Unravelling the Chemistry of the [Cu(4,7-Dichloroquinoline) 2 Br 2 ] 2 Dimeric Complex through Structural Analysis: A Borderline Ligand Field Case

: Large dark prismatic crystals (P 1) consisting of closely packed centrosymmetric [Cu(4,7-dichloroquinoline) 2 ] 2 Br 4 binuclear units are formed when 4,7-dichloroquinoline (DCQ, C 9 H 5 NCl 2 ) binds copper(II). Cu 2 + adopts a strongly distorted square pyramidal coordination geometry, perturbed by electrostatic interactions with two axial µ –Br ligands acting as highly asymmetric bridges. It is shown that, as electronic states of ligands are higher in energy than the metal ones, antibonding orbitals bear signiﬁcant ligand-like character and electronic charge is partially transferred from inner-sphere coordinated halogen atoms to copper. Overall, the title compound sits on the Ho ﬀ man’s border between main group and transition chemistry, with non-negligible contributions of the ligands to the frontier orbitals. The relative energy placement of metal and ligand states determines an internal redox process, where the metal is slightly reduced at the expense of partial oxidation of the bromide ligands. In fact, the crystal structure is partially disordered due to the substitution of some penta-coordinated Cu(II) centers with tetra-coordinated Cu(I) ions. The geometry of the complex is rationalized in terms of electrostatic-driven distortions from an ideal octahedral prototype. Implications on the reactivity of Cu(II)–quinoline complexes are discussed.


Introduction
Because of its versatility, Cu 2+ has been defined as a chameleon in coordination chemistry [1]. The stereochemistry of copper complexes is frequently dominated by a subtle interplay of Jahn-Teller, dynamic and steric effects [2,3] that cause it to depart from that expected based on a simple crystal field framework [4]. The discovery of an inverted ligand field in Cu-based coordination compounds [5][6][7], prototyped by the square planar anion Cu(CF 3 ) 4 − , deepened the general understanding of coordinative bonding [8] and provided new ways to exploit the reactivity of unusual chemical states of both the metal and the ligands. In a recent review [8], Hoffmann and co-workers pointed out that late transition elements like Cu and Zn lie on the borderline of what they define as "transition metal thinking" and "main group thinking". In other words, the metal itself might present a sort of σ-noninnocence, that is, its 3d states could be as much important as the 4s-4p ones in determining the measured geometrical and electronic properties of the complex. This kind of analysis definitely suggests the existence of a very rich territory of yet unexplored chemistry. For some years now, we have been studying the reactivity of transition metals with quinoline-based antimalarial drugs in order to understand their mechanism of action at the molecular level [9][10][11]. Quinoline compounds can actively enter the metabolism by binding specific metal targets, including late transition elements like copper and zinc [12]. Iodochlorhydroxyquin (clioquinol) [13] and 7-chloroaminoquinolines [14], for example, are effective Cu(II) scavengers, with potential application against Alzheimer's disease [13][14][15]. Chloroquine and hydroxychloroquine were recently claimed to even exploit antiviral activity against pandemic SARS-CoV2 virions, even though the exact mechanism of action remains to be elucidated [16]. Cu:quinoline complexes can also promote the decarboxylation of aromatic acids, as cuprous ions stabilize anionic transition states by setting up π bonds with the occupied p-like orbitals of the substrate [17,18]. Due to manifest implications on general reactivity and medicinal applications, a deeper understanding of chemical bonding in copper:quinoline complexes is desirable. Moreover, these systems are good candidates for probing chemical and structural properties on the edge of Hoffmann's traced boundary.
Here, a newly synthesized binuclear Cu(II) coordination compound with 4,7-dichloroquinoline (4,7-DCQ, C 9 H 5 NCl 2 , Figure 1) and bromide ligands is discussed (hereinafter, CDCQB). To date, only the structures of trichloroacetate and benzoate Cu(II) copper complexes with 4,7-DCQ are known [19], even though a similar binuclear core structure was reported in quinoline:Cu(I) complexes with Cl, Br and I as µ 2 -bridging ligands [20,21]. The main goal is to clarify how chemical bonding in the title compound is related to the metal valence state, from which the observed coordination geometry stems. CDCQB was probed by single-crystal X-ray diffraction experiment at T = 100 K and magnetic measurements. Experimental results were complemented by quantum simulations at the DFT M06 level, while the real-space analysis of the experimental electron density, carried out in the framework of the quantum theory of atoms in molecules [22], was exploited to translate the Hilbert space picture into a more familiar chemical lexicon. For some years now, we have been studying the reactivity of transition metals with quinolinebased antimalarial drugs in order to understand their mechanism of action at the molecular level [9][10][11]. Quinoline compounds can actively enter the metabolism by binding specific metal targets, including late transition elements like copper and zinc [12]. Iodochlorhydroxyquin (clioquinol) [13] and 7-chloroaminoquinolines [14], for example, are effective Cu(II) scavengers, with potential application against Alzheimer's disease [13][14][15]. Chloroquine and hydroxychloroquine were recently claimed to even exploit antiviral activity against pandemic SARS-CoV2 virions, even though the exact mechanism of action remains to be elucidated [16]. Cu:quinoline complexes can also promote the decarboxylation of aromatic acids, as cuprous ions stabilize anionic transition states by setting up π bonds with the occupied p-like orbitals of the substrate [17,18]. Due to manifest implications on general reactivity and medicinal applications, a deeper understanding of chemical bonding in copper:quinoline complexes is desirable. Moreover, these systems are good candidates for probing chemical and structural properties on the edge of Hoffmann's traced boundary.
Here, a newly synthesized binuclear Cu(II) coordination compound with 4,7-dichloroquinoline (4,7-DCQ, C9H5NCl2, Figure 1) and bromide ligands is discussed (hereinafter, CDCQB). To date, only the structures of trichloroacetate and benzoate Cu(II) copper complexes with 4,7-DCQ are known [19], even though a similar binuclear core structure was reported in quinoline:Cu(I) complexes with Cl, Br and I as μ 2 -bridging ligands [20,21]. The main goal is to clarify how chemical bonding in the title compound is related to the metal valence state, from which the observed coordination geometry stems. CDCQB was probed by single-crystal X-ray diffraction experiment at T = 100 K and magnetic measurements. Experimental results were complemented by quantum simulations at the DFT M06 level, while the real-space analysis of the experimental electron density, carried out in the framework of the quantum theory of atoms in molecules [22], was exploited to translate the Hilbert space picture into a more familiar chemical lexicon. Single-crystal X-ray structure of the centrosymmetric CDCQB complex at 100 K, with the atom numbering scheme, as viewed down the a axis. The center of symmetry (red dot) coincides with the center of coordinates. Thermal ellipsoids are drawn at the 50% probability level. Anisotropic displacement parameters were assigned to hydrogen atoms according to the procedure implemented in the Shade [23] server. (b): Chemical connectivity of CDCQB. The Br atom drawn in red corresponds to Br(1) and is occupationally disordered with site occupation factor (s.o.f.) of 0.89 (see Section 2). Single-crystal X-ray structure of the centrosymmetric CDCQB complex at 100 K, with the atom numbering scheme, as viewed down the a axis. The center of symmetry (red dot) coincides with the center of coordinates. Thermal ellipsoids are drawn at the 50% probability level. Anisotropic displacement parameters were assigned to hydrogen atoms according to the procedure implemented in the Shade [23] server. (b): Chemical connectivity of CDCQB. The Br atom drawn in red corresponds to Br(1) and is occupationally disordered with site occupation factor (s.o.f.) of 0.89 (see Section 2).

