Analyses on Molecular Properties of the Diamidinate CrIâCrI Complex

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Analyses on Molecular Properties of the Diamidinate Cr-Cr Complex by Multireference and DFT Approaches I

I

Gou-Tao Huang, and Jen-Shiang K. Yu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b04423 • Publication Date (Web): 19 Aug 2019 Downloaded from pubs.acs.org on August 28, 2019

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The Journal of Physical Chemistry

Analyses on Molecular Properties of the Diamidinate CrI−CrI Complex by Multireference and DFT Approaches Gou-Tao Huang† and Jen-Shiang K. Yu∗,†,‡,¶,§ †

Department of Biological Science and Technology, ‡ Institute of Bioinformatics and

Systems Biology, ¶ Institute of Molecular Medicine and Bioengineering, and § Center for Intelligent Drug Systems and Smart Bio-devices (IDS2 B), National Chiao Tung University, Hsinchu City 300, Taiwan E-mail: [email protected]

∗

To whom correspondence should be addressed National Chiao Tung University ‡ National Chiao Tung University ¶ National Chiao Tung University § National Chiao Tung University †

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ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The model system of the diamidinate CrI −CrI complex is investigated by wave function theory (WFT) and Kohn-Sham density functional theory (KS-DFT). The multireference perturbation theory (RASPT2) estimates a stabilization energy of ca. 20 kcal mol−1 for the δ bonding. The multiconfiguration pair-density functional theory (MC-PDFT) with the ftPBE functional well predicts the singlet energy curve comparable to the RASPT2 level. For the KS-DFT scheme based on a single determinant, seven functionals including BP86, BLYP, PBE, B3LYP, M06-L, M06 and ωB97X-D are assessed: two types of functionals are classified according to the nature of the restricted and broken symmetry potential energy curves. The broken symmetry scheme with the type I functionals can give good results for the energy curve in agreement with the multireference calculations. In regard to the metal-metal bonding, the restricted KS-DFT calculations performed by all of the seven functionals yield inferior description due to the lack of significant multiconfigurational character. The Mayer bond order, the electron localization function and electron density predicted by the broken symmetry formalism with the type II functionals are consistent with those obtained with the multireference theory.

Keywords Dichromium(I) complexes, CASPT2, MC-PDFT, KS-DFT

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1

Introduction

Transition metal (TM) chemistry plays an important role in biocatalytic reactions where the mononuclear TM core is the most common at active sites while multicentered TM clusters, such as Fe-S clusters responsible for electron transfer, are also ubiquitous. 1–5 TM clusters, in addition to catalytic functions in enzymes, exhibit more fascinating magnetic properties than mononuclear TM systems. 6,7 Dinuclear systems, which are the simplest form of metallic clusters, have been extensively investigated, and applied in the field of catalysis as well as the design of magnetic materials. 7–11 The two TM centers in bimetallic systems usually interact with each other by antiferromagnetic/ferromagnetic coupling, which is theoretically elucidated by the Heisenberg-Dirac-van Vleck model. Under antiferromagnetic conditions, the energy gaps between the singlet ground state and low lying excited states are small, and thereby thermal effects promote a considerable population in the excited states, which leads to a temperature-dependent behavior in magnetic susceptibility. The separation between two first-row TM centers is around 2.6 ˚ A when antiferromagnetic/ferromagnetic couplings dominate. 12–14 Inspired by a chromium dimer with a bond length of 1.68 ˚ A identified by vibrational spectroscopy, 15,16 scientists were interested in search of a very short metal-metal bond. Theoretical studies have indicated that the short Cr−Cr bond arises from the contribution of δ bonds. Furthermore, dichromium complexes have been synthesized in the three composites of CrII −CrII , CrI −CrII and CrI −CrI . The metal-metal distances in the CrII −CrII compounds range from 1.8 to 2.6 ˚ A depending on the nature of ligands. 17–22 A quadruply-bonded CrI −CrI complex was first isolated in 2005: the bimetallic core was coordinated by terphenyl ligands (Figure 1a), and the metal-metal bond length was 1.84 ˚ A. 23,24 Since then, bridged ligands, such as diazadiene and amidinate, have also been employed to reduce the metal-metal bond length by holding the central TM core more tightly. 14,25–30 With the coordination of the amidinate and guanidinate ligands, the Cr−Cr bond decreased to 1.70−1.75 ˚ A. In aspects of magnetic characterization, these dinuclear CrI −CrI compounds shown in Figure 1a were 3



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temperature independent in magnetic susceptibility. On the other hand, a long CrI −CrI separation of 2.65 ˚ A was observed in the complex where each metal was terminally chelated by one bulky guanidinato ligand, and the chelate compound exhibited an antiferromagnetic behavior. 14 In addition to the homobimetallic species, heterobimetallic complexes in Cr−Fe and Cr−Mn composites were also synthesized, featuring short metal-metal bonds. 31–33

Figure 1: a) Synthesized dinuclear CrI −CrI compounds. amidinate-bridged complexes.

b) Structures of simplified

The typical potential energy curve of a covalent bond, such as a carbon-carbon bond, is shown on the left handed side in Figure 2a; in contrast, an antiferromagnetic interaction causes more complicated energy curves where the energy gaps among different spin states 4


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are small. In the case of dichromium systems, covalent and antiferromagnetic effects interact with each other. As dCr−Cr increases, the interaction between the Cr spin centers changes from covalent dominance to a major antiferromagnetic pattern. As a consequence, two possible conditions occur: 1) the inner and outer wells caused by the covalent and antiferromagnetic interactions coexist (Figure 2b); 2) the outer well vanishes to a shoulder, which leads to the inner well only (Figure 2c). For convenience of description below, the areas near the energy minima of the covalent bonding and the antiferromagnetic coupling are referred to as the CB and AF regions, respectively. A chromium dimer demonstrates a typical case without the existence of the outer well. Qualitative and quantitative descriptions for such a complicated energy curve require high level multireference theories, particularly in the AF region. Complete active space second-order perturbation theory 34–36 (CASPT2) is frequently used to deal with such a near-degenerate problem. In addition to the simplest Cr2 molecule, the dinuclear CrI −CrI complexes in Figure 1a have been computationally investigated by the Kohn-Sham density functional theory 37,38 (KS-DFT) calculations 39–42 based on a single determinant, and by more reliable multireference approaches. 43–48 These computational studies, however, focused on the analysis of electronic structures at the equilibrium geometries with a short Cr−Cr bond length of about 1.7 ˚ A. In the present study, we examine the potential energy curves of the amidinate-based complex with respect to the Cr−Cr separation over the range between 1.6 and 2.6 ˚ A. According to experimental X-ray crystal structures, the metal-metal bond lengths in the amidinate-based compounds were little affected by ligand substituents, and therefore the simplified amidinate ligands capped by methyl groups (Figure 1b) are employed to reduce computational cost. 26 The potential energy curves of S = 0 − 5 are computed by multireference perturbation theory and multiconfiguration pair-density functional theory 49,50 (MC-PDFT). The conventional KS-DFT methodology is also compared with the multiconfigurational approach.

