Tuning the Reactivity and Bonding Properties of Metal Square-Planar Complexes by the Substitution(s) on the Trans-Coordinated Pyridine Ring

Abstract

The kinetics of the hydration reaction on trans-[Pt(NH₃)₂(pyrX)Cl]⁺ (pyr = pyridine) complexes (X = OH^–, Cl^–, F^–, Br^–, NO₂^–, NH₂, SH^–, CH₃, C≡CH, and DMA) was studied by density functional theory calculations in the gas phase and in water solution described by the implicit polarizable continuum model method. All possible positions ortho, meta, and para of the substituent X in the pyridine ring were considered. The substitution of the pyr ligand by electron-donating X’s led to the strengthening of the Pt–N1(pyrX) (Pt–N_pyrX) bond and the weakening of the trans Pt–Cl or Pt–O_w bonds. The electron-withdrawing X’s have exactly the opposite effect. The strengths of these bonds can be predicted from the basicity of sigma electrons on the N_pyrX atom determined on the isolated pyrX ligand. As the pyrX ring was oriented perpendicularly with respect to the plane of the complex, the nature of the X···Cl electrostatic interaction was the decisive factor for the transition-state (TS) stabilization which resulted in the highest selectivity of ortho-substituted systems with respect to the reaction rate. Because of a smaller size of X’s, the steric effects influenced less importantly the values of activation Gibbs energies ΔG^⧧ but caused geometry changes such as the elongation of the Pt–N_pyrX bonds. Substitution in the meta position led to the highest ΔG^⧧ values for most of the X’s. The changes of ΔG^⧧ because of electronic effects were the same in the gas phase and the water solvent. However, as the water solvent dampened electrostatic interactions, 2200 and 150 times differences in the reaction rate were observed between the most and the least reactive mono-substituted complexes in the gas phase and the water solvent, respectively. An additional NO₂ substitution of the pyrNO₂ ligand further decelerated the rate of the hydration reaction, but on the other hand, the poly-NH₂ complexes were no more reactive than the fastest o-NH₂ system. In the gas phase, the poly-X complexes showed the additivity of the substituent effects with respect to the Pt–ligand bond strengths and the ligand charges.

Introduction

Platinum anticancer complexes are administered in their inactive neutral form as prodrugs, and at least one hydrolysis step is needed for their activation. The activated drug reacts rapidly with DNA or proteins, and the hydrolysis step is the rate-determining step of the whole process. Because platinum binding to proteins is probably responsible for the side effects of the drug,¹ the activation should not be too fast to enable the drug to reach the nuclei of the malignant cells. Thus, the rate of hydrolysis is one of the important factors which should be considered for new drug development.

The reactivity of square-planar Pt(II)-complexes is driven by the trans effect; that is, the stability of the ligand is strongly influenced by the ligand in the trans position.²⁻⁹ It is a kinetic phenomenon whose origin lies in reactant destabilization and/or the transition state (TS) stabilization. The reactant destabilization is manifested itself by the Pt–trans ligand bond elongation, and it is sometimes called the trans influence.¹⁰ The trans effect can be explained by different σ-donation and π-back-donation abilities of the ligands⁶ and depends on the nature of the coordinating atom and its hardness.⁷ However, the chemistry of currently used drugs¹¹ is rather limited because only slowly hydrolyzing compounds are needed, considering the length of the delivery route. Thus, the non-leaving groups are always bound to the central Pt(II) by a nitrogen atom and are either two ammines or a diammine with an attached carbohydrate residue. The non-leaving group influence interactions with the proteins affecting cellular uptake of the drug and the repair of DNA-drug lesions.¹² The influence of the leaving groups on the biotransformation kinetics of the drug is less clear but two chlorine atoms in the first-generation drug cisplatin were displaced by bidentate groups (e.g. cyclobutanedicarboxylate or oxalate group) bound by the oxygen atom to the platinum central atom in the second- and third-generation drugs. The mechanism of hydrolysis of bidentate groups is still not well understood, and it is not clear in which form these drugs react with DNA.¹³⁻¹⁵

The substitution effects were explored on Pt(II)-complexes with different N,N,N-tridentate and N,N-bidentate ligands which mainly differ in π-back-donation ability. Strong π-acceptor ligands increase the electrophilicity of the Pt(II) center increasing the rate of the substitution.¹⁶⁻²²

Complexes with aromatic monodentate ligands having anticancer properties were also reported including those based on pyridine and its derivatives.²³⁻²⁷ To minimize the inactivating interactions with thiols, a sterically hindered complex AMD 473 with 2-picoline (2-methylpyridine) ligand was synthesized.²⁸ The reactivity of Pt(II) complexes with 2- and 3-picoline as ligands was experimentally compared by Sadler and co-workers. The complex with 2-picoline showed a 45 times slower hydration reaction of the Cl^– ligand in the trans position which was attributed to the steric effect of the methyl group on the pyridine ring.²⁹ Hydrolysis of AMD 473 and its binding to guanine were studied also theoretically.³⁰⁻³² The influence of the substitution in the para position of the pyridine ring on the spin densities and NMR spectra was studied for analogues of the Ru(III) complex NAMI.³³

Monofunctional Pt complexes, which offer unique ways of transmembrane transport and DNA interactions, form another promising group of anticancer drugs. Pyriplatin and phenanthriplatin contain three non-leaving ligands: two ammines with pyridine and phenanthridine, respectively.^23,34 Despite rather negligible DNA structure deformation, the inhibition of transcription was seen in vitro as well as in vivo.^35,36 The antineoplastic effect of phenanthriplatin was discovered by Lippard and co-workers.^37,38 Very recently, the importance of stacking interactions for the binding of phenanthriplatin to DNA was shown in studies of Veclani at al. and Almaqwashi et al.^39,40

The replacement of chloride ligands by water ligands in cisplatin and its derivatives was a subject of many previous studies⁴¹⁻⁴⁶ and was recently reviewed by Ahmad⁴⁷ and by Kozelka.⁴⁸

The substitution on the pyr ring affects the electron density on the coordinating atom through the inductive and resonance effects. In this study, we explored how the substitutions on the aromatic non-leaving group in the trans position influence the reactivity of the Pt(II)-complexes. We used trans-[Pt(NH₃)₂(pyrX)Cl]⁺ (pyrX = pyridine with the X substituent) complexes (X = OH^–, Cl^–, F^–, Br^–, NO₂^–, NH₂, SH^–, CH₃, C≡CH, DMA = dimethylamine) as the model compounds. We studied how the stability of Pt–pyrX, Pt–Cl, and Pt–w (w = water) bonds and the kinetics of the hydration reaction are affected by the nature and the position of the X in the pyrX ligand (Scheme 1).

Scheme 1. Reaction Mechanism of the Hydration Reactions Studied in This Contribution.

All reaction pathways proceeded over pentacoordinated X-TS transition state structures.

All possible positions ortho, meta, and para of the X in the pyr ring were considered. X was represented by electron-donating (NH₂, OH, and SH) and electron-withdrawing (C≡CH, and NO₂) groups as well as by halides (F, Cl, and Br) with mixed (resonance) donating and (inductive) withdrawal effects.

Because of a large number of optimized reaction pathways, only results for X = NH₂ and X = NO₂ as the main representatives of electron-donating and electron-withdrawing groups, respectively, together with reference non-substituted X = H structures are shown in most tables in the text. Complete versions of the respective tables can be found in the Supporting Information.

Finally, the metal complexes with poly-substituted pyrX (poly-X) ligands were considered. The reasons were threefold: (1) to evaluate more generally the limits for ΔG^⧧ values due to substituent effects; (2) to test the additivity of substituent effects with respect to the bond strengths, bond lengths, NPA ligand charges, and ΔG^⧧ values; and (3) to provide an independent set of structures for the validity testing of the 2p_x(N_pyrX) natural atomic orbital (NAO) energy as the predictor of the Pt–ligand bond strengths and ΔG^⧧ activation free energies (see below). We used NH₂ and NO₂ ligands as the representatives of electron-donating and electron-withdrawing groups, respectively. Furthermore, we used fluorine as the ligand with a small size and high electronegativity. Its derivatives may have interesting properties and found many applications mainly as agrochemicals and pharmaceuticals.⁴⁹ All poly-X ligands considered in this contribution are shown in Scheme 2.

Scheme 2. Poly-X Ligands Considered in This Study and Their Designation (X = F, NH₂, NO₂).

Results and Discussion

Structure Labeling

The designation of the complexes with pyrX ligands reflects the position of the X on the pyr ring with respect to the N_pyrX atom: ortho (o-), meta (m-), and para (p-). Thus, reactant structures are denoted as o-(m-, p-)X-R. For corresponding transitions states and product structures, the letter ‘R’ is replaced by ‘TS’ and ‘P’, respectively. X-R and X-P structures represent isolated complexes without weakly bound H₂O and Cl^– ligands, respectively, and they were used for the evaluation of bonding properties and the electronic structure.