Synthesis
Reagent-grade chemicals were purchased from Aldrich and used without further purification. A~120 mM transparent solution was prepared by dissolving under stirring 47.2 mg of DCQ into 2.0 mL of CH 2 Cl 2 and then poured in a glass test tube (∅ 9 mm). A~60 mM yellow solution of CuBr 2 was also prepared by dissolving 26.9 mg of CuBr 2 into 2.0 mL of methanol under stirring. Then, the copper solution was layered gently over the DCQ solution with a Pasteur pipette. The test tube was sealed with Parafilm and was allowed to rest at ambient temperature for roughly 76 h. After~24 h, the mixture became homogeneously pale yellow-colored. In the next two days, a number of yellow, tiny acicular crystals appeared in the bulk liquor. Their quality was generally low; preliminary single-crystal X-ray diffraction analysis showed that they consisted of a copper-containing P2 1 /c monoclinic phase, which will be described in detail in a forthcoming study on the reactivity of such complexes. After 5 days, the test tube was put in a refrigerator at T = 6-8 • C, where it rested for roughly a month. Thirteen days after the preparation, the first tiny black crystal appeared in the liquor; in the next days, the crystals of the new phase grew in number and dimensions, coexisting with the pristine yellow ones. The crystallization was deemed concluded roughly 30 days after the preparation. Upon extensive testing, a charge-density quality specimen of the black phase ( Figure S1) was selected for the diffraction analysis.

Single-Crystal X-ray Diffraction and Model Refinement
Diffraction experiments at 100 K were carried out on a Bruker AXS Smart Apex three-circle diffractometer equipped with an Apex II CCD area detector and an Oxford Cryosystem N 2 blower. Graphite-monochromated X-rays at the characteristic Mo Kα wavelength (λ = 0.71073 Å) were produced with a sealed tube at a nominal 50 kV × 30 mA power of the generator. Diffraction data were acquired in ω-scan mode up to a maximum resolution of 0.44 Å. No phase transitions were detected in the RT to 100 K range. The data were integrated with SAINT+, while frame scale factors and an empirical absorption correction were applied with SADABS [24]. Attempts to develop analytical absorption correction models were unsatisfactory, as the deep black color of the specimen made very difficult to accurately reconstruct the boundaries of the crystal faces. The empirical absorption procedure nevertheless gave satisfactory results for our regularly shaped specimen. It consists in fitting a multipole-based transmission surface against expected average intensities of multiple measures of equivalent intense reflections and determining an overall internal agreement factor of 2.6% up to sinθ/λ = 1.0 Å −1 (Table 1). Moreover, statistical analysis (see Figure S4) demonstrated that no significant residual systematic errors were present in the reduced dataset. The structure was solved by direct methods and refined in the spherical atom formalism framework implemented in the SHELX suite of programs [25]. A bromide ion in the first coordination shell of one of the two Cu atoms was found to be occupationally disordered, with the site occupation factor refining to 0.8870 (6). Table 1 summarizes the most relevant crystallographic results. CCDC 2002857 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/structures.

