2.2. Description of the Crystal Structures
The crystal structures of the reported complexes (
1 and
2) are made up of neutral hexanuclear Mn(III) complexes, so-called Mn
6 SMMs [
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27]. Compound
1 crystallizes in the space group Pī of the triclinic system and compound
2 crystallizes in the space group C2/c of the monoclinic system (see
Table 1). The crystallization solvent molecules MeOH (
1), H
2O (
2) and EtOH (
2) are also present in the structures of these compounds. The characteristic Mn
6 complexes found in
1 and
2 are shown in
Figure 1. In this family of compounds, the core is formed by two {Mn
3(μ
3-O)} subunits, which display a connection between them through phenolate and oximate O atoms (
Figure 1). Three Mn(III) metal ions of each {Mn
3(μ
3-O)} triangular subunit are mainly connected by three –N–O– bonds of salicylamidoxime molecules and a oxo group which is located approximately in the plane containing the triangle in
1 and
2.
In compound
1 there are two crystallographically independent Mn
6 complexes. The Mn(III) metal ions in the center of
1 and
2 show a metal environment very close to those of earlier published amidoxime-based Mn
6 compounds [
32,
33], exhibiting elongated Oh geometries with axial axes pretty much located at 90° about the main plane of the triangular subunits. The Mn-N-O-Mn angles of the {Mn
3(μ
3-O)} triangular subunits are 43.7, 41.2 and 26.1° and 38.0, 36.2 and 26.3° for
1 and 42.9, 36.9 and 24.4° for
2. These torsion angles values are very important to explain the magnetic properties of this type of Mn
6 complexes [
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33]. In both compounds, the coordinated lipoate ligand is bonded to the Mn(3) ion and to its symmetry equivalent [Mn(3a); (a) = -x, -y, -z+1 for
1 and (a) = -x+1, -y+1, -z+1 for
2], by means of the carboxylate group in a monodentate fashion, as previously reported for other carboxylate-based ligands in this family of complexes [
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27]. In both cases, the lipoate ligand exhibits average values of the S–S, C–S and C–C bond lengths of the dithiolane ring that are in agreement with those previously reported [
31].
In the molecules arrangement of
1, the neutral Mn
6 entities are linked through H-bonding interactions promoted by solvent MeOH molecules, oximate oxygen atoms and −NH
2 groups of neighboring neutral Mn
6 units via the N(9)···O(10)···O(24) pathway [N(9)···O(10) distance of ca. 2.89(1) Å and O(10)···O(24) distance of ca. 2.80(1) Å], thus generating a 1D motif based on Mn
6 complexes (
Figure 2). The shortest intermolecular S···S distance in
1 is approximately 11.44(1) Å [S(2)···S(1b) distance; (b) = x, y+1, z]. Further intermolecular crystal interactions formed through S atoms of the dithiolane rings and −C-H groups of salicylamidoxime ligands of adjacent Mn
6 complexes [S···C distances cover the 3.4(1)-3.8(1) Å range; (c) = -x+1, -y+1, -z+1 and (d) = -x+2, -y+1, -z+2] link the Mn
6 pseudo-chains leading to a 2D structure of alternating Mn
6 complexes in
1 (
Figure 3).
In the molecules arrangement of
2, adjacent discrete Mn
6 entities are connected each other by means of hydrogen bonds, which involve −NH
2 groups and O atoms of phenolate groups of close salicylamidoxime ligands [N(2)···O(4b) separation of ca. 2.99(1) Å; (b) = -x+3/2, -y+3/2, -z+1], leading to a 1D arrangement (
Figure 2). Further H-bonded Mn
6 molecules are linked by means of additional −NH
2 and carboxylate groups of neighboring Mn
6 entities [N(6)···O(11c) separation of approximately 3.05(1) Å; (c) = -x+1, y, -z+3/2], generating a 2D structure in
2 (
Figure 3). The shortest intermolecular S···S distance in
2 is much more reduced than that found in
1 [S(1)···S(1d) separation of ca. 5.14(1) Å; (d) = -x+2, -y+1, -z+2]. Finally, weak interactions between S atoms of the dithiolane rings and −C-H groups of salicylamidoxime ligands of neighboring complexes [S···C separations spanning the ca. 3.4(1)-3.8(1) Å range; (c) = -x+1, -y+1, -z+1 and (d) = -x+2, -y+1, -z+2] link the Mn
6 pseudo-chains leading to a 2D structure of alternating Mn
6 complexes in
2 (
Figure 3).