The same principle will be used for the complexes with the poly-X ligand for which o-(m-, p-)X will be replaced by the designation from Scheme 2.

The reaction energetics of the hydration reactions were determined by the supermolecular approach. Here, “_w” and “_Cl” suffixes in o-(m-, p-)X-R_w reactants and o-(m-, p-)X-P_Cl products represent entering water and leaving chloride anion, respectively, being associated to Pt-complexes by H-bonding.

Electronic Structure of the Isolated pyrX Ligands

The influence of substitution effects on the reactivity of aromatic systems was studied in many previous studies.⁵⁰⁻⁵² In the pyrX ring, the π-electrons are shifted in accordance with the mesomeric effect. For electron-donating NH₂ substituent, π-electron density is increased on atoms in the ortho and para positions with respect to NH₂ while the opposite is true for the electron-withdrawing X such as NO₂ (Figure S1). However, the σ-electrons are shifted independently and in fact contrarily with respect to π-electrons.⁵⁰ For p-NH₂, the density of σ-electrons is decreased on the N_pyrX atom while the opposite is true for p-NO₂ (Figure S1).

Looking at atomic NPA charges, the shifts of the σ-electrons are masked by quantitatively larger shifts of the π-electrons. Values of NPA charge of the N_pyrX atom (q(N_pyrX)) in pyrX molecules are shown in Table 1. As expected, in the isolated pyrX molecule, q(N_pyrX) is increased in electron-donating groups in ortho or para positions. The electron-withdrawing NO₂ group lowers electron density in all ring atoms with the least effect for atoms in the meta position. Thus, q(N_pyrX) is almost independent on the nature of the X when being bound in the meta position.

Table 1. Gas Phase NPA Charges of the N_pyrX Atom (q(N_pyrX), in e) Calculated in the Isolated pyrX Ligands and in the X-R and X-P Complexes.

	PyrX			X-R			X-P
X/position	o-	m-	p-	o-	m-	p-	o-	m-	p-
H	–0.459			–0.503			–0.452
DMA	–0.527	–0.444	–0.504	–0.530	–0.482	–0.553	–0.504	–0.423	–0.480
NH2	–0.522	–0.443	–0.497	–0.551	–0.481	–0.547	–0.493	–0.426	–0.499
Br	–0.509	–0.476	–0.493	–0.535	–0.491	–0.510	–0.462	–0.439	–0.490
SH	–0.501	–0.443	–0.471	–0.537	–0.488	–0.522	–0.486	–0.436	–0.478
OH	–0.491	–0.442	–0.485	–0.564	–0.486	–0.530	–0.510	–0.433	–0.482
F	–0.486	–0.440	–0.470	–0.544	–0.489	–0.516	–0.502	–0.440	–0.467
Cl	–0.472	–0.442	–0.460	–0.531	–0.491	–0.510	–0.485	–0.441	–0.464
CH3	–0.479	–0.456	–0.467	–0.514	–0.496	–0.511	–0.460	–0.444	–0.462
C≡CH	–0.437	–0.453	–0.453	–0.492	–0.498	–0.508	–0.445	–0.446	–0.464
NO2	–0.420	–0.446	–0.430	–0.503	–0.497	–0.490	–0.467	–0.449	–0.445

Strength of the Pt–pyrX Bonds

The differences of q(N_pyrX) between the positional isomers in metallic X-R and X-P complexes were qualitatively similar to the isolated pyrX ligands (Table 1) and are discussed in more detail below. The Pt–pyrX bond was stabilized mainly by electrostatic energy ΔE_elst due to +e and +2 e total charges of metal complex fragments in X-R and X-P (Table 2 and Table S1), respectively. The binding was accompanied by the charge transfer and polarization effects whose extent strongly depended on the charge of the complex. As expected, the amount of transferred negative charge from pyrX toward the metal was much higher in doubly charged X-P products compared to X-R reactants. For X = H, the respective pyrH charges were 0.424 and 0.241 (Table 2). The amounts of ΔE_orb energy are about one-half (52 ± 2%) and two-thirds (69 ± 3%) of the values of ΔE_elst energy in X-R and X-P, respectively (cf. below).

Table 2. Pt–pyrX Interaction (X = H, NH₂, NO₂) in the Gas Phase Optimized X-R, X-TS, and X-P Structures: Pt–N_pyrX Bond Lengths (in Å); Total NPA Charges of the Pt Atom (q(Pt)) and pyrX Ligands (q(pyrX)) (in e); and ETS-NOCV Energy Decomposition Terms ΔE_Pauli, ΔE_elst, ΔE_orb, ΔE_disp, ΔE_orb^σ, and ΔE_orb Obtained at the BLYP-D3BJ/TZ2P//B3LYP/BS1 Level^a.

		Pt–NpyrX	q(Pt)	q(pyrX)	ΔEPauli	ΔEelst	ΔEorb	ΔEdisp	ΔEorbσ	ΔEorbπ	ΔEbind
X-R
H		2.081	0.617	0.241	127.6	–122.5	–61.6	–7.2	–40.7	–11.6	–65.7
NH2	o-	2.086	0.601	0.257	135.6	–129.9	–64.5	–9.0	–41.2	–10.9	–69.9
	m-	2.078	0.616	0.254	129.7	–127.4	–63.4	–7.4	–41.8	–10.3	–70.4
	p-	2.077	0.612	0.268	130.5	–131.0	–64.0	–7.3	–42.5	–12.1	–73.8
NO2	o-	2.111	0.613	0.205	114.4	–103.3	–57.7	–10.2	–34.7	–11.6	–57.5
	m-	2.089	0.618	0.220	120.3	–108.0	–59.5	–7.3	–38.0	–10.4	–55.6
	p-	2.084	0.618	0.221	122.8	–109.6	–60.6	–7.2	–38.6	–12.7	–57.5
X-TS
H		2.046	0.791	0.294	174.2	–147.2	–78.6	–7.6	–53.4	–12.5	–62.7
NH2	o-	2.050	0.770	0.312	192.7	–160.6	–85.9	–9.8	–57.4	–12.5	–67.1
	m-	2.044	0.789	0.304	176.9	–152.4	–80.8	–7.8	–54.8	–10.7	–67.5
	p-	2.043	0.784	0.319	177.0	–155.4	–81.5	–7.7	–55.7	–12.7	–71.1
NO2	o-	2.072	0.799	0.243	159.6	–128.2	–73.2	–10.7	–45.6	–12.5	–54.5
	m-	2.053	0.797	0.269	166.8	–133.1	–75.8	–7.7	–49.8	–10.9	–52.5
	p-	2.050	0.799	0.268	169.6	–134.8	–77.1	–7.6	–50.5	–13.7	–52.4
X-P
H		2.011	0.749	0.424	147.3	–153.1	–101.7	–7.5	–64.2	–19.6	–114.3
NH2	o-	2.016	0.736	0.439	152.7	–159.0	–105.1	–9.5	–63.9	–18.9	–120.4
	m-	2.007	0.745	0.437	151.0	–162.4	–105.8	–7.7	–66.0	–19.3	–123.7
	p-	2.005	0.738	0.450	152.6	–168.4	–107.5	–7.6	–66.8	–22.3	–130.0
NO2	o-	2.038	0.780	0.369	131.8	–128.7	–97.0	–10.1	–55.2	–19.1	–102.7
	m-	2.016	0.757	0.404	139.4	–132.5	–100.1	–7.6	–61.4	–19.6	–99.3
	p-	2.014	0.757	0.404	141.0	–133.1	–100.1	–7.5	–61.5	–21.1	–98.6

^aΔE_bind energy values were calculated at the B3LYP-D3BJ/BS2//B3LYP/BS1 level. All energy values are in kcal/mol. The data for all X’s are shown in Table S1.

Pt–pyrX interaction energies were almost two (1.77 ± 0.03) times higher for X-P than for X-R, and all stabilizing terms contributed to this difference (Table 2 and Table S1). The nature of the X on the pyrX ring influenced strongly the strength of the Pt–pyrX bond being weakened by electron-withdrawing X’s and made stronger by electron-donating ones. The binding energies were usually larger for para-X complexes than for otho-X and meta-X ones (Figure 1). For X-R, the highest value of the binding energy was obtained for p-DMA-R (−76.8 kcal/mol) while the lowest for m-NO₂-R (−55.6 kcal/mol).

Figure 1.

Relative Pt–pyrX (upper panels) and Pt–Cl and Pt–w (lower left and right panels, respectively) gas phase binding energies calculated with respect to the strength of the bonds in the non-substituted H-R and H-P complexes (set as 100%). The values of reference Pt–pyrH binding energies in H-R and H-P complexes are −65.7 and −114.3 kcal/mol, respectively (Table 2). Reference values for Pt–Cl and Pt–w bonds are −248.7 and −46.8 kcal/mol, respectively (Table 3).

