CASPT2 Study of Inverse Sandwich-Type Dinuclear Cr(I) and Fe(I

Article pubs.acs.org/JPCA

CASPT2 Study of Inverse Sandwich-Type Dinuclear Cr(I) and Fe(I) Complexes of the Dinitrogen Molecule: Significant Differences in Spin Multiplicity and Coordination Structure between These Two Complexes Masayuki Nakagaki and Shigeyoshi Sakaki* Fukui Institute for Fundamental Chemistry, Kyoto University, Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan S Supporting Information *

ABSTRACT: Inverse sandwich-type complexes (ISTCs), (μ-N2)[M(AIP)]2 (AIPH = (Z)-1-amino-3-imino-prop-1-ene; M = Cr and Fe), were investigated with the CASPT2 method. In the ISTC of Cr, the ground state takes a singlet spin multiplicity. However, the singlet to nonet spin states are close in energy to each other. The thermal average of effective magnetic moments (μeff) of these spin multiplicities is close to the experimental value. The η2-side-on coordination structure of N2 is calculated to be more stable than the η1-end-on coordination one. This is because the d-orbital of Cr forms a strong dπ−π* bonding interaction with the π* orbital of N2 in molecular plane. In the ISTC of Fe, on the other hand, the ground state takes a septet spin multiplicity, which agrees well with the experimentally reported μeff value. The η1end-on structure of N2 is more stable than the η2-side-on structure. In the η1-end-on structure, two doubly occupied d-orbitals of Fe can form two dπ−π* bonding interactions. The negative spin density is found on the bridging N2 ligand in the Fe complex but is not in the Cr complex. All these interesting differences between ISTCs of Cr and Fe are discussed on the basis of the electronic structure and bonding nature.

1. INTRODUCTION In the past decade, inverse sandwich-type complexes (ISTCs) have drawn a lot of interest in coordination chemistry, organometallic chemistry, and physical chemistry, as follows:1−12 In these complexes, an organic moiety is sandwiched by two metal moieties. This is reverse to the usual sandwichtype complex in which a metal is sandwiched by organic moieties. In ISTCs, one metal moiety interacts with another metal moiety through molecular orbitals of the sandwiched organic moiety. Because such interaction depends on the electron configuration and spin state of each metal moiety and also the shape and energy of molecular orbitals of the organic moiety, one can expect that a variety of electronic structures are found in the ISTC. For instance, Tsai and his co-workers found that the Cr(I) ISTCs of benzene and toluene exhibit a high spin multiplicity of septet;5,6 see Figure 1A for this complex. This spin multiplicity is considered to be surprisingly high; remember that most of organometallic compounds tend to take a low spin state. A high spin multiplicity of quintet was also reported for the similar ISTC of V.7 We theoretically investigated the series of ISTCs of benzene for the 3d transition-metal elements and found that the spin multiplicity increases from a singlet to a nonet when going from Sc to Mn and then decreases to a singlet at Fe.11 This interesting behavior of spin multiplicity can be easily explained by orbital diagram in the early transition-metal element but cannot in the late transition-metal element in which we need to consider © 2014 American Chemical Society

Figure 1. (μ-C6H6)[M(N∧N)]2 and (μ-N2)[M(N∧N)]2 (M = Cr, Fe; N∧N = DDP (DDPH = 2-(4-{(2,6-diisopropylphenyl)imino}pent-2ene): R = Me, R′ = 2,6-iPr2C6H3) or AIP (AIPH = (Z)-1-amino-3iminoprop-1-ene): R = H, R′ = H).

sufficiently the static electron correlation. In the 4d transitionmetal elements, our theoretical study shows that the maximum spin multiplicity is found at the Nb (group V) and it is quintet;12 in other words, the maximum spin multiplicity becomes smaller and the position of the maximum spin Received: October 21, 2013 Revised: January 29, 2014 Published: January 30, 2014 1247

dx.doi.org/10.1021/jp410410j | J. Phys. Chem. A 2014, 118, 1247−1257

The Journal of Physical Chemistry A

Article

Figure 2. Optimized structure of (μ-N2)[M(AIP)]2 (M = Cr, Fe) calculated by the CASSCF method. The spin state is singlet in Cr and septet in Fe. Experimental values are in parentheses.

N−N bond in the Cr ISTC, which is parallel too to the M(AIP) plane in both Cr and Fe ISTCs (Figure 1). We employed here an active space consisting of such twelve orbitals as five d orbitals of each metal and two π* orbitals of the dinitrogen molecule. The second-order perturbation (PT2) calculation was carried out with a CASSCF-optimized structure, using a CASSCF wave function as a reference.15,16 The energy denominator shift (EDS) technique17 was employed in the PT2 calculation, where the EDS value of 0.2 au was used throughout the present study. Edmiston−Ruedenberg localization18 was applied to CASSCF active orbitals and then the CASCI calculations were carried out with these localized orbitals to evaluate the occupation number and the spin density of each localized orbitals. To separate electron density between two M(AIP) and N2 moieties, D2h symmetry was kept in the localized orbitals. The restricted active space self-consistent field (RASSCF) calculation with large active space was also carried out to check the double-shell effect. The active space of RAS2, in which all electron configurations are considered, was taken to be the same as that of the above CASSCF calculation. For the active space of RAS3, five 4d-type orbitals of each transition metal were employed. In RAS-SCF calculations, single and double excitations from RAS2 to RAS3 were considered. In addition, DFT calculations of (μ-η2:η2-N2)[Cr(AIP)]2 were carried out for comparison. The usual B3LYP functional19,20 was used for geometry optimization and such functionals as B3LYP*, 21 BP86, 22 PW91PW91, 23 and M06L24,25 were employed for evaluating relative energies and spin multiplicities with the B3LYP-optimized structure. For metal atoms, (311111/22111/411/1) basis sets were employed with the effective core potentials of the Stuttgart group.26 For C, N, and H, cc-pVDZ basis sets were employed,27 where one augmented function was added to each N atom in the AIP because of its anionic character. The CASSCF and RASSCF calculations were carried out by GAMESS28 and the CASPT2 calculation were carried out by MOLCAS 6.4.29 The DFT calculations were carried out by Gaussian09 program package.30