Magnetic Measurements
The molar magnetic susceptivity of the powdered material was measured with an Alfa Aesar magnetic susceptibility balance Mark 1 at T = 291 K. Diamagnetic corrections due to atoms, ions and chemical bonds in CDCQB were calculated from tabulated Pascal constants [26].

Quantum Simulations (Gas Phase)
The structure of the title compound was optimized in vacuo with Gaussian09 [27], starting from the X-ray geometry. The Minnesota-class meta-GGA M06 DFT functional [28] was exploited to account for long-range dispersion effects [29], in conjunction with the triple zeta valence polarization (TZVP) basis set proposed by Peintinger [30]. A restricted basis was employed, considering both the singlet and triplet spin states of the complex. As the ground state charge density does not depend on the spin state, only the singlet results are considered in the discussion of chemical bonding, unless otherwise specified. Vibrational frequencies were calculated to confirm that the optimized structures correspond to true potential energy minima. Energy differences always account for zero-point vibrational corrections.

Experimental Charge Density Analysis
The deposited X-ray geometry at 100 K was corrected a posteriori by lengthening all the covalent C-H bond distances to their best neutron estimates [31]. Then, anisotropic displacement parameters (ADPs) of hydrogen atoms were evaluated with the TLS+U procedure [32], as implemented in the SHADE2.1 web server [23]. The site occupation factor of the disordered bromide ion was kept identical to that estimated based on the independent atom model (see above). The aspherical Hansen-Coppens rigid pseudoatom formalism [33] available in the XD2016 program suite [34] was exploited to fit all the symmetry-independent observed intensities (|F hkl | 2 > 0) up to sinθ/λ = 1.00 Å −1 . The Su and Coppens [35] radial functions for core and valence densities of neutral atoms were taken from the embedded SCM databank and used throughout. The complexity of the least-squares model was incremented progressively, until quadrupoles (l = 2) for H; octupoles (l = 3) for C and N; and hexadecapoles (l = 4) for heavier Cl, Br and Cu atoms were included. Third-order Gram-Charlier coefficients were used for chlorine and bromine atoms to account for residual anharmonicity at low Crystals 2020, 10, 477 5 of 16 temperature [36,37]. Radial scaling parameters κ and κ' for each atomic species were also refined. The experimental multipole model was compared with a theoretical one, obtained by projecting the same multipole expansion onto a set of synthetic structure factor amplitudes, F theo , predicted from DFT single-point calculations of the CDCQB structure (see Section S1.4 of the Supplementary Materials). The interested reader can find full details in the Supplementary Materials (Section S1). Experimental and theoretical structure factor amplitudes, as well as input XD files, were also deposited. Relevant agreement factors are reported in Table 1.

Crystal Packing
The CDCQB crystal is made by centrosymmetric neutral building blocks, each formed by two inversion-related asymmetric units. Only weak C-H hydrogen bond donors are present, not able to form strong extended networks. Thus, only dispersive interactions and high-order electrostatic moments are expected to determine the crystal packing [38]. The structure consists indeed of weakly bonded, isolated metal-organic units, the main inertial axis of the aromatic rings being oriented roughly along the [10] direction ( Figure 2a).

5
to fit all the symmetry-independent observed intensities (|Fhkl| >0) up to sinθ/λ = 1.00 Å . The Su and Coppens [35] radial functions for core and valence densities of neutral atoms were taken from the embedded SCM databank and used throughout. The complexity of the least-squares model was incremented progressively, until quadrupoles (l = 2) for H; octupoles (l = 3) for C and N; and hexadecapoles (l = 4) for heavier Cl, Br and Cu atoms were included. Third-order Gram-Charlier coefficients were used for chlorine and bromine atoms to account for residual anharmonicity at low temperature [36,37]. Radial scaling parameters κ and κ' for each atomic species were also refined. The experimental multipole model was compared with a theoretical one, obtained by projecting the same multipole expansion onto a set of synthetic structure factor amplitudes, Ftheo, predicted from DFT single-point calculations of the CDCQB structure (see Section S1.4 of the Supplementary Materials). The interested reader can find full details in the Supplementary Materials (Section S1). Experimental and theoretical structure factor amplitudes, as well as input XD files, were also deposited. Relevant agreement factors are reported in Table 1.