Electron-donating X’s promoted higher charge transfer from the pyrX ligand to the Pt atom by up to 10% (Table 2 and Table S1) being caused by stronger σ-donation. Five most important ETS-NOCV deformation density contributions describing the formation of the Pt–N_pyrX bond in H-R, H-TS, and H-P structures are shown in Figure S2. The σ-donation energy ΔE_orb^σ and π-donation energy ΔE_orb contributions were the most stabilizing terms for all structures. The σ-donation energy ΔE_orb^σ contributions correlated well with total ΔE_orb energies for meta-X and para-X subsets (Figure 2B and Figure S3) accounting for 65.2 ± 0.8, 67.1 ± 0.9, and 61.7 ± 0.8% of their values for X-R, X-TS, and X-P structures, respectively.

Figure 2.

X-R structures: panel A: dependence of pyr-X ligand binding energies on the Pt–N_pyrX bond lengths. The o-DMA point was not included in the regression analysis for the ortho-X subset (blue line). Panel B: dependence of the σ-donation energy ΔE_orb^σ contributions on total ΔE_orb energies. One regression line was constructed for both meta-X and para-X subsets in the two graphs (black lines). The graphs for X-TS and X-P structures are shown in Figure S3.

For ortho-X’s, the correlation was worse (Figure 2B and Figure S3), and relative importance of ΔE_orb^σ was slightly lower (by 2–3%) due to the existence of X···Pt and X···ligand nonbonding interactions in some structures (Figure S4). Similar information can be also seen from the dependence of Pt–pyrX binding energy on the transferred q(pyrX) charge. The amount of the total transferred charge from the pyrX ligand to the metal complex correlated very well with the Pt–N_pyrX bond strength for m-X and p-X subsets (Figure S5). For the o-X subset, the correlation was worse with a less steep slope compared to m-X and p-X subsets and R² values 0.807, 0.690, and 0.799 for X-R, X-TS, and X-P structures, respectively (Figure S5). It reflected the existence of additional charge transfer channels (nonbonding interactions of X with Pt or NH₃ ligands) besides the Pt–N_pyrX bond (cf. Figure S4).

The dependence of ΔE_bind^pyrX on the Pt–N_pyrX bond lengths was steeply linear for meta-X and para-X complexes (Figure 2A). The ortho-X complexes had clearly larger Pt–N_pyrX bond lengths for given values of ΔE_bind, and the correlation between the two variables was also linear for all o-X’s including those not involved in any nonbonding interactions (o-CH₃) but with exception of o-DMA as the bulkiest X. o-DMA complexes showed a substantial Pt–N_pyrX bond elongation at a large value of ΔE_bind^pyrX (Figure 2A and Figure S3). Thus, the steric hindrance should be responsible for the Pt–N_pyrX bond elongation.

No clear trends were found for the π-bonding energy ΔE_orb^ππ and ΔE_orb contributions which involve π and σ orbitals of the pyrX ring, respectively, as the main source of the transferred electrons (Figure S2). ΔE_orb^ππ was always the second most stabilizing contribution, and it was enhanced slightly for the CCH and NO₂ X’s with conjugated multiple bonds with respect to the pyr ring. This term was much more important than ΔE_orb which could be mixed with the σ-back-donation or nonbonding interaction contributions in some ortho-X systems (Figure S4). Note that the π-back-donation was not apparent in the NOCV analysis possibly due to the positive charge of the Pt(II) fragment. For example, the π-back-donation transferred charges of 0.005, 0.001, and 0.009 e were calculated by the charge decomposition analysis,⁵³ as provided by the Multiwfn program⁵⁴ for the Pt–N_pyrX bonds in H-R, p-NH₂-R, and p-NO₂-R structures, respectively.

Despite the positive charge of pyrX ligands, the negative NPA charge on the N_pyrX atom (q(N_pyrX)) increased by about 10% (varying from 5.6% for o-NH₂-R up to 19.7% for o-NO₂-R, cf. Table 1) in X-R reactants and almost did not change in X-P products compared to the isolated pyrX ligand. It was caused by the polarization of the aromatic pyrX ligand upon binding with the positively charged metal complex. The transferred charge was drained from the CH and CX groups of the pyrX ligand roughly following the order para > meta > ortho (cf. ETS-NOCV deformation density contributions in Figure S2).

The changes of total electron densities with respect to the H-R structure caused by the H → X substitution are shown in Figure 3 for p-NH₂-R and p-NO₂-R structures. These differences reflected only pure electronic effects caused by the H → X substitution not considering accompanying changes of molecular structures. The shifts of electron density within the pyrX ligand were very similar to those in the isolated pyrX system (cf. Figure S1). With respect to the Pt(II) fragment, the substitution by the electron-donating NH₂ group led to exactly opposite changes of electron density compared to the electron-withdrawing NO₂ group (Figure 3). Thus, let us describe only the changes caused by the H → p-NH₂ substitution here: (1) the strengthening of the Pt–pyrX bond could be clearly documented by an increase of electron density roughly in the middle of this bond. (2) The electron density was increased in the p_x orbital of the trans Cl^– ligand (if the x axis is oriented along the Pt–Cl bond). It reflected the lower σ-donation and the weakening of the Pt–Cl bond (cf. below). (3) The changes of the total charge on the Pt atom (q(Pt)) were small for X-R structures (Table 2 and Table S1) due to compensating effects on the 5d NAO’s: electron density was increased in 5d_xy but decreased in 5d_x²–y² orbital (Figure 3). However, for the water trans ligand as a weaker electrophile, the changes of q(Pt) were larger and q(Pt) was decreased/increased for electron-donating/withdrawing X’s (Table 2 and Table S1).

Figure 3.

Electron density difference isosurfaces of p-NH₂-R (A) and p-NO₂-R (B) structures with respect to the reference H-R structure which show electron accumulation (blue: 0.0004 a.u.) and depletion (red: −0.0004 a.u.) regions caused by p-NH₂ (A) and p-NO₂ (B) substitution of the pyr ring. Electron densities were calculated on the H-R geometry for all atoms of respective complexes except the atoms of the X substituent whose positions were optimized.

We used also the concept of the activation strain model⁵⁵ and performed the fragment energy decomposition of the Pt–pyrX bond for the structures in Figure 3. For p-NH₂-R (p-NO₂-R), the Pauli, electrostatic, orbital, and dispersion energies were 130.5 (125.0), −130.9 (−111.4), −63.7 (−61.3), and −7.2 (−7.3) kcal/mol, respectively. A comparison of these values and also the ones for H-R (Table 2) confirmed the influence of X on the strength of the Pt–pyrX bond mainly through electrostatic energy which is in agreement with the analyses on fully optimized structures (cf. above).

Trans Influence: The Strength of the Pt–Cl and Pt–w Bonds

Trans influence is a thermodynamic phenomenon in which the binding of a more strongly bound ligand weakens the Pt–trans ligand bond which becomes elongated. Thus, the electron-withdrawing X’s strengthened the Pt–trans ligand bond, and the opposite was true for electron-donating ones (Table 3 and Table S2). The influence of the X on the strengths of Pt–Cl and Pt–w bonds was roughly 8 and 14% of their relative value, respectively. These values were obtained from a comparison of binding energies of the strongest respective bond with the weakest one (Figure 1). Such low values reflected a rapid weakening of the electronic effects with increasing distance from the bound X because the relative change of the Pt–pyrX bond strength was more than 32%. This trend is visible in Figure 3 as the decrease of the isosurface volume with the increasing distance from the X group. However, the increase of electron density in the 3p_x natural bond orbital (NBO) of the trans Cl^– ligand in the p-NH₂-R structure can be still clearly seen as the result of smaller electron donation from Cl^– toward the central Pt(II) atom forming a weaker Pt–Cl bond. Exactly the opposite was true for p-NO₂-R. Note that due to much larger absolute strength of the Pt–Cl bond, the changes of the absolute values of its binding energies (Table 3 and Table S2) are comparable with the binding energy changes of the Pt–pyrX bond (Table 2 and Table S1).

Table 3. Interactions of Cl^– and Water Ligands with the Rest of the Complex in the Gas Phase Optimized X-R and X-P Structures (X = H, NH₂, NO₂), Respectively: Pt–Cl, Pt–O_w Bond Lengths (in Å); the Total NPA Charges of the Cl^– and Water Ligands (q(Cl), q(w)); and ETS-NOCV Energy Decomposition Terms ΔE_Pauli, ΔE_elst, ΔE_orb, ΔE_disp, ΔE_orb^σ, and ΔE_orb Obtained at the BLYP-D3BJ/TZ2P//B3LYP/BS1 Level^a,^b.