multiplicity moves to the group V from the group VII in the periodic table. These interesting differences between the 3d and the 4d transition-metal elements arise from the difference in d orbital expansion.12 Not only the arene compound but also the dinitrogen molecule is sandwiched by two chromium moieties to afford a dinitrogen-bridged dichromium complex4 (Figure 1B). In this complex, the magnetic moment was reported to be 3.9 μB. This value is much lower than that reported for the Cr ISTC of benzene (6.93 μB), indicating that the antiferromagnetic coupling occurs between two chromium atoms. Another interesting feature of this complex is found in its structure; this dinitrogen molecule takes a η2-side-on coordination structure, which is different from the well-known η1-end-on N2 structure reported in a chromium(I) dinitrogen complex with tetrakis phosphine ligands.13 In the diiron(I) analogue, on the other hand, the dinitrogen molecule takes a η1-end-on coordination structure.3 Its μeff value was reported to be 7.9 μB, which corresponds to a septet spin multiplicity. These spin multiplicities are reverse to those of the ISTCs of benzene, in which the iron complex takes a singlet but the chromium complex takes a septet spin state.11 These features suggest that the interesting differences can be found in bonding nature and electronic structure between the ISTCs of benzene and dinitrogen molecules. In this work, we theoretically investigated a dinitrogenbridged dichromium(I) and diiron(I) complexes, because its electronic structure and coordination geometry are interesting, as mentioned above. Our purposes here are to clarify the electronic structure, spin multiplicity, and spin distribution of these complexes, elucidate why the dichromium complex takes the η2-side-on coordination structure but the diiron complex takes the η1-end-on coordination one, and find determining factors for the electronic structure and spin multiplicity.

2. COMPUTATIONAL DETAILS We employed a model ligand AIP (AIPH = 1-amino-3iminoprop-1-ene) instead of the DDP ligand to save the computational cost (Figure 1B,C). This type of model complex was successfully employed in our previous studies of V and Cr ISTCs of benzene.11 Geometry optimization was carried out at each spin state by the complete active space self-consistent field (CASSCF) method.14 Two coordination structures of η1-endon and η2-side-on N2 were investigated under D2h symmetry, considering the experimental geometry.3,4 The z-axis was taken to be the same as the M−M line and the y-axis is parallel to the

3. RESULTS AND DISCUSSION 3.1. Geometry of (μ-N2)[Cr(AIP)]2 and Relative Energies of Various Spin States. Important structural parameters optimized for the singlet state by the CASSCF method are shown in Figure 2. The CASSCF results for other spin states and DFT results are shown in Supporting 1248



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Table 1. Relative Energies (kcal/mol) of Various Spin Multiplicities with the η1-End-On and the η2-Side-On N2 Coordination Modes Calculated by the CASPT2 Method Cr

Fe

η2-side

η1-end

η2-side

η1-end

spin multiplicity

B3LYP

CASSCF

CASPT2

CASPT2

CASPT2

CASPT2

undecet nonet septet pentet triplet singlet

38.9 0.0 22.6 51.8 70.9 70.5

51.7 1.4 0.8 0.4 0.1 0.0

107.7 3.1 2.1 1.2 0.4 0.0

24.6 19.9 15.3 12.2 10.5

29.2 3.9 10.0 15.9 22.3

50.2 0.0 7.3 14.2 21.9

Figure 3. Schematical orbital pictures of (μ-N2)[Cr(AIP)]2.

On the other hand, the CASSCF and CASPT2 calculations indicate that the ground state takes a singlet state. Also, it should be noted that the energy difference between the singlet and the nonet spin states is very small. This means that the experimentally observed magnetic moment corresponds to the thermal average of these spin multiplicities. According to the Boltzmann distribution law, the average of effective magnetic moments is estimated to be μeff = 4.6 and 2.7 μB with CASSCF and CASPT2 calculated relative energies, respectively, at 293 K. The calculated value is not vey different from the experimental one, indicating that CASSCF and CASPT2 provide reliable results of the spin multiplicity and hence the electronic structure. The relative energies of various spin states calculated by the RASSCF method are shown in Supporting Information Table S3. The energy differences between spin states are not very different from those calculated by the CASSCF method, and the occupation numbers of 4d-type orbitals are very small. These results suggest that the double-shell effect is not large. We will present our discussion based on the CASSCF and CASPT2 computational results hereafter. Though the B3LYP optimized structure at the nonet state agrees well with the experimental one, the CASSCF optimized structures were adopted for calculations of other (μ-N2)[M(AIP)]2 because the correct spin multiplicity is calculated at the CASSCF and CASPT2 levels; see Supporting Information Figure S1 for the CASPT2-optimized geometry. 3.2. Electronic Structure of (μ-η2:η2-N2)[Cr(AIP)]2. The molecular orbital (MO) interaction diagram of (μ-η2:η2N2)[Cr(AIP)]2 is shown in Figure 3, where important orbitals

Information Table S1. The CASSCF optimized structures at the singlet to nonet spin states resemble each other. Though the Cr−Cr distance is about 0.12 Å longer than the experimental value, the Cr−N distance is moderately longer than the experimental values. Considering that a direct bonding interaction is formed between the Cr and N atoms but is not between two Cr atoms, this deviation is not very large. The B3LYP-optimized structures of singlet, quintet, and nonet spin states agree with experimental values of (μ-η2:η2-N2)[Cr(DDP)]2, whereas the optimized structures in the triplet and septet states are much different from the experimental and CASSCF-optimized structures (Supporting Information Table S1). In particular, the Cr−Cr distance is considerably shorter than the experimental value. This is probably because the δ bonding interaction between the dxy orbitals of Cr and the πx* of N2 is overestimated by the single reference wave function, remember that the single reference method cannot treat well the occupation numbers in the δ-type bonding and antibonding MOs.31 The relative energies of various spin states of (μ-η2:η2N2)[Cr(AIP)]2 are listed in Table 1. In the DFT computational results, the nonet state is much more stable than the other spin states. All functionals employed here indicate that the ground state takes a nonet spin multiplicity and other spin states exist at much high energy (Supporting Information Table S2). However, these results disagree with the experimental fact that the effective magnetic moment of (μ-η2:η2-N2)[Cr(DDP)]2 is 3.9 μB, which corresponds to the spin state between the triplet and quartet spin states. 1249