Crystal Packing
The CDCQB crystal is made by centrosymmetric neutral building blocks, each formed by two inversion-related asymmetric units. Only weak C-H hydrogen bond donors are present, not able to form strong extended networks. Thus, only dispersive interactions and high-order electrostatic moments are expected to determine the crystal packing [38]. The structure consists indeed of weakly bonded, isolated metal-organic units, the main inertial axis of the aromatic rings being oriented roughly along the [010] direction ( Figure 2a).   Figure 2b,c shows the Hirshfeld surface fingerprint plot of CDCQB in its crystalline environment at 100 K. As quinoline nitrogen atoms are directly involved in coordinative bonds with copper, the only available H-bond acceptors are Cl and Br species. The two spikes at d i + d e ≈ 2.7-2.9 Å fingerprint close contacts of aromatic CH with halogens, together accounting for~40% of the total surface of the plot. More information is available in Section S2 of the Supplementary Materials.
Other statistically relevant contacts are the Cl· · · Cl ones, which appear as a sharp plume along the main diagonal of the diagram. They correspond to weak type I halogen bonds [39] involving atoms Cl1 and Cl12 of neighboring 4,7-dichloroquinoline ligands, which form infinite chains running approximately along the [1 11] direction ( Figure S7) and connected to each other through type II Cl2· · · Cl12 contacts ( Figure S8). As expected, direct Br· · · Br interactions are missing, as negatively charged Br − ions tend to be as far apart as possible from each other [10,29]. As they are included in the first coordination sphere of Cu atoms, Br − ions are also unavailable to set up Br· · · Cl contacts.
The last significant feature appreciable from Figure 2 is a large blue leaf at d i + d e ≈ 3.8 Å, roughly halfway the main diagonal, which signals π· · · π interactions. These are due to extended stacking arrangements of the quinoline rings, which all lie roughly orthogonal to the [10 1] direction (Figure 2a), along which they form parallel displaced ladders similar to those observed in other quinoline [10,11] and aromatic compounds [40]. Inversion-related organic moieties are stacked in a perfectly parallel fashion (Supplementary Materials, Section S2), but whenever symmetry-independent rings are close to each other, a slanted arrangement is preferred [40], with quinoline least-squares planes displaying an offset angle of 12.60 (2) • with respect to each other.

6
Cl2···Cl12 contacts ( Figure S8). As expected, direct Br···Br interactions are missing, as negatively charged Brions tend to be as far apart as possible from each other [10,29]. As they are included in the first coordination sphere of Cu atoms, Brions are also unavailable to set up Br···Cl contacts.
The last significant feature appreciable from Figure 2 is a large blue leaf at di + de ≈ 3.8 Å, roughly halfway the main diagonal, which signals π···π interactions. These are due to extended stacking arrangements of the quinoline rings, which all lie roughly orthogonal to the [10⎯1] direction ( Figure  2a), along which they form parallel displaced ladders similar to those observed in other quinoline [10,11] and aromatic compounds [40]. Inversion-related organic moieties are stacked in a perfectly parallel fashion (Supplementary Materials, Section S2), but whenever symmetry-independent rings are close to each other, a slanted arrangement is preferred [40], with quinoline least-squares planes displaying an offset angle of 12.60(2)° with respect to each other.

Coordination Geometry
The stoichiometry of the CDCQB binuclear complex is [Cu(4,7-DCQ)2Br2]2, with the metal centers in a formal +2 oxidation state. Inversion-related copper ions are connected through strongly asymmetric μ 2 -Brligands, resulting in two edge-sharing, distorted square pyramidal units ( Figure  3). Each bridging Br(1) atom acts as both an equatorial and axial ligand for the different Cu centers. Similar structures have been reported for Cu complexes with heterocycle aromatics [41][42][43][44] or Schiff bases [45][46][47][48]. Equatorial bond distances are within the expected range for organometallic compounds with either pyridine-like (1.998-2.142 Å) or bromide (2.303-2.521 Å) ligands [49]. Distortions in this plane are mainly due to the much larger covalent radius of bromine (1.20(3) Å) with respect to nitrogen Equatorial bond distances are within the expected range for organometallic compounds with either pyridine-like (1.998-2.142 Å) or bromide (2.303-2.521 Å) ligands [49]. Distortions in this plane are mainly due to the much larger covalent radius of bromine (1.20(3) Å) with respect to nitrogen (0.71(1) Å) [50]. The metal center is also significantly pyramidalized, as Cu 2+ ions are displaced by 0.31 Å toward the axial Br(1) ligand (Figure 3a). While the two equatorial Cu-Br interactions bear similar coordination distances, the axial Br(1) bromide is farther from the metal center by~0.35 Å, due to the different nature of the chemical bond in which it is involved (see below). Despite apparent similarities, the coordination geometries of the only other two known Cu(II):4,7-DCQ binuclear complexes (CSD refcodes KUHHEA and KUBJOG [19]) are significantly different, as they both bear k 2 chelating COO − groups that make copper centers significantly closer to each other (2.7 and 2.8 Å) with respect to CDCQB (d Cu· · · Cu 3.8 Å). No direct metal-metal interactions are set up in CDCQB, resulting in much stronger Cu-N coordinative bonds (e.g., d Cu· · · N 2.16 Å in KUHHEA and 2.24 Å in KUBJOG).
The crystal field has slight influence on the coordination geometry. Section S3 (Supplementary Materials) reports on in vacuo DFT-optimized geometries, compared with the X-ray one ( Figure S11). For the stoichiometric complex, the only relevant change is a~10.0 • relative rotation of the quinoline rings bonded to the same Cu center. This is clearly a packing effect, as in the solid state 4,7-DCQ ligands are constrained by stacking interactions in a more space-saving arrangement (see above and Supplementary Materials, Section S2). However, the Cu local valence shell concentration (VSCC) and depletion coordination geometry are essentially identical, with deviations between bond lengths and angles not exceeding 2% and 3% on average, respectively, regardless of the spin state of the metal (Table S13). In the DFT-optimized structure, the pyramidalization of Cu atoms is less appreciable but still significant, with the metal being displaced by 0.22 Å towards the axial bromide.