2.3. Analysis of the Hirshfeld Surfaces
The intermolecular interactions involving the neutral Mn
6 complexes of
1 and
2 were further studied through the CrystalExplorer program [
34]. By mapping the distances of the 3D surface formed having into account the nearest atom outside (d
e) and inside (d
i) distances of each studied molecule and a normalized contact distance (d
norm), that overcomes some limitations generated by the atom size, this program allowed the qualitative and quantitative study of the significant molecular contacts [
34,
35,
36]. It is displayed with a set of colors. Red color is used for short contacts, white indicates contacts interactions close to the van der Waals distances, and blue is assigned to long interactions. With all this information, it is generated a fingerprint, which is a 2D plot outline of the involved molecular interactions [
35,
36,
37,
38]. The Hirshfeld surfaces for complexes
1 and
2 are the first ones reported for oxime-based Mn
6 entities and are given in
Figure 4 and
Figure 5, respectively. The intermolecular O···H contacts formed among the -NH
2 groups of salicylamidoxime ligands and solvent MeOH molecules, which connect the Mn
6 complexes in
1, are approximately 14% of the complete fingerprint plot (
Figure 4). Besides, intermolecular weak S···H contacts involving S atoms of the dithiolane rings and –C-H groups of salicylamidoxime ligands of adjacent Mn
6 entities cover ca. 6% of the graphic outline of complex
1 (
Figure 4). In complex
2, intermolecular O···H contacts generated by H-bonding interactions, which are formed between the -NH
2 groups of salicylamidoxime ligands and carboxylate groups of neighboring Mn
6 molecules, are close to 11% of the complete fingerprint plot (
Figure 5) and, therefore, it is a somewhat lower percentage than that detected for O···H contacts in complex
1. Finally, intermolecular S···H contacts are also observed in complex
2, in this case, displaying a higher percentage (ca. 12% of the complete fingerprint plot) than that shown in complex
1 (
Figure 4 and
Figure 5).
2.4. Study of the Magnetic Properties
Dc magnetic susceptibility studies were carried out on microcrystalline samples of both compounds in the temperature range from 300 to 1.9 K. An external magnetic field of H
dc = 0.5 T was employed. χ
MT vs T curves of
1 and
2 are shown in
Figure 6. At T = 300 K, the initial χ
MT values are approximately 19.2 (
1) and 18.3 cm
3mol
-1K (
2). These χ
MT values are very close to that expected for six isolated Mn(III) metal ions, with S = 2 and g = 1.99 values for each metal ion, which are in accordance with those earlier published for amidoxime-based hexanuclear Mn(III) complexes [
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27]. With cooling, the χ
MT value in complex
1 remains pretty much constant to 200 K, before χ
MT slightly increases to reach a value of ca. 21.2 cm
3mol
-1K at 60 K. Afterwards, χ
MT value decreases very fast to finish with a value of ca. 6.5 cm
3mol
-1K at 1.9 K (
Figure 6). In complex
2, χ
MT value follows the Curie law with reducing temperature to 150 K, before χ
MT somewhat rises to get a number of approximately 19.2 cm
3mol
-1K at 35 K. Finally, χ
MT decreases very fast reaching a final number of ca. 8.3 cm
3mol
-1K at 2 K (
Figure 6). The decrease of the χ
MT values displayed at low temperature by
1 and
2 are likely due to the ocurrence of molecular magnetic exchange and/or zero-field splitting (ZFS) consequence, which have been earlier published for close Mn
6 systems [
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27].
The experimental magnetic susceptibility values of the
χMT vs
T curves of
1 and
2 were analyzed employing a 2
J model which can be exemplified through the isotropic Hamiltonian shown in equation (1), where
J1 and
J2 are the magnetic exchange constants for the molecular manganese-manganese couplings assuming the pathway based on the Mn–N–O–Mn set of atoms in the Mn
6 entity.
