Theoretical Study of Inverted Sandwich Type Complexes of 4d

Jan 27, 2012 - These spin multiplicities are much lower than the septet of ISTC of Cr and the nonet of that of Mn. When going from 3d to 4d, the posit...
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Theoretical Study of Inverted Sandwich Type Complexes of 4d Transition Metal Elements: Interesting Similarities to and Differences from 3d Transition Metal Complexes Yusaku I. Kurokawa,† Yoshihide Nakao, and Shigeyoshi Sakaki* Fukui Institute for Fundamental Chemistry, Kyoto University, Nishihiraki-cho 34-4, Sakyo-ku, Takano, Kyoto 606-8103, Japan S Supporting Information *

ABSTRACT: Inverted sandwich type complexes (ISTCs) of 4d metals, (μ-η6: η6-C6H6)[M(DDP)]2 (DDPH = 2-{(2,6-diisopropylphenyl)amino}-4-{(2, 6-diisopropylphenyl)imino}pent-2-ene; M = Y, Zr, Nb, Mo, and Tc), were investigated with density functional theory (DFT) and MRMP2 methods, where a model ligand AIP (AIPH = (Z)-1-amino-3-imino-prop-1-ene) was mainly employed. When going to Nb (group V) from Y (group III) in the periodic table, the spin multiplicity of the ground state increases in the order singlet, triplet, and quintet for M = Y, Zr, and Nb, respectively, like 3d ISTCs reported recently. This is interpreted with orbital diagram and number of d electrons. However, the spin multiplicity decreases to either singlet or triplet in ISTC of Mo (group VI) and to triplet in ISTC of Tc (group VII), where MRMP2 method is employed because the DFT method is not useful here. These spin multiplicities are much lower than the septet of ISTC of Cr and the nonet of that of Mn. When going from 3d to 4d, the position providing the maximum spin multiplicity shifts to group V from group VII. These differences arise from the size of the 4d orbital. Because of the larger size of the 4d orbital, the energy splitting between two dδ orbitals of M(AIP) and that between the dδ and dπ orbitals are larger in the 4d complex than in the 3d complex. Thus, when occupation on the dδ orbital starts, the low spin state becomes ground state, which occurs at group VI. Hence, the ISTC of Nb (group V) exhibits the maximum spin multiplicity.

1. INTRODUCTION Recently, Tsai et al.1 and Monillas et al.2 synthesized inverted sandwich type complexes (ISTCs) of chromium (μ-η6:η6C6H5CH3)[Cr(DDP)]2 (DDPH = 2-{(2,6-diisopropylphenyl)amino}-4-{(2,6-diisopropylphenyl)imino}pent-2-ene, which is often referred to as nacnac, and (μ-η6:η6-C6H6)[Cr(DDP)]2 RCr, respectively. Interestingly, these complexes take very high spin multiplicity of septet. Also, Tsai et al. reported that ISTC of vanadium (μ-η6:η6-C6H5CH3)[V(DDP)]2 takes very high spin multiplicity of quintet.3 These spin states are surprisingly high considering that organometallic compounds tend to take low spin state in general. Thus, electronic structures and spin multiplicities of these ISTCs are of considerable interest from the points of view of physical chemistry, material science, and coordination chemistry. Recently, we theoretically investigated ISTCs of the 3d transition-metal (TM) elements and elucidated the reason why ISTCs of vanadium and chromium take such high spin multiplicities.4 Also, we calculated the spin multiplicities of their analogues, RM (M = Sc, Ti, Mn, and Fe), though they have not been synthesized yet, and reported that the Sc, Ti, Mn, and Fe complexes take closed-shell singlet, triplet, nonet, and open-shell singlet spin states in the ground state, respectively. In other words, the spin multiplicity of RM interestingly increases from singlet to nonet when going to Mn (group VII) from Sc (group III) in the 3d TM series of the periodic table but then suddenly decreases to singlet at Fe (group VIII). © 2012 American Chemical Society

Because the spin multiplicity of the ISTC of 3d TM shows interesting changes upon going from the left-hand side to the right-hand side in the periodic table, it is also interesting to clarify what changes occur upon going down to the 4d TM complex from the 3d in the periodic table. Remember that dinuclear TM complex bearing a M−M multiple bond exhibits several important differences between 3d (Cr) and 4d (Mo);5 for instance, the bond distance is calculated to be much longer in M = Mo than in M = Cr by the MRMP2 method, but the static correlation is much larger in the Cr complex than in the Mo complex. These results provide us with motivation to investigate what changes occur in the spin multiplicity and electronic structure of the ISTC when going down to the 4d from the 3d. In the present work, we theoretically investigated various ISTCs of the 4d TM elements such as Y, Zr, Nb, Mo, and Tc. Our main purposes here are to clarify the electronic structures and spin multiplicities of the ISTCs of these 4d TM elements, to show how much the 4d ISTCs are similar to and different from the 3d ISTCs, and to elucidate the reasons why. Though these 4d ISTCs have not been experimentally reported yet, we believe that the theoretical knowledge of their electronic structures and spin multiplicities provides new motivation for development of the chemistry of these ISTCs. Received: November 9, 2011 Revised: January 26, 2012 Published: January 27, 2012 2292

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2. MODELS AND COMPUTATIONAL DETAILS 2.1. Model Complexes. In our previous study of the ISTCs of the 3d TM elements,4 we employed AIP (AIPH = (Z)-1-amino-3-imino-prop-1-ene) ligand as a model of the DDP; see Scheme 1 for AIP and DDP. The geometries and the

their valence electrons were represented with (311111/22111/ 411) basis sets.16 For C, N, and H, cc-pVDZ basis sets were employed,17 where one augmented function was added to N because it is anionic in the AIP. Gaussian 03 package was used for DFT calculation,18 and GAMESS package was used for CASSCF and MRMP2 calculations.19 Molecular orbitals were drawn with Molekel program version 5.3.20

