, P. L. Phys. Rev. B 2005, 71, 155108.(49) Gritsenko, O. V.; Schipper, P. R. T.; Baerends, E. J. Chem. Phys.Lett. 1999, 302, 199.(50) Neese, F. ORCA-An ab Initio, Density Functional andSemiempirical Program Package, version 2.8; Universitat Bonn: Bonn,Germany. The program can be downloading free of charge fromhttp://www.mpibac.mpg.de/bac/index_en.php.(51) Schafer, A.; Huber, C.; Ahlrich, R. J. Chem. Phys. 1994, 100,5829−5836.(52) Becke, A. D. J. Chem. Phys. 1993, 98, 5648−5653.(53) Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. Rev. B 1988, 27, 785.(54) Nesse, F. J. Chem. Phys. 2005, 122, 034107.(55) Hess, B. A.; Marian, C. M.; Wahlgren, U.; Gropen, O. Chem.Phys. Lett. 1996, 251, 365.(56) Jutzi, P.; Burford, N. Main Group Metallocenes. In Metallocenes:Synhtesis, Reactivity, Applications; Togny, A., Halterman, R., Eds.;Wiley-VCH Verlag CmbH: Weinheim, Germany, 1998; Chapter 1.(57) Schumacher, E.; Taubenest, R. Helv. Chim. Acta 1964, 47,1525−1529.

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp3039576 | J. Phys. Chem. A 2012, 116, 7584−75927591

(58) Dubler, E.; Textor, M.; Oswald, H.-R.; Salzer, A. Angew. Chem.1974, 55, 125.(59) Lamanna, W. M.; Glesson, W. B.; Britton, D. Organometallics1987, 16, 1553−1561.(60) Hoshino, K.; Kurikawa, T.; Takeda, H.; Nakajima, A.; Kaya, K. J.Phys. Chem. 1995, 99, 3053−3055.(61) Weis, P.; Kemper, P. R.; Bowers, M. T. J. Phys. Chem. A 1997,101, 8207−8213.(62) Kurikawa, T.; Takeda, H.; Hirano, M.; Judai, K.; Arita, T.;Nagao, S.; Nakajima, A.; Kaya, K. Organometallics 1999, 18, 1430−1438.(63) Nakajima, A.; Kaya, K. J. Phys. Chem. A 2000, 104, 176−191.(64) Pandey, R.; Rao, B. K.; Jena, P.; Blanco, M. A. J. Am. Chem. Soc.2001, 123, 3799−3808.(65) Paez-Hernandez, D.; Murillo-Lopez, J. A.; Arratia-Perez, R. J.Phys. Chem. A 2011, 115, 8997−9003.

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp3039576 | J. Phys. Chem. A 2012, 116, 7584−75927592