J1 is assigned to higher Mn–N–O–Mn torsion angles and
J2 with the lower ones (
Figure S1). A term to account for the Zeeman result is also added to the final part of the Hamiltonian. The magnetic
g parameter is the Landé factor for the involved metal ions. The best theoretical fit thus obtained gave the following parameters:
g = 1.98,
J1 = +1.95 cm
-1 and
J2 = -2.07 cm
-1 for complex
1, and
g = 1.99,
J1 = +1.78 cm
-1 and
J2 = -2.04 cm
-1 for complex
2. This theoretical 2
J model reproduces very well the experimental magnetic susceptibility data in the reported temperature range (see solid red lines in
Figure 6). The numbers computed for
J1 and
J2 are in line with the Mn–N–O–Mn angles obtained in the structures of both compounds, and are in agreement with earlier reported values of similar Mn
6 compounds [
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28]. In both compounds, the global antiferromagnetic interaction (associated with
J2) is the main magnetic exchange between the implicated Mn(III) ions, even though both magnetic contributions are important in both
1 and
2, as observed in their experimental curves (
Figure 6), and both compounds exhibit at least a torsion angle value lower than the critical value of 27°, as indicated in the 2.2 section [
21,
22,
23,
24,
25,
26,
27].
In general, in this family of Mn
6 systems, the antiferromagnetic compounds display a spin S = 4 value, whereas the ferromagnetic compounds show a spin S = 12 value [
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27]. The reported
χMT vs
T plot for both
1 and
2 would be consistent with a global antiferromagnetic interaction and, a priori, a spin S = 4 value for the ground state would be expected for both
1 and
2. In fact, the simulation of the magnetic susceptibility data of
1 and
2 generated the plots of the energy vs spin value displayed in the respective insets in
Figure 6, which was performed as in previous studies focused on Mn
6 complexes [
17,
18,
19,
20,
21]. In both compounds, the ground state spin value would be S = 4 and the first excited state would be S = 5, which is placed at 3.50 (
1) and 2.97 cm
-1 (
2). In many other amidoxime-based Mn
6 complexes with S = 4, which were previously studied, the first excited state was S = 3 [
32,
33]. These results match the S values obtained from the reduced magnetization data fits (
Figure S2 and
Figure S3).
Ac magnetic susceptibility studies were carried out on microcrystalline samples of
1 and
2 in the temperature range from 7 to 2 K. An ac magnetic field of H
ac = 5.0 G oscillating at several frequency values (10
2-10
4 Hz range) was used. Slow relaxation of the magnetization is detected in
1 and
2 through out-of-phase ac signals (χ″
M) that were detected at H
dc = 0 G. In this way, both
1 and
2 display Single-Molecule Magnet (SMM) behavior, which is typical for all the members of this oxime-based family of Mn
6 compounds [
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27]. The magnetic relaxation of
1 and
2 was investigated by means of out-of-phase (χ
M″) ac susceptibilities vs frequency (ν/Hz) plots and out-of-phase (χ
M″) ac susceptibilities vs temperature (T/K) plots, which are given in
Figure 7 and
Figure 8, respectively. In the two types of ac plots, the data of each maximum in
1 show much higher intensity than those data of
2. Nevertheless, a similar magnetic relaxation would be observed for
1 and
2.
We have reported previous works dealing with systems where two Mn
6 molecules coexist in the crystal structure and, hence, two clearly distinguishable χ
M″ peaks are observed and associated with the two Mn
6 molecules [
21,
24]. This fact is not detected in the ac experimental data of compound
1.
In the insets of
Figure 8 it is shown the ln(τ) vs 1/
T plots for
1 and
2. In both compounds, the plotted data follows a straight line covering the ranges of approximately 0.27–0.38 (
1) and 0.33–0.47 K
−1 (
2). These data were fitted through the same mechanism for the relaxation of magnetization, namely, Orbach, and following the Arrhenius equation or eqn (2), where
τo is the pre-exponential factor,
τ is the relaxation time, U
eff is the barrier to relaxation of the magnetization, and k
B is the Boltzmann constant. The fitted data were plotted in their respective insets (
Figure 8). Once fitted the experimental data of
1 and
2 by means of a least-squares fit of eqn (2), these parameters were obtained:
τo = 2.54(1) × 10
−10 s and U
eff = 40.9(1) K [28.4(1) cm
−1] for
1 and
τo = 2.80(2) × 10
−10 s and U
eff = 33.0(2) K [22.9(2) cm
−1] for
2.
The
τo values reported for
1 and
2 are in concordance with those earlier published for Mn
6 SMMs with S = 4 [
13,
17], and their computed U
eff values fall into the range previously reported for this family of compounds [24.0 K (16.7 cm
-1) < U
eff < 86.0 K (59.8 cm
-1)] [
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27].