Scheme 1. (μ-η6:η6-C6H6)(MDDP)2 (RM) and (μ-η6:η6C6H6)(MAIP)2 (MM) (M = Y-Tc, DDPH = 2-{(2,6Diisopropylphenyl)amino}-4-{(2,6-diisopropylphenyl)imino}pent-2-ene, AIPH = (Z)-1-Amino-3-imino-prop-1-ene)

3. RESULTS AND DISCUSSION 3.1. DFT Computed Spin Multiplicities and Geometries of MM (M = Y, Zr, Nb, Mo, and Tc). We optimized the geometry of MM (M = Y, Zr, Nb, Mo, or Tc) in various spin states with various functionals. The most stable spin state is calculated to be singlet, triplet, and quintet for M = Y, Zr, and Nb, respectively, by all functionals employed here as shown in Table 1 and in Table S1 of theSupporting Information. Table 1. Relative Energiesa of Various Spin Multiplicities Calculated by the DFT Method with the (a) B3LYP and (b) BP86 Functionals

spin multiplicities of RV and RCr were reproduced well by the model complexes MV and MCr consisting of the AIP.4 Though toluene was employed in real systems, substitution of toluene for benzene little changes the geometry and does not alter the most stable spin multiplicity at all.4 On the basis of these results, we mainly employed the model complex, (μ-η6:η6-C6H6)[M(AIP)]2 M M, in the present study unless otherwise mentioned. The real complexes were theoretically investigated with only density functional theory (DFT) method to make comparison of spin multiplicity with that of the model complex. 2.2. Computational Details. The geometry of MM (M = Y, Zr, Nb, Mo, and Tc) was optimized in each spin state by the DFT method with B3LYP,6,7 B3LYP*,8 BP86,6,9 and PW91PW9110 functionals. The initial geometry of MM was set to D2 symmetry,11 where the M(AIP) moiety was assumed to be planar because the six-member ring of the Cr(DDP) moiety in (μ-η6:η6C6H5CH3)[Cr(DDP)]2 was experimentally observed to be almost planar.1−3 The geometry of real complex RM was also optimized at each spin state by the DFT method with BP86 functional, where the same basis sets were employed. The geometries of MMo and MTc were optimized by the CASSCF method for each spin state, too, where the M−M distance was taken as a coordinate and the geometry of the remaining moiety was optimized under D2 symmetry at various M−M distances. Because Mo(I) has five d electrons, the active space containing 10 electrons in 8 orbitals was employed for MMo. These eight orbitals are six d derived orbitals and two π* MOs (lowest unoccupied molecular orbitals (LUMOs)) of benzene; the reason to employ this active space will be discussed in the Results and Discussion. In MTc, the active space of 12 electrons in 10 orbitals was employed; here, the size of active space was increased because the number of d electrons increases by two in this complex compared to MMo. Using the CASSCFoptimized geometry at each M−M distance, the potential energy surface (PES) was evaluated by the MRMP2 method.13−15 In the MRMP2 calculation, the CASSCF wave function was taken as the reference wave function. We employed the energy denominator shift (EDS) in the MRMP2 calculations, where the EDS value of 0.02 au was used throughout the present study. Core electrons (up to 3d) of the metals were replaced with Stuttgart−Dresden−Bonn effective core potentials (ECPs), and

(a) B3LYP Y septet quintet triplet singlet

septet quintet triplet singlet

Zr

Nb

Mo

Tc

51.5 0.0 13.4 32.5

21.0 19.8 0.0 0.9

21.6 1.2 0.0

Nb 51.9 0.0 8.5 102.8

Mo 32.4 17.4 2.4 0.0

51.5 26.9 0.0

44.1 17.4 0.0 0.8 (b) BP86

Y

Zr

25.7 0.0

25.4 0.0 3.3

Tc 31.8 4.6b 0.0

a

Energy differences from the most stable spin state are shown in kcal/ mol. See Table S2 of theSupporting Information for thermal corrections. The geometry was optimized under the D2 symmetry except for the BP86 calculation of the triplet of the Tc complex. bThe C2 symmetrical geometry only in this case; see ref 11.

However, some discrepancy is observed between the B3LYP computational results and others in MMo and MTc. In MMo, the triplet state is calculated to be the most stable by the B3LYP functional, but the singlet is the most stable by the B3LYP*, BP86, and PW91PW91 functionals, while the energy difference between the triplet and the singlet states is small. The result that the ground state is calculated to be singlet by the B3LYP* is consistent with the general understanding that the B3LYP functional tends to overestimate the stability of high spin state and that the B3LYP* improves the overestimation.21 In MTc, the ground state is calculated to be singlet by all functionals here, while the relative stability of the triplet is much different between the B3LYP and the other functionals; the energy difference is only 1.2 kcal/mol in the B3LYP calculation but about 10 kcal/mol in the other calculations. These results indicate that the spin multiplicities of MMo and MTc must be carefully investigated. The geometry of the real complex RM was optimized by the DFT method with the BP86 functional; see Figure S1 and Table S3 of the Supporting Information for the optimized geometries. The spin multiplicity of the ground state is the same as that of the model AIP complex, MM, as shown in Table 2. This indicates that the AIP ligand is a good model for the real DDP 2293

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Table 2. Relative Energiesa of Various Spin Multiplicities of the Real Complexes (RM) Calculated by the DFT Method with the BP86 Functionals septet quintet triplet singlet

Y

Zr

22.3 0.0

22.0 0.0 0.7

Nbb

Mo

Tc

38.4 0.0 7.8

72.0 24.7 14.1 0.0

30.1 13.2 0.0

3.2. Molecular Orbital Diagram and Spin Multiplicity of MM (M = Y, Zr, and Nb). First, we will present a brief explanation of the molecular orbital (MO) diagram and its difference between 3d and 4d ISTCs because they were discussed in our previous work.4 In M(AIP), degenerate five d orbitals of M become nondegenerate five d orbitals by the interaction with the AIP moiety. We named them σd, δd1, δd2, πd1, and πd2 orbitals as shown in Scheme 2 (right-hand side).

a

Energy differences from the most stable spin state are shown in kcal/mol. bThe geometry optimization did not converge in the singlet spin state.