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a) singlet triplet quintet septet

...

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

antiferromagnetic

primarily covalent

b)

c)

antiferromagnetic interaction (AF region)

antiferromagnetic interaction (AF region) covalent bonding (CB region)

covalent bonding (CB region)

Figure 2: Potential energy curves of a) covalent/antiferromagnetic interactions between two atoms as well as their combining patterns, b) with, and c) without the outer well in the AF region.

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2

Computational Details

The relaxed potential energy curve scan in the broken symmetry (BS) singlet state was performed at the BP86 51,52 /def2-TZVP 53 level by elongating the Cr−Cr bond length from 1.6 to 2.6 ˚ A (Figure 1b). Using the relaxed structures, the scanned energy curve was refined with multireference approaches. Note that the condition at a longer Cr−Cr separation than 2.6 ˚ A was not discussed in the present study because bridged ligands supported the two metal centers in the range of 1.7 − 2.6 ˚ A observed in the X-ray structures of dinuclear CrI −CrI and CrII −CrII complexes. 14,17–30 The basis set superposition error (BSSE) correction was thus not included. The D2h symmetry was imposed in the multiconfigurational calculations since the DFT-scanned geometries were almost D2h -symmetric. The ground states in S = 0 − 5 belong to 1Ag , 3B1u , 5Ag , 7B1u , 9Ag , and

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B1u representations. Scalar

relativistic effects were described by the second-order Douglas-Kroll-Hess 54,55 (DKH) Hamiltonian, and the Cholesky decomposition 56,57 with a threshold of 10−6 was used to speed up two-electron integrals. The ANO-RCC 58–60 basis sets were employed with the contractions of [10s10p8d6f4g2h] for Cr, [4s3p1d] for C/N, and [2s] for H. The active orbitals of complete active space self consistent field 34 (CASSCF) and the restricted formalism (RASSCF) were chosen from the 3d and 4d orbitals of the two CrI ions, as well as the bonding orbitals of 4s and 4px . Table 1 lists the active spaces in the eight sets of CASSCF/RASSCF (Figures 3 and S1−S6). In RASSCF, only double excitation was allowed from the RAS2 to the RAS3 orbitals. The strength of the metal-metal bond was analyzed by the effective bond order 46,61 (EBO), defined by half of the difference between the electron occupation numbers of the 3d bonding and antibonding natural orbitals. Based on the CASSCF/RASSCF reference wavefunction, the second order perturbation theory 35,36 (CASPT2/RASPT2) was used to recover dynamic correlation energy. The intruder state was avoided by applying an imaginary shift 62 of 0.1. The recommended IPEA value of 0.25 was set in all CASPT2/RASPT2 computations. 63 Alternatively, the MC-PDFT approach has been recently developed to tackle the dynamic correlation energy. MC-PDFT directly uses the CAS wavefunction to incorporate 7



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the static correlation effect, and then the part of the dynamic correlation is computed by the on-top density functional with respect to the one-particle density ρ and the on-top two particle density Π. The on-top density functional of tPBE 49 derived from the translation of the PBE 64 functional, and its fully translated 65 (ftPBE) form was formulated by including the gradients of the electron density and the on-top density. In order to distinguish MCPDFT from the conventional KS-DFT, the prefix RAS is added to stand for the MC-PDFT calculations, such as RAS-ftPBE. In aspects of the KS-DFT methodology, BP86 51,52 , BLYP 51,66 , B3LYP 66–68 , PBE 64 , M06-L 69 , M06 70 , and ωB97X-D 71 were tested with the same ANO-RCC basis sets, in combination of the relativistic DKH2 treatment. The analysis of wavefunction stability was performed to verify whether restricted and broken symmetry solutions are stable under the perturbations. 72,73 Because the EBO value can only be obtained from multiconfigurational wavefunctions, the Mayer bond order 74,75 was alternatively used to examine the bond strength in KS-DFT. In addition, the metal-metal bond was also analyzed by the electron localization function 76 using the Multiwfn 77 software. The multireference and KS-DFT computations were done by Molcas 8.2 78 and Gaussian 09 packages, 79 respectively. Table 1: Active orbitals in the CASSCF/RASSCF calculations. The maximal electron number of 2 is allowed in the RAS3 orbitals in the RASSCF computations. types of active orbitals RAS2 CASSCF-A CASSCF-B CASSCF-C RASSCF-D RASSCF-E CASSCF-F CASSCF-G RASSCF-H

1σ 1σ 1σ 1σ 1σ 1σ 1σ 1σ

∗

1σ 1σ ∗ 1σ ∗ 1σ ∗ 1σ ∗ 1σ ∗ 1σ ∗ 1σ ∗

1π 1π 1π 1π 1π 1π 1π 1π

∗

1π 1π ∗ 1π ∗ 1π ∗ 1π ∗ 1π ∗ 1π ∗ 1π ∗

2π 2π 2π 2π 2π 2π 2π 2π

∗

2π 2π ∗ 2π ∗ 2π ∗ 2π ∗ 2π ∗ 2π ∗ 2π ∗

1δ 1δ 1δ 1δ 1δ 1δ 1δ 1δ

∗

1δ 1δ ∗ 1δ ∗ 1δ ∗ 1δ ∗ 1δ ∗ 1δ ∗ 1δ ∗

2δ 2δ 2δ 2δ 2δ 2δ 2δ 2δ

RAS3 ∗

2δ 2δ ∗ 2δ ∗ 2δ ∗ 2δ ∗ 2δ ∗ 2δ ∗ 2δ ∗

3δ 2σ 2σ 3π 3π 2σ 2σ 3π

8

3π 4π 3δ 4δ 3π 4π 3δ 4δ σligand 3δ 3δ 2σ ∗ 3σ 3δ 3δ ∗ 2σ ∗ 3σ 3δ 3δ ∗ σligand 3δ


2σ 3σ 2σ ∗ 5π 4π 3δ ∗ 4δ 4δ ∗ 2σ 3σ 2σ ∗ 5π 3π ∗ 4π 4π ∗ 3δ ∗ 4δ 4δ ∗

2σ 3σ 2σ ∗ 3δ ∗ 4δ 4δ ∗

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Figure 3: Natural orbitals of RASSCF-E at the equilibrium structure (dCr−Cr : 1.74 ˚ A). Electron occupation numbers are listed in parentheses: the red and blue values represent the RAS2 and RAS3 orbitals, respectively.