X-R		Pt–Cl	q(Cl)	ΔEPauli	ΔEelst	ΔEorb	ΔEdisp	ΔEorbσ	ΔEorbπ	ΔEbind
H		2.315	–0.477	130.5	–283.4	–95.3	–3.0	–67.5	–9.8	–248.7
NH2	o-	2.316	–0.482	130.4	–282.6	–94.4	–3.1	–67.0	–9.4	–247.4
	m-	2.317	–0.486	131.8	–278.3	–95.8	–3.0	–68.5	–9.7	–243.6
	p-	2.320	–0.492	128.4	–275.0	–92.5	–3.0	–65.2	–10.1	–240.0
NO2	o-	2.301	–0.444	135.0	–289.8	–100.4	–2.8	–70.9	–10.4	–255.5
	m-	2.308	–0.460	135.2	–288.7	–100.7	–2.9	–72.4	–9.9	–256.0
	p-	2.309	–0.462	131.9	–289.8	–98.0	–3.0	–69.0	–10.7	–255.5

X-P		Pt–Ow	q(w)	ΔEPauli	ΔEelst	ΔEorb	ΔEdisp	ΔEorbσ	ΔEorbπ	ΔEbind
H		2.137	0.177	60.9	–64.4	–37.9	–3.0	–27.9	–5.9	–46.8
NH2	o-	2.141	0.174	60.1	–63.2	–37.0	–3.0	–27.3	–5.7	–45.6
	m-	2.141	0.172	60.7	–63.4	–36.9	–3.0	–27.2	–5.7	–45.2
	p-	2.147	0.170	59.3	–62.3	–36.1	–2.9	–26.6	–5.5	–44.4
NO2	o-	2.116	0.191	64.1	–67.6	–40.7	–3.1	–29.7	–6.5	–49.7
	m-	2.131	0.183	63.5	–66.2	–39.8	–3.0	–29.2	–6.2	–48.6
	p-	2.130	0.182	61.5	–65.6	–39.1	–3.0	–28.8	–6.2	–48.6

^aAll energy values are in kcal/mol. The data for all X’s are shown in Table S2.

^bΔE_bind energies were calculated at the B3LYP-D3BJ/BS2//B3LYP/BS1 level.

Prediction of the Pt–Ligand Bond Strengths

In previous studies, the strength of the Pt–ligand bonds was proportional to the properties such as the Pt–ligand bond lengths^6,56 (cf. Figure 2A and Figure S3), the linear combinations of electron densities at bond critical bonds,^56,57 or the populations in 5d orbitals of the Pt(II) atom.^5,6 These properties were calculated for the optimized structures of whole metal complexes.

However, our aim was to propose a predictor for the Pt–pyrX bond strength, which would be based just on the property of the isolated pyrX ligand as the putative reactant. First, we started with predictors typical for electrostatic energy such as the q(N_pyrX) atomic NPA charge, the total dipole moment of pyrX, and the projection of the dipole moment into the C4–N_pyrX bond direction. These predictors worked well for para-X subset but completely failed for meta-X and ortho-X ones (Figure S6).

The minimum surface electrostatic potential calculated on the surface of the N atom of the amino groups enabled accurate estimation of their basicities and pK_b values.⁵⁸ Here, these calculations were performed on the surface of the N_pyrX atom, and a very good prediction of the Pt–pyrX bond strength was obtained for meta and para subsets but not for some ortho-X’s (o-DMA, o-NO₂, o-NH₂, o-OH, and o-F) (Figure S7) probably due to a strong interference of o-X and N_pyrX local electrostatic fields.

The electron shifts caused by the H → X substitution in the isolated pyrX ring (see above and Figure S1) were accompanied by changes of the energies of NAO’s on the N_pyrX atom. The energy of the 2p_x(N_pyrX) NAO considering N_pyrX and C4 atoms of the pyrX ring were oriented along the x axis (Figure 4I) reflected the origin of electrons which were involved in σ-donation as the decisive contributor to the formation of the Pt–pyrX dative bond (Figure 2B and Figure S3). Thus, the 2p_x(N_pyrX) NAO energy quantified σ-electron basicity of the pyrX ligand, and it was increased for electron-donating X substituents while the opposite was true for electron-withdrawing X’s.

Figure 4.

Dependence of the Pt–pyr(X) (panels A, B), Pt–Cl (panel C), and Pt–w (panel D) gas phase binding energies in X-R and X-P complexes (A, C and B, D panels, respectively) on the 2p_x(N_pyrX) NAO energies calculated on the isolated pyrX ligands. Panels E, F, G, and H represent analogous results calculated in the water solvent. Points for the poly-X complexes were not included in the regression analyses (cf. below). Relative orientation of the 2p_x(N_pyrX) orbital with respect to the isolated pyrX ligand (panel I). 2p_x(N_pyrX) represents 2p(N_pyrX) NAO orbital oriented along the C4–N_pyrX axis which is the direction of the pyrX nucleophilic attack to form the Pt–N_pyrX bond.

Differences in ΔE_orb contributions to ΔE_bind^pyrX were in the order of units of kcal/mol when systems with different X’s were compared while differences in ΔE_elst could be by up to one order of magnitude higher (see Table 2 and Table S1). However, 2p_x(N_pyrX) NAO energy is still a good predictor of the Pt–pyrX bond strength because prevailing ΔE_elst is linearly correlated with ΔE_orb (see below and Figure S8), as it was already shown in our previous studies on similar systems.^6,59 Polarization and charge transfer effects as parts of ΔE_orb are strongly influenced by ΔE_elst.

The steric effect was quantified from the relation between complex stability and ligand basicity.⁶⁰ The graphs on panels A, B, E, F in Figure 4 have a similar meaning because 2p_x(N_pyrX) NAO energies and Pt–N_pyrX binding energies can be expected to be related to ligand basicities and complex stabilities, respectively. Ortho-X substituents had mostly a stabilizing effect showing higher Pt–N_pyrX bond strengths at a given value of 2p_x(N_pyrX) NAO energy compared to meta-X and para-X counterparts (see Figure 4A,B).

Because Pt–pyrX and Pt–trans ligand binding energies are dependent quantities due to the trans influence (see above), the 2p_x(N_pyrX) NAO energies calculated on the isolated pyrX ligand could be used also for the Pt–trans ligand bond strength prediction. This predictor worked very well for the Pt–Cl bond strengths in X-R structures especially for para-X and meta-X subsets (cumulative R² = 0.897) but gave less satisfactory results for ortho-X (R² = 0.604) (Figure 4C). On the other hand, the Pt–w bond strengths in X-P structures could be well-predicted by this parameter regardless of the X position (cumulative R² = 0.864) (Figure 4D) probably due to much higher relative importance of the ΔE_orb contribution.

Note that the energy of the lone pair on the N_pyrX atom (LP(N_pyrX) NBO) gave slightly worse correlation with Pt–ligand binding energies than 2p_x(N_pyrX) NAO energy (Figure S9) although both these parameters quantified a dative ability of the pyrX ligand. The reason may lie in the fact that LP(N_pyrX) NBO is an sp² hybrid NBO (Figure S9I) with a variable contribution of 2s(N_pyrX) NAO which depended on the nature and the position of X and ranged from 27.9% (o-Cl) to 29.9% (p-DMA).

Trans Effect: The Binding Properties of the Transition State X-TS Structures and Kinetics of the Substitution Reactions

Pt–pyrX bonds in the X-TS structures were shortened by about 0.02–0.03 Å as observed for cisplatin in our previous study,⁴¹ but contrary to our expectation, they were also weakened by about 4 ± 3% compared to X-R structures. It was caused by a large increase of ΔE_Pauli as the leaving Cl^– and entering water ligands lied in the plane of the pyrX ligand in most X-TS structures. This increase of ΔE_Pauli was not compensated by a rise of ΔE_elst and ΔE_orb terms (Table 2 and Table S1).

The influence of X on binding energies of ligands in X-TS is similar to X-P and X-R structures: Pt–N_pyrX bonds are stronger for electron-donating X’s, while Pt–Cl and Pt–w interactions are more stabilized for electron-withdrawing X’s (cf. above, Tables 4and 5and Tables S3 and S4).

Table 4. Pt–Cl and Pt–O_w Bonds in the Gas Phase Optimized X-TS Structures (X = H, NH₂, NO₂): Pt–Cl, Pt–O_w Bond Lengths (in Å); the Total NPA Charges of the Cl and Water Ligands (q(Cl), q(w); in e)^a.

		Pt–Cl	Pt–Ow	q(Cl)	q(w)
H		2.770	2.327	–0.765	0.058
NH2	o-	2.710	2.384	–0.761	0.064
	m-	2.768	2.344	–0.765	0.054
	p-	2.776	2.344	–0.768	0.051
NO2	o-	2.752	2.302	–0.735	0.073
	m-	2.760	2.307	–0.758	0.068
	p-	2.759	2.309	–0.763	0.067

^aThe data for all X’s are shown in Table S3.

Table 5. Gas Phase Optimized X-TS Structures (X = H, NH₂, NO₂): ETS-NOCV Energy Decomposition Terms ΔE_Pauli, ΔE_elst, ΔE_orb, ΔE_disp, and ΔE_orb^σ for the Interaction of the Joint (Cl + w) Fragment (Leaving and Entering Ligands) with the Rest of the Complex Were Obtained at the BLYP-D3BJ/TZ2P//B3LYP/BS1 Level^a,^b.