Scheme 2. MO Diagram of ISTC of 4d Metal, (μ-η6:η6C6H6)[M(AIP)]2, [M(AIP)]2, and M(AIP) and the Natural Orbitals Calculated by the CASSCF Method

ligand in the 4d ISTCs like in the 3d ISTCs. Hereafter, we will mainly discuss the spin multiplicity and electronic structure of model ISTCs. Because the spin state has not been determined well by the DFT calculations in Mo and Tc complexes, we will concentrate on Y to Nb complexes here. In these complexes, the spin multiplicity increases from singlet to quintet when going to Nb (group V) from Y (group III). This result is the same as that of ISTCs of 3d TMs. The maximum spin multiplicity is provided by Nb which is earlier than that of the 3d ISTCs; remember that the maximum spin multiplicity is presented at M = Mn (group VII) in the 3d ISTCs.4 Also, the maximum spin multiplicity of quintet is much lower than that of the 3d ISTC which is nonet.4 It is of considerable interest to clarify the reason why the maximum position shifts to the group V and why the maximum spin multiplicity becomes much lower in the 4d ISTC than in the 3d ISTC. These results will be discussed below in detail. The M−M distance also shows interesting change when going from the left-hand side to the right-hand side in the periodic table. In the 4d ISTCs, the M−M distance gradually decreases by about 0.12 Å when going to Tc from Y as shown in Figure 1. In the 3d ISTCs, the M−M distance decreases The πd2 orbital mainly consists of the dxz orbital of M with which the N lone pair of the AIP moiety strongly interacts in an antibonding way; see Scheme 2 for x, y, and z axes. Because these two orbitals overlap well with each other in a σ manner with respect to the M−N bond, the πd2 orbital is much destabilized in energy. The πd1 orbital mainly consists of the dyz orbital of M with which the π orbital of the AIP moiety somewhat interacts in an antibonding way. Because the π-type overlap is smaller than the σ-type one, the πd1 orbital is less destabilized than the πd2 orbital. These πd1 and πd2 orbitals are more unstable in the 4d M(AIP) complex than in the 3d M(AIP) complex because the larger 4d orbital interacts stronger with the lone pair and π-orbitals of the AIP ligand in an antibonding way than does the smaller 3d.22 The δd1 and δd2 orbitals mainly consist of the dxy and dy2 orbitals, respectively. The δd2 orbital is somewhat more unstable than the δd1 orbital because the dxy orbital somewhat more strongly interacts with the π orbital of the AIP ligand in an antibonding way than does the dy2 orbital. The σd orbital mainly consisting of the dz2−x2 lies at the lowest energy because it little interacts with the AIP ligand. The energy gaps between the δd1 and δd2 orbitals and between the πd1 and πd2 orbitals are larger in the 4d M(AIP) than in the 3d M(AIP); remember the 4d orbital is larger than the 3d.22 These differences induce the difference in spin multiplicity between the 3d and 4d ISTCs, which will be discussed below.

Figure 1. DFT optimized geometry of MM in the most stable spin state. (The most stable spin states are singlet, triplet, quintet, triplet, and singlet for M = Y, Zr, Nb, Mo, and Tc, and singlet, triplet, quintet, septet, and nonet for M = Sc, Ti, V, Cr, and Mn, respectively.) (A) Important distances (Å) of MMo and MCr (in parentheses is distance for MCr) and (B) metal−metal distances of MM.

when going from Sc to V like the 4d TM series but then somewhat increases when going to Mn from V. This difference between 3d and 4d ISTCs will be discussed below in detail. 2294

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In MNb, two more d electrons are added because Nb(I) has four d electrons. There are two possibilities in electron configuration: one is quintet (ϕ1)2(ϕ2)2(ϕ3)1(ϕ4)1(ϕ5)1(ϕ6)1 and another is closed-shell singlet (ϕ1)2(ϕ2)2(ϕ3)2(ϕ4)2; see Scheme 3. The electron configuration depends on the energy differences among ϕ3−ϕ6 MOs; when they are not large, the ground state takes quintet and vice versa. All DFT calculations show that MNb takes a (ϕ1)2(ϕ2)2(ϕ3)1(ϕ4)1(ϕ5)1(ϕ6)1 electron configuration with the quintet spin multiplicity though the energy differences among ϕ3−ϕ6 MOs are larger in the 4d ISTC than in the 3d ISTC. This result is reasonably understood in terms that the quintet state contains enough molecular exchange integrals to overcome the energy destabilization by electron occupation of ϕ5 and ϕ6 MOs. These spin multiplicities are the same as those of the ISTCs of the 3d TM elements. In these 4d ISTCs, we can understand the spin multiplicity in terms of the MO diagram and the number of d electrons. 3.3. Spin Multiplicities of MMo and MTc by the MRMP2 Method. Though the spin multiplicity can be easily understood in terms of the MO diagram and the number of d electrons for M = Y to Nb, as discussed above, that of MMo cannot be easily understood because the electronic state becomes complicated as follows: Because MMo has 10 d electrons, two more d electrons are added to the MOs of MNb, which leads to either (ϕ1)2(ϕ2)2(ϕ3)2(ϕ4)2(ϕ5)2 or (ϕ1)2(ϕ2)2(ϕ3)2(ϕ4)2(ϕ5)1(ϕ6)1 electron configuration. The former is closed-shell singlet and the latter is triplet spin state. If the energy gap between the ϕ5 and ϕ6 is small, the triplet state is more stable. If it is large, the closed-shell singlet state is more stable. Though the energy gap is small in the 3d ISTCs, it becomes larger in the 4d ISTC than in 3d ISTC as mentioned above; see also Figure S2 of the Supporting Information. Thus, the relative stabilities of these two electron configurations cannot be obviously determined. Actually, the spin multiplicity of MMo depends on the functionals employed for computation as shown in Table 1 and in Table S1 of the Supporting Information. In this complex, therefore, we should perform careful examination. Here, we investigated MMo with the MRMP2 method. In the CASSCF calculations, we employed an active space containing 10 electrons in eight MOs such as ϕ1−ϕ8 because the ϕ3−ϕ6 MOs are in similar energies and the ϕ7 and ϕ8 MOs are antibonding counterparts of the ϕ1 and ϕ2; see Scheme 2.23 The energy minimum of MMo is presented at R(Mo−Mo) = 3.6 Å in the 1A state as shown in Figure 2A. The PES by CASSCF calculation is repulsive like the dinuclear complex bearing the

