Single Molecule Magnetism in Linear Fe(I) Complexes with Aufbau and non-Aufbau ground-state

With the ongoing efforts on synthesizing mono-nuclear single-ion magnets (SIMs) with promising applications in high-density data storage and spintronics devices, the linear Fe(I) complexes emerge as the enticing candidates possessing large unquenched angular momentum. Herein, we have studied five experimentally synthesized linear Fe(I) complexes to uncover the origin of single-molecule magnetic behavior of these complexes. To begin with, we benchmarked our methodology on the experimentally and theoretically well studied complex, [Fe{C(SiMe3)}3]] (1) (SiMe3 = trimethylsilyl) which is characterized with large spin-reversal barrier of 226 cm−1 [Nat. Chem. 2013, 5, 577–581]. Further, the two Fe(I) complexes, i.e., [Fe(cyIDep)2] (2) ((cyIDep = 1,3-bis(2,6-diethylphenyl)-4,5-(CH2)4-imidazol-2-ylidene) and [Fe(sIDep)2]] (3) (sIDep = 1,3-bis(2′,6′-diethylphenyl)-imidazolin-2-ylidene) are studied that do not possess SIM behavior under ac or dc magnetic fields, however, they are reported to exhibit large opposite axial zero field splitting (-62.4 and +34.0 cm−1 respectively) from ab initio calculations. Employing state-of-the-art ab initio calculations, we have unwrapped the origin of this contrasting observation between experiment and theory by probing 1 their magnetic relaxation pathways and the pattern of d-orbitals splitting. Additionally, the two experimentally synthesized Fe(I) complexes, i.e., [(η-C6H6)FeAr*-3,5-Pr2] (4) (Ar*-3,5-Pr2 = C6H-2,6-(C6H2-2,4,6-Pr3)2-3,5-Pr2) and [(CAAC)2Fe] (5) (CAAC = cyclic (alkyl)(amino)carbene) are investigated for SIM behavior, since there is no report on their magnetic properties. To this end, complex 4 presents itself as the potential candidate for SIM.


Introduction
Single-ion magnets (SIMs) are the centrepiece of numerous areas of research with promising applications in quantum computing, 1,2 molecular spintronics, 3 classical data storage 4 etc.
These are distinct molecules displaying slow relaxation of magnetization that is characterized by an energy barrier (U ef f ) for reversal of total molecular spin. The energy barrier further depends on the total spin of the system and is given by U ef f = S 2 |D| and (S 2 -1/4)|D| (for integer and non-integer spin states respectively), where D is the axial zero field splitting parameter. 5 Complexes based on lanthanides (Ln) have gained much popularity as propitious candidates for SIMs since the report of phthalocyanine Tb(III) complex, TbPc 2 in 2003 owing to huge magnetic anisotropy and large spin ground state. 6 Followed by this, a plethora of Ln-based complexes have been synthesized and characterized with high anisotropic energy barriers. They exhibit large unquenched angular momentum and strong spin-orbit coupling, which are solely responsible for their magnetic behaviors. [7][8][9][10][11][12] Transition metal (TM) complexes have also entered the spotlight in recent years, offering tantalizing alternatives to be utilized in prospective applications. [13][14][15] In this regard, in mononuclear complexes containing 3d-metal ions, it is essential to maintain the first-order orbital angular momentum to accomplish large magnetic anisotropy on a level comparable with Ln based complexes. 16,17 Controlling various chemical modifications in the coordination environment, such as the coordination number, geometry of the complex and nature of ligand atoms directly bonded to the metal center, assists in the conservation of the first-order orbital angular momentum. In TM complexes with coordination number greater than 4, the ligand field largely quenches the orbital angular momentum as a result of Jahn Teller distortion. 18 However, the complexes with high axial symmetry, show signs of unquenched angular momentum and hence moderate magnetic anisotropy, but the molecules with high local symmetry are quite scarce. 19 The breaking of symmetry significantly lowers the magnitude of magnetic anisotropy as elegantly reported by Feng 21 To overcome these ligand field effects, the low-coordinate complexes (coordination number <4) renewed the interest of researchers, since, they favor degenerate ground states resulting in minimal quenching of orbital angular momentum. To this end, linear or quasi-linear two-coordinate complexes emerge as the choicest complexes for mitigating these effects and eventually resulting in large anisotropic energy barriers. [22][23][24][25] The stability and isolation of these low coordinated complexes necessitate sterically encumbered ligands. A copious number of two-and three-coordinate complexes featuring Fe(II) center are already reported with intriguing magnetic properties. 13,15,[26][27][28] Nearly, all these complexes anchorage sterically bulky ligands. However, in Fe(II) based complexes, the slow relaxation of magnetization is observed only in the presence of d.c. field owing to Fe(II) being a non-Kramer ion. Therefore, taking advantage of Kramer's theorem and thus, attenuating one T-shaped Fe(I) complexes employing bulky NHC (N-heterocyclic carbene) ligands were synthesized by Ouyang et al. 33 Later on, they carried the magnetic characterization of these complexes explaining multiple magnetic relaxation pathways existing in the three co-ordinate complexes. 34 Another Fe(I) complex [Cp Ar Fe(IiPr 2 Me 2 )] (Cp Ar =C 5 (C 6 H 4 -4-Et) 5 ; IiPr 2 Me 2 =1,3-diiso-propyl-4,5-dimethylimidazolin-2-ylidene) has been synthesized and characterized with spin-reversal barrier of 64 cm −1 by Chakraborty et al. 35 In recent years, although two-coordinate Fe(I) complexes with sterically bulky ligands have been synthesized, 33,36,37 but a thorough study to underpin the origin of magnetic anisotropy in these complexes has not been done yet. The present work aims to gain an in-depth understanding of magnetic anisotropy in a series of linear two-coordinate Fe(I) complexes, employing state-of-the-art ab initio calculations. To this end, we have chosen 5 exper- 33 [(η 6 -C 6 H 6 )FeAr*-3,5-Pr i 2 ] (4) 36