		ΔEPauli	ΔEelst	ΔEorb	ΔEdisp	ΔEorbσ	ΔEbind	ΔG⧧
H		88.0	–236.2	–69.8	–6.0	–37.7	–222.9	33.2
NH2	o-	93.6	–243.6	–69.6	–6.8	–36.7	–225.3	29.9
	m-	87.3	–231.2	–68.5	–6.0	–37.5	–217.9	32.7
	p-	85.8	–227.4	–67.3	–6.0	–36.1	–214.2	32.6
NO2	o-	91.4	–242.2	–74.0	–6.1	–39.8	–230.0	33.3
	m-	92.2	–241.8	–74.6	–6.1	–41.5	–230.4	34.4
	p-	90.8	–243.2	–73.2	–6.1	–39.4	–230.8	34.3

^aAll energy values are in kcal/mol. The data for all X’s are shown in Table S4.

^bΔE_bind energies of the (Cl + w) fragment and activation Gibbs energies ΔG^⧧ were calculated at the B3LYP-D3BJ/BS2//B3LYP/BS1 level.

The substitution reaction proceeded by the associative interchange mechanism⁶ which assumed a comparable importance of the leaving ligand (Cl^–) destabilization in the reactant X-R structures and the X-TS transition state stabilization for the height of the activation barrier (ΔG^⧧). Thus, ΔG^⧧ values resulted from a complex event of the X-TS formation which should not be predictable by a single variable. However, TS stabilization was important only for o-X-TS structures (see below), and thus, we obtained a reasonable correlation between the 2p_x(N_pyrX) NAO energy calculated on the isolated pyrX ligand (see above) and ΔG^⧧ values for m-X and p-X reaction pathways (Figure 5). Only the points which corresponded to the stabilized o-NH₂-TS, o-OH-TS, and o-SH-TS structures (see below) were considerably outside the linear correlation.

Figure 5.

Dependence of the gas phase activation Gibbs free energies (ΔG^⧧) on the energies of 2p_x(N_pyrX) NAO’s calculated on the isolated pyrX ligand (see Figure 4I). One regression line was constructed for m-X and p-X reaction paths while excluding all o-X and poly-X (see below) points.

Nucleophilicity of organic compounds was estimated by the Hirshfeld charges.⁶¹ However, here the Hirshfeld charge on the Pt(II) center offered a slightly worse correlation with the ΔG^⧧ energies for meta and para subsets (R² = 0.596) than 2p_x(N_pyrX) NAO energies (Figure S11).

In accordance with the influence of X on the stability of the Pt–Cl bond (see above), the electron-donating X’s tend to lower the activation ΔG^⧧ energy while the opposite was true for electron-withdrawing X’s (Figure 6). It was caused by much higher relative importance of the Pt–Cl bond destabilization compared to Pt–water ligand stabilization in X-TS structures.

Figure 6.

Dependence of the relative values of the activation Gibbs free energy barriers (Δ(ΔG^⧧)) of the hydration reactions of the trans-[Pt(NH₃)₂(pyrX) Cl]⁺ complexes on the nature and the position of the X in the gas phase and in the water solvent. Δ(ΔG^⧧) was calculated with respect to the reference values (33.2 and 25.7 kcal/mol in the gas and water solvent, respectively) determined for the X = H pathway. Absolute values of ΔG^⧧ are shown in Table 5, Table S4 and Table 7, and Table S6 for the gas phase and the water solvent, respectively.

In the ortho position, the electronic effects were probably stronger than in para and meta positions (cf. NPA charges in Table 1) but were hardly distinguishable from the structural (de)stabilizations (see below), giving together the widest range of ΔG^⧧ values of 3.8 kcal/mol between the analyzed reaction profiles (Figure 6). For para-X’s, the structural effects were negligible, and the ΔG^⧧ range of 1.8 kcal/mol could be attributed purely to electronic effects.

The meta-X substitution always decreased the electron density on the N_pyrX atom (Table 1), which led to the formation of electron-deficient Pt(II) complexes compared to ortho and para analogues. It may be responsible for the highest ΔG^⧧ values and the least reactivity of meta substituted systems. Thus, the dependence of ΔG^⧧ on the position of X in the order ortho–meta–para has usually the shape of inverted “V”. The exceptions are DMA and CH₃ substituents, but they show very small ΔG^⧧ differences of just tenths of kcal/mol between the three isomers’ reaction pathways (Figure 6).

Considering both the nature and the position of X on the pyrX ligand, we obtained the total difference of 4.6 kcal/mol in the height of the reaction free energy barrier between the slowest reaction for m-CCH and the fastest one for o-NH₂. It corresponds to ca. 2200-fold difference in the reaction rate at 298 K.

TS Structure (de)stabilizations

X-TS structures preserved all X···HNH₂ and X···Pt nonbonding interactions (Figure 7) which were established already in X-R structures, and thus, these interactions did not contribute importantly to the decrease of ΔG^⧧ (cf. below the case of o-DMA pathway). However, for most X-TS structures, the entering water and leaving Cl^– ligands are roughly coplanar with the pyrX ligand which means that the nucleophilic attack of the water ligand occurred in the plane of the pyrX ligand. Depending on the nature of X, it may dictate the direction of the water attack and stabilize/destabilize the TS structures through the electrostatic field of X. The most striking examples are o-NH₂, o-OH, and o-SH pathways, which showed the lowest activation energies (Figure 6) having the leaving Cl^– ligand stabilized by internal HNH···Cl, OH···Cl, and SH···Cl contacts with distances 2.745 Å, 2.673 Å, and 2.560 Å in o-NH₂-TS, o-OH-TS, and o-SH-TS structures, respectively (Figure 7). NOCV analysis revealed neither any contribution of these contacts to the orbital energy nor any corresponding bond critical points were found by QTAIM analysis. Thus, these contacts had fully electrostatic nature (cf. ΔE_elst values in Table 5 and Table S4) but still led to the substantial lowering of the reaction free energy barrier of corresponding substitution reactions compared to meta- and para-analogues (Figure 6). The conformation of the entering water ligand in the TS structure then clearly referred to the favored direction of the nucleophilic attack on the Pt(II) center being from the opposite semispace with respect to o-NH₂, o-OH, and o-SH substituents (Figure 7).

Figure 7.

Energetically the most feasible structures of o-NH₂-TS, o-OH-TS, o-NO₂-TS, and o-DMA-TS in the gas phase (upper structures) and in the water solvent (lower structures) with depicted distances of the X···HNH₂, X···Pt nonbonding, and X···Cl (X···w) electrostatic interactions. The Gibbs energy conformational preferences (Δ(ΔG_conf^⧧)) of the water nucleophilic attack from the semispace defined by the plane of the Pt complex and the position of the o-X group relative to the opposite direction are also shown (in kcal/mol). Pt–N_pyrX, Pt–Cl, and Pt–O_w bond lengths are shown in Table 2, Table S1 and Table 4, and Table S3, respectively, for the gas phase optimized structures and in Table 7and Table S6 for the water solvent ones.

On the other hand, o-NO₂, o-F, o-Cl, and o-Br groups made a nucleophilic attack more difficult because their contact with the entering water ligand was destabilizing due to unsuitable orientation of the water ligand in o-NO₂-TS (see Figure 7), o-F-TS, o-Cl-TS, and o-Br-TS structures, respectively; nevertheless, it was more advantageous than the contact with the leaving Cl^– ligand (by 2.7, 1.9, 0.9, and 1.1 kcal/mol for o-NO₂, o-F, o-Cl, and o-Br reaction pathways, respectively). It is probably the main reason of their highest activation energies compared to other ortho-X’s (Figure 6).

The steric hindrance manifested itself by the elongation of the Pt–N_pyrX bond (see above). It also changed the conformation of the o-DMA-R, o-DMA-TS, and o-DMA-P structures which had deformed geometries with the twist angles of 56.3, 54.4 (Figure 7), and 58.9°, respectively, between the pyrX plane and the plane of the complex defined by Pt and two N_NH3 and N_pyrX atoms. This deformation enabled unfavorable interactions to be avoided between the o-DMA substituent and the NH₃ ligands. However, similar deformation was found also for structures along o-F, o-Cl, and o-Br pathways, but here it enabled the formation of the attractive halogen X···HNH₂ H-bond. For the other structures, the twist angle between the two planes is close to 90° (Figure 7) but its influence on ΔG^⧧ is unclear.

The steric hindrance should lead to an increase of ΔG^⧧. o-DMA, o-CH₃, o-Br, o-Cl, and o-F pathways have elevated ΔG^⧧ values which are within 0.1 kcal/mol compared to their meta counterparts. However, the differences in ΔG^⧧ are too small to find a clear reason. For example, as the above described deformation is similar for all structures along the o-DMA pathway, it has little effect on ΔG^⧧ as it can be manifested by the values of 7.2, 7.2, and 8.8 kcal/mol which represent the free energy destabilizations of o-DMA-R, o-DMA-TS, and o-DMA-P structures, respectively, with respect to their p-DMA isomeric counterparts. Note that ΔG^⧧ is even by 0.1 kcal/mol lower for the o-DMA pathway than for the p-DMA one (Figure 6 and Table S4).