[M(AIP)]2 consists of two M(AIP) moieties, where d derived πd2, πd1, δd1, δd2, and σd orbitals of one M(AIP) interact with those of another M(AIP) to form bonding and antibonding pairs such as π2 and π2*, π1 and π1*, δ2 and δ2*, δ1 and δ1*, and σ and σ* orbitals, respectively, as shown in Scheme 2. Because two M(AIP) moieties are sufficiently separated by benzene, the bonding orbital and its antibonding counterpart are almost degenerate with each other. In MM, the LUMOs of benzene largely interact with these orbitals of [M(AIP)]2 because the metal center takes +1 oxidation state which is low oxidation state; the δ1* and δ2* orbitals of [M(AIP)]2 strongly interact with the LUMOs of benzene to form bonding MOs, ϕ1 and ϕ2, and their antibonding counterparts, ϕ7 and ϕ8 as shown in Scheme 2; see also previous work.4 The π1, π2, δ1, δ2, σ, and σ* orbitals of [M(AIP)]2 do not interact with the LUMOs of benzene because they have different symmetry from the LUMOs of benzene. The π1* and π2* orbitals have the same symmetry as the highest occupied molecular orbitals (HOMOs) of benzene but exist at much higher energy than the HOMOs of benzene. Thus, these MOs of MM exist at almost the same energy as those of the M(AIP) moiety. We named all these MOs ϕ1− ϕ12 as shown in Scheme 2. In MY, one Y(I) has two d electrons. Totally, four d electrons occupy these MOs of MY. The possible electron configuration is (ϕ1)2(ϕ2)2 because the ϕ1 and ϕ2 MOs exist at considerably lower energy than the others; see Scheme 3. Thus, it is clearly concluded that MY takes the closed-shell singlet spin state. Scheme 3. Schematical Occupation of Inverted Sandwich Type Complexes of Y, Zr, and Nb

In MZr, two more d electrons are involved because Zr(I) has three d electrons. The ϕ3 and ϕ4 MOs are nearly degenerate because they consist of the σd orbitals which little interact with the HOMOs and LUMOs of benzene. Thus, MZr takes (ϕ1)2(ϕ2)2(ϕ3)1(ϕ4)1 electron configuration with the triplet spin multiplicity (Scheme 3).

Figure 2. The PES of MMO (left) and MTc (right) calculated by the MRMP2 method. 2295

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M−M direct bond;5 see Figure S3 of the Supporting Information. The main electron configuration and the second leading one are (ϕ1) 2 (ϕ2) 2 (ϕ3) 2 (ϕ4) 2 (ϕ5) 2 and (ϕ1)2(ϕ2)2(ϕ3)2(ϕ4)2(ϕ6)2, respectively, indicating that the ground state of MMo is closed-shell singlet. Their weights are 0.766 and 0.095, respectively. The weights of the other electron configurations are less than 0.04. The occupation numbers of natural orbitals which are calculated by the CASSCF method are given in Scheme 4. Those of the ϕ1−ϕ4 are close to two

Because the most stable closed-shell singlet state of MMo is energetically close to the triplet state in all calculations including the MRMP2, it is difficult to present a definite answer about the spin multiplicity in the model complex. However, it is likely to conclude that the real Mo complex takes singlet ground state because the BP86 computational results show a somewhat large energy difference between the singlet and triplet states (Table 2); see also Table S2 of the Supporting Information and its footnote for the relative stabilities of the singlet and triplet states. Thus, it should be concluded that the spin multiplicity of the Mo complex is much lower than the septet state of the Cr analogue. This is an important difference between the 3d and 4d ISTCs, which will be discussed below in detail. In MTc, the ground state is calculated to be triplet (3B3) by the MRMP2 method23 as shown in Figure 2B. The next is a different triplet (3B2) which is only 1.4 kcal/mol above the 3B3 state. Though the singlet is calculated to be ground state by the DFT(B3LYP) method, it is much more unstable than the triplet by about 10.1 kcal/mol in the MRMP2 calculation indicating that the closed-shell singlet is very unstable. This result cannot be understood on the basis of the orbital diagram of MMo (Scheme 4) as follows: Because the Tc(I) has six d electrons, two more d electrons occupy the ϕ6 in this scheme, which leads to the closed-shell singlet state. This electron configuration is not consistent with the triplet state presented by the MRMP2 calculations. This means that MTc has a different MO diagram. As shown in Scheme 5, the ϕ6 and ϕ9

Scheme 4. Natural Orbitals and Their Occupation Numbers Calculated by CASSCF(10e,8o) of Inverted Sandwich Type Complex of Mo, MMoa

a

Scheme 5. Natural Orbitals and Their Occupation Numbers Calculated by CASSCF(12e,10o) of Inverted Sandwich Type Complex of Tc, MTca

Numbers in parentheses are occupation numbers.