Computational Details
All the ground and excited state energies and wave function calculations are performed on the experimentally reported X-ray crystal structures' geometries. The molecular coordinate system is chosen in such a way that Fe(I) is the origin of the coordinate system and the z-axis points approximately towards the ligands. The correlated calculations are done using Complete Active Space Self Consisent Field (CASSCF) 38 together with N-Electron Valence Perturbation Theory (NEVPT2). 39 The Fe(I) possess d 7 electronic configuration giving rise to 10 quartets (S=3/2) and 40 doublets (S=1/2) states. To benchmark the methodology, we performed the calculation for complex 1 considering all the roots of quartet and doublet and another calculation with all roots of quartet only. However, the doublet states do not show any significant contribution to the D values, therefore, the calculations are performed accounting for only 10 quartet states (see Table S1 in SI). The CASSCF energy levels are obtained by state-averaging these states in the active space consisting of 7 electrons distributed in 5 3d orbitals i.e., CAS (7,5). The effect of dynamical correlations is included by performing  49 To account for spin-orbit effects, AMFI spin-orbit operator is used and DKH Hamiltonian is considered for scalar relativistic effect. The AMFI (atomic mean field integral) spin-orbit operator is introduced to account for the spin-orbit effects. The scalar relativistic effect is considered using the DKH Hamiltonian. The resolution-of-identity approximation is employed to accelerate the calculation. 50  For complexes with negative value of D, the Kramers doublet with the maximum spin projection is the ground-state while reverse is true with positive D value. 51 The negative value of D for all complexes except 3 implies that the Kramers doublets (KDs), with the projection of total angular momentum m J = ±7/2 is the ground state for these complexes.

ZFS parameters and g tensors
However, for complex 3 with positive D value, the ground state KDs has m J = ±1/2 as the projection of total angular momentum.   For a molecule to possess uniaxial anisotropy with slow relaxation of magnetization under no applied field, apart from negative axial ZFS (D), the negligibly small rhombicity i.e., |E/D| ratio is required. 52 The non-zero value of E allows mixing of ±M s levels, leading to relaxation of electron through quantum tunneling. 53 The SA-CASSCF/NEVPT2 computed |E/D| ratio of all the complexes are collected in Table 1. Complexes 1 and 4 exhibit negligibly small rhombicity i.e., |E/D| <0.005 (Table 1)  Besides ZFS parameters, the g tensor corresponding to a pair of KDs, which imparts the preferential direction of magnetization in a particular spin-orbit state, is an important parameter for governing the efficiency of SIMs. 54 Complexes with g z > g y ≈ g x are characterized with easy axis anisotropy with g z as the favorable direction of magnetization. In contrast, g y ≈ g x > g z signifies easy plane anisotropy and g z > g y > g x represents the case of triaxial anisotropy. 55 The g tensors for the ground-state and the lowest three excited states of all the complexes are shown in Table 2. For complexes 1 and 4, the computed g tensors in the groundstate KDs are observed to show g z >> g y ≈ g x , indicating g z as the favorable direction of magnetization with strong Ising type nature. This uniaxial magnetic anisotropy signifies negligible relaxation of magnetization from the ground state Kramers pair. However, for the first and higher excited states, the extent of uniaxiality is reduced. Moreover, along with the changes in g, the direction of magnetization of the excited state from the ground state (measured as g z angle in Table 2) also deviates. These decreased uniaxiality and noncoincidence of the anisotropy axis of excited state with respect to the ground-state leads to faster relaxation of magnetization from the corresponding state. 54 For complexes 2 and 5, although the g-tensor show axiality with g z >> g y ≈ g x , but lacks pure Ising nature. This suggests partial tunneling within the ground state KDs along with faster tunneling through the excited state with reduced uniaxiality and deviation of anisotropy axis from the ground state. Complex 3 is a peculiar case possessing triaxial anisotropy with g z > g y > g x . This triaxial anisotropy has been observed earlier also for Co(II) compounds by Møller et al. 55 and Korchagin et al. 56