Solvent Effects

Water environment dampened the electrostatic forces which were the most contributive to the stabilization of the Pt–ligand bonds of our charged complexes in the gas phase (see above). Thus, binding energies of all Pt–ligand bonds were lowered in the water environment (Tables 6and 7and Tables S5 and S6). Similarly as in the gas phase, the Pt–ligand binding energies could be estimated from 2p_x(N_pyrX) NAO energies calculated for the isolated pyrX ligand immersed in the polarizable continuum model (PCM) water solvent (Figure 4E–H). The linear correlations are even slightly better here than in the gas phase probably due to a smaller relative importance of electrostatic interactions. Note also that the changes of electron density induced by X’s are qualitatively the same as in the gas phase (cf. Figure 3 and Figure S10). Thus, the findings described above for the gas phase should be qualitatively valid also for the water phase.

Table 6. Bonding Interactions in X-R and X-P Structures (X = H, NH₂, NO₂) Optimized in the Water Solvent and Calculated by the B3LYP-D3BJ-PCM/BS2//B3LYP-PCM/BS1 Method: Pt–N_pyrX, Pt–Cl, and Pt–O_w Bond Lengths (in Å); the Total NPA Charges of the pyrX, Cl, and Water Ligands (q(pyrX), q(Cl) and q(w), Respectively) (in e); ΔE_bind Energy Values are in kcal/mol^a.

X-R		Pt–NpyrX	q(pyrX)	ΔEbindpyrX	Pt–Cl	q(Cl)	ΔEbindCl
H		2.052	0.284	–43.9	2.370	–0.597	–38.7
NH2	o-	2.064	0.292	–46.2	2.363	–0.594	–38.2
	m-	2.051	0.289	–45.3	2.363	–0.599	–38.5
	p-	2.047	0.312	–47.7	2.378	–0.610	–37.0
NO2	o-	2.084	0.231	–35.4	2.341	–0.560	–42.3
	m-	2.067	0.251	–38.8	2.353	–0.576	–41.2
	p-	2.056	0.247	–39.7	2.360	–0.580	–40.8

X-P		Pt–NpyrX	q(pyrX)	ΔEbindpyrX	Pt–Ow	q(w)	ΔEbindw
H		2.011	0.356	–54.3	2.118	0.195	–20.5
NH2	o-	2.021	0.371	–56.7	2.123	0.195	–19.7
	m-	2.008	0.364	–55.9	2.120	0.194	–19.9
	p-	2.010	0.383	–58.9	2.123	0.189	–19.7
NO2	o-	2.034	0.306	–44.2	2.098	0.211	–21.7
	m-	2.014	0.327	–48.5	2.114	0.202	–21.0
	p-	2.011	0.322	–49.1	2.108	0.203	–21.4

^aThe data for all X’s are shown in Table S5.

Table 7. Activation Free Energies (ΔG^⧧) and Bonding Interactions in X-TS Structures (X = H, NH₂, NO₂) Optimized in the Water Solvent and Calculated by the B3LYP-D3BJ-PCM/BS2//B3LYP-PCM/BS1 Method: Pt–N_pyrX,Pt–Cl, and Pt–O_w Bond Lengths (in Å); Total NPA Charges of the pyrX, Cl and Water Ligands (q(pyrX), q(Cl) and q(w), Respectively) (in e); and ΔE_bind and ΔG^⧧ Energy Values in kcal/mol^a.

X-TS		Pt–NpyrX	q(pyrX)	ΔEbindpyrX	Pt–Cl	q(Cl)	Pt–Ow	q(w)	ΔEbind(w+Cl)	ΔG⧧
H		2.034	0.318	–42.9	2.837	–0.837	2.476	0.050	–18.6	25.9
NH2	o-	2.042	0.333	–45.0	2.806	–0.832	2.482	0.053	–18.5	24.3
	m-	2.032	0.327	–44.3	2.843	–0.841	2.469	0.050	–18.1	26.0
	p-	2.029	0.350	–47.0	2.846	–0.841	2.495	0.044	–17.3	25.4
NO2	o-	2.074	0.252	–33.0	2.783	–0.821	2.431	0.067	–21.9	26.5
	m-	2.042	0.281	–37.2	2.822	–0.830	2.447	0.059	–20.2	27.3
	p-	2.035	0.272	–38.1	2.816	–0.828	2.448	0.059	–19.6	27.2

^aThe data for all X’s are shown in Table S6.

The weakening of the Pt–ligand bonds did not automatically lead to their elongation because bond length changes were inversely related to the changes of the ligand → Pt transferred charge. The trend of the change (increase/decrease) of the charge transfer and polarization effects depended on the nature of the interaction and nature of the complex.

As expected, Pt–Cl was the most affected bond in the X-R structures being ca. six times weaker in the solvent than in the gas phase because the arising Cl^– anion was stabilized by hydration. The charge donation from the Cl^– ligand was by 22 ± 0.8% lower in the water solvent which resulted in 0.047 ± 0.006 Å Pt–Cl bond elongation. The ligand environment was crucial for the behavior of the pyrX ligand: the charge transfer from pyrX is higher/lower by 14.1 ± 1.7%/17.3 ± 1.3% in the solvent, and Pt–N_pyrX bond lengths were shortened/slightly elongated by 0.026 ± 0.003 Å/0.002 ± 0.002 Å in R-X/P-X structures. The Pt–N_pyrX bond was always weakened: by 54 ± 1.5% in P-X structures and by 34.4 ± 2.0% in R-X ones. The Pt–w bonds in the water solvent-optimized X-P structures were shortened by 0.019 ± 0.004 Å compared to the gas phase. The transferred charge from the water ligand increased by 11.7 ± 0.8%, and the Pt–O_w bond was weakened by 56 ± 0.7%. As the result, the NPA charge of the Pt center was by 10.2 ± 0.8 and 7.9 ± 0.8% more positive in the solvent than in the gas phase in R-X and P-X structures, respectively.

The activation Gibbs energies (ΔG^⧧) were substantially reduced: by 6.9 ± 0.5 kcal/mol compared to the gas phase (Table 7 and Table S6). 2p_x(N_pyrX) NAO energies worked substantially worse as the predictor of ΔG^⧧ values giving the R² value of 0.483 for meta and para subsets (cf. Figure 5). It could be caused by higher complexity of the reaction in the water solvent and/or by a lower precision of our calculations.

Despite a general weakening of the Pt–ligand coordination bonds, the relative values of the activation barriers for different X’s were similar to the gas phase when driven by the electronic effects. Thus, the meta and para subsets gave almost the same maximum Δ(ΔG^⧧) differences of 1.5 and 1.8 kcal/mol (cf. with respective values of 1.8 and 1.8 kcal/mol for the gas phase, see Figure 6). However, the water environment caused substantial weakening of the electrostatic forces which lowered spatial preferences of the nucleophilic attack in the TS structures and the importance of the long-range X···Cl and X···w interactions therein (cf. Δ(ΔG_conf^⧧) differences in Figure 7). The weakening of HNH···Cl and HO···Cl stabilization interactions in o-NH₂-TS and o-OH-TS, respectively (cf. above), resulted in the decrease of Δ(ΔG^⧧) variance for the ortho subset to the value of 2.4 kcal/mol. Taken the results for all three subsets together, Δ(ΔG^⧧) between the fastest (o-NH₂) and the slowest (m-NO₂) reaction was 3.0 kcal/mol in the water solvent which corresponded to ca. 150 times change in the reaction rate at 298 K. It is by about one order of magnitude smaller value than for the gas phase.

Complexes with the Poly-X Ligand

The 2p_x(N_pyrX) NAO energies and the Pt–ligand bond strengths for poly-substituted complexes were compatible with the results for the mono-substituted ligand complexes (cf. above). The mean deviations of 2.5 ± 1.3, 4.0 ± 2.8, 1.3 ± 0.9, and 0.7 ± 0.3 kcal/mol from the linear functions derived for the mono-substituted complexes (Figure 4) were calculated for Pt–pyrX (in X-R), Pt–pyrX (in X-P), Pt–Cl, and Pt–w binding energies, respectively, in the gas phase. In the water solvent, the respective values were 1.4 ± 1.2, 1.9 ± 1.2, 0.4 ± 0.3, and 0.2 ± 0.2 kcal/mol. The highest deviation values of 6.3 and 11.2 kcal/mol were detected for Pt–pyrX bonds of the gas phase 2op-NH₂-R and 2op-NH₂-P structures, respectively (Figure 4). This underestimation of the binding energies was caused by the presence of two strong H₂NH···NH₂ H-bonds (Figure S12) whose energies were not compensated by the elongation of the Pt–N_pyrX bond (by about 0.01 Å) (cf. above and values in the Tables S9 and S10).