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3

Results and Discussion

3.1 3.1.1

Multiconfigurational computations CASPT2 and RASPT2

Figure 4 shows the singlet and triplet potential energy curves in the eight sets of multireference calculations. The 3δ orbital is rotated out of the active space at large Cr−Cr separation in the CASSCF-A calculation so that the active orbitals are inconsistent over the scanned range (Figure S1). This orbital rotation can be avoided by the inclusion of five 4d-type bonding orbitals, leading to the decreasing energy difference between the CB and AF regions for the singlet curve (CASPT2-A v.s. CASPT2-B in Figure 4a). As the antibonding orbitals are incorporated, the energy difference between the CB and AF regions is enlarged (from CASPT2-B to RASPT2-E), and notably the minimum for the triplet curve shifts from 2.5 ˚ A to 2.0 ˚ A. Next, we examine the situation that simultaneously contains the 4d-type bonding and antibonding orbitals. For the singlet curves in the three cases of CASPT2-F, RASPT2-H and RASPT2-E, the AF region shown in Figure 4b is kept 15−20 kcal mol−1 above the CB region. The triplet states feature the equilibrium Cr−Cr bond length between 2.0 ˚ A and 2.2 ˚ A. Hence, the 4d bonding orbitals must be accompanied by their corresponding antibonding orbitals in the active space, otherwise the shape of the curves would be incorrect, which is exemplified by the triplet curve characterized by an outer well. In addition, the σ-donor orbital of the ligand has little effects on the potential energy curve (CASPT2-B/CASPT2-C in Figure 4a and CASPT2-F/CASPT2-G in Figure 4b). The following RASPT2 and MC-PDFT calculations are based on the RASSCF-E reference wavefunction. Figure 5 shows the energy curves for all of the spin states. The Cr−Cr bond length at the singlet equilibrium structure is 1.74 ˚ A, which agrees well with experimental results. The energy minimum of the triplet curve at 1.99 ˚ A in dCr−Cr lies ca. 20 kcal mol−1 higher than the singlet equilibrium geometry. The curves of S = 2 − 5 are characterized by outer wells, which is similar to the RASSCF curves (Figure S7). Qualitatively, the dynamic correlation 10


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a)

b) 40

40 singlet triplet

singlet triplet

CASPT2-A CASPT2-B CASPT2-C RASPT2-D RASPT2-E

35 30

30

25 20

25 20

15

15

10

10

5

5

0

1.6

1.8

2

2.2

CASPT2-A CASPT2-F CASPT2-G RASPT2-H RASPT2-E

35

E (kcal/mol)

E (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.4

0

2.6

1.6

Cr−Cr (Å)

1.8

2

2.2

2.4

2.6

Cr−Cr (Å)

Figure 4: Potential energy curves for a) singlet and b) triplet states, plotted by the solid and dashed lines, respectively. The energies are relative to the singlet equilibrium geometry. plays a more significant role for the curves of S = 0 and 1. The calculations demonstrate that the curves shown in Figure 5 correspond to the scenario in Figure 2c, implying that the antiferromagnetic property cannot be observed in the amidinate-bridged complex of a short Cr−Cr bond due to the lack of the outer well in the singlet ground state. Electronic structures of the CrI −CrI compounds have been investigated by multiconfigurational methods. 43–48 A short Cr−Cr bond is due to δ-bonding interactions by two sets of dxy and dx2 −y2 orbitals. Herein, the δ-bonding contribution is re-examined by the comparison of three electronic structures of S = 0 − 2 (Table 2). The weights of the leading configurations for the three spin states are about 52% (41% + 12% in the triplet state) while the rest configurations account for 47%, which implies the deficiency of the restricted KS-DFT methodology based on only one electronic configuration, 1σ 2 1π 2 2π 2 1δ 2 2δ 2 . The primary difference of the leading configurations among S = 0 − 2 is the arrangement of the four electrons filled in the four δ orbitals (1δ 2 2δ 2 , 1δ 2 2δ ↑ 2δ ∗↑ /1δ ↑ 1δ ∗↑ 2δ 2 and 1δ ↑ 1δ ∗↑ 2δ ↑ 2δ ∗↑ for the singlet, triplet and quintet states, respectively). In order to analyze the effect of the Cr−Cr bond length on the δ bond, the EBO composed of σ, π and δ portions is plotted

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against dCr−Cr in Figure 6. The decreasing trends of the σ and π bond orders are consistent in the three spin states, and accordingly the δ bonding contribution is the dominant factor leading to the EBO difference, which indicates that the position of the minima shifting from an inner to an outer well is affected by the magnitude of the δ bond order. At the singlet equilibrium geometry, the multireference calculations give a total EBO of 3.73, in which the δ bonding contribution accounts for 1.40. The triplet energy curve is characterized by the flat bottom with a minimum at 1.99 ˚ A, as a result of the decreasing δ bond order. Actually, the dominant configurations in the triplet state, 1σ 2 1π 2 2π 2 1δ 2 2δ ↑ 2δ ∗↑ /1σ 2 1π 2 2π 2 1δ ↑ 1δ ∗↑ 2δ 2 , correspond to a formal quadruple bond (Table 2). The nature of the flat bottom also implies a flexible Cr−Cr distance, which can be reflected by the broad Cr−Cr range of 1.8−2.6 ˚ A observed in dinuclear CrII −CrII compounds. 17–22,80 For the quintet state, four unpaired electrons are aligned in the four δ-type orbitals (Table 2) so as to contribute the δ bond order of smaller than 0.5 in the total EBO. The analyses confirm that the formation of the short metal-metal bond arises from the δ bonding, otherwise the energy minimum would reside in the AF region. Thus, the energy difference of approximately 20 kcal mol−1 in going from the CB (1.74 ˚ A) to the AF region (2.5 ˚ A) can be considered as the stabilization energy of the δ bond. Table 2: Major configurations and the corresponding weights. The RASPT2 energies (in kcal mol−1 ) are relative to the singlet equilibrium geometry at 1.74 ˚ A in dCr−Cr . dCr−Cr 1.74

major configuration singlet triplet quintet

1.99

triplet

weight

ERASPT2

1σ 2 1π 2 2π 2 1δ 2 2δ 2 1σ 2 1π 2 2π 2 1δ 2 2δ ↑ 2δ ∗↑ 1σ 2 1π 2 2π 2 1δ ↑ 1δ ∗↑ 2δ 2 1σ 2 1π 2 2π 2 1δ ↑ 1δ ∗↑ 2δ ↑ 2δ ∗↑

