*3.1. Direct Interactions between PdCl4 Units*

The initial calculation focuses on the isolated PdCl4 <sup>2</sup><sup>−</sup> dimer, in the absence of any counterions. The first row of Table 1 documents the strong repulsion between the two naked dianions. The interaction energy of the pair within their X-ray structure is +212 kcal/mol. Most of that can be attributed to a highly repulsive electrostatic component of +218 kcal/mol. Indeed, it would be difficult to generate any degree of attraction for the negatively charged Cl atom when the maximum of the MEP above the Pd atom is −371 kcal/mol, especially when coupled with the VS,min on the Cl of −387 kcal/mol.

**Table 1.** Interaction energy and its electrostatic component for interactions between subunits, and the maximum and minimum of the MEP of the uncomplexed subunits (kcal/mol), and total charge (Q, e) assigned to PdCl4 segment within complexes.


<sup>a</sup> L refers to the butyl ligands with amino groups on both ends. L<sup>0</sup> has NH2 on both ends, L<sup>+</sup> has NH3 <sup>+</sup> on one end near the PdCl4, L2+ has NH3 <sup>+</sup> on both ends for total charge of +2. <sup>b</sup> PC refers to the constellation of point charges that approximate L0, L+, or L2+, respectively. <sup>c</sup> total charge on each PdCl4 unit (average of two).

The next rows of Table 1 indicate the effects of adding four neutral ligands around this dianion pair. For the purposes of examining the interactions of the two principal dianions, two of these ligands were assigned to each PdCl4 unit to compose a [PdCl4] <sup>2</sup>−L2 subunit. The MEP was computed for each [PdCl4] <sup>2</sup>−L2 subunit, and the interaction energy between them was computed as the energy of the dimerization reaction (1)

$$2\left[\text{PdCl}\_4\right]^{2-}\text{L}\_2 \rightarrow \left[\text{PdCl}\_4\right]^{2-}\text{ }\_2\text{L}\_4\tag{1}$$

The Ar atoms were placed at the positions of the proximate N atoms of the NH3- (CH2)4-NH3 2+ counterions within the X-ray structure, as were the N atoms of the NH3 units. The H atoms of the latter were optimized and thus engaged in NH···Cl H-bonds with the anions. The Ar atoms have essentially no effect on the repulsive energy between the two anions, diminishing it by only 3 kcal/mol. The Ar atoms do reduce the negative value of VS,max, lowering its magnitude from −371 to −184 kcal/mol. They also strongly reduce the negative potential on Cl, lowering VS,min from −387 to −202 kcal/mol. However, the electrostatic component of the interaction is little changed, dropping from +218 to +206 kcal/mol. Nor does Ar absorb any of the negative charge of these anions, leaving their total charge at −2.00.

The H-bonds connected with NH3 have a larger impact, albeit still fairly small. VS,max drops a bit more, down to −172 kcal/mol, and VS,min is reduced as well, causing a drop in EES to +173 kcal/mol. The NH3 units absorb a small amount of density, leaving the charges on the PdCl4 dianions at −1.96. Nevertheless, the interaction energy remains high at +182 kcal/mol. Extending the NH3 units to the full NH2(CH2)4NH2 ligands, likewise capable of engaging in NH···Cl H-bonds, has a further stabilizing effect. These longer species absorb a bit more of the anion's charge, reducing it to −1.92, and raises VS,max a small amount, up to −162 kcal/mol and also reducing the magnitude of VS,min. The electrostatic component and interaction energy are accordingly reduced as well, both down below +160 kcal/mol.

In order to distinguish the effects of this longer ligand arising from purely electrostatic considerations, from H-bonding, polarization, dispersion, and so on, these four NH2(CH2)4NH2 ligands were each replaced by a series of point charges. There was a oneto-one replacement of each atom of the ligand by such a charge, which was superimposed on the atomic position, and was assigned the natural charge equal to that of the ligand within the complex. The next row of Table 1 shows that this constellation of point charges has a small stabilizing effect on the dianion repulsion, less than that of the true ligand, and only roughly equivalent to the much smaller NH3 molecule. Of course, as simply a collection of charges, these pseudoligands cannot absorb any charge, so that of each ligand remains at −2.00. So, it is clear that the H-bonds connected with the full ligands, as well as any charge which they can accept from the anions, have a significant effect on stabilizing the anion pair, albeit far too small to make this interaction attractive.