The gas phase ΔG^⧧ free energy values could be also estimated from the 2p_x(N_pyrX) NAO energies of the poly-substituted ligand complexes except for the om-NH₂, op-NH₂, and 2op-NH₂ pathways which involved o-NH₂···Cl electrostatic stabilization of the TS structures (cf. above). For the other poly-X pathways, the mean deviation of the ΔG^⧧ values from the linear function in Figure 5 was 0.5 ± 0.3 kcal/mol.

The additivity of the substituent effects on the pyr ring was already shown for proton affinities and gas phase basicities of the substituted pyridines⁶² while electron shifts within the pyrX ring were non-additive.⁶³ In this contribution, the values (X_poly) of NPA charges, binding energies, and bond lengths of the poly-substituted complexes could be estimated by a simple additive approach based on eq 1

1

where the summation goes over all positions (i = ortho, meta, para); X_H is the value for the non-substituted complex (X = H); Δx_i is the measured changes of the monosubstituted complexes with respect to the non-substituted complex (X = H); and n_i is the number of substituents in the position i. The plots of calculated versus estimated values for the ligand binding energies are shown in Figure 8. Numerical values are shown in Tables S7–S12. In the gas phase, the absolute differences between calculated and estimated values were within the experimental error for the binding energies (≤2.5 kcal/mol), NPA charges (≤0.01 e), and bond lengths (≤0.01 Å). For poly-F and poly-NO₂ complexes, the relative errors were below 20% (Tables S7, S8, S11, and S12). For the most sterically hindered complexes with the 2op-NH₂ ligand, this error reached almost 50% for q(Cl) and q(w) NPA charges (Tables S9 and S10). However, for the poly-NH₂ complexes, the additive approach failed to predict the subtle changes of Pt–ligand bond lengths. Note that the relative error of 30% was measured for the additivity of substituent effects on much simpler (de)protonation processes of substituted pyridines in the gas phase.⁶²

Figure 8.

Plots of estimated vs calculated (eq 1) values of Pt–ligand binding energies for complexes with poly-substituted ligands in the gas phase (panels A–D) and the water solvent (panels E–H). Panels A, C, E, and G and B, D, F, and H correspond to poly-X-R and poly-X-P structures, respectively. The solid line represents equality of the two values.

In the water solvent, the additive approach worked less satisfactory especially for the weakest Pt–w interaction (Figure 8H and Tables S8, S10, and S12). Partly, it might be caused by a lower precision of PCM calculations.

For ΔG^⧧ activation energies, the additive approach did not offer useable results due to high relative errors (Tables S7, S9, and S11). The largest errors were for poly-NH₂ pathways (Figure S13). While any single NH₂ substitution of the non-substituted pyrH system led to the decrease of ΔG^⧧ activation free energy (except m-NH₂ in the water solvent), any additional NH₂ substitution of o-NH₂ led to the ΔG^⧧ value increase (Table S9). The electron-withdrawing poly-F and poly-NO₂ systems worked more predictably and offered an increase of the ΔG^⧧ values (with exception of the op-F system and in the water solvent of the om-F one, too) compared to mono-substituted systems. The 2m-NO₂ and op-NO₂ pathways showed the highest ΔG^⧧ values of 35.1 and 27.7 kcal/mol (Table S11), which are by 0.6 and 0.5 kcal/mol larger than the ones for the slowest hydration reactions of complexes with mono-functional pyrX ligands (Tables S4 and S6) in the gas phase and the water solvent, respectively. Thus, the ΔG^⧧ value ranges (cf. above) increased up to 5.2 and 3.4 kcal/mol for the gas phase and the water solvent, respectively, which corresponded to ca. 6400 and 320 times differences in the reaction rate at 298 K.

Reliability of Our Results

To obtain accurate absolute values of observables, one has to choose the appropriate combination of the density functional theory (DFT) functional, the solvation method, and the basis set.⁶⁴⁻⁶⁶ In this contribution, we rely on the relative values which should be much less sensitive in this respect.

To check the influence of the B3LYP functional on the height of the activation barriers and Pt–ligand bond lengths, the X-R_w and X-TS structures were also optimized and energy of optimized structures was evaluated by M06-2X, PBE0 functionals⁶⁷ using BS1 and BS2 basis sets, respectively, in the gas phase (M062X/BS2//M062X/BS1, and PBE0-D3BJ/BS2//PBE0/BS1 calculations). In the solvent, these calculations were performed only with the M06-2X functional.

All M062X and PBE0 gas phase optimized Pt–ligand bond lengths correlated very well linearly with the B3LYP counterparts (R² > 0.94) and were systematically shorter with the exception of Pt–O distances in M06-2X optimized X-TS structures (Figures S14 and S15). Reasonable correlation was found also for activation Gibbs free energies which were systematically lower by 2.8 ± 0.5 kcal/mol and higher by 0.9 ± 0.4 kcal/mol for the M06-2X and PBE0-D3BJ functionals, respectively. Thus, for the gas phase, the relative changes of the variables studied in this paper should be not sensitive on the chosen functional.

For the M06-2X/PCM optimizations, the correlation was generally worse and not very satisfactory for Pt–Cl distances in X-TS structures (R² = 0.430) (Figure S16). No correlation was found for solvent phase activation energies. In agreement with the B3LYP results, the fastest reaction was detected for the o-NH₂ substitution (Figure S17), but for the other X’s, the Δ(ΔG^⧧) differences are probably too small compared to the precision of our calculations. Thus, except of the ΔG^⧧ values and the properties of the Pt–Cl bond in X-TS structures, the other relative changes of variables studied in this contribution and calculated in the water solvent should be described in our opinion satisfactorily and should be little dependent on the chosen functional.

Comparison with Experimental Data

We have not found experimental data about any of the complexes studied in this contribution. 2-Picoline and 3-picoline complexes are related compounds to o-CH₃-R and m-CH₃-R, respectively, but one of the ammine NH₃ groups is replaced by the chlorine Cl^– ligand. We obtained slightly longer Pt–N_pyrX (by 0.070 and 0.071 Å) and Pt–Cl bond lengths (by 0.019 and 0.007 Å) compared to the crystal structures of the 2- and 3-picoline complexes²⁹ (cf. Tables S1 and S2). In the crystal structure, the 3-picoline ligand is tilted by 48.9° while 2-picoline ligand is almost perpendicular (102.7°).^29,68 In o-CH₃-R and m-CH₃-R, both o-CH₃ and m-CH₃ ligands were perpendicular to the plane of the complex (90.0 and 87.7°). The difference for the 3-picoline complex has to be attributed to the Cl^– ligand in the cis position because the gas phase mPW1PW1 DFT-optimized geometries of 2-picoline and 3-picoline complexes were in very good agreement with the crystal structures.⁶⁹

According to our calculations, the rates of hydrolysis were the same for two related complexes: the experimental trans-[Pt(NH₃)(H₂O)(3-picoline)Cl]⁺ complex²⁹ and m-CH₃-R which differed only by the nature of the group in the cis position (H₂O vs NH₃). However, in the water solvent, we did not observe any steric hindrance of the o-CH₃ ligand (unlike the gas phase) and the kinetic constant for the o-CH₃ pathway was by two orders of magnitude higher compared to the trans-[Pt(NH₃)(H₂O)(2-picoline)Cl]⁺ experimental analogue.²⁹

The meta-X substitution of the pyrX ligand led to the slowest reaction for most X’s in both the gas phase and the water solvent, which is in agreement with experimental evidence.^68,70

Conclusions

Substitution of the pyridine ligand by electron-donating groups in the trans-[Pt(NH₃)₂(pyrX)Cl]⁺ complexes led to the strengthening of the Pt–N_pyrX bond and the weakening of the bonds in the trans direction (Pt–Cl and Pt–O_w in X-R and X-P structures, respectively). The electron-withdrawing groups had exactly the opposite effect. In both the gas phase and the water solvent, the strengths of Pt–N_pyrX, Pt–Cl, and Pt–O_w bonds in the X-R and X-P complexes were dependent on σ-electron basicity of the N_pyrX atom which correlated linearly best with the energy of the 2p(N_pyrX) NAO oriented in the C4–N_pyrX direction and calculated on the isolated pyrX ligand. These correlations were successfully validated on the complexes with the poly-substituted ligand.

The electron-donating/withdrawing groups tend to decrease/increase ΔG^⧧ free activation energies. In the gas phase, the 2p(N_pyrX) NAO energy can be used also as a predictor for the estimation of ΔG^⧧ of the meta-X and para-X reaction pathways with dominating influence of electronic effects.

Because of the perpendicular orientation of the pyrX ligand with respect to the metal complex plane, the substitution reactions occurred in the pyrX plane. The attractive X···Cl electrostatic interaction was established for o-X’s with the H-bond donor ability (o-NH₂, o-OH, o-SH) which led to the o-X-TS structure stabilization and a substantial decrease of the ΔG^⧧ values. The fastest reaction rate was observed for the o-NH₂ pathway. On the other hand, steric hindrance in o-X-TS structures led only to a moderate increase of ΔG^⧧ probably due to a small size of X’s considered in this study. Anyway, taken together the activation free ΔG^⧧ energy of the hydration reactions can be most easily modified by the substitution of the pyridine ring in the ortho position giving the ΔG^⧧ values range of 3.8 kcal/mol between the fastest o-NH₂ and slowest o-Br pathways (Table S4). Substitutions in the meta position led usually to the highest activation energies.