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Table 2. Main Electron Configuration of the CASSCF Wavefunctions of (μ-η2:η2-N2)[Cr(AIP)]2 and (μ-η1:η1-N2)[Fe(AIP)]2 configurationa state

ψ1

ψ2

ψ3

ψ4

ψ5

ψ6 2

9

2

α

α

α

α

7

(2) (2) (2) (2) (2) (2)

(2) (2) (2) (2) (2) (2)

2 2 α 2 0 α

2 α 2 0 2 α

α α α α α α

Ag B1g

a

ψ7

ψ8

ψ9

ψ10

ψ11

ψ12

α

α

0

0

0

0.9565

α α α α α α

α α α α α α

α α α α α α

0 β 0 2 0 β

0 0 β 0 2 β

0.5804 0.3707 0.3236 −0.2284 −0.2096 0.1861

coefficient

2

(μ-η :η -N2)[Cr(AIP)]2 α α (μ-η1:η1-N2)[Fe(AIP)]2 α α α α α α α α α α α α

These orbitals correspond to those of Figures 2 and 3.

Figure 4. CASSCF(10,12) optimized orbitals for the 1Ag state of (μ-η2:η2-N2)[Cr(AIP)]2. The subscript represents irreducible representation under D2h symmetry and in parentheses are occupation numbers of natural orbitals. The natural orbital resembles well the CASSCF-optimized MO. Isovalue of 0.01 was employed for occupied orbitals (φ1 to φ9) and that of 0.05 for unoccupied orbitals (φ10 to φ12).

between the dyz of [Cr(AIP)]2 and the in-plane πz* MO of N2. The ψ2 to ψ9 MOs are essentially nonbonding, though the φ2b MO consisting of Cr dxy slightly overlaps with the πx* MO of N2; see Supporting Information Figure S2 for a brief explanation. Because each Cr center takes +I oxidation state with a d5 electron configuration, a total of ten d electrons occupy these MOs. In the nonet 9Ag state, which is the highest spin multiplicity, two electrons occupy the most stable ψ1 and the remaining eight α-spin electrons occupy eight MOs, as shown in Figure 3A. Actually, the occupation numbers of the CASSCF(10,12)-calculated natural orbitals of (μ-η2:η2-N2)[Cr(AIP)]2 in the 9Ag state are consistent with this understanding, as shown in Figure S3 (Supporting Information). The ψ10 to ψ12 MOs are essentially unoccupied; their small occupation numbers arise from excited electron configurations to these two MOs mainly from the ψ1 due to the electron correlation effect.

of the [Cr(AIP)]2 moiety are displayed on the right-hand side. In Cr(AIP), the Cr dyz orbital is considerably destabilized in energy by the antibonding overlap with the two lone pair orbitals of the AIP ligand.11 Four other d orbitals are nearly degenerate at lower energy because they are nearly nonbonding. When going from Cr(AIP) to [Cr(AIP)]2, one d orbital of the Cr(AIP) moiety above the N2 ligand overlaps with the corresponding d orbital of the other Cr(AIP) below the N2 ligand to form bonding and antibonding pairs (Figure 3A). These bonding and antibonding MOs are nearly degenerate because of the long Cr−Cr distance. They are named φia and φib (i = 1−5) for antibonding and bonding pairs, respectively; for instance, φ5a is an antibonding pair of dyz orbitals of two Cr centers. This φ5a overlaps well with the πz* MO of N2 to form a bonding ψ1 MO and an antibonding ψ12 MO in (μ-η2:η2-N2)[Cr(AIP)]2 (Figure 3A). The ψ1 MO is very stable in energy because of the good π-type overlap 1250



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experimental result that only the η1-end-on structure is isolated in (μ-N2)[Fe(DDP)]2. Several important differences between ISTCs of Fe and Cr and between ISTCs of dinitrogen and benzene are summarized here:; (1) the Fe ISTC of dinitrogen takes the η1-end-on coordination structure but the Cr analogue takes the η2-side-on structure, (2) the singlet state is the ground state in the Cr ISTC of dinitrogen but the septet spin state is the ground state of the Cr ISTC of benzene, and (3) the high spin septet state is the ground state in the Fe ISTC of dinitrogen and the singlet is the ground state of the Fe ISTC of benzene. These differences will be discussed below. 3.4. Electronic Structure of (μ-N2)[Fe(AIP)]2. The MO diagram of (μ-η1:η1-N2)[Fe(AIP)]2 is shown in Figure 5. Each