and those of the others are close to zero except for the ϕ5 and ϕ6; the occupation number is 0.32 for the ϕ6 and 1.70 for the ϕ5 suggesting that the ϕ5→ϕ6 excited electron configuration considerably contributes to the total wave function. Besides, the 3 B1 and 3A electronic states are only 1.3 and 0.3 kcal/mol above the closed-shell singlet 1A state at R(Mo−Mo) = 3.6 Å and 3.5 Å, respectively. In the 3B1 state, the main, second, and third leading configurations are (ϕ1)2(ϕ2)2(ϕ3)2(ϕ4)2(ϕ5)1(ϕ6)1, (ϕ1)2(ϕ2)2(ϕ3)1(ϕ4)2(ϕ5)1(ϕ6)1(ϕ8)1, and (ϕ1)2(ϕ2)2(ϕ3)2(ϕ4)1(ϕ5)1(ϕ6)1(ϕ7)1, respectively, whose weights are 0.815, 0.039, and 0.030, respectively, at R(Mo− Mo) = 3.6 Å. Those of the 3A state are (ϕ1)1(ϕ2)2(ϕ3)2(ϕ4)2(ϕ5)2(ϕ6)1, (ϕ1)2(ϕ2)1(ϕ3)2(ϕ4)1(ϕ5)2(ϕ6)1(ϕ8)1, and (ϕ1)2(ϕ2)2(ϕ3)2(ϕ4)2(ϕ5)1(ϕ6)1, whose weights are 0.744, 0.037, and 0.031, respectively, at R(Mo−Mo) = 3.5 Å. The weights of the other configurations are less than 0.03 in both the 3B1 and 3A states. Though the main configuration of the 3B1 state is consistent with our expectation, the main configuration of the 3A state is against our simple expectation on the basis of the orbital energy because the most stable ϕ1 becomes singly occupied and one electron excitation from the ϕ1 to the ϕ5 is involved in this main configuration. Considering the configuration energy, we can understand the reason why this electron configuration becomes the main configuration as follows: The ϕ1 mainly consists of the δ2* of Mo(AIP) and the ϕ6 is essentially the same as the δ2; in other words, both ϕ1 and ϕ6 mainly consist of δd2. As a result, the molecular Coulombic repulsion integral between ϕ1 and ϕ6 is large, which leads to a small ϕ1→ϕ6 excitation energy. Thus, the ϕ1→ϕ6 excited configuration becomes a main configuration.

a

The numbers in parentheses are occupation numbers.

are singly occupied in the 3B2 state and the ϕ5 and ϕ9 are singly occupied in the 3B3 state. These electron configurations become possible when the ϕ9 and ϕ10 become more stable 2296

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than the ϕ7 and ϕ8 in MTc. The plausible MO diagram for these electron configurations is shown in Scheme 5. The reason why this MO diagram is reasonable will be discussed in the next section. In the 3B2 state, the main, second, and third configurations are (ϕ1) 2 (ϕ2) 2 (ϕ3) 2 (ϕ4) 2 (ϕ5) 2 (ϕ6) 1 (ϕ9) 1 , (ϕ1) 2 (ϕ2) 1 (ϕ3) 2 (ϕ4) 2 (ϕ5) 1 (ϕ6) 1 (ϕ8) 1 (ϕ9) 1 , and (ϕ1)2(ϕ2)2(ϕ3)2(ϕ4)2(ϕ5)1(ϕ6)2(ϕ10)1 where their weights are 0.503, 0.094, and 0.054, respectively. The occupation number of the natural orbital ϕ2 decreases to 1.72 and that of the ϕ10 is 0.28, that of the ϕ9 is much smaller than 1.0, but those of the ϕ7 and ϕ8 are somewhat larger than 0.0. These results indicate that the excitations from the ϕ2 and ϕ9 to the ϕ7, ϕ8, and ϕ10 contribute to the total wave function. Actually, the third leading term contains one such excited electron configuration. In the 3B3 state, the main configuration is (ϕ1)2(ϕ2)2(ϕ3)2(ϕ4)2(ϕ5)1(ϕ6)2(ϕ9)1 and the second leading term is (ϕ1)2(ϕ2)2(ϕ3)2(ϕ4)2(ϕ5)1(ϕ6)1(ϕ7)1(ϕ9)1, where their weights are 0.632 and 0.029, respectively. The occupation numbers of the natural orbitals ϕ2 and ϕ6 are considerably smaller than 2.0 and that of the ϕ9 is considerably smaller than 1.0, while those of the ϕ7, ϕ8, and ϕ10 are somewhat larger than 0.0. These results suggest that the excitation configurations from the ϕ2, ϕ6, and ϕ9 to the ϕ7, ϕ8, and ϕ10 considerably contribute to the total wave function. The second leading term is one such excited electron configuration. In summary, the spin multiplicity increases from singlet to quintet when going from M = Y to M = Nb like the 3d ISTCs of Sc to V, where the spin multiplicity is determined by the MO diagram and the number of d electrons. However, then the spin multiplicity suddenly decreases to either closed-shell singlet or triplet at M = Mo and triplet at M = Tc unlike the 3d ISTCs of Cr and Mn. This is an interesting difference between 3d and 4d ISTCs, which will be discussed below. 3.4. Reason Why Mo and Tc Analogues Take Low Spin States. It is worth investigating the reason why MMo takes low spin state unlike MCr which takes the septet spin state in the ground state. Before starting the discussion of MMo, let us remember the MO diagram of MCr: Because the 3d orbital expands less than the 4d orbital, the energy gap between ϕ6 and ϕ9−ϕ10 is considerably smaller in MCr than in MMo. As a result, the ϕ9 and ϕ10 exist below the ϕ7 and ϕ8 MOs in MCr; see MO diagram in Scheme 6 which is the same as Scheme 4 of