51% 41% 12% 51%

0.0 25.2

1σ 2 1π 2 2π 2 1δ 2 2δ ↑ 2δ ∗↑ 1σ 2 1π 2 2π 2 1δ ↑ 2δ 2 1δ ∗↑

19% 10%

19.5

12


55.1

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40 35

E (kcal/mol)

30 25 20 15 undectet nonet septet quintet triplet singlet

10 5 0

1.6

1.8

2

2.2

2.4

2.6

Cr−Cr (Å)

Figure 5: Potential energy curves computed at the RASPT2-E level.

a) singlet

b) triplet 4

total EBO π δ σ effective bond order (EBO)

3

2

1

0

c) quintet 4

total EBO π δ σ

3

effective bond order (EBO)

4

effective bond order (EBO)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2

1

1.6

1.8

2

2.2 Cr−Cr (Å)

2.4

2.6

0

total EBO π δ σ

3

2

1

1.6

1.8

2

2.2

2.4

2.6

Cr−Cr (Å)

0

1.6

1.8

2

2.2

2.4

2.6

Cr−Cr (Å)

Figure 6: Variation of the EBO with the Cr−Cr bond length for a) singlet, b) triplet and c) quintet states. The total EBO bond order is composed of three components of the σ, π and δ bond orders.

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3.1.2

MC-PDFT calculations

The MC-PDFT methodology is used to assess the potential energy curves in comparison with RASPT2. Among the MC-PDFT calculations utilizing tLSDA, ftLSDA, tPBE, ftPBE, trevPBE, ftrevPBE, tBLYP and ftBLYP functionals, the best performance giving similar results to the RASPT2 is obtained with ftPBE and ftBLYP (Figure S8). Figure 7 shows the potential curves computed by RAS-ftPBE. In the CB region, the equilibrium Cr−Cr bond length is ca. 1.70 ˚ A; the curve near the AF region is flatter than that of RASPT2-E. Except tLSDA and ftLSDA, the other six functionals of MC-PDFT predict an outer well for the triplet curve, and fail to reproduce a minimum of 1.99 ˚ A in the triplet curve of RASPT2. The four spin states of S = 2 − 5 are characterized by the outer wells, as observed in Figure 5. 40 35 30

E (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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25 20 15 undectet nonet septet quintet triplet singlet

10 5 0

1.6

1.8

2

2.2

2.4

2.6

Cr−Cr (Å)

Figure 7: Potential energy curves computed at the RAS-ftPBE level based on the RASSCF-E reference wavefunction. The RASPT2-E curves are shown by the gray dashed lines for comparison.

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3.2

KS-DFT calculations

3.2.1

Potential energy curves

For the KS-DFT methodology, the seven functionals of BP86, BLYP, B3LYP, PBE, M06-L, M06 and ωB97X-D are employed to examine the singlet potential energy curve in both restricted and broken symmetry formalisms. Two distinct scenarios are classified according to the nature of the singlet curves shown in Figures 8 and S12: I) BP86, BLYP and PBE, categorized as the type I functionals, reveal that the restricted and broken symmetry curves tend to coincide when dCr−Cr shrinks to 1.7 ˚ A; II) the restricted energy curves of B3LYP, M06-L, M06 and ωB97X-D, categorized as the type II functionals, always lie above the broken symmetry curves. Similar results were found in the literature, 81,82 and the formation of an outer well was relevant to the percentages of Hartree-Fock exchange (however, this might also be related to the nature of the functionals since the pure functional of M06-L yields an outer well in the case shown in Figure S12c). 83 The analysis of wavefunction stability shows that all restricted wavefunctions have an internal instability except the overlap of the restricted and broken symmetry curves. Next, we take BP86 and B3LYP as representatives to illustrate the difference between the type I and II functionals (Figure 8). The prefixes Rand BS- added to the functionals denote the restricted and broken symmetry formalisms for S = 0, respectively. Both R-BP86 and R-B3LYP (blue curves in Figure 8) yield an inner well with an equilibrium Cr−Cr bond length of 1.67 ˚ A that is shorter than 1.74 ˚ A estimated at the RASPT2 level. The two R-P86 and BS-BP86 energy curves overlap at dCr−Cr < 1.68 ˚ A (Figure 8a). In contrast, the R-B3LYP and BS-B3LYP curves never coincide with each other. The BS-B3LYP curve features an outer well with a minimum at 2.5 ˚ A. In addition, we have attempted to correct the BS-B3LYP potential energy curve with the Yamaguchi’s approximate spin projection procedure to eliminate spin contamination, but the pure singlet energy curve was not improved (Figure S13a). 84–87 On the other hand, the alternative correction based on the weak coupling limit derived by Noodleman 82,88,89 is

15



able to qualitatively yield an inner well (Figure S13b), and the equilibrium Cr−Cr bond length (1.57 ˚ A), however, is underestimated. The information in Figure 8 indicates that at short dCr−Cr , BS-BP86 tends to form a closed shell electronic structure, whereas BS-B3LYP holds the broken symmetry properties, giving an overlap integrals of 0.79 and 0.69 in the δ-type corresponding orbitals (Figure S11). In the section below, the Cr−Cr bonding character is to be analyzed using the BP86 and B3LYP functionals in comparison with the RASPT2-E result. a) BP86

b) B3LYP

60

60

S=5

50

50

40

restricted S=0

40 E (kcal/mol)

E (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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30 broken symmetry S=0

restricted S=0

20

S=5

30

20

10

10 broken symmetry S=0

0

1.6

1.8

2

2.2

2.4

0

2.6

1.6

1.8

Cr−Cr (Å)

2

2.2

2.4

2.6

Cr−Cr (Å)

Figure 8: Potential energy curves computed with the KS-DFT of a) BP86, and b) B3LYP functionals.

