In this paper we will report the study of nineteen compounds corresponding to the general formula depicted in
Scheme 1 and named by a simple code that allows to easy identification: (R-pzAg)
2(L)
n. Firstly, the substituents (R) on the pyrazole ring are indicated: Pz, 4NO
2pz, DMepz and 4Clpz for the unsubstituted (H), 4-nitro, 3,5-dimethyl, and 4-chloro derivatives, respectively. Secondly, the ligands (L) interacting with the silver atoms are indicated. Thus, for instance, (4NO
2pzAg)
2(PH
3)
4 corresponds to the (4-nitropyrazole:Ag)
2 cyclic structure with four phosphines interacting with the silver atoms (two phosphines per each silver atom).
3.1. CSD Search
A search in the Cambridge Structural Database has been carried out and the resulting compounds with the structure represented in
Scheme 1 were summarized and reported in
Table 1 ordered by increasing Ag–Ag intramolecular distance. Two simplified views of these structures can be found in
Table S1 of the Supplementary Materials. Structures with dinuclear silver(I) pyrazolates without ligands were not found within the CSD search.
As observed by the crystallographic data, the Ag–Ag distance ranges between 4.305 Å (ZIGSEQ) and 3.392 Å (FINWOR). The shortest distances correspond to complexes with only two ligands present concomitantly with the 3,5-bis-CF3 substituent on the pyrazole. It is also clear that the larger the number of ligands, the longer the intramolecular Ag–Ag distance. Moreover, it is noteworthy that, in structures with four phosphines ligands, the Ag–Ag distance increases as the substitutes of the pyrazole are H < 4-Cl < 4-NO2. These results will be compared against our theoretical calculations in the following sections.
Concerning the conformation of the six-membered rings in the crystal structures (similar to those of 1,4-cyclo-hexadiene, 9,10-dihydroanthracenes, phenothiazines, etc.), very little energy differences between those conformations in the crystals were found, in agreement what was proposed by Rasika Dias [
78]. Regarding the tetrahedral configuration of Ag(I) atom, we have used Houser’s τ
4 index [
79] as recommended by Raptis [
80]. This index is defined as:
where, α and β correspond to the two largest angles of the six angles around the tetrahedral silver atom. The values of τ
4 range from 1 (perfect tetrahedral geometry, i.e., τ
4 = [360 − (109.5 + 109.5)]/141 = 1) to 0 (perfect square planar geometry). The τ
4 values obtained for three substituents, 0.9 (RATFEX and ZIGSIU) are very similar to those for 4 substituents (ZIGROZ and ZIGSEQ, 0.89 and 0.88 respectively) with both identical Ag atoms. The two lowest values (0.78) correspond to a substituent that differs from PPh
3 (see notes (a) and (b) of
Table 1).
3.4. Effect of the Ligands and Substituents on the Structure and Dissociation Energy (De)
After studying the free (PzAg)
2 system
, the complexes with two ligands simultaneously interacting with the (PzAg)
2 system have been optimized, i.e., each silver atom interacts with a single ligand. The minimum structures obtained show that the interacting atom of the ligand is coplanar with the plane defined by the (PzAg)
2 system. The molecular graphs of two illustrative examples are shown in
Figure 3 and the Cartesian coordinates of all of them were summarized in
Table S3.
The complexation with ligands produces an elongation of the Ag–Ag distance up to 1.1 Å (
Table 2) in agreement with the large variety of structures and the range of Ag–Ag distances found in the CSD search. For example, the crystal structure RATPAT (L = (PPh
3)
2) shows an Ag–Ag distance of 3.870 Å while in the calculated (PzAg)
2(PH
3)
2 complex this value is 3.689 Å. It is known that ligands coordinated by O, C or P atoms are strong, while those ligands coordinated by N atoms are weak. In the cases of CNH and HCN ligands are both -donors and -acceptors but the former is coordinated by the C atom while the latter is coordinated by the N atom. This results in larger dissociation energies for the (PzAg)
2(CNH)
2 complex in comparison with (PzAg)
2(NCH)
2. Similarly, this happens with CO and NH
3 ligands (both -donors), but while CO is a good -acceptor NH
3 is not, resulting in smaller values of De. In the case of the PH
3 ligand, it is both a -donor and -acceptor ligand, which is in agreement with the (PzAg)
2(PH
3)
2 complex, showing the second largest De. Chalcogen ligands, OH
2 (-donor) and SH
2 (-donor) present similar trends. In addition, it is also observed that the distance between both pyrazole rings decreases with the elongation of the Ag–Ag distance.