Chemical Bonding
Local topological descriptors of chemical bonds [22] of CDCQB in the solid state were evaluated to extract qualitative, real-space information on the nature of the coordinative interactions. The purpose is to rank, at least on a relative scale, the relative strength of metal-ligand bonds. Experimental outcomes were compared with those from the multipole-projected charge density, as evaluated by theoretical structure factor amplitudes (F theo ) from solid-state DFT M06/pVZT simulations at the same X-ray multipole geometry (Supplementary Materials, Section S1.4). The agreement among experimental and theoretical multipole models is quantitative (Table S16 and Figure S12), indicating that the X-ray charge density is sufficiently accurate to gain reliable insights on the copper first coordination shell.
As expected, the charge density Laplacian, ∇ 2 ρ(r), is invariably positive at the bond critical points (bcp's) of the Cu-N and Cu-Br bonds (Table S16), as these interactions fall in the valence shell charge depletion (VSCD) region of the metal [37,51]. No direct metal-metal bonds [52] are detected: the two copper centers are connected through an asymmetric µ-Br bridge that involves Br(1) ions on axial positions ( Figure 3). The axial Cu-Br(1) bonds bear a low degree of covalency, with halved ρ(r) bcp with respect to equatorial Cu-Br bonds.
The Abramov's functional [53] can be exploited to estimate the kinetic energy density at the bcp, G(r) bcp , from the corresponding charge density and its Laplacian, according to the following equation: This expression is strictly correct only when the gradient of the charge density is null, such as at a critical point. It relies on the Kirzhnitz-corrected Thomas-Fermi expression for the electron kinetic energy [53], thus being valid only in low-density areas that are far from core electrons, such as the copper valence region of CDCQB (Table S16). The local form of the virial theorem [22] relates kinetic and potential energy densities to the corresponding Laplacian: where V(r) bcp is the potential energy density, negative for bonded states. The Laplacian of the charge density, together with the total kinetic energy density, H(r) = V(r) + G(r), distinguishes electron-shared interaction, characterized by a prevalent contribution of V(r), from the closed-shell (CS) ones, where G(r) dominates. Following Espinosa et al. [54], we compared the bond degree parameter (BD = H(r) bcp /ρ(r) bcp ) with the |V(r)|/G(r) ratio for all bonds in the valence coordination region of Cu 2+ , where direct metal-ligand interactions take place. Experimental estimates are compared with multipole-projected DFT ones in Figure 4 (black squares vs. red triangles). Differences are very small on absolute grounds. Moreover, the least-squares trends of the two series are quantitatively identical, i.e., BD = −6.2(4)·|V(r)|/G(r) + 6.0(4) (R 2 = 0.98) for F exp and BD = −6.0(4)·|V(r)|/G(r) + 5.8(4) (R 2 = 0.97) for F theo . The atomic interaction lines whose energy parameters lie in the upper left quadrant of Figure 4 are produced by full closed shell (CS) Br· · · H hydrogen bonds ( Figure 2 and Figure S13). Equatorial Cu-Br and Cu-N coordinative bonds fall instead in the lower right region of the diagram, meaning that the nuclear potential is prevailing at their bcp's. Nevertheless, the corresponding Laplacians remain positive as, according to Equation (2), G(r) < V(r) < 2·G(r). In other words, these bonds fall in a "transit" region, characterized by negative H(r) and positive Laplacian, that is, they experience a certain degree of electron sharing [54,55]. Both theoretical and experimental estimates agree in predicting the Cu-N bonds as more covalent than the Cu-Br ones. On the contrary, the axial Cu· · · Br(1) interaction is instead almost entirely closed-shell, with no appreciable electron sharing (H(r) = 0) or, equivalently, a main electrostatic character. This energy classification can be related only to the relative strength of homologous bonds, as topological descriptors are only indirectly related to attractive Coulomb interactions between formal Cu 2+ and Br − ions. The axial Cu· · · Br(1) is certainly weaker than the equatorial Cu-Br ones, as a null electron sharing is accompanied by a significantly greater metal-ligand distance.  Experimental estimates are compared with multipole-projected DFT ones in Figure 4 (black squares vs. red triangles). Differences are very small on absolute grounds. Moreover, the leastsquares trends of the two series are quantitatively identical, i.e., BD = -6.2(4)·|V(r)|/G(r) + 6.0(4) (R 2 = 0.98) for Fexp and BD = -6.0(4)·|V(r)|/G(r) + 5.8(4) (R 2 = 0.97) for Ftheo. The atomic interaction lines whose energy parameters lie in the upper left quadrant of Figure 4 are produced by full closed shell (CS) Br···H hydrogen bonds (Figures 2 and S13). Equatorial Cu-Br and Cu-N coordinative bonds fall instead in the lower right region of the diagram, meaning that the nuclear potential is prevailing at their bcp's. Nevertheless, the corresponding Laplacians remain positive as, according to Equation (2), G(r) < V(r) < 2·G(r). In other words, these bonds fall in a "transit" region, characterized by negative H(r) and positive Laplacian, that is, they experience a certain degree of electron sharing [54,55]. Both theoretical and experimental estimates agree in predicting the Cu-N bonds as more covalent than the Cu-Br ones. On the contrary, the axial Cu···Br(1) interaction is instead almost entirely closed-shell, with no appreciable electron sharing (H(r) = 0) or, equivalently, a main electrostatic character. This energy classification can be related only to the relative strength of homologous bonds, as topological descriptors are only indirectly related to attractive Coulomb interactions between formal Cu 2+ and Brions. The axial Cu···Br(1) is certainly weaker than the equatorial Cu-Br ones, as a null electron sharing is accompanied by a significantly greater metal-ligand distance.
The valence shell concentration (VSCC) and depletion zones of the charge density scalar field around Cu 2+ ions provide hints as to the actual filling of d orbitals. Figure 5 displays the electron density Laplacian along the mutually orthogonal N(1)-Cu-N(2) and Br(1)-Cu-Br(2) equatorial coordinative bonds. The Laplacian distribution around the metal has a spherical shape. VSCC regions form an almost isotropic belt, according to the relatively low amount of electron sharing experienced by these bonds. If, from the viewpoint of the metal, Cu-Br and Cu-N bonds are qualitatively similar The valence shell concentration (VSCC) and depletion zones of the charge density scalar field around Cu 2+ ions provide hints as to the actual filling of d orbitals. Figure 5 displays the electron density Laplacian along the mutually orthogonal N(1)-Cu-N(2) and Br(1)-Cu-Br(2) equatorial coordinative bonds. The Laplacian distribution around the metal has a spherical shape. VSCC regions form an almost isotropic belt, according to the relatively low amount of electron sharing experienced by these bonds. If, from the viewpoint of the metal, Cu-Br and Cu-N bonds are qualitatively similar (Figure 5), lone pairs of quinoline N atoms are instead neatly polarized toward the metal, in agreement with the σ-donor character of this interaction.
As d orbitals on Copper are almost filled, we checked whether some kind of π-backdonation occurs, possibly involving antibonding π* orbitals of the quinoline system. We computed HOMED (Harmonic Oscillator Model of Electron Delocalization) indices [56] of 4,7-DCQ in the experimental and in vacuo DFT-optimized structures, and we compared them with the isolated 4,7-dichloroquinoline ligand ( Table 2).