3.3 3.3.1

Analysis of the Cr−Cr bond Mayer bond order

The bonding strength between the two Cr centers is evaluated by the Mayer bond order (MBO). As anticipated, the restricted KS-DFT methods give a high MBO of ca. 4.5 in the CB region (Figure 9). The MBO values at the BS-BP86 level are higher than those of BSB3LYP at any dCr−Cr . The varying trend of the bond order computed by BS-B3LYP agrees 16


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nicely with that obtained by the multireference theory. It is concluded that the restricted KS-DFT formalism is inevitable to overestimate the Cr−Cr bond order, particularly in the CB region at 1.7 ˚ A in dCr−Cr (Figure S14). The broken symmetry scheme in combination of the type II functionals is capable to well describe the bond order. In addition, a similar trend is also obtained with the Wiberg bond index 90,91 shown in Figure S15. R-BP86 BS-BP86 R-B3LYP BS-B3LYP RASPT2-E

4

Mayer bond order

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3

2

1

0

1.6

1.8

2

2.2

2.4

2.6

Cr−Cr (Å)

Figure 9: Variation of the Mayer bond order between the two metal centers with respect to dCr−Cr .

17



3.3.2

Electron localization function

In addition to the Mayer bond order, the electron localization function (ELF) provides an alternative to analyze the bonding pattern. The ELF analysis using the singlet wavefunction of RASPT2-E displays two disynaptic basins V1 (Cr1, Cr2) and V2 (Cr1, Cr2) between the metal center (Figure 10), and their attractors pass the x axis. The calculated electron number of 0.79e for each of the two basins indicates a weakly covalent metal-metal bonding around the lateral region. This value is decreased to 0.69e and 0.56e in the triplet and quintet states, respectively, which suggests that the disynaptic basins are contributed partially from the δ bond. In aspect of KS-DFT, BS-B3LYP yields an electron population of 0.82e integrated over the basin, which is similar to that obtained by RASPT2. R-BP86, BS-BP86 and RB3LYP give higher electron numbers of 0.93e, 92e and 96e, respectively.

Figure 10: ELF attractors of the disynaptic basins with respect to Cr. The values in the table indicate the electron numbers integrated over the basin domain. The distances between the V1 (Cr1, Cr2) and the origin are shown in brackets.

18


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3.3.3

Electron density

The computed electron density and the Laplacian at the midpoint between two Cr atoms are compared with experimental data (Table S2), and the multireference approach well predicts these values in accord with experiments. 40 Figure 11 shows the electron density plotted along the x, y and z axes. The electron density calculated at the BS-B3LYP level is closest to that of the RASPT2-E computation. The BP86 functional and the restricted B3LYP obviously overestimate the electron density.

Figure 11: Electron density, ρ(~r) in e/˚ A3 , along the x, y and z axes around the midpoint between two Cr atoms. The structure is taken from the RASPT2-E equilibrium geometry.

19



4

Conclusions

The potential energy curves with respect to dCr−Cr in the amidinate-bridged CrI −CrI complex are investigated by the multiconfigurational CASPT2/RASPT2 and MC-PDFT approaches as well as the KS-DFT methodology. The RASPT2 calculations demonstrate that no outer well is formed at large Cr−Cr separation along the singlet potential energy curve, and the equilibrium bond length of 1.74 ˚ A agrees with experimental data. According to the EBO analysis, the increasing δ bonding is the dominant factor leading to the formation of the inner well in the CB region, and the stabilization energy of the δ bonding is estimated at ca. 20 kcal mol−1 . Among the eight functionals (tLSDA, ftLSDA, tPBE, ftPBE, trevPBE, ftrevPBE, tBLYP, and ftBLYP) of MC-PDFT, ftPBE and ftBLYP can yield the most similar energy curves to RASPT2; however, the triplet curve can not be reproduced qualitatively. For the KS-DFT formalism, the functionals of BP86, BLYP, PBE, B3LYP, M06-L, M06 and ωB97X-D fall into two categories according to the nature of the singlet potential energy curves. The types I and II functionals complement each other to well describe the CrI −CrI complex. The potential energy curves generated by the broken symmetry formalism with the type I functionals of BP86, BLYP and PBE agree with the RASPT2 curve. However, the analyses of the bond order, ELF and electron density regarding the Cr−Cr bond should rely on the broken symmetry scheme with the type II functionals of B3LYP, M06-L, M06 and ωB97X-D. We recommend that if one intends to use the KS-DFT scheme to study the dichromium system, the restricted formalism could be employed to locate the equilibrium structure despite a underestimated Cr−Cr bond length, and then single-point calculations are performed by the broken symmetry formalism using the type II functionals to analyze molecular properties.

20


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Acknowledgement The authors are indebted to the Ministry of Science and Technology (MOST), Taiwan, for financial support under Grants MOST 106-2113-M-009-018-MY3, and the ”Center for Intelligent Drug Systems and Smart Biodevices (IDS2 B)” from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan. G.T.H. acknowledges the postdoctoral fellowship from MOST 106-2811-M-009-005 and 106-2811-M-009-040.

Supporting Information This material is available free of charge via the Internet at http://pubs.acs.org. Natural orbitals of the CASSCF/RASSCF calculations, potential energy curves computed by the MC-PDFT and KS-DFT methodologies, analysis of the bond order, and coordinates of the scanned structures. Author Contributions All authors have given approval to the final version of the manuscript. The authors declare no competing financial interest.

References (1) Johnson, D. C.; Dean, D. R.; Smith, A. D.; Johnson, M. K. Structure, function, and formation of biological iron-sulfur clusters. Annu. Rev. Biochem. 2005, 74, 247–281. (2) Mitić, N.; Smith, S. J.; Neves, A.; Guddat, L. W.; Gahan, L. R.; Schenk, G. The catalytic mechanisms of binuclear metallohydrolases. Chem. Rev. 2006, 106, 3338– 3363. (3) Holm, R. H.; Lo, W. Structural conversions of synthetic and protein-bound iron-sulfur clusters. Chem. Rev. 2016, 116, 13685–13713.