ref 4. For MOs of MCr, we employ notations of φ1−φ10 to avoid confusion with MOs of 4d ISTCs. In Scheme 6, four electrons occupy φ1 and φ2 and six electrons occupy the φ3−φ8; because the energy gap between φ3 and φ8 is small, they are nearly nonbonding d orbitals. This electron configuration leads to the septet spin state; see the discussion of previous work.4 In Mo(AIP), the energy gap between the δd1, δd2 πd1, and πd2 orbitals is considerably larger than that in Cr(AIP) because the 4d orbital expands more toward the AIP ligand than does the 3d orbital.22 The energy gap between the ϕ6 and ϕ9−ϕ10 MOs becomes larger in MMo than in MCr because these MOs mainly consist of the πd1 and δd2 orbitals, respectively, and the energy gap between the πd1 and δd2 orbitals is larger in the Mo(AIP) moiety than in the Cr(AIP) as mentioned above; see Scheme 2. Also, the energy gap between the ϕ5 and ϕ6 becomes larger in MMo than in MCr because these MOs consist of δd1 and δd2, respectively, and the energy gap between δd1 and δd2 becomes larger in Mo(AIP) than in Cr(AIP); see Figure S2 of the Supporting Information for this energy gap. Because of these larger energy gaps, four electrons occupy the ϕ1 and ϕ2 like those of MCr, but the next six electrons occupy the ϕ3−ϕ5 unlike those of MCr as shown in Scheme 4, which corresponds to the closed-shell singlet spin state. Of course, the energy gap between ϕ5 and ϕ6 is not sufficiently large. As a result, the ϕ5→ϕ6 excited configuration considerably contributes to the total wave function of the closed-shell singlet as discussed above; see occupation numbers of natural orbital shown in Scheme 4. Also, the triplet state, in which the ϕ5 and ϕ6 are singly occupied, is calculated to be only slightly above the closed-shell singlet. From this discussion, it is concluded that the larger energy gap between the δd1, δd2 πd1, and πd2 orbitals of Mo(AIP) is the origin of the lower spin state of MMo. However, the electronic state and spin multiplicity of MTc cannot be understood with the MO diagram of Scheme 4. In MTc, we must consider two more d electrons than in MMo. If we employed Scheme 4, the closed-shell singlet became ground state in this complex. However, not the closed-shell singlet but the triplet was calculated for the ground state of MTc. In the case of the triplet, Scheme 4 suggests that the ϕ6 and the ϕ7 (or ϕ8) are singly occupied. However, such an electron configuration is not presented by the MRMP2 calculation as discussed above. These results request us to consider some other factors here. One of the important factors is the d orbital energy shift along the TM series and another is the size of the d orbital. As is well-known, the d orbital becomes lower in energy, and its size becomes smaller when going from the lefthand side to the right-hand side in the periodic table.22 On the other hand, the ϕ7 and ϕ8 MO energies change little upon going from M = Y to M = Tc because they mainly consist of the benzene π* orbitals. As a result, the ϕ9 and ϕ10 become lower in energy than the ϕ7 and ϕ8, which is the reason of the MO diagram shown in Scheme 5. Thus, two additional d electrons occupy both ϕ6 and ϕ9 in MTc. This electron configuration corresponds to the triplet state (3B2), which is consistent with the occupation numbers of the natural orbitals discussed above; see also Scheme 5. In addition, because the 4d orbital of Tc is smaller than that of Mo, the energy gap between δd1 and δd2 becomes smaller in Tc(AIP) than in Mo(AIP) leading to a smaller energy gap between the ϕ5 and ϕ6. As a result, another triplet state (3B3) is formed in which the ϕ5 and ϕ9 are singly occupied; this electron configuration is consistent with the occupation numbers of natural orbitals shown in Scheme 5, too.

Scheme 6. Orbital Diagram of ISTC of Cr, MCra

The positions of the φ7 and φ8 are different from those in Scheme 2. The φ7 and φ8 correspond to the ϕ9 and ϕ10 in Scheme 2, and the φ9 and φ10 correspond to the ϕ7 and ϕ8 in Scheme 2. Because the d−d orbital energy gap is smaller in the Cr complex than in the Mo analogue, the φ7 and φ8 derived from πd1 and πd2 become at lower energy than the φ9 and φ10 derived from benzene π* orbitals. a