of 16
Crystals 2020, 10, x FOR PEER REVIEW 9 of 16 9 ( Figure 5), lone pairs of quinoline N atoms are instead neatly polarized toward the metal, in agreement with the σ-donor character of this interaction. As d orbitals on Copper are almost filled, we checked whether some kind of π-backdonation occurs, possibly involving antibonding π* orbitals of the quinoline system. We computed HOMED (Harmonic Oscillator Model of Electron Delocalization) indices [56] of 4,7-DCQ in the experimental and in vacuo DFT-optimized structures, and we compared them with the isolated 4,7dichloroquinoline ligand ( Table 2).
HOMED relies on the idea that extended electron delocalization should reflect into the equalization of covalent bond lengths, whereas any deviation from an otherwise ideal symmetry implies some loss of aromaticity. R0 is the reference bond length for a fully delocalized (aromatic) system, Ri is the i-th bond length of each of the n bonds in the ring considered, and α is an empirical calibration parameter chosen so that HOMED is exactly 0 for the Kekulé structure of benzene and is 1 for aromatic benzene [56]. Table 2. HOMED indices for aromaticity in symmetry-independent 4,7-dichloroquinoline ligands. Calibration parameters proposed in [56] have been employed (α(C=C) = 88.09 Å -2 ; α(C=N) = 91.60 Å -2 ; R0(C=C) = 1.394 Å; R0(C=N) = 1.334 Å). Data in Table S18.  Table 2. HOMED indices for aromaticity in symmetry-independent 4,7-dichloroquinoline ligands. Calibration parameters proposed in [56] have been employed (α(C=C) = 88.09 Å −2 ; α(C=N) = 91.60 Å −2 ; R 0 (C=C) = 1.394 Å; R 0 (C=N) = 1.334 Å). Data in Table S18.  Figure 1 for numbering. Atoms of the "quinoline 2" molecule all have 2-digit ID numbers, ending with "2". d This is the heterocyclic ring and bears the N atom which is connected to copper. e All atoms in this ring are carbons.
HOMED relies on the idea that extended electron delocalization should reflect into the equalization of covalent bond lengths, whereas any deviation from an otherwise ideal symmetry implies some loss of aromaticity. R 0 is the reference bond length for a fully delocalized (aromatic) system, R i is the i-th bond length of each of the n bonds in the ring considered, and α is an empirical calibration parameter chosen so that HOMED is exactly 0 for the Kekulé structure of benzene and is 1 for aromatic benzene [56].
No significant differences are detected when aromaticity indices computed on the experimental structure are compared with those from the isolated complex or ligand. As expected [57], the heterocycle part of the condensed quinoline system is slightly more asymmetric-and thus less aromatic-due to the incorporation of the nitrogen atom. However, Cu-N bonding does not determine any appreciable effect on the aromatic π system of 4,7-DCQ, ruling out any backdonation from the metal. This result is also in line with the electronic structure analysis (see below).
In conclusion, the chemical bonding analysis demonstrates that each Cu 2+ ion acts as a Lewis acid, accepting pure σ coordinative bonds from lone pairs of organic nitrogen atoms and Br − ions, with no appreciable perturbation of π aromatic systems of the 4,7-dichloroquinoline moieties. Axial Br(1) atoms are instead involved in essentially closed-shell interactions, mainly electrostatic in nature and significantly weaker than equatorial Cu-Br ones.