21



(4) Valdez, C. E.; Smith, Q. A.; Nechay, M. R.; Alexandrova, A. N. Mysteries of metals in metalloenzymes. Acc. Chem. Res. 2014, 47, 3110–3117. (5) Wolle, D.; Dean, D.; Howard, J. Nucleotide-iron-sulfur cluster signal transduction in the nitrogenase iron-protein: The role of Asp125. Science 1992, 258, 992–995. (6) Craig, G. A.; Murrie, M. 3D single-ion magnets. Chem. Soc. Rev. 2015, 44, 2135–2147. (7) Liu, K.; Shi, W.; Cheng, P. Toward heterometallic single-molecule magnets: Synthetic strategy, structures and properties of 3d-4f discrete complexes. Coord. Chem. Rev. 2015, 289-290, 74–122. (8) Chen, H. Z.; Liu, S. C.; Yen, C. H.; Yu, J. S. K.; Shieh, Y. J.; Kuo, T. S.; Tsai, Y. C. Reactions of metal-metal quintuple bonds with alkynes: [2+2+2] and [2+2] cycloadditions. Angew. Chem. Int. Ed. 2012, 51, 10342–10346. (9) Powers, I. G.; Uyeda, C. Metal−metal bonds in catalysis. ACS Catal. 2017, 7, 936–958. (10) Huang, Y. S.; Huang, G. T.; Liu, Y. L.; Yu, J. S. K.; Tsai, Y. C. Reversible cleavage/formation of the chromium−chromium quintuple bond in the highly regioselective alkyne cyclotrimerization. Angew. Chem. Int. Ed. 2017, 56, 15427–15431. (11) Rej, S.; Tsurugi, H.; Mashima, K. Multiply-bonded dinuclear complexes of earlytransition metals as minimum entities of metal cluster catalysts. Coord. Chem. Rev. 2018, 355, 223–239. (12) Chai, J.; Zhu, H.; St¨ uckl, A. C.; Roesky, H. W.; Magull, J.; Bencini, A.; Caneschi, A.; Gatteschi, D. Synthesis and reaction of [{HC(CMeNAr)2 }Mn]2 (Ar = 2,6-i Pr2 C6 H3 ): The complex containing three-coordinate manganese(I) with a Mn−Mn bond exhibiting unusual magnetic properties and electronic structure. J. Am. Chem. Soc. 2005, 127, 9201–9206.

22


Page 22 of 33

Page 23 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(13) Lu, D.-Y.; Yu, J.-S. K.; Kuo, T.-S.; Lee, G.-H.; Wang, Y.; Tsai, Y.-C. Theory-guided experiments on the mechanistic elucidation of the reduction of dinuclear zinc, manganese, and cadmium complexes. Angew. Chem. Int. Ed. 2011, 50, 7611–7615. (14) Noor, A.; Bauer, T.; Todorova, T. K.; Weber, B.; Gagliardi, L.; Kempe, R. The ligandbased quintuple bond-shortening concept and some of its limitations. Chem. Eur. J. 2013, 19, 9825–9832. (15) Casey, S. M.; Leopold, D. G. Negative ion photoelectron spectroscopy of chromium dimer. J. Phys. Chem. 1993, 97, 816–830. (16) Bondybey, V. E.; English, J. H. Electronic structure and vibrational frequency of Cr2 . Chem. Phys. Lett. 1983, 94, 443–447. (17) Cotton, F. A.; Koch, S. A.; Millar, M. Tetrakis(2-methoxy-5-methylphenyl)dichromium. Inorg. Chem. 1978, 17, 2084–2086. (18) Cotton, F. A.; Rice, G. W.; Sekutowski, J. C. 1,3-Diphenyltriazine complexes of dichromium(II), dimolybdenum(II), and chromium(III). Inorg. Chem. 1979, 18, 1143– 1149. (19) Cotton, F. A.; Murillo, C. A.; Pascual, I. An unprecedented quadruply bonded compound with a bridging chlorine atom: Cr2 [(o-ClC6 H4 N)2 CH]3 (µ-Cl). Inorg. Chem. Commun. 1999, 2, 101–103. (20) Cotton, F. A.; Hillard, E. A.; Murillo, C. A.; Zhou, H. C. After 155 years, a crystalline chromium carboxylate with a supershort Cr−Cr bond. J. Am. Chem. Soc. 2000, 122, 416–417. (21) Cotton, F. A.; Daniels, L. M.; Murillo, C. A.; Schooler, P. Chromium(II) complexes bearing 2,6-substituted N, N 0 -diarylformamidinate ligands. J. Chem. Soc. Dalt. Trans. 2000, 2001–2005. 23



(22) Cotton, A. F.; Daniels, L. M.; Murillo, C. A.; Schooler, P. Chromium(II) complexes bearing 2-substituted N, N 0 -diarylformamidinate ligands. J. Chem. Soc. Dalt. Trans. 2000, 2007–2012. (23) Nguyen, T. Synthesis of a stable compound with fivefold bonding between two chromium(I) centers. Science 2005, 844, 844–848. (24) Wolf, R.; Ni, C.; Nguyen, T.; Brynda, M.; Long, G. J.; Sutton, A. D.; Fischer, R. C.; Fettinger, J. C.; Hellman, M.; Pu, L.; Power, P. P. Substituent effects in formally quintuple-bonded ArCrCrAr compounds (Ar = terphenyl) and related species. Inorg. Chem. 2007, 46, 11277–11290. (25) Kreisel, K. A.; Yap, G. P.; Dmitrenko, O.; Landis, C. R.; Theopold, K. H. The shortest metal-metal bond yet: Molecular and electronic structure of a dinuclear chromium diazadiene complex. J. Am. Chem. Soc. 2007, 129, 14162–14163. (26) Hsu, C. W.; Yu, J. S. K.; Yen, C. H.; Lee, G. H.; Wang, Y.; Tsai, Y. C. Quintuplybonded dichromium(I) complexes featuring metal−metal bond lengths of 1.74 ˚ A. Angew. Chem. Int. Ed. 2008, 47, 9933–9936. (27) Tsai, Y. C.; Hsu, C. W.; Yu, J. S. K.; Lee, G. H.; Wang, Y.; Kuo, T. S. Remarkably short metal−metal bonds: A lantern-type quintuply bonded dichromium(I) complex. Angew. Chem. Int. Ed. 2008, 47, 7250–7253. (28) Noor, A.; Wagner, F. R.; Kempe, R. Metal-metal distances at the limit: A coordination compound with an ultrashort chromium−chromium bond. Angew. Chem. Int. Ed. 2008, 47, 7246–7249. (29) Noor, A.; Glatz, G.; M¨ uller, R.; Kaupp, M.; Demeshko, S.; Kempe, R. Metal−metal distances at the limit: Cr−Cr 1.73 ˚ A – The importance of the ligand and its fine tuning. Z. Anorg. Allg. Chem. 2009, 635, 1149–1152.