However, the wave function of the nonet state can be clearly represented by one dominant configuration, as shown in Table 2. In the 1Ag state, the occupation numbers of the CASSCF(10,12)-calculated natural orbitals are similar to that of the 9Ag state; in other words, only ψ1 is doubly occupied and the other eight MOs (ψ2 to ψ9) are singly occupied, as shown in Figure 4; see the Supporting Information Table S4 for the wave function. This feature suggests that the singlet spin state is described by the combination of the four α-spin electrons in four MOs and the four β-spin ones in the other four MOs. This is not unreasonable because these eight electrons can afford singlet, triplet, quintet, septet, and nonet spin states through various combinations. In such a case, the energy differences between these states are small, as shown in Table 1. This is why the experimentally observed magnetic moment corresponds to an intermediate value between triplet and quartet spin states. According to Hund’s rule, the nonet state is expected to be the ground state because eight singly occupied d-orbitals are close in energy to each other, as shown in Figure 3. However, the ground state takes a singlet spin multiplicity against the simple understanding. It is of considerable interest to elucidate why the singlet is the ground state here. The knowledge of such a reason is necessary for correctly understanding the electronic structure of the ISTCs. In Figure 4, it should be noted that the occupation numbers of the ψ4 and ψ8 are moderately larger than 1.00 but those of ψ5 and ψ9 are moderately smaller than 1.00. If the molecular orbitals completely consistent of bonding or antibonding combination of d orbitals, their orbital energies are almost the same because of the long Cr−Cr distance and hence the occupation numbers are 1.0. However, φ2b interacts with the πx* of N2 and φ4b interacts with the πx of N2 (Figure 4 and Supporting Information Figure S2). As a result, ψ4 is more stable than ψ5. Because the same situation is observed in ψ8 and ψ9, ψ8 is more stable than ψ9. To provide larger occupation numbers in more stable MOs than in their counterparts, the ground state must take a singlet rather than the nonet spin state; remember that the occupation numbers of the bonding pair MO is almost the same as that of the antibonding counterpart MO in the high spin state. The difference in spin multiplicity between ISTCs of benzene and dinitrogen will be discussed below. 3.3. Geometries and Relative Energies of Various Spin States of (μ-N2)[Fe(AIP)]2. The CASSCF-optimized structural parameters of (μ-η1:η1-N2)[Fe(AIP)]2 in a septet spin state are shown in Figure 2B. The N−N distance of the N2 ligand agrees with the experimental value, whereas the CASSCF-optimized Fe−N distance is somewhat longer than the experimental one. However, we employed this CASSCF-optimized geometry hereafter, because the spin multiplicity of the ground state and the relative stabilities of the η1-end-on and η2-side-on structures were reproduced well by this geometry and also with the experimental one, as will be discussed below; see also Supporting Information Table S5 and Figure S4 and the explanation there. The relative energies of various spin states of (μ-N2)[Fe(AIP)]2 with η1-end-on and η2-side-on coordination structures of N2 are listed in Table 1. In (μ-η1:η1-N2)[Fe(AIP)]2 with the η1-end-on coordination structure, the septet state is the most stable, which agrees well with the experimentally reported μeff value. In the η2-side-on structure, the septet state is the most stable too but it is less stable than in the η1-end-on N2 structure. This result agrees with the

Figure 5. Schematical orbital pictures of (μ-N2)[Fe(AIP)]2.

Fe(AIP) moiety has seven d electrons (right-hand-side of Figure 5). In Fe(AIP), the dx2 and dz2−y2 orbitals are doubly occupied and the other three d orbitals are singly occupied in the A1 state; see Supporting Information for why dx2 is doubly occupied here. Two important differences are found in this orbital diagram (Figure 5) between the η 2 -side-on and η 1 -end-on N 2 complexes: Two dπ−π* bonding interactions are formed in the η1-end-on structure, whereas only one dπ−π* bonding interaction is formed in the η2-side-on structure. Actually, both φ4a and φ5a overlap with the πx* and πy* MOs of N2 to form 1251



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Figure 6. CASSCF(10,10) natural orbitals for the 7B1g state of (μ-η1:η1-N2)[Fe(AIP)]2. The subscript represents irreducible representation under D2h symmetry and in parentheses are occupation numbers of natural orbitals. An isovalue of 0.03 was employed.

bonding ψ3 and ψ4 MOs and antibonding ψ11 and ψ12 MOs in the η1-end-on N2 complex (Figure 5A). Another important difference is found in the participation of the lone pair of N2; it overlaps well with the φ1(dz2−y2) orbital in an antibonding way to push up the ψ5 and ψ6 in the η1-end-on structure but such an interaction is absent in the η2-side-on structure. When going from CrI to FeI, four more d electrons are added to (μ-η2:η2N2)[Fe(AIP)]2. As a result, two MOs, ψ1 and ψ2, which mainly consist of φ3(dx2), become doubly occupied, as discussed above. The bonding ψ3 and ψ4 MOs are doubly occupied too, because they are stable in energy. Because the ψ11 and ψ12 MOs are the antibonding counterpart of the ψ3 and ψ4, their orbital energies are considerably high. The remaining six electrons occupy the nearly nonbonding ψ5 to ψ10 MOs, as shown in Figure 5A. Hence, the septet spin multiplicity is the most favorable, here. Table 2 shows the wave function of the 7B1g state of (μ-η1:η1N2)[Fe(AIP)]2. Both the second and the third leading terms consist of single- and double-excitations from the bonding ψ3 and ψ4 MOs to the antibonding ψ11 and ψ12. Their coefficients are considerably large, indicating that the electron correlation is large. Because those antibonding ψ11 and ψ12 MOs contain a considerably large N2 component, as shown in Figure 6, the second and the third leading terms are responsible for the negative spin population on the N2 ligand, which will be discussed below. The CASSCF(10,10)-calculated natural orbitals of (μ-η1:η1N2)[Fe(AIP)]2 are shown in Figure 6, where in parentheses are the occupation numbers of the septet state. These occupation numbers are consistent with our qualitative understanding except for the ψ3 and ψ4, whose occupation numbers are about 1.5. Because the occupation numbers of the antibonding ψ11 and ψ12 are about 0.5, these results indicate that the electron excitation configurations from the ψ3 and ψ4 to the ψ11 and ψ12