Electronic States
The occupational Br(1) defect (see Section 2) implies that a~11% non-negligible minority of Cu 2 (4,7-DCQ) 4 Br 3 moieties with a single bridging Br − ion coexist with stoichiometric Cu 2 (4,7-DCQ) 4 Br 4 ones. To ensure electroneutrality, the bromide vacancy must be compensated by a lower charge on Cu ions. Thus, we expect to have a mixture of +1/+2 oxidation states of copper in the crystal. This view is supported by magnetic susceptibility measurements on the CDCQB complex. An effective magnetic moment µ eff = 2.47 Bohr magnetons (BM) is reported (Section S5). This estimate is compatible with two unpaired electrons on the two Cu centers and is also consistent with DFT simulations, which predict the triplet spin state as 29.9 kcal·mol −1 more stable than the singlet one. However, the measured µ eff has a~12% lower magnitude than that expected for spin-only paramagnetism produced by two unpaired electrons (2.83 BM). In other words, the missing spin polarization can be attributed to the occurrence of an equal amount of Cu centers in a diamagnetic d 10 configuration. The conformity of views between structural, DFT and magnetic results is remarkable. Figure 6 displays a simplified molecular orbital (MO) scheme of the neutral asymmetric unit of the CDCQB complex, Cu(4,7-DCQ) 2 Br 2 . The geometry is close to a rectangular pyramid, so C 2v symmetry labels are used. Only σ-bonding interactions are shown, as they are the most relevant in this system. Moreover, the scheme includes only equatorial ligands, as the axial Br(1) − ion does not significantly participate in electron sharing (see above). Moreover, the quinoline system acts as a σ-donor (see above); thus, only the sp 2 hybrids of N atoms directed toward the metal along the y laboratory axis have been included in the calculation of the corresponding symmetry-adapted linear combination (SALC) of atomic orbitals.
The electronic states of ligands, and specifically those of bromide ions, are higher in energy than the metal ones. Therefore, frontier orbitals bear a significant ligand character, at a variance of what is expected in a normal ligand field. For example, the first virtual states bear large contributions from π* orbitals localized on the quinoline rings, while the highest occupied MO (HOMO) is invariably an antibonding combination of the d x 2 −y 2 metal state with ligand-centered SALC of a 1 symmetry (see Figure S13). However, the ligand field is not inverted in the Hoffman's sense [8], as the MO sequence is the same as expected for a distorted square pyramidal crystal field ( Figure 6). The reason can be traced back to the relatively low electronegativity of ligands. Therefore, frontier orbitals still bear a significant metal character, and the geometry of the title compound can be rationalized in terms of distortions due to an anisotropic ligand environment, according to the predictions of the crystal field theory.
The higher energy of ligand states, however, makes them possible reducing agents with respect to metal. Following Snyder [5], we believe that copper in CDCQB is partly reduced by bromide ligands. Keeping in mind that many arguments arise when one tries to assign physical meaning to quantities sensible to arbitrary partitioning criteria, such as atomic charges, some consistent trends can at least be deduced by comparing the outcomes of DFT simulations. Table 3 shows condensed Mulliken charges of metal, quinoline ligands and bromide ions for the stoichiometric Cu 2 (4,7-DCQ) 4 Br 4 structure, at the experimental and in vacuo DFT optimized geometries. DFT results from the triplet spin state are qualitatively identical (Table S21).  The higher energy of ligand states, however, makes them possible reducing agents with respect to metal. Following Snyder [5], we believe that copper in CDCQB is partly reduced by bromide ligands. Keeping in mind that many arguments arise when one tries to assign physical meaning to quantities sensible to arbitrary partitioning criteria, such as atomic charges, some consistent trends can at least be deduced by comparing the outcomes of DFT simulations. Table 3 shows condensed Mulliken charges of metal, quinoline ligands and bromide ions for the stoichiometric Cu2(4,7-DCQ)4Br4 structure, at the experimental and in vacuo DFT optimized geometries. DFT results from the triplet spin state are qualitatively identical (Table S21).
While the dichloroquinoline ligands are neutral, some electron density is transferred to copper, whose net charge is lower than that expected from its formal +2 oxidation state. DFT results thus provide a rationale to explain the observed amount of nonstoichiometric Cu2(4,7-DCQ)4Br3 molecules in the crystal, with reduced (or partially reduced) copper centers (see above).   While the dichloroquinoline ligands are neutral, some electron density is transferred to copper, whose net charge is lower than that expected from its formal +2 oxidation state. DFT results thus provide a rationale to explain the observed amount of nonstoichiometric Cu 2 (4,7-DCQ) 4 Br 3 molecules in the crystal, with reduced (or partially reduced) copper centers (see above).
It is likely that the redox process takes place in solution when CuBr 2 is mixed with the 4,7-DCQ ligand (see Section 2). We hypothesize that a minority of bromide ions are oxidized to Br 2 and produce Cu(I) centers, which are included in the crystal at the growth stage. The reaction is expected to be Cu 2+ (solv) + 2Br − (solv) Cu + (solv) + Br 2 (g) (4) where "solv" indicates the 1:1 dichloromethane/methanol reaction liquor (see Section 2). Based on the amount of formal Cu + centers found in the crystal, a degree of progress of 11% is reasonable, corresponding to an equilibrium constant K = 5.15 × 10 −4 . Overall, the process is endergonic, with ∆G o = 18.14 kJ·mol −1 as computed from the known thermodynamic boundary conditions (T = 15 • C, p = 1 bar; see Section 2). From the Nernst equation, applicable at our dilutions, the expected standard cell potential is -0.188 V for the Cu 2+ /Br − redox pair. To the sake of comparison, the reduction of Cu 2+ by bromide in water is much more endergonic, with 5 times higher ∆G o (+89.6 kJ·mol −1 ), as estimated from standard reduction potentials. However, in aqueous solution, Cu(I) is completely instable and disproportionates to give metallic copper and Cu(II) ions. Copper(I) oxidation state can be stabilized only by forming stable complexes (e.g., [CuCl 2 ] − ) or insoluble salts (e.g., CuI). The difference between the two ∆G o values can be partly attributed to the different chemical environments [58,59], although the role of 4,7-DCQ may not be negligible. Indeed, it is known that the Cu(I)-Cu(II) redox system can be strongly influenced by the presence of N-donor ligand depending on the strength of the copper-nitrogen bond [60]. Actually, stabilization effects towards an oxidation state in a copper complex are governed by a tricky combination of structural and reduction-oxidation properties of both organic components and Cu counter-anions [61,62]. Even some environmental factors, such as temperature and solvent polarity, can also produce a drastic change in the position of the redox equilibrium [63]. To corroborate this model and fully clarify the role of any system elements, the inclusion of further experimental evidence is needed, which will be discussed in a forthcoming study.