24


Page 24 of 33

Page 25 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(30) Huang, Y. L.; Lu, D. Y.; Yu, H. C.; Yu, J. S. K.; Hsu, C. W.; Kuo, T. S.; Lee, G. H.; Wang, Y.; Tsai, Y. C. Stepwise construction of the Cr−Cr quintuple bond and its destruction upon axial coordination. Angew. Chem. Int. Ed. 2012, 51, 7781–7785. (31) Rudd, P. A.; Liu, S.; Planas, N.; Bill, E.; Gagliardi, L.; Lu, C. C. Multiple metal−metal bonds in iron−chromium complexes. Angew. Chem. Int. Ed. 2013, 52, 4449–4452. (32) Eisenhart, R. J.; Rudd, P. A.; Planas, N.; Boyce, D. W.; Carlson, R. K.; Tolman, W. B.; Bill, E.; Gagliardi, L.; Lu, C. C. Pushing the limits of delta bonding in metal−chromium complexes with redox changes and metal swapping. Inorg. Chem. 2015, 54, 7579–7592. (33) Eisenhart, R. J.; Clouston, L. J.; Lu, C. C. Configuring bonds between first-row transition metals. Acc. Chem. Res. 2015, 48, 2885–2894. (34) Malmqvist, P. ˚ A.; Rendell, A.; Roos, B. O. The restricted active space self-consistentfield method, implemented with a split graph unitary group approach. J. Phys. Chem. 1990, 94, 5477–5482. (35) Andersson, K.; Malmqvist, P. ˚ A.; Roos, B. O.; Sadlej, A. J.; Wolinski, K. Secondorder perturbation theory with a CASSCF reference function. J. Phys. Chem. 1990, 94, 5483–5488. (36) Andersson, K.; Malmqvist, P. ˚ A.; Roos, B. O. Second-order perturbation theory with a complete active space self-consistent field reference function. J. Phys. Chem. 1992, 96, 1218–1226. (37) Hohenberg, P.; Kohn, W. Inhomogeneous electron gas. Phys. Rev. 1964, 136, B864– B871. (38) Kohn, W.; Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140, A1133–A1138.

25



(39) Ponec, R.; Feixas, F. Peculiarities of multiple Cr−Cr bonding. Insights from the analysis of domain-averaged fermi holes. J. Phys. Chem. A 2009, 113, 8394–8400. (40) Wu, L. C.; Hsu, C. W.; Chuang, Y. C.; Lee, G. H.; Tsai, Y. C.; Wang, Y. Bond characterization on a Cr−Cr quintuple bond: A combined experimental and theoretical study. J. Phys. Chem. A 2011, 115, 12602–12615. (41) Ndambuki, S.; Ziegler, T. A theoretical analysis of supported quintuple and quadruple chromium−chromium bonds. Inorg. Chem. 2013, 52, 3860–3869. (42) Falceto, A.; Theopold, K. H.; Alvarez, S. Cr−Cr quintuple bonds: Ligand topology and interplay between metal−metal and metal−ligand bonding. Inorg. Chem. 2015, 54, 10966–10977. (43) Brynda, M.; Gagliardi, L.; Widmark, P. O.; Power, P. P.; Roos, B. O. A quantum chemical study of the quintuple bond between two chromium centers in [PhCrCrPh]: trans-Bent versus linear geometry. Angew. Chem. Int. Ed. 2006, 45, 3804–3807. (44) La Macchia, G.; Gagliardi, L.; Power, P. P.; Brynda, M. Large differences in secondary metal−arene interactions in the transition-metal dimers ArMMAr (Ar = terphenyl; M = Cr , Fe, or Co): Implications for Cr−Cr quintuple bonding. J. Am. Chem. Soc. 2008, 130, 5104–5114. (45) La Macchia, G.; Aquilante, F.; Veryazov, V.; Roos, B. O.; Gagliardi, L. Bond length and bond order in one of the shortest Cr−Cr bonds. Inorg. Chem. 2008, 47, 11455–11457. (46) Brynda, M.; Gagliardi, L.; Roos, B. O. Analysing the chromium−chromium multiple bonds using multiconfigurational quantum chemistry. Chem. Phys. Lett. 2009, 471, 1–10. (47) La Macchia, G.; Li Manni, G.; Todorova, T. K.; Brynda, M.; Aquilante, F.; Roos, B. O.;

26


Page 26 of 33

Page 27 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Gagliardi, L. On the analysis of the Cr−Cr multiple bond in several classes of dichromium compounds. Inorg. Chem. 2010, 49, 5216–5222. (48) Li Manni, G.; Dzubak, A. L.; Mulla, A.; Brogden, D. W.; Berry, J. F.; Gagliardi, L. Assessing metal−metal multiple bonds in Cr−Cr, Mo−Mo, and W−W compounds and a hypothetical U−U compound: A quantum chemical study comparing DFT and multireference methods. Chem. Eur. J. 2012, 18, 1737–1749. (49) Li Manni, G.; Carlson, R. K.; Luo, S.; Ma, D.; Olsen, J.; Truhlar, D. G.; Gagliardi, L. Multiconfiguration pair-density functional theory. J. Chem. Theory Comput. 2014, 10, 3669–3680. (50) Gagliardi, L.; Truhlar, D. G.; Manni, G. L.; Carlson, R. K.; Hoyer, C. E.; Bao, J. L. Multiconfiguration pair-density functional theory: A new way to treat strongly correlated systems. Acc. Chem. Res. 2017, 50, 66–73. (51) Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38, 3098–3100. (52) Perdew, J. P. Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys. Rev. B 1986, 33, 8822–8824. (53) Weigend, F.; Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297–305. (54) Reiher, M.; Wolf, A. Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order. J. Chem. Phys. 2004, 121, 10945–10956. (55) Hess, B. A. Relativistic electronic-structure calculations employing a two-component

27



no-pair formalism with external-field projection operators. Phys. Rev. A 1986, 33, 3742–3748. (56) Aquilante, F.; Pedersen, T. B.; Lindh, R. Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals. J. Chem. Phys. 2007, 126, 194106. (57) Aquilante, F.; Pedersen, T. B.; Lindh, R.; Roos, B. O.; Sánchez de Merás, A.; Koch, H. Accurate ab initio density fitting for multiconfigurational self-consistent field methods. J. Chem. Phys. 2008, 129, 024113. (58) Widmark, P.-O.; Malmqvist, P. ˚ A.; Roos, B. O. Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions. Theor. Chim. Acta. 1990, 77, 291–306. (59) Roos, B. O.; Lindh, R.; Malmqvist, P. ˚ A.; Veryazov, V.; Widmark, P.-O. New relativistic ANO basis sets for transition metal atoms. J. Phys. Chem. A 2005, 109, 6575–6579. (60) Pierloot, K.; Dumez, B.; Widmark, P.-O.; Roos, B. O. Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions. Theor. Chim. Acta. 1995, 90, 87–114. (61) Roos, B. O.; Borin Antonio, C.; Laura, G. Reaching the maximum multiplicity of the covalent chemical bond. Angew. Chem. Int. Ed. 2007, 46, 1469–1472. (62) Forsberg, N.; Malmqvist, P. ˚ A. Multiconfiguration perturbation theory with imaginary level shift. Chem. Phys. Lett. 1997, 274, 196–204. (63) Vancoillie, S.; Malmqvist, P. ˚ A.; Veryazov, V. Potential energy surface of the chromium dimer re-re-revisited with multiconfigurational perturbation Theory. J. Chem. Theory Comput. 2016, 12, 1647–1655.