considerably contribute to the electronic structure. These excited electron configurations correspond to the second and the third leading terms of the CASSCF wave function mentioned above. The occupation numbers of the remaining ψ5 to ψ10 are almost the same as 1.0, which is characteristic feature of the high spin electronic structure. The MO diagram of a η2-N2 side-on complex (μ-η2:η2N2)[Fe(AIP)]2 is shown in Figure 5B. This diagram is essentially the same as that of the η1-end-on complex except for the ψ4 bonding MO, which consists of the Fe dxy and N2 πx* orbitals in η2-side-on but the Fe dyz and N2 πx* orbitals in η1end-on. Though the electronic structure is essentially the same between the η1-end-on and η2-side-on structures, the η1-end-on is more stable than the η2-side-on, as described above, the reason of which will be elucidated below. 3.5. Comparison between the η1-End-On and η2-SideOn Structures. As shown in Table 1, the ISTC of Cr takes a η2-side-on structure but the Fe analogue takes a η1-end-on one. Because the η2-side-on structure provides the well overlap between the dyz orbital of metal and the πz* MO of N2, one strong dπ−π* bonding interaction is formed in the yz plane. The dxy of metal overlaps with the πx* MO of N2 to form a δtype dxy−πx* bonding interaction which is much weaker than the π-type dyz−πz* interaction. In the η1-end-on structure, on the other hand, two πx* and πy* orbitals of N2 interact with the dxz and dyz orbitals of metal to form two dπ−π* bonding interactions. Important is that the dxz−πx* π-type interaction in the η1-end-on structure is stronger than the dxy−πx* δ-type interaction in the η2-side-on because the π-type overlap is larger than the δ-type one. But, the dyz−π* π-type interaction in the η1-end-on structure is weaker than in the η2-side-on, because the η2-side-on provides better orbital overlap than the η1-endon. In general, the d-orbital energy becomes lower and the 1252



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Table 3. Spin Densities on the N2 Moiety Calculated by the CASCI Method with the Localized Molecular Orbitals Cr

Fe

η2-side 1

Ag

ΔE (kcal/mol) N2

πz/y* πx* total

0.0 0.00 0.00 0.00

η1-end 9

1

Ag

3.1 −0.09 0.08 0.00

Ag

10.5 0.00 0.00 0.00

η2-side 9

Ag

24.6 −0.15 0.25 0.10

7

B3g

3.9 −0.57 −0.72 −1.29

η1-end 7

B1g

0.0 −0.62 −0.64 −1.26

calculation with localized MOs to evaluate the spin populations on the πx* and πy* MOs of N2; see Supporting Information Tables S6 and S7 for details of CASCI. The CASCI wave function with the localized orbitals presents clearer understanding of the electronic structure of (μ-η1:η1-N2)[Fe(AIP)]2. In the 7B1g state of (μ-η1:η1-N2)[Fe(AIP)]2, the weight of the main configuration increases and the weights of the second and third leading terms decrease, compared to that of CASSCF natural orbital wave function; see the CI expansion coefficients in Tables 2 and S6 (Supporting Information). As shown in Table 3, the significantly large negative spin density is observed on the N2 ligand in both η1end-on and η2-side-on N2 complexes of Fe. In the 1Ag of (μη2:η2-N2)[Cr(AIP)]2, on the other hand, many electron configurations participate in the wave function even with the localized orbitals, as shown in Table S6 (Supporting Information), where only one part is presented as an example. However, it should be noted that the β-component of the N2 moiety is completely canceled by the α-component, indicating that the spin population is not found on the N2 moiety at all. The similar feature is found in the 9Ag state (Table S6, Supporting Information). As a result, the spin population is not found on the bridging N2 ligand at all in the η2-side-on (μη2:η2-N2)[Cr(AIP)]2, as clearly shown in Table 3, and very small spin population is found on the N2 ligand even in the η1end-on analogue with the nonet spin state. This difference in spin distribution between the Cr and Fe complexes is of considerable interest from the viewpoint of their electronic structures. As is well-known, the stabilization by the exchange interaction becomes larger when the α-spin density increases on the metal d orbitals. Hence, the MOs mainly consisting of the metal d orbital must polarize to increase the α-spin density on the d orbitals. As a result, the β spin density increases in the other moieties such as the πx* and πz* of N2. This can be understood by the spin polarization32,33 on the basis of the CAS natural orbitals, as follows: In the Fe complex, the ψ10 is singly occupied by one α-spin electron (Figures 5A and 7A). The ψ10 mainly consists of the dyz of Fe. To increase the α-spin density on the dyz, the ψ12 mixes into the ψ3, as shown in Figure 7B, where the mixing coefficient λ is positive so as to increase the α-spin density on the dyz. On the other hand, in β-spin space, the ψ12 mixes into the ψ3 with opposite sign coefficient so as to increase the β-spin density on N2 πz* orbital. This mixing corresponds to the mixing of configurations with the single- and double-excitations from ψ3 to ψ12 into a main configuration. This mechanism is spin-polarization similar to that of allyl radical in which the positive spin density is found on the terminal carbon atoms but the negative one is found on the central carbon atom;32 in other words, this feature corresponds to a three-center three-electron (3c−3e) interaction, as shown in Figure 7B. In the Cr complex, on the other hand, such polarization does not necessarily occur because the nonbonding

