Neutral All Metal Aromatic Half-Sandwich Complexes Between Alkaline Earth and Transition Metals: An Ab-initio Exploration

Sandwich complexes nd their interests among the chemists after the breakthrough discovery of ferrocene. Since then, a number of sandwich and half sandwich complexes were predicted and synthesized. Herein, we have theoretically proposed a series of half-sandwich complexes involving a neutral Be 3 ring and transition metal. Quantum chemical calculations have shown that the proposed complexes are quite stable involving high bond dissociation energies. The thermodynamics of their formation is also favorable. The Be 3 ring in all cases posses dual aromaticity which has been ascertained based on magnetic as well as topological feature of electron density.


Introduction
Discovery of the rst sandwich complex (C 5 H 5 ) 2 Fe, commonly known as "ferrocene", drew the attention of the chemistry fraternity in no time [1][2][3]. The detail structural analyses revealed that the complex may adopt two close energy conformations [4]. This was followed by the discovery of sandwich complexes involving benzene and other arene systems coordinated to transition metals via delocalized π-electrons [5]. Since then, the journey of this domain has been spectacular as numerous sandwich complexes were proposed and synthesized along and their bonding analyses were carried out [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. As compared to that of a full sandwich complex where the metal centre is enclosed on both sides, half-sandwich metallocenes involve a metal atom or ion enclosed on one particular side only. The inception of half-sandwich complex took place almost parallel to the discovery of ferrocene when Fischer and Hafner carried out the synthesis of tetracarbonyl (cyclopentadienyl) vanadium complex, C 5 H 5 V(CO) 4 [24]. This was followed by the synthesis of half-sandwich compounds containing manganese and cobalt as metal centers [25][26].
Although all metal sandwich complexes have so far been signi cantly explored, the library of such complexes involving s-block metal as ligand fragment is not adequate so far [36][37]. Through this ab initio study, we have designed a series of all metal neutral half sandwich complexes (Scheme 1) involving Be 3 fragment attached to transition metals. The reason of taking cyclic Be 3 fragment is due to the fact that it can act like a Z-type ligand owing to the presence of vacant π symmetric orbital. The structure and reactivity of Be 3 is well established [38][39][40]. The proposed half sandwich complexes feature donoracceptor interaction between the transition metals and the Be 3 fragment. These complexes are quite stable owing to their high bond dissociation energies and also with favorable thermodynamics.

Computational Details
All the molecules were fully optimized without any symmetry constraints in their gas phase at PBE1PBE [41], MP2 [42] and CCSD level of theory using 6-311 + + G** basis set for Be atom and SDD [43] basis set for transition metals. Harmonic frequency calculations were performed at the same level of theory to characterize the nature of stationary states. The global minima structures have all real values of frequencies. All energies are zero point and thermal corrected. Natural bond orbital analyses (NBO) [44] were performed at PBE1PBE/SDD level of theory to get the precise idea of the frontier orbitals as well as electronic structure of the molecules. All calculations were performed using Gaussian 16 suite of program [45]. Quantum theory of atoms in molecules (QTAIM) [46], electron localization function (ELF) [47][48] and Charge decomposition analysis (CDA) [49] were performed at PBE1PBE level of theory using Multiwfn program code [50].
Results And Discussion  Table S1, supporting information. Among the studied systems, the frontier molecular orbitals of the Be 3 -Fe and Be 3 -Zn has been shown (Fig 2). The Be-Be distance in metal free cyclic Be 3 molecule is 2.210 Å which signi cantly shortens in the half sandwich complexes (Fig 1). The Wiberg bond indices for the TM-Be bonds, a measure of bond strength, are close to 0.9 for Fe, Ru and Os complexes while they are lower (~0.2) for the Zn, Cd and Hg complexes.
To investigate the mode of binding of Be 3 fragment with the transition metals, we calculated the energy changes while displacing the transition metal atom from the centre to a distance r as shown in Scheme 2.
Results based on single point calculations at PBE1PBE level of theory (Fig 3) reveals that all these complexes have the lowest energy at r = 0, i.e., Be 3 fragment in these complexes feature η 3 coordination mode.
Further to investigate the nature of bonding, we have performed charge decomposition analysis (CDA) Fe and Zn complexes respectively as representative case. Fig 4 shows the interaction diagram. The LUMO (lowest unoccupied molecular orbital) and LUMO+1 of Be 3 fragment interact with the metal d z 2 and s orbital. It is to be noted that the LUMO of Be 3 fragment is a delocalized unoccupied π symmetric oribital while the LUMO+1 is the σ orbital. Occupation of these orbitals in the sandwich complex is expected to enhance aromaticity in the cyclic Be 3 fragment.
We then turned to the aromaticity of the proposed molecules by performing nucleus independent chemical shift (NICS) calculations at the centre of the Be 3 fragment in the complexes which is known as NICS(0) and 1 Å above the plane which we designated as NICS(1) [49] (Scheme 3, Table 1). It is worth mentioning that Be 3 ring is anti-aromatic which is backed by positive NICS(0) value of 20 ppm. Upon complexation with the considered transition metals, signi cant aromaticity is induced in the Be 3 -TM complexes. In all the complexes, aromaticity is dominated by NICS(0), a measure of σ aromaticity.
However, NICS(1) values, a measure of π aromaticity, are also signi cant. Thus, the calculated values of NICS suggest that the proposed sandwich complexes have dual σ and π aromaticity [51]. The presence of dual aromaticity is expected to increase the stability of the complexes. We therefore, calculated the bond dissociation energies (BDE, Table 2) and change in Gibbs free energies (∆G 298 ) of their formation according to the following equation  We then further analyzed the topological feature of electron density within the realm of quantum theory of atoms in molecules (QTAIM) [46] and electron localization function (ELF) [47][48]. QTAIM is based on topological properties of electron density and its derivatives. It describes the concept of bonding with the help of bond paths and critical points. The electron density (q) exhibits a maximum, a minimum, or a saddle point in space. These points are referred to as Critical Points (CPs). At this point, the rst derivatives of q(rc) vanishes. The Laplacian (∇ 2 ρ) plays a very vital role in the characterization of chemical bonding. Generally, for covalent interactions (also referred to as ''open-shell" or ''sharing" interactions), the electron density at the bond critical point (BCP), ρb, is large (>0.2 a.u) while its laplacian, ∇ 2 ρ is large and negative. On the other hand, for closed-shell interactions (e.g., ionic, van der Waals, or hydrogen bonds), ρb is small (<0.10 au) and ∇ 2 ρ is positive. However, a clear distinction between the closed-shell and covalent type of interaction is impossible without determination of the local electronic energy density, H(r). The local electronic energy density, H(r), given by H(r) = G(r) + V(r), where G(r) and V(r) are the local kinetic and potential energy densities, is negative for an interaction with signi cant covalent character and accounts for the lowering of potential energy of electrons at BCPs. The magnitude of H(r) re ects the ''degree of covalency" present in a given interaction. Thus, some covalent (some polar bonds, donor-acceptor bonds, etc.) bonds are associated with positive values of r2 q and negative values of H(r) [52]. Table 3   negative for the all the geometries. Nucleus independent chemical shift (NICS) calculations suggest the presence of dual aromatic character in the cyclic Be 3 fragment of the complexes which were substantiated by topological analyses. We feel that our ab initio study will attribute to the possible synthesis and characterization of the proposed complexes.   Plot of energy against the displacement (r) of the transition metal centre in the sandwich complexes.