28


Page 28 of 33

Page 29 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(64) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (65) Carlson, R. K.; Truhlar, D. G.; Gagliardi, L. Multiconfiguration pair-density functional theory: A fully translated gradient approximation and its performance for transition metal dimers and the spectroscopy of Re2 Cl2– 8 . J. Chem. Theory Comput. 2015, 11, 4077–4085. (66) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37, 785–789. (67) Stephens, P.; Devlin, F.; Chabalowski, C.; Frisch, M. J. Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J. Chem. Phys. 1994, 98, 11623–11627. (68) Vosko, S.; Wilk, L.; Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis. Can. J. Phys. 1980, 58, 1200–1211. (69) Zhao, Y.; Truhlar, D. G. A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions. J. Chem. Phys. 2006, 125, 194101. (70) Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: Two new functionals and systematic testing of four M06-class functionals and 12 other function. Theor. Chem. Acc. 2007, 120, 215–241. (71) Chai, J.-D.; Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615– 6620.

29



(72) Seeger, R.; Pople, J. A. Self-consistent molecular orbital methods. XVIII. Constraints and stability in Hartree-Fock theory. J. Chem. Phys. 1977, 66, 3045–3050. (73) Bauernschmitt, R.; Ahlrichs, R. Stability analysis for solutions of the closed shell KohnSham equation. J. Chem. Phys. 1996, 104, 9047–9052. (74) Mayer, I. On bond orders and valences in the Ab initio quantum chemical theory. Int. J. Quantum Chem. 1986, 29, 73–84. (75) Mayer, I. Bond order and valence indices: A personal account. J. Comput. Chem. 2007, 28, 204–221. (76) Becke, A. D.; Edgecombe, K. E. A simple measure of electron localization in atomic and molecular systems. J. Chem. Phys. 1990, 92, 5397–5403. (77) Lu, T.; Chen, F. Multiwfn: A multifunctional wavefunction analyzer. J. Comput. Chem. 2012, 33, 580–592. (78) Aquilante, F.; Autschbach, J.; Carlson, R. K.; Chibotaru, L. F.; Delcey, M. G.; De Vico, L.; Fdez. Galván, I.; Ferré, N.; Frutos, L. M.; Gagliardi, L. et al. Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table. J. Comp. Chem. 2016, 37, 506–541. (79) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Revision E.01; Gaussian, Inc.: Wallingford, CT, 2009. (80) Sadique, A. R.; Heeg, M. J.; Winter, C. H. A weak, short metal−metal bond in a chromium(II) amidinate complex. J. Am. Chem. Soc. 2003, 125, 7774–7775. (81) Arcisauskaite, V.; Spivak, M.; McGrady, J. E. Structure and bonding in trimetallic arrays containing a Cr−Cr quadruple bond: A challenge to density functional theory. Inorg. Chim. Acta 2015, 424, 293–299. 30


Page 30 of 33

Page 31 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(82) Edgecombe, K. E.; Becke, A. D. Cr2 in density-functional theory: Approximate spin projection. Chem. Phys. Lett. 1995, 244, 427–432. (83) Schultz, N. E.; Zhao, Y.; Truhlar, D. G. Databases for transition element bonding: Metal-metal bond energies and bond lengths and their use to test hybrid, hybrid meta, and meta density functionals and generalized gradient approximations. J. Phys. Chem. A 2005, 109, 4388–4403. (84) Yamaguchi, K.; Takahara, Y.; Fueno, T.; Houk, K. N. Extended Hartree-Fock (EHF) theory of chemical reactions - III. Projected Møller-Plesset (PMP) perturbation wavefunctions for transition structures of organic reactions. Theor. Chim. Acta 1988, 73, 337–364. (85) Yamaguchi, K.; Okumura, M.; Mori, W.; Maki, J.; Takada, K.; Noro, T.; Tanaka, K. Comparison between spin restricted and unrestricted post-Hartree-Fock calculations of effective exchange integrals in Ising and Heisenberg models. Chem. Phys. Lett. 1993, 210, 201–210. (86) Yamanaka, S.; Okumura, M.; Nakano, M.; Yamaguchi, K. EHF theory of chemical reactions Part 4. UNO CASSCF, UNO CASPT2 and R(U)HF coupled-cluster (CC) wavefunctions. J. Mol. Struct. 1994, 310, 205–218. (87) Kitagawa, Y.; Saito, T.; Ito, M.; Shoji, M.; Koizumi, K.; Yamanaka, S.; Kawakami, T.; Okumura, M.; Yamaguchi, K. Approximately spin-projected geometry optimization method and its application to di-chromium systems. Chem. Phys. Lett. 2007, 442, 445–450. (88) Noodleman, L. Valence bond description of antiferromagnetic coupling in transition metal dimers. J. Chem. Phys. 1981, 74, 5737–5743. (89) Noodleman, L.; Davidson, E. R. Ligand spin polarization and antiferromagnetic coupling in transition metal dimers. Chem. Phys. 1986, 109, 131–143. 31



(90) Wiberg, K. B. Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane. Tetrahedron 1968, 24, 1083–1096. (91) Glendening, E. D.; Landis, C. R.; Weinhold, F. NBO 6.0: Natural bond orbital analysis program. J. Comput. Chem. 2013, 34, 1429–1437.

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Graphical TOC Entry δ bonding

1.74 Å

antiferromagnetic

ΔEδ: 20 kcal mol−1

2.50 Å

Methodologies: CASPT2, MC-PDFT, and KS-DFT

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Analyses on Molecular Properties of the Diamidinate CrIâCrI Complex

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