But, does this have any impact on the dissociation energy? Or, in other words, is there any relationship between the Ag–Ag intramolecular distance and the dissociation energy? The dissociation energy values corresponding to the (PzAg)
2L
2 complexes range between 23 kJ mol
−1 for L = N
2 to 137 kJ mol
−1 for L = CNH (
Table 2). In general, despite observing a trend between the dissociation energy and the elongation of the Ag–Ag distance (
Figure S1), no good fitting has been found (logarithmic fitting, R
2 = 0.73). The only outlier corresponds to the (PzAg)
2(CO)
2 complex, and when this point is neglected the fitting is more evident (R
2 = 0.90). A better exponential relationship has been found for the distance between the pyrazole rings vs. De (De = 5.55·e
−0.114Pz-Pz, R
2 = 0.92) which may suggest that the repulsion between pyrazole groups is partially responsible for the increase of the De energy but somehow compensated by the Ag–Ligand interaction.
The effect of the substituents (pyrazole ring) within the Ag–Ag distance and dissociation energies have been explored by considering four different pyrazole derivatives, R = H, 3,5-di(CH
3), 4-Cl and 4-NO
2. These isolated (R-pzAg)
2 systems have been fully optimized as well as in the presence of two phosphine molecules ligands with the results gathered in
Table 3.
In relation to the Ag–Ag distance in the isolated (R-pzAg)2 systems, it increases in the following order: 3,5-di(CH3) < H < 4-Cl < 4-NO2 with a variation of 0.05 Å between both extremes. The same order was found within the (R-pzAg)2(PH3)2 complexes but with a slightly larger range of 0.12 Å. This evolution was also found in the CSD search for complexes with three PPh3 ligands: RATFEX (R = H) (3.706 Å) < ZIGRUF (R = 4-Cl) (3.707 Å) < ZIGSIU (R = 4-NO2) (3.827 Å), and for complexes with four PPh3 ligands: KIRVIX (R = H) (3.900 Å) < ZIGROG (R = 4-Cl) (4.209 Å) < ZIGSEQ (R = 4-NO2) (4.305 Å).
The dissociation energies for the (R-pzAg)
2(PH
3)
2 complexes increase following the same trend of Ag–Ag distances (
Table 3 and
Figure S2). Furthermore, linear correlation with R
2 value of 0.97 was obtained between Ag–Ag distances and the De.
So far, only the systems with no ligands, (R-pzAg)
2, and complexes with two identical ligands, (R-pzAg)
2L
2, have been studied. In
Table 4, the results corresponding to the complexes with 0, 1, 2 and 4 phosphine ligands bonded to (PzAg)
2 and (4NO
2pzAg)
2 systems are shown. In both series, the intramolecular Ag–Ag distance increases with the number of phosphine ligands bonded. When one PH
3 is bonded the increase in the Ag–Ag distance with respect to the isolated system is 0.286 and 0.311 Å for (PzAg)
2 and (4NO
2pzAg)
2 systems respectively. However, the change is two times larger when moving from 1 to 2 simultaneous ligands. Finally, the change is again moderate when 4 PH
3 ligands interacting with each Ag are considered. The CDS search also shows an increase of the Ag–Ag distance with the number of ligands. For example in the unsubstituted complexes (R=H) the Ag–Ag distance in RATFET (L = 3) is 3.706 Å and increases to 3.900 Å with four ligands (KIRXIV). This is also observed for substituted complexes with R=4-Cl: ZIGRUF (L = 3) 3.707 Å to ZIGROZ (L = 4) 4.209 Å and for R = 4NO
2: ZIGSIU (L = 3) 3.827 Å) to ZIGSEQ (L = 4) 4.305 Å. In addition, it is interesting to notice that in complexes with four phosphines, the (R-PzAg)
2 system adopts a chair conformation (
Figure 4) vs. the planar one observed with one or two ligands. The experimental Ag–Ag distances are longer than the calculated ones; this could be due to the fact that the ligand found in the crystals are bulkier (for instance PPh
3 vs. PH
3). This can be also related with the ratio of σ-donor/π-acceptor capacity in phosphorus ligands. In principle P(CH
3)
3 is a better σ-donor than PH
3, while the latter is a better π-acceptor [
81]. However, the σ-donor/π-acceptor ratio indicates that the P(CH
3)
3 is a stronger ligand than PH
3. The same can be expected for PPh
3 and therefore the Ag–Ag distance will be larger for complexes that are PPh
3-coordinated compared with those for PH
3 ones.
Regarding the τ4 index for (PzAg)2(PH3)4 and (4NO2pzAg)2(PH3)4: the values for both Ag are 0.81 and 0.83 respectively, in between of those found for ZIGSAM (0.78) and ZIGROZ (0.89) crystal structures.
The values of De show an anticooperativity effect as the number of phosphines increases, thus the De’s of the systems with two phosphines are smaller than twice the corresponding ones with one phosphine and the same happens when the results between the systems with two and four phosphines are compared. Looking at the values shown in
Table 4, (PzAg)
2(PH
3) complex yields a De of 64.2 kJ·mol
−1, whereas (PzAg)
2(PH
3)
2 complex’s is 122.9 kJ·mol
−1, 5.5 kJ·mol
−1 smaller than twice the corresponding value for (PzAg)
2(PH
3). This is an indication of an anti-cooperativity effect, which is more evident when (PzAg)
2(PH
3)
4 complex is taken into account (~42 kJ·mol
−1 less than four times the De of (PzAg)
2(PH
3)). This is also observed for (4NO
2pzAg)
2 and the corresponding complexes, but the differences, i.e., the anti-cooperativity, is rather smaller (4.0 kJ·mol
−1) for (4NO
2pzAg)
2(PH
3)
2 and slightly larger for (4NO
2pzAg)
2(PH
3)
4 (57.9 kJ·mol
−1).