number of d electrons increases when going from the left-hand side to the right-hand side in the periodic table. This suggests that the CT from metal center to N2 becomes weaker, when going from Cr to Fe, but the number of dπ−π* interaction increases. Because the Cr center takes a d5 electron configuration, the πz* orbital of N2 can form only one strong dπ−π* bonding interaction with the φ5a MO in the η2-side-on structure, to afford the ψ1 MO with a very large stabilization energy, as shown in Figure 3. Another πx* orbital of N2 can overlap with the φ2b MO to form a δ-type bonding interaction, but it is very weak. In the η1-end-on structure, on the other hand, the two dπ−π* bonding interactions are formed, but only one (ψ1) is doubly occupied and another (ψ2) is singly occupied, because this dichromium complex has totally ten d electrons. Hence, the π-type dxz−πx* interaction does not provide enough stabilization energy in the η1-end-on structure. Because the dyz−πz* interaction in the η2-side-on structure is strong enough to compensate the weak δ-type dxz−πx* interaction, as discussed above, the η2-side-on structure is more stable than the η1-end-on one in (μ-N2)[Cr(AIP)]2. In (μ-N2)[Fe(AIP)]2, the Fe center takes a d7 electron configuration. In the η1-end-on coordination structure, both ψ3 and ψ4 including the dxz−πx* and dyz−πy* interactions are doubly occupied. In the η2-side-on coordination structure, both of them are doubly occupied too. However, the δ-type dxz−πx* bonding interaction in the ψ4 MO of the η2-side-on structure is much weaker than the π-type dxz−πx* bonding one of the ψ4 of the η1-end-on. Also, the dyz−πz* interaction in the η2-side-on is not strong enough to compensate the weak δ-type interaction in the Fe complex unlike in the Cr complex, because the d orbital becomes lower in energy when going from the left-hand side to the right-hand side in the periodic table. In addition, the lone-pair orbital of N2 overlaps with the singly occupied φ1(dz2−y2) to participate in the stabilization of the η1-end-on structure. Thus, (μ-N2)[Fe(AIP)]2 prefers the η1-end-on structure to the η2-side-on one. In conclusion, the η2-side-on structure is more stable than the η1-end-on one in (μ-N2)[Cr(AIP)]2 because of the presence of only one doubly occupied dπ orbital, which can form a strong π-type bonding interaction with the π* orbital of N2. In the (μ-N2)[Fe(AIP)]2, the η1-end-on structure is more stable than the η2-side-on one because two doubly occupied dπ orbitals can participate in the π-type bonding interaction with the π* orbital of N2 and in addition the singly occupied φ1(dz2−y2) somewhat contributes to the bonding interaction with the lone pair of N2. These results arise from the general trend found in the periodic table; the d orbital energy becomes lower but the number of d electrons increases when going from the left-hand side to the right-hand side in the periodic table. 3.6. Spin Distributions and Bonding Nature between N2 and M(AIP). We found significantly different spin distributions between (μ-N2)[Cr(AIP)]2 and (μ-N2)[Fe(AIP)]2, as shown in Table 3, where we performed CASCI 1253



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the high spin state, where the notation ψd is employed to represent the nonbonding ψ9 and ψ10 MOs in the η1-end-on Fe complex and the ψ10 MO in the η2-side-on Cr analogue. In the Fe complex, the exchange interaction between the bonding MO ψ3 and the nonbonding MO ψ10 orbital (b3u in D2h symmetry) is larger than that between the ψ3 and the other nonbonding d orbitals because ψ3 and ψ10 contain the same dyz orbital component (Figure 5 and Supporting Information Table S8). Another bonding MO ψ4 in the Fe complex also induces the large exchange interaction with the nonbonding MO ψ9 because they contain the same dxz orbital component. Thus, when the nonbonding ψd MOs including dxz and dyz orbitals are singly occupied, the spin polarization occurs to increase the αspin density on these dxz and dyz orbitals and as a result the high spin state becomes more stable than the low spin state. To provide clearer evidence of the important role of the singly occupied ψd MO, we carried out several calculations with assumed electron configurations. In one, one d electron is added to (μ-η2:η2-N2)[Cr(AIP)]2 and in another two d electrons are removed from (μ-η1:η1N2)[Fe(AIP)]2. The relative energies of various spin states of monoanionic (μη2:η2-N2)[Cr(AIP)]2− and mono- and dicationic (μ-η1:η1N2)[Fe(AIP)]2n+ (n = 1 or 2) are calculated by the CASSCF method, where their geometries were assumed to be the same as those of the neutral Cr and Fe analogues to focus on the difference in electronic structure. In the monoanionic [(μ-η2:η2-N2)[Cr(AIP)]2]−, the high spin state becomes more stable than the low spin state, as shown in Table 4. This result is consistent with the above Table 4. Relative Energies (kcal/mol) of Various Spin Multiplicities in [(μ-η2:η2-N2)[Cr(AIP)]2]−1 and [(μ-η1:η1N2)[Fe(AIP)]2]x (x = +1 or +2)

Figure 7. Mechanism of spin polarization in (μ-N2)[Fe(AIP)]2.

ψd (ψ10) is unoccupied, as shown in Figure 7C. This is why the negative spin density is not found on the bridging N2 ligand of the Cr complex. 3.7. Why (μ-η1:η1-N2)[Fe(AIP)]2 Takes a High Spin Septet State but the Cr Analogue Takes a Singlet State. It is of considerable interest why (μ-N2)[Cr(AIP)]2 takes a singlet state in both η1-end-on and η2-side-on structures but the Fe analogue takes a high spin septet state. In (μ-η2:η2-N2)[Cr(AIP)]2, the most stable ψ1 is doubly occupied and its antibonding counterpart is unoccupied in a formal sense. The situation is the same as in the Fe analogue. However, one important difference is found in the nonbonding d orbital consisting of two dyz orbitals, which is the ψ10 MO in the η2-side-on Cr and the ψ9 and ψ10 in the η1-end-on Fe complexes. The ψ9 and ψ10 MOs of the Fe complex are singly occupied but the ψ10 MO of the Cr analogue is unoccupied, because the number of d electron is smaller in the Cr complex than in the Fe analogue. In the Fe complex, the presence of αspin electrons on the ψ9 and ψ10 induce spin polarization on the ψ3 and ψ4, as discussed above. As a result, the α-spin density increases on the Fe dyz. Because of the larger α-spin density on the dyz, the other d orbitals tend to possess α-spin electron too, which stabilizes the high spin state; remember that high spin state become stable when the exchange interaction between two d orbitals is large. In the η2-side-on Cr analogue, on the other hand, the absence of the α-spin on the nonbonding ψ10 does not request such situation. Hence, the high spin is not the ground state. We wish to discuss here why the singly occupied nonbonding ψd including the dyz orbital plays an important role in providing