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The 3B2 state is more stable than the 3B3 because the ϕ5 is more stable than the ϕ6 as shown in Scheme 5. At the end of this discussion, we wish to explain the reason why the nonet cannot be taken in the ground state of MTc unlike in MMn. Because the 4d orbital expands more toward the ligand than the 3d, the ϕ11 and ϕ12 are considerably destabilized in energy by the antibonding interaction with the AIP lone pair orbitals in MTc; see Scheme 4. In MMn, on the other hand, these two MOs are not destabilized very much because of the small size of the 3d orbital. As a result, the ϕ11 and ϕ12 can become singly occupied in MMn, which leads to the nonet ground state. In summary, the spin multiplicities of MMo and MTc are reasonably understood in terms of the larger expansion of the 4d orbital than the 3d and the energy lowering of the 4d orbital upon going to the right-hand side from the left-hand side in the periodic table. 3.5. Metal−Metal Distance of MM. We found several important and interesting results about the M−M distance in Figure 1 as mentioned above: (1) The M−M distance becomes monotonously shorter when going to Tc from Y in the 4d ISTCs. (2) In the 3d ISTCs, however, the M−M distance becomes shorter when going from Sc to V like the 4d ISTCs but then becomes longer when going from V to Mn. Finally, (3) the Cr−Cr distance is almost the same as the Mo−Mo distance and the Mn−Mn distance is longer than the Tc−Tc distance despite the larger 4d orbital than the 3d. The decrease in the M−M distance observed when going to group V from group III is interpreted by the size of the d orbital: The size of the d orbital becomes smaller when going from the left-hand side to the right-hand side in the periodic table as is well-known.22 When going to Ti from Sc, the φ3 and φ4 become singly occupied; we employ Scheme 6 for the discussion of the 3d ISTCs. Because these MOs expand toward benzene, the occupation of these MOs induces exchange repulsion between benzene and M(AIP), which leads to the elongation of the M−M distance. On the other hand, the decrease in the d orbital size induces the shortening of the M−M distance in the bonding MOs φ1 and φ2. Because the φ1 and φ2 are doubly occupied but the φ3 and φ4 are singly occupied, the M−M shortening by the occupations of φ1 and φ2 becomes larger than the M−M elongation by the single occupations of φ3 and φ4, and hence, the M−M distance becomes shorter in the Ti complex. When going to V from Ti, the φ5 and φ6 become singly occupied in addition to the φ3 and φ4. However, the occupation of these MOs little contributes to the M−M elongation because these MOs expand parallel to the benzene plane. Thus, the decrease in d orbital size leads to the decrease in the exchange repulsions by the φ1 and φ2 with benzene, and hence, the M−M distance becomes shorter in MV. However, the different feature starts to contribute to the increase in the M−M distance when going from V to Mn in the 3d ISTCs. To present correct understanding here, we need to inspect the electron configuration of these ISTCs. Remember that the φ7 and φ8 MOs become singly occupied in MCr and that the φ7−φ10 MOs become singly occupied in MMn in addition to the φ3−φ6;4 see Scheme 6. Because the φ7−φ10 expand toward benzene, four MOs (φ3, φ4, φ7, and φ8) give rise to the exchange repulsion between M(AIP) and benzene in MCr and two more MOs (φ9 and φ10) participate in the exchange repulsion in MMn. These exchange repulsions induce

the M−M distance elongation, and as a result, the M−M distance becomes longer in the order V < Cr < Mn. Almost the same story can be presented for the M−M distance of 4d ISTCs of Y to Nb. Next is to provide an answer to the question of why the M−M distance becomes shorter when going from Nb to Tc unlike the increasing order of V < Cr < Mn. This difference is understood in terms of the MO occupations of MMo and MTc. As discussed above, either closedshell singlet or triplet is the ground state in MMo. This means that when going from Nb to Mo, either the ϕ5 becomes doubly occupied or the ϕ5 and ϕ6 become singly occupied in MMo; see Scheme 5. However, the occupation of the ϕ5 and ϕ6 contributes little to the M−M elongation because they expand parallel to the benzene plane. In MTc, either ϕ5 or ϕ6 becomes doubly occupied and the ϕ9 becomes singly occupied. Though the ϕ9 expands toward the benzene plane, it is only singly occupied. Hence, the exchange repulsion between M(AIP) and benzene moderately increases, which is not enough to induce the M−M distance elongation in MTc. In other words, the 4d metal tends to take lower spin multiplicity than the 3d metal, which does not contribute to the M−M distance elongation; the MO expanding toward benzene is not occupied in the Mo complex and is singly occupied in the Tc complex, and hence, the exchange repulsion is not enough to induce the Mo−Mo and Tc−Tc distances. Thus, the distance becomes shorter in the order Nb > Mo > Tc. Because the M−M distance becomes shorter in MMo and MTc but becomes longer in MCr and MMn, the Cr−Cr distance is almost the same as the Mo−Mo distance, and the Mn−Mn distance becomes even longer than the Tc−Tc distance despite the larger 4d orbital than the 3d.

4. CONCLUSION We theoretically investigated ISTCs (μ-η6:η6-C6H6) [M(AIP)]2 MM (M = Y, Zr, Nb, Mo, and Tc; AIPH = (Z)-1-amino-3imino-prop-1-ene) and (μ-η 6 :η 6 -C 6 H 6 )[M(DDP)] 2 R M (DDPH = 2-{(2,6-diisopropylphenyl)amino}-4-{(2,6-diisopropylphenyl)imino}pent-2-ene). All DFT calculations with B3LYP, B3LYP*, BP86, and PW91PW91 functionals indicate that the most stable spin state of MM and RM is singlet, triplet, and quintet for M = Y, Zr, and Nb, respectively. These results are essentially the same as those observed for the 3d ISTCs, which is clearly understood by the MO diagram and the number of d electrons. However, the ground state of MMo is calculated to be triplet by the B3LYP functional but to be singlet by the other functionals. In MTc, the ground state is calculated to be singlet by all functionals, while the energy difference between the singlet and the triplet states is very small in the B3LYP calculation but considerably large in the other functionals. Considering these results, we applied the MRMP2 method to these two complexes. MRMP2 calculations indicate that the closed-shell singlet is slightly more stable than the triplet in MMo though the energy difference between them is very small, within 1.3 kcal/mol. In MTc, the ground state is triplet (3B3), but the other triplet state lies slightly above the 3 B3 state by only 1.4 kcal/mol. The singlet spin multiplicity is much less stable. Though the 4d ISTCs take the same spin multiplicity as those of the 3d ISTCs for group III to group V, the 4d ISTCs take lower spin multiplicity than the 3d ISTCs for groups VI and VII. The maximum spin multiplicity of 4d ISTCs is quintet for M = Nb (group V) unlike that of the 3d ISTCs. All these results arise from the fact that the 4d orbital expands more than 2298