Conclusions
The stereochemistry of Cu 2+ complexes is often determined by a subtle interplay of electronic effects that are hardly rationalized in a classical coordination chemistry framework. In this work, the binuclear [Cu(4,7-dichloroquinoline) 2 Br 2 ] 2 complex (CDCQB) was studied by single-crystal X-ray crystallography and quantum chemical methods as a possible borderline case between transition and main group chemistry. The basic coordination geometry of CDCQB is distorted square pyramidal, with each Cu center bonded to four equatorial ligands and one axial bridging bromide ion. There are striking similarities with inverted field complexes. However, likely due to the low electronegativity of 4,7-DCQ and bromide, the MO sequence remains that expected for a distorted square pyramidal crystal field, that is, no inversion of the d ladder occurs.
From the reactivity viewpoint, we provided several points of experimental evidence that formal Cu 2+ centers in this complex act as Lewis acids and tend to accept electrons from the inner shell ligands, in agreement with the known reactivity and catalytic ability of this kind of complex [17,18,64]. To date, only two crystal structures of Cu(II):4,7-dichloroquinoline complexes have been reported (CSD refcodes KUBJOG and KUHHEA), and a few dozen Cu:quinoline complexes are known, with copper mainly in the +1 oxidation state. We proved that 4,7-DCQ ligands, in conjunction with bromide counterions, can promote a change of the metal redox state. In further detail, it is found that~11% Br − vacancies are included in the crystal, determining defective Cu 2 (4,7-DCQ) 4 Br 3 binuclear units, with a missing µ 2 -type bromide ion, that coexist with stoichiometric Cu 2 (4,7-DCQ) 4 Br 4 ones. To ensure electroneutrality, copper in Cu 2 (4,7-DCQ) 4 Br 3 must thus be partially reduced. An endergonic redox pair where Br 2 is produced by the partial oxidation of Br − is probably set up in solution, and the resulting Cu(I) centers are included in the crystal during the growth process. Even though no appreciable π-backdonation toward the 4,7-DCQ moieties was detected, we note that the availability of low-energy virtual π* 4,7-DCQ orbitals may provide opportunities to activate the aromatic ring of the ligand, opening new perspectives for aromatic chemistry applications.