[(μ-η2:η2-N2) [Cr(AIP)]2]x

[(μ-η1:η1-N2)[Fe(AIP)]2]x

x = −1 10

B3u B2g 6 B3u 4 B2g 2 B3u 8

0.0 3.8 7.8 12.1 16.7

x = +1 10

B2g B2g 6 B3u 4 B2g 2 B3u 8

17.8 0.0 1.8 3.7 5.7

10

B3g B3g 6 B2u 4 B3g 2 B2u 8

x = +2 15.9 1.7 3.1 4.6 6.1

7

B1u Ag 3 B1u 1 Ag 5

0.5 0.2 0.1 0.0

qualitative explanation. Occupation numbers of CASSCF natural orbitals are shown in Table 5. One additional d electron formally exists in the nonbonding MO ψ10. Another important difference from the neutral analogue is that the occupation number of the antibonding MO ψ12 remarkably increases but that of ψ1 somewhat decreases, suggesting that the presence of α-spin electron on the nonbonding MO ψ10 induces the spin polarization by electron excitation from ψ1 to ψ12. This situation is the same as that shown in Figure 7B. Actually, the large negative spin density is calculated on the N2 π*z orbital by the LMO-CASCI analysis (Table 5 and Supporting Information Table S9). These results show that the α-spin occupation of the nonbonding ψ10 is crucial to provide the high spin state and the negative spin density on the bridging N2 ligand like (μ-η2:η2-N2)[Fe(AIP)]2. In the monocationic [(μ-η1:η1-N2)[Fe(AIP)]2]+, the octet spin state is the ground state in both B2g and B3g electronic states, as shown in Table 4. In both 8B2g and 8B3g states, one d electron is removed from the bonding ψ4 or ψ3 MO, respectively. As a result, the ψ4 or ψ3 becomes singly occupied 1254



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Table 5. Occupation Numbers of the CASSCF Natural Orbitals in [(μ-η2:η2-N2)[Cr(AIP)]2]x (x = 0 or −1) and [(μ-η1:η1N2)[Fe(AIP)]2]x (x = 0, +1, or +2) [(μ-η2:η2-N2)[Cr(AIP)]2]x x=0 1

Ag

[(μ-η1:η1-N2)[Fe(AIP)]2]x

x = −1 10

x=0 7

B3u

ψ1 ψ2 ψ3 ψ4 ψ5 ψ6 ψ7 ψ8 ψ9 ψ10 ψ11 ψ12

b2g ag b1u b1g au ag b1u b3g b2u b3u b1g b2g

1.96 0.99 1.01 1.02 0.97 1.00 1.00 1.06 0.94 0.02 0.01 0.01

1.81 1.00 1.00 1.00 0.99 1.00 1.00 1.00 1.00 1.00 0.01 0.19

π*z/y π*x

b2g b1g

0.00 0.00

−0.40 0.22

B3g

ag (2.00) b1u (2.00) b2g 1.55 b3g 1.45 b1u 1.00 ag 1.00 au 1.00 b1g 1.00 b2u 1.00 b3u 1.00 b3g 0.55 b2g 0.45 Spin Density on N2 b2g −0.62 b3g −0.64

x = +1 8

B2g

x = +2 8

B3g

(2.00) (2.00) 1.43 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.01 0.56

(2.00) (2.00) 1.00 1.39 1.00 1.00 1.00 1.00 1.00 1.00 0.61 0.01

−0.68 0.06

0.06 −0.70

1

Ag

(2.00) (2.00) 1.06 1.05 1.01 0.99 1.00 1.00 0.95 0.94 0.00 0.00 0.00 0.00

MOs are doubly occupied. Because the φ2b and φ3b MOs of Cr(AIP) exist at the second and third lowest energies, they are singly occupied, which lead to the presence of the nonbonding ψ5 and ψ6 MOs in (μ-C6H6)[Cr(AIP)]2. These MOs are singly occupied. Remember that the singly occupied nonbonding ψ5 and ψ6 MOs consist of the same d orbital components as the doubly occupied bonding ψ1 and ψ2 MOs. In this situation, the spin polarization of the bonding orbital necessarily occurs, which increases the exchange interaction among the d orbitals. Hence, (μ-C6H6)[Cr(AIP)]2 takes the high spin septet state, as reported experimentally5,6 and theoretically.11

but the ψ3 or ψ4 remains as doubly occupied MO in the 8B2g or 8 B3g state, respectively (Table 5). Because this monocation species contains one doubly occupied ψ3 or ψ4 MO and two singly occupied nonbonding ψ9 and ψ10 MOs (Table 5), the spin polarization occurs so as to increase α-spin density on the metal center like the neutral analogue. Hence, the high spin state becomes stable and the considerably large negative spin density is calculated on one πz* MO of N2, as shown in Table 5. In the dicationic species, on the other hand, two electrons are removed from the bonding MO ψ3 and ψ4. The singlet state becomes the most stable, but the triplet, quintet, and septet states are very close in energy to each other like the neutral Cr complex, as shown in Table 4. Because the spin polarization does not occur in this case, the negative spin density disappears on the N2 and the moderately positive spin density is calculated due to the spin delocalization, as shown in Table 5 (see also Supporting Information Table S9). On the basis of the above results, it is concluded that the presences of the doubly occupied bonding MO (ψ1 and ψ2 in the Cr complex and ψ3 and ψ4 in the Fe complex) and the singly occupied nonbonding ψd are crucial for stabilizing the high spin multiplicity. In this case, the spin polarization necessarily occurs to increase the exchange interaction on the metal center, which leads to the presence of negative spin density on the N2. 3.8. Comparison between the (μ-N2)[Cr(AIP)]2 and (μC6H6)[Cr(AIP)]2. (μ-N2)[Cr(AIP)]2 takes a singlet state in contrast to the septet spin state of (μ-C6H6)[Cr(AIP)]2. As discussed above, the high spin state becomes stable when the spin polarization of the bonding MO is induced by the singly occupied nonbonding ψd MO, because such polarization increases the exchange interaction among d orbitals of metal center. In (μ-N2)[Cr(AIP)]2, the nonbonding ψ10 MO exists at a much higher energy than the other d orbitals and hence it is unoccupied. As a result, the spin polarization does not occur and this complex takes a singlet state. In (μ-C6H6)[Cr(AIP)]2, the LUMOs of benzene have two nodes. Thus, antibonding φ2a and φ3a MOs of Cr(AIP), which mainly consist of dxy and dx2 orbitals, interact with the LUMOs of benzene to form two pairs of δ-type bonding ψ1 and ψ2 MOs and antibonding ψ11 and ψ12 MOs (Supporting Information Figure S5). The δ-type bonding