In the gas phase, the X’s on the pyridine ring can be ordered according to their ability to promote the hydration reaction as follows: NH₂ > OH ≥ SH ≈ CH₃ > DMA > H > F ≥ Cl ≈ CCH ≈ Br > NO₂.

Water solvent weakens all coordination Pt–ligand bonds and lowers the activation free energies compared to the gas phase. Both shortenings and elongations of the bond lengths are possible being inversely related to the changes of the ligand → Pt transferred charge. The dampening of electrostatic interactions lowered the range of the ΔG^⧧ values for the ortho subset to 2.4 kcal/mol. The ranges of ΔG^⧧ for meta and para subsets being driven mainly by electronic effects remained almost unchanged with respect to the gas phase (ca. 1.8 kcal/mol).

Considering all three ortho, meta, and para positions (all mono-substituted systems), the ranges of ΔG^⧧ values for all X’s were 4.6 and 3.0 kcal/mol, which corresponded to ca. 2200 and 150 times differences in the reaction rate at 298 K in the gas phase and the water solvent, respectively.

The acceleration of the hydration reaction by an additional NH₂ substitution of the o-NH₂ ligand was not observed. On the other hand, a further slowdown of the Pt(II) complex reactivity with respect to the complexes with mono-substituted ligands was possible. The 2m-NO₂ and op-NO₂ pathways increased the maximum value of ΔG^⧧ by 0.6 and 0.5 kcal/mol in the gas phase and the water solvent, respectively. As the result, if poly-X complexes were considered, the ranges of possible ΔG^⧧ values were increased up to 5.2 and 3.4 kcal/mol which corresponded to ca. 6400 and 320 times differences in the reaction rate at 298 K for the gas phase and the water solvent, respectively.

The additivity of substituent effects on poly-X complexes was shown with respect to the Pt–ligand bond strengths and the ligand NPA charges in the gas phase which had the relative errors below 30%.

Computational Methods

All geometries of the structures were optimized at the DFT level with the hybrid B3LYP functional⁷¹ and 6-31+G(d) basis set for the first and second row elements. Heavier atoms were treated by Dresden–Stuttgart quasirelativistic energy-averaged effective pseudopotentials^72,73 with a pseudo-orbital basis set augmented by the set of diffuse (for Pt with exponents α_s = 0.0075, α_p = 0.013, α_d = 0.025; for Cl: α_s = 0.09, α_p = 0.0075) and polarization (α_f(Pt) = 0.98; α_d(Cl) = 0.618) functions.⁷⁴ These calculations are labeled as B3LYP/BS1 in further text. The nature of the obtained stationary points was always checked by the Hessian matrix evaluation. Thermal contributions to the energetic properties were calculated using the canonical ensemble at standard gas phase conditions (T = 298 K, p = 101.325 kPa).

The energy profiles and wave function properties were determined at the B3LYP-D3BJ/MWB-60(2fg)/6-311++G(2df,2pd) single point calculations which combined the B3LYP functional with Grimme’s DFT-D3 dispersion correction and Becke–Johnson damping⁷⁵ (labeled as D3BJ). The Pt atom was augmented by the set of diffuse functions in analogy to BS1 and by the set of polarization functions (α_f(Pt) = 1.419; 0.466, α_g(Pt) = 1.208)⁷⁴ (B3LYP-D3BJ/BS2 calculations). All possible rotamers were considered for the reactant and product structures, and the energy of the given minimum structure was obtained by Boltzmann averaging over all optimized rotamers at T = 298 K. For calculation of activation free energies (ΔG^⧧), the lowest lying TS structure was considered. In calculations of binding energies ΔE_bind, the basis set superposition error (BSSE) was included by the counterpoise correction.⁷⁶ Deformation energies were not included.

Additional single-point calculations on selected optimized structures were conducted using the Amsterdam Density Functional 2014.05 package (ADF)⁷⁷ to calculate fragment energy decompositions according to the extended transition state theory⁷⁸ combined with natural orbitals for chemical valence (ETS-NOCV).^79,80 Gas phase interaction energies ΔE_INT^gas were decomposed to Pauli (ΔE_Pauli), electrostatic (ΔE_elstat), orbital (ΔE_orb), and dispersion (ΔE_disp) energy contributions

2

In these calculations, scalar relativistic effects were treated within the zeroth order regular approximation (ZORA).⁸¹ The BLYP-D3BJ functional was used with the all-electron TZ2P (ZORA) basis set for all atoms.

To include solvent effects, the above described B3LYP/BS1 optimizations and B3LYP-D3BJ/BS2 single point calculations were performed also in the water environment for all structures using IEFPCM (PCM) implicit solvent approach. BSSE corrections with the PCM regime were calculated with ghost atomic orbital functions localized inside the cavity having the same size as the whole complex.⁸²

All optimizations and single point calculations were carried out by the Gaussian 09, revision D.01 (G09) program package.⁸³ Atoms in molecules (AIM) topological analysis of the electron density in bond critical points was performed on selected structures by the AIMAll program.⁸⁴ NBO analysis was carried out, and atomic charges based on NAO’s (natural population analysis (NPA) charges) were determined by the NBO 3.1 program.⁸⁵ Wave function properties were analyzed by the Multiwfn 3.7 program.⁵⁴

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c01161.

• Complete versions of Tables 2–7 with the data for all X’s; electron density difference isosurfaces of p-NH₂ and p-NO₂ structures with respect to the reference pyrH structure; five most important ETS-NOCV deformation density contributions describing the formation of the Pt–N_pyrX bond in H-R, H-TS, and H–P structures; dependence of pyr-X ligand binding energies on the Pt–N_pyrX bond lengths and the dependence of the σ-donation energy ΔE_orb^σ contributions on total ΔE_orb energies for X-TS and X-P structures; ETS-NOCV deformation density contributions for the formation of the Pt–N_pyrX bond in X-R structures which involve contribution from Pt···H (o-NH₂-R, o-OH-R), Pt···S (o-SH-R) nonbonding interactions or NH₃···N (o-DMA-R), NH₃···O (o-NO₂-R) H-bond interactions; dependence of the Pt–pyrX binding energy on the transferred q(pyrX) charge for X-R, X-TS, and X-P structures; dependence of the gas phase Pt–pyrX binding energy on the NBO charge of the N_pyrX atom (q(N_pyrX)), the total dipole moment of pyrX (p(pyrX)), and the projection of the dipole moment into C4–N_pyrX direction (p_x(pyrX)) for X-R, X-TS, and X-P structures; dependence of the gas phase Pt–pyrX binding energies for X-R, X-TS, and X-P structures on the minimum surface electrostatic potential calculated on the surface of the N_pyrX atom in the isolated pyrX ligand; correlation between ΔE_elst and ΔE_orb terms for the Pt–pyrX interaction in X-R, X-TS, and X-P structures; dependence of Pt–ligand binding energies on the LP(N_pyrX) NBO energy in the gas phase and the water solvent; electron density difference isosurfaces of p-NH₂-R and p-NO₂-R structures with respect to the reference H-R structure calculated in the water solvent; dependence of the gas-phase activation Gibbs free energies (ΔG^⧧) on the Hirschfeld charges calculated on the Pt(II) atom; bonding energies, bond lengths, and ligand NPA charges in poly-X-R and poly-X-P structures (X = F, NH₂, NO₂) optimized in the gas phase and water solvent, ΔG^⧧ activation free energies, and estimated values of all these variables (eq 1) with absolute and relative errors; stabilizing H-bonds in the 2op-NH₂-R and 2op-NH₂-P structures; plots of calculated versus estimated (eq 1) values of ΔG^⧧ activation free energies for complexes with poly-substituted ligands in the gas phase and the water solvent; correlations between B3LYP/BS1 and M06-2X/BS1 bond lengths for the X-R_w and X-TS structures and the correlations between B3LYP-D3BJ//BS2//B3LYP/BS1 and M06-2X/BS2//M06-2X/BS1 activation free energies in the gas phase and the water solvent; correlations between B3LYP/BS1 and PBE0/BS1 bond lengths for the X-R_w, X-TS structures and the correlations between B3LYP-D3BJ//BS2//B3LYP/BS1 and PBE0-D3BJ/BS2//PBE0/BS1 activation free energies in the gas phase; and dependence of the relative values M06-2X/BS2//M06-2X/BS1 calculated activation free energy barriers (Δ(ΔG^⧧)) of the hydration reactions of the trans-[Pt(NH₃)₂(pyrX) Cl]⁺ complexes on the nature and the position of the X in the gas phase and in the water solvent (PDF)

• Optimized Cartesian coordinates of all TS and the most stable minimum structures (XYZ)

The authors declare no competing financial interest.