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Notes

the 3d orbital as follows: Because the 4d orbital expands more toward ligand than does the 3d, the energy gap between the ϕ6 and the ϕ9 orbitals becomes larger in MMo than in MCr, which stabilizes such low spin multiplicity as closed-shell singlet and triplet states. Because the d orbital energy becomes lower when going from the left-hand side to the right-hand side in the periodic table, the ϕ9 and ϕ10 MOs become lower in energy than the ϕ7 and ϕ8 MOs in MTc. However, the ϕ11 and ϕ12 do not become lower in energy than the ϕ7 and ϕ8 because they contain very large antibonding overlap between the dxz and the AIP lone pair. As a result, not the nonet but the triplet becomes the ground state of MTc unlike MMn. The M−M distance becomes shorter when going from group III to group VII in the 4d ISTCs. This result arises from the fact that the size of the d orbital becomes smaller when going from the left-hand side to the right-hand side in the periodic table. On the other hand, the M−M distance of 3d ISTCs becomes shorter going from group III to group V but then becomes longer when going from group V to group VII. The increase in the M−M distance from V (group V) to Mn (group VII) arises from the occupation of nonbonding d orbitals expanding toward benzene in these 3d ISTCs. Such occupation becomes possible in high spin multiplicity. However, those d orbitals are not occupied in the 4d ISTCs because the 4d ISTCs take lower spin multiplicity. Hence, the M−M distance monotonously decreases upon going from Y to Tc in the 4d ISTCs. In conclusion, the difference in d orbital expansion leads to different occupation of MOs of 4d ISTC, which further provides the different change of the M−M distance between 3d and 4d ISTCs. Though it is well-known that the 4d TM complex tends to take lower spin multiplicity than the 3d TM complex, the difference in spin multiplicity between the 3d and 4d ISTCs is of considerable interest as follows: The spin multiplicity increases from singlet to quintet when going from group III to group V in both 3d and 4d ISTCs, but then it suddenly becomes either singlet or triplet at the group VI in the 4d ISTCs unlike in the 3d ISTCs in which a such sudden decrease in the spin multiplicity occurs at the group VIII. All these results of electronic structures and spin multiplicities of 3d and 4d ISTCs indicate that these ISCTs are interesting compounds from the viewpoints of physical chemistry, material science, and coordination chemistry.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported in part by the Grant-in-Aids on Specially Promoted Science and Technology (No. 22000009) and the Grand Challenge Project (IMS) of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan and the Japan Society for the Promotion of Science. Some of the theoretical calculations were performed in the Institute for Molecular Science (Okazaki, Japan).

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(1) Tsai, Y.-C.; Wang, P.-Y.; Chen, S.-A.; Chen, J.-M. J. Am. Chem. Soc. 2007, 129, 8066. (2) Monillas, W. H.; Yap, G. P. A; Theopold, K. H. Angew. Chem., Int. Ed. 2007, 46, 6692. (3) Tsai, Y.-C.; Wang, P.-Y.; Lin, K.-M.; Chen, S.-A.; Chen, J.-M. Chem. Commun. 2008, 205. (4) Kurokawa, Y. I.; Nakao, Y.; Sakaki, S. J. Phys. Chem. A 2010, 114, 1191. (5) Kurokawa, Y. I.; Nakao, Y.; Sakaki, S. J. Phys. Chem. A 2009, 113, 3202. (6) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (7) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (8) Reiher, M.; Salomon, O.; Hess, B. A. Theor. Chem. Acc. 2001, 107, 45. (9) Perdew, J. P. Phy. Rev. B 1986, 33, 8822. (10) Perdew, J. P. Electronic Structure of Solids; Akademie: Berlin, 1991. (11) In DFT(BP86) calculations, we performed frequency calculations. In the triplet state of the Tc complex, the imaginary frequency did not disappear in the D2 symmetry, and we continued to perform the geometry optimization under the C2 symmetry until no imaginary frequency; see Table S2 of the Supporting Information and its footnote. In other cases, the imaginary frequency disappears or becomes very small (less than 100i cm−1). The frequency was not calculated in the B3LYP optimized geometry because the BP86 computational results are close to the MRMP2 one, but the B3LPY calculated results are different in some cases. (12) Roos, B. O. Adv. Chem. Phys. 1987, 69, 399. (13) Hirao, K. Chem. Phys. Lett. 1992, 190, 374. (14) Hirao, K. Chem. Phys. Lett. 1992, 196, 397. (15) Nakano, H. J. Chem. Phys. 1993, 99, 7983. (16) Bergner, A.; Dolg, M.; Kuchle, W.; Stoll, H.; Preuβ, H. Mol. Phys. 1993, 80, 1431. (17) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007. (18) Frisch, M. J.; Pople, J. A.; et al. Gaussian 03; Gaussian Inc.: Wallingford, CT, 2003. (19) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347. (20) Varetto, U. Molekel, ver. 5.3; Swiss National Supercomputing Centre: Manno, Switzerland, 2009. (21) Koch, W.; Holthausen, M. C. A Chemist’s Guide to Density Functional Theory, 2nd ed.; Wiley-VCH: Weinheim, Germany, 2001. (22) Frenking, G.; Frohlich, N. Chem. Rev. 2000, 100, 717. (23) In the Mo complex, we also carried out the CASSCF calculation with 10 orbitals of ϕ1−ϕ10, but we failed to obtain the converged result in spite of a lot of efforts. In the Tc complex, we failed to have convergence of CASSCF calculation when we added the ϕ11 to ϕ12 orbitals to the active space unlike the CASSCF calculation of the Mn complex. The reason is not clear at this moment.

ASSOCIATED CONTENT

* Supporting Information S

Complete references for Gaussian 03, GAMESS, and Molekel 5.3. The DFT calculations with B3LYP* and PW91PW91 functionals of MM (Table S1). Thermal-corrected energies of MM calculated by the BP86 functional (Table S2). Optimized geometries of RM (Table S3 and Figure S1). Orbital energies of MBCr and MBMo calculated by RO-B3LYP method (Figure S2). The PES of MMO method and MTc calculated by the CASSCF (Figure S3). This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

Quantum Chemistry Research Institute, Kyodai Katsura Venture Plaza, 1-36 Goryo-Oohara, Nishikyo-ku, Kyoto 6158245, Japan. 2299

dx.doi.org/10.1021/jp210781v | J. Phys. Chem. A 2012, 116, 2292−2299