4. CONCLUSIONS We theoretically investigated inverse sandwich-type complex (μ-N2)[M(AIP)]2 (M = Cr, Mn, Fe; AIPH = 1-amino-3iminoprop-1-ene). The CASPT2 energies with the CASSCF optimized structures are in good agreement with the experimental results of the spin state and coordination structure of N2. In (μ-N2)[Cr(AIP)]2, the ground state of the η2-side-on coordination structure takes a singlet spin multiplicity. It is more stable than the ground state (singlet) of the η1-end-on coordination structure. The wave function of (μ-η2: η2N2)[Cr(AIP)]2 with the singlet spin state is constructed by the low-spin couplings of eight electrons in nearly degenerate nonbonding d orbitals. Wave functions of such spin states as triplet to nonet spin states are constructed by various coupling of those eight electrons, and hence, singlet to nonet spin states are close in energy to each other. In (μ-N2)[Fe(AIP)]2, the ground state of the η1-end-on N2 coordination structure takes a septet spin multiplicity. It is more stable than the ground state of the η2-side-on N2 coordination structure, which also takes a septet spin multiplicity. The wave function of the septet spin state is constructed by two doubly occupied nonbonding ψ1 and ψ2 MOs, two doubly occupied bonding ψ3 and ψ4 MOs, and six singly occupied nonbonding d MOs ψ5 to ψ10. Because the nonbonding ψ9(dxz) and ψ10(dyz) MOs are singly occupied and the doubly occupied bonding ψ3 and ψ4 MOs consist of the same dxz and dyz components as those of ψ9(dxz) and ψ10(dyz), the configuration mixings of (ψ3 and ψ4 → ψ11 and ψ12) occur so as to increase the exchange 1255



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interactions with the α-spin electrons on these dyz and dxz orbitals. As a result, the septet spin state becomes the ground state and the β-spin density increases on the bridging N2 ligand. The above discussion and several computational results of anionic (μ-N2)[Cr(AIP)2]− and cationic (μ-N2)[Fe(AIP)2]n+, it is reasonably concluded that when doubly occupied bonding MO(s) and singly occupied nonbonding ψd MO(s) consist of the same d orbital component, the spin polarization occurs so as to increase the α-spin density on the d orbital, and hence, the high spin state becomes stable, and as a result, the β-spin density is observed on the bridging N2 ligand. The difference in coordination structure of N2 between (μN2)[Cr(AIP)]2 and the Fe analogue is of considerable interest. This difference is reasonably interpreted in terms of the interaction between the π* orbital of N2 and the doubly occupied dπ orbital of [M(AIP)]. When going from the lefthand side to the right-hand side in the periodic table, the d orbital energy becomes lower and the number of d electrons increases. In the Cr complex, only dyz is doubly occupied, which can form one strong bonding interaction with the πz* MO of the η2-side-on coordinated N2. The πx* MO of N2 can form a δ-type bonding MO with the dxz of Cr but its δ-type bonding interaction is weak. In the η1-end-on coordination structure, two π* MOs of N2 can participate in the bonding interaction with the dπ orbital. In the Cr complex with the η1-end-on structure, only one dyz−πz* bonding MO is doubly occupied and the dxz−πx* π-type bonding MO is singly occupied. In this situation, the η2-side-on is more stable than the η1-end-on structure because the dyz−π* interaction of the η2-side-on is strong enough to overcome the sum of stabilization interactions in the η1-end-on which are provided by one doubly occupied dyz−πz* interaction and one singly occupied dxz−πx*interaction. In (μ-N2)[Fe(AIP)]2, the number of d electrons increases by four compared to that of the Cr analogue. As a result, two dxz and dyz orbitals become doubly occupied, which can provide enough stabilization energy by two dπ−π* bonding MOs in the η1-end-on coordination structure. The sum of stabilization energies by these two dπ−π* interactions of the η1-end-on is larger than the stabilization energy by one strong dπ−π* interaction in the η2-side-on coordination structure, and in addition, the σ-donation of the N2 lone pair to the singly occupied φ1(dz2−y2) of metal center participates in the coordinate bond in the η1-end-on structure. Hence, the η1-end-on mode is more stable than the η2-side-on structure in the (μ-N2)[Fe(AIP)]2. Our theoretical study clearly shows that the number of d electrons, the d orbital energy, and the MOs of bridging ligand provide interesting differences in spin multiplicity and coordination structure between Cr and Fe ISTCs and between benzene and dinitrogen ISTCs.

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S4); CASCI wave functions with the localized orbitals (Table S6); occupation numbers and spin densities of localized orbitals (Table S7); exchange integrals between active orbitals (Table S8); spin densities of the N2 moiety (Table S9); MO diagram of the benzene Cr complex (Figure S5); the reason dx2 exists at a low energy in Fe(AIP); complete ref 30 for Gaussian09. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*S. Sakaki: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by Grant-in-Aids of Specially Promoted Science and Technology (No. 22000009) and Grand Challenge Project (IMS) from Ministry of Education, Culture, Science, Sports, and Technology. We are also thankful to the computational facility at the Institute of Molecular Science, Okazaki, Japan.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Structural parameters of the Cr complex (Table S1); relative energies of the Cr complex calculated by several DFT functionals (Table S2) and the RASSCF method (Table S3); potential energy curves along the Cr−Cr distance (Figure S1); localized orbitals of the Cr complex under D2h symmetry (Figure S2); CASSCF optimized orbitals of the Cr complex in the nonet state (Figure S3); main electron configuration of the Cr complex in the singlet state (Table S4); relative energies of the Fe complex at the experimental Fe−N2 distance (Table S5); potential energy curve along the Fe−Fe distance (Figure 1256



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CASPT2 Study of Inverse Sandwich-Type Dinuclear Cr(I) and Fe(I

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