A second iteration of this analysis would involve placing a positive charge on each ligand. The simplest such counterion, and one incapable of engaging in a H-bond, would be a monatomic cation such as K+. As exhibited in the next row of Table 1, the inclusion of four such cations makes the interaction exothermic with negative values of Eint. The presence of these cations also strongly reduces the negative values of both VS,max and VS,min, both smaller in magnitude than −80 kcal/mol. These changes are partly responsible for the negative, attractive electrostatic component at −94 kcal/mol.

The Eint of −97 kcal/mol is enhanced to −111 kcal/mol if the K<sup>+</sup> is morphed into the NH4 <sup>+</sup> ion of roughly the same size, but with the added capability of forming NH···Cl Hbonds. This mutation has a small reducing effect on the MEP extrema and drops the formal charge on the PdCl4 unit to −1.80, adding to a slightly more negative EES, which contributes to the more negative interaction energy. Enlarging the ammoniums to the much longer NH2(CH2)4NH3 <sup>+</sup> was done in such a way that it is the positively charged NH3 <sup>+</sup> unit that is placed close to the PdCl4 species. This counterion enlargement has a slightly deleterious effect, increasing Eint from −111 to −101 kcal/mol, as well as dropping the electrostatic

attraction energy by 5 kcal/mol. This rise in Eint may be due to the lesser concentration of the positive charge in the larger cation. Each of these counterions, whether NH4 <sup>+</sup> or NH2(CH2)4NH3 +, involves itself in two NH··Cl H-bonds for a total of four such bonds with each PdCl4 unit. The replacement of the ligand atoms by their corresponding point charges is just slightly less effective, with Eint becoming less exothermic by 3 kcal/mol.

It may be noted further from Table 1 that the electrostatic components are all quite attractive when any of these monocations are added, nearly −100 kcal/mol. On the other hand, even with these counterions present, VS,max on Pd remains negative by between 53 and 58 kcal/mol. This contradiction argues against taking a positive VS,max as a condition for an exothermic association. In sum, adding a +1 charge to the surrounding ligands enables them to absorb a bit more of the (PdCl4) <sup>2</sup><sup>−</sup> dianion's negative charge. Most effective in this regard is the set of four ammonium cations which drop the dianion's charge down to −1.80.

The last few rows of Table 1 refer to the addition of two dications instead of the four monocations. (The smaller number of the former is necessary in order to maintain overall electroneutrality. Equation (1) must be modified to describe each subunit as [PdCl4] <sup>2</sup>−L2+). Despite the reduction in their number, the dications prove more effective at promoting a more exothermic association. Whether the small monatomic Ca2+ or the much larger NH3(CH2)4NH3 2+ dications, Eint drops below −120 kcal/mol. Even the collection of point charges designed to mimic the long ligand dication is effective in this regard, with Eint of –108 kcal/mol. The comparison of the Ca2+ and the L2+ systems enables some assessment of H-bonds, which are only possible for the latter. It is intriguing that although the Hbonding ligands leave both VS,max and VS,min more negative, the total electrostatic term is nonetheless more attractive when compared to Ca2+.

In fact, upon moving the analysis to the dications, the electrostatic component diverges substantially from the full Eint. These two quantities differ by some 60–80 kcal/mol. More specifically, while the transition from monatomic K<sup>+</sup> monocation to Ca2+ dication makes Eint more negative, and the same sort of change can be seen from L<sup>+</sup> to L2+, it has the opposite effect on EES, which becomes substantially less negative. This change to a less attractive electrostatic term contrasts with the less negative VS,max quantities associated with the monatomic ions. Despite their smaller number, the Ca2+ dications are much better at dispersing the negative charge on the central dianions than K+, dropping this charge down to −1.73. There is much less distinction between the longer ligands, where the dications are slightly poorer at absorbing this charge than the monocations.