3.5. Electron Density
The critical points of the electron density of all systems have been characterized using the quantum theory of atoms in molecules (QTAIM) method. As aforementioned, a bond critical point (BCP) is obtained for the (PzAg)
2 system in between both Ag atoms. A similar feature has been obtained for all the systems with Ag–Ag distances shorter than 3.3 Å. The electron density values, ρ
BCP, of this BCP (
Table S4) range between 0.032 and 0.014 a.u., with positive values of the Laplacian, ∇
2ρ (between 0.098 and 0.041 a.u.) and negative values of the total energy density, H
BCP, except for the system with the largest Ag–Ag bond in this set ((PzAg)
2(NH
3)
2). Excellent exponential relationships are obtained between the ρ
BCP and ∇
2ρ
BCP and the interatomic distance in agreement with previous reports (
Figure 5) [
82,
83].
Concering the Ag–L bonds, the corresponding bond critical points between the silver atom and the different ligands have been gathered in
Table S5. In all the cases, the interactions exhibit positive values of the ∇
2ρ
BCP and negative values of H
BCP, which indicates a partial covalent character of the bond formed [
84,
85]. The only exception corresponds to the weakest complex, (PzAg)
2(N
2)
2, which shows a small positive H
BCP value. The 14 unique Ag–P contacts found in this set show similar relationships between ρ
BCP and ∇
2ρ
BCP vs. the Ag–P distance to those previously mentioned for Ag–Ag BCPs.
3.6. Magnetic Properties and Aromaticity
Among the different nuclei suitable for NMR spectra present in these systems (
1H,
13C and
15N),
109Ag is the one with the largest range of chemical shifts. The calculated
109Ag chemical shielding for all the systems studied in this article are listed in
Table 5. It is worth noting that upon complexation
109Ag can change its chemical shielding by more than 1200 ppm to lower field, from 3765 ppm ((PzAg)
2) to 2550.48 ppm ((PzAg)
2(PH
3)
4). Furthermore, a good relationship between the chemical shielding and the intramolecular Ag–Ag distance (only for complexes with two ligands) was found (
Figure S3). Unfortunatelly, there are no experimental data on (PzAg)
2 compounds but a recent report on (PzAg)
3 derivatives show that the methodology used here provides δ
109Ag values within 10 ppm of the experimental ones [
46].
In order to explore the potential aromaticity of the six membered ring formed by the nitrogen atoms of the pyrazoles and the two silver atoms, the NICS(0) and NICS(1) have been calculated (
Table 5). Despite NICS isotropic values being widely used and well established, there is still a controversy about the reliability of NICS values for assessment of the aromaticity of certain molecules [
86,
87]. Nevertheless, and following our previous experience, the isotropic values have in several cases been shown to present an accurate description of the aromatic behaviour in poly-aromatic systems [
88,
89,
90].
Despite almost all the systems studied presenting negative NICS(0) values in the six-membered ring, only those with short Ag–Ag distances (2.8−3.0 Å) present very negative values close to the benzene molecule (−8 ppm) [
91], and, also, those NICS(0) values decrease in absolute value as the Ag–Ag distance increases. NICS(1) are smaller, in absolute value, than NICS(0), but follow the same trend as the latter. Also, NICS(1) are very small compared with benzene ones (−10.2 ppm) [
91] which suggest non-aromatic character. But, those values should be taken carefully, since the two silver atoms are very close and the proximity of the nuclei may affect the NICS(0) measure. To provide a further insight on this,
Figure 6 clearly shows that there is a unique dependence between the NICS(0) and NICS(1), the distance between the location where the NICS is measured and the silver atom. The scan of the NICS values for (PzAg)
2 from 0 to 2.0 Å above the centre of the six-membered ring (
Table S6) have also been plotted in
Figure 6 showing a similar evolution to the NICS(0) and NICS(1) of the rest of the molecules. This indicates that, as aforementioned, this ring is not aromatic but the NICS values obtained are somehow affected by the proximity of the silver atom.
In contrast the NICS(0) and NICS(1) values of the pyrazole rings are negative and large in all cases and very close to the ones obtained by Kusakiewicz-Dawid (−13.5 and −11.4 ppm respectively) [
92].
On the other hand, the substituents on the pyrazole ring have a greater effect on the NICS values than the different ligands on the (PzAg)2L2 complexes, most likely due to changes in the electron density on the ring current electrons. For instance the NICS(0) in the (Rpz-Ag)2 systems ranges between −10.5 and −13.1 ppm while in the (PzAg)2L2 complexes it is between −12.3 and −13.1 ppm.