Origin of ZFS
To gain a better understanding of the observed magnitude as well as the sign of D values for the studied complexes, we have analyzed the pattern of molecular d-orbitals splitting of these complexes obtained from AILFT analysis as shown in the top panel of Figure 2. For 1, the d-orbital splitting is observed where the d z 2 is lowest in energy followed by closely degenerate pairs of d x 2 −y 2 and d xy and then by d xz and d yz . The stabilization of d z 2 is a result of strong 3d z 2 -4s mixing as reported by Zadrozny et al. 29 Visual inspection of the shape of d z 2 orbital (bottom of Figure 2) reveals an appreciable overlap where the donut-like ring in the xy plane of d z 2 orbital mixes with the 4s orbital. This 3d z 2 -4s mixing is observed for all the complexes.
Moreover, this 3d z 2 -4s is also evident from the analysis of Löwdin orbital composition of the 3d-orbitals (  (Table 3) and the excitation of an electron from ground to first excited state takes place between the same |m l | states, thus, the spin-conserved transition from d x 2 −y 2 to d xy leads to large negative contribution to the D value. The second excited state is composed of several determinants with major contribution Here, the electron promotes to the states with different |m l | values and the energy difference between the ground and second excited state is quite large (Table   3) (Table S4). Since these d-orbitals are quasi-degenerate, therefore, to avoid inter-electronic repulsion for the Aufbau configuration i.e., d 2 Further, the first excited state will be attained by promoting an electron from d xy to d x 2 −y 2 with small energy difference (52.0 cm −1 ) and between same |m l | states leading to large negative contribution to the D value. The second excited state has the major contribution from d 2  In complex 3, the imidazolin ylidine ligand is substituted which, due to better π accepting ability than imidazol ylidine 58 (in complex 2), renders more pronounced dπ-pπ interactions and hence, stabilizes the d xz orbital compared with the d z 2 and d yz which are almost degenerate ( Figure S1). As a consequence of this pattern of d-orbital splitting, the ground state acquires non-Aufbau electronic configuration, d 2 xz d 1 (similar to 2). Since, the first and second excited states are achieved by promoting an electron from d yz to d x 2 −y 2 and d xy respectively with different |m l | states, both of them give a positive contribution to the D value. Hence, the complex exhibits an overall positive D value. Thus, the different splitting pattern due to better π-acceptor imidazoline ylidine than imidazol ylidine (in 2) results in opposite signs of magnetic anisotropy for the two complexes. Another difference between the two molecules is the dihedral angle between the ligands attached to the complexes. Complex 2 renders dihedral angle of 14°in contrast to the large dihedral angle of 70°exhibited by complex 3 (tabulated in Table S10). The different dihedral angles can also be the underlying rationale for the contrasting signs of magnetic anisotropy for the complexes 2 and 3 as also observed in Co complexes by Meng et al. 58 The complex 4 is a peculiar case where quasi-degenerate d xy and d x 2 −y 2 are lower in energy as compared to d z 2 . The analysis of molecular orbitals as shown in Figure 2 reveals a substantial overlap between the d xy and d x 2 −y 2 orbitals of Fe with the π-electron cloud of the benzene ring which is binding to the Fe through η 6 fashion making a half-sandwich complex. The π-electron cloud of the benzene ring and the d xy and d x 2 −y 2 orbitals of the Fe atom are lying perpendicular to the molecular axis. These orbitals can be considered as a linear combination of pπ orbitals of the benzene ring and d-orbitals (d xy and d x 2 −y 2 ) of Fe atom indicating significant interactions and hence leading to substantial stabilization of these orbitals followed by d z 2 and subsequently by a closely degenerate pair of d xz and d yz orbitals.
The outcome of this d-orbital ordering is the ground-state with electronic configuration The promotion of electron from d xy to d x 2 −y 2 i.e., between same |m l | states and with small energy difference (298.3 cm −1 ) leads to first excitation providing large negative contribution to D value. Further, the second excited state is obtained by transfer of electron from d z 2 to d x 2 −y 2 causing small positive contribution to the D value, with overall negative magnetic anisotropy for the complex.

Mechanism of magnetic relaxation
To have a qualitative understanding of the mechanism of magnetic relaxation, we have plot-  These relaxation pathways provide the plausible reason for no SIM behaviors under any applied field for complexes 2 and 3 as observed by Meng et al. 34 Since for complex 2, due to multiple relaxation pathways i.e., partial QTM through the ground-state KDs and Orbach relaxation, the complex shows absence of SIM behavior. In contrast, complex 3 possessing barrierless potential well leads to relaxation within the ground-state KDs. Thus, both the complexes do not show any signatures of SIM behavior.

Conclusion
We