Exploring the Potential Energy Surface for the Interaction of Sterically

Article pubs.acs.org/JPCA

Exploring the Potential Energy Surface for the Interaction of Sterically Hindered Trichloro(diethylenetriamine)gold(III) Complexes with Water Hélio F. Dos Santos,*,† Diego Paschoal,† and Jaroslav V. Burda‡ †

NEQC: Núcleo de Estudos em Química Computacional, Departamento de Química−ICE, Universidade Federal e Juiz de Fora, 36036-330 Juiz de Fora, MG, Brazil ‡ Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague 2, Czech Republic ABSTRACT: The reactivity of gold(III) complexes is analyzed for a series of derivatives of 3-azapentane-1,5-diamine (dien) tridentate ligand that can contain some bulky substituents. Two distinct series of compounds are considered where the dien ligand is either deprotonated (R-dien-H) or protonated (R-dien) at the secondary amine where R = ethyl (Et) or methyl (Me). While the deprotonated species will occur in neutral and basic solutions, the protonated forms are likely to be present in acidic environment. Hydration reaction (water/Cl− ligand exchange) of 14 complexes is modeled with quantum chemical calculations. Our calculations predict that the reactivity decreases with the increase in the molecular volume of the substituted dien ligand, and the calculated rate constants are in satisfactory agreement with experimental results. In addition, quantitative structure/reactivity models are proposed where the angle between the entering and leaving groups in the transition state structure (the reactivity angle) is used as a molecular descriptor. These models explain the trend of the relative reactivity of these complexes and can be used to design new ligands for gold(III) complexes aiming to adjust the reactivity of the complex.

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frequently2,4−7 due to their high reactivity and potential as an antitumor drug. Some novel ligands have been designed and synthetized for Pd(II), while using the basic triamine skeleton as the chelating group.8 As expected, the reaction rate decreases with the increase in the volume of the alkyl groups above and below the plane containing the nitrogen atoms, although the reactivity order has not been completely understood. Some discussions have focused on few gold(III) derivatives such as [Au(R-dien-H)Cl]+ and have addressed the steric effect of the alkyl groups.9 For these Au(III) complexes, the ligand exchange rate was higher using 1,1-Et2-dien-H ligand (3) than 1,1,7,7Me4-dien-H (2) when bromide was the entering group. Two hypotheses were proposed in an attempt to explain this trend: (1) the role of the higher effective positive charge on the gold center in the complex with 1,1-Et2-dien-H ligand and (2) a distinct substitution mechanism passing through an open-ring intermediate, where the Au−N(Et)2 bond is broken. Both hypotheses are reasonable; however, they were not explored further. We recently studied the substitution reactions of [Au(dien)Cl]2+ and [Au(dien-H)Cl]+ (Scheme 1) complexes by considering water and stronger nucleophiles such as OH−,

INTRODUCTION Substitution reactions of square-planar complexes, mainly complexes of Pt(II) and Pd(II), have been widely addressed in the literature since they have a primary role in catalytic and medical applications.1 Besides the electronic structure of the metal center, which is the target for nucleophilic attack, the reactivity of those coordination complexes is adjusted or tuned by properly choosing the steric and electronic features of the ligand. Generally, a role of ligand has a much more subtle effect than the variation of metal itself. For example, the standard hydration reactions of [Pd(dien)Cl]+ and [Pd(1,4,7-Me3dien)Cl]+ (for numbering sequence, see Scheme 1) have rate constants of 37.8 and 25.7 s−1, respectively,2 which corresponds to a 32% decrease when the methyl groups are present on the nitrogen atoms. However, hydration process for [Pt(dien)Cl]+ occurs much more slowly, with a rate constant of the order of 10−5 s−1.3 Therefore, it is possible to achieve fine-tuning in the kinetics of substitution reactions by using bulky ligands to shield the metal center of the complex. Tridentate N-ligands have been used often for chelating to add steric hindrance in square-planar complexes and, consequently, decrease the substitution reaction rate. Among these ligands, the simplest example is the diethylenetriamine (3azapentane-1,5-diamine: dien as mentioned above), which is used in its unsubstituted form or substituted with bulky alkyl groups (Scheme 1). Pd(II) complexes have been studied © 2012 American Chemical Society

Received: August 10, 2012 Revised: October 24, 2012 Published: October 29, 2012 11015

dx.doi.org/10.1021/jp307977p | J. Phys. Chem. A 2012, 116, 11015−11024

The Journal of Physical Chemistry A

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Scheme 1. N-Alkyl-Substituted Diethylenetriaminegold(III) Complexes: (a) R-dien-H Derivatives, Found in Neutral and Basic Solutions (pH > 5), and (b) R-dien Derivatives, Found in Acidic Solution

Scheme 2. Hydration Reaction Path Calculated in the Present Study

N3−, and SCN−.10 Our results show that, for these complexes, ring-opening does not compete with the chloride exchange when water is involved. Despite that the ring-opening is significantly faster for N3− and SCN−, it is still slower than the direct dechlorination process. We also noted that the deprotonation of the central nitrogen (N4 in Scheme 1) weakened the Au−Cl bond due to trans-influence and increased the chloride release rate. In this work, we extend our previous study by evaluating the hydration reaction of sterically hindered [Au(R-dien-H)Cl]+ and [Au(R-dien)Cl]2+ complexes with R = CH2CH3 and CH3 at the positions shown in Scheme 1a,b, respectively. Fourteen structures are modeled, and the rate constants of the hydration is calculated (Scheme 2). In addition to the chemical interest in these processes, the substitution reactions for Au(III) complexes are of paramount importance for their use as anticancer drugs11−13 and have not been explored to the same extent as Pt(II) complexes in the recent literature. Moreover, the computational studies addressing their substitution reaction mechanisms are even sparser than the experimental works.13−15

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Initial estimates of transition-state (TS) structures are proposed on the basis of a standard associative mechanism for square-planar complexes, with the entering and leaving groups in the equatorial plane of a distorted trigonalbipyramidal geometry. These geometries were further optimized and characterized as saddle point (1st-order TS) on the potential energy surface (PES) using the Becke three-parameter hybrid functional B3LYP,16 with the 6-31+G(d) basis set for ligand atoms and the Stuttgart RSC 1997 ECP (also known as Stuttgart/Dresden ECP−SDD),17 augmented with one set of f (αf = 1.14) polarization functions for the gold atom.18 The solvent effect (water, ε = 78.35) was taken into account, including geometry optimization, by using the integral equation formalism PCM (IEF-PCM)19 with the cavity constructed using the UFF radii20 scaled by α = 1.10 (the default in Gaussian0921). From the saddle point, each reaction path was followed by the intrinsic reaction coordinate (IRC)22 with 50 points calculated along the reverse direction and a step size of 0.1 a.m.u1/2 Bohr. The final point in the reverse IRC direction (called intermediate, I) was then further optimized to guarantee full geometric convergence and characterized as a true minimum on the PES at the level of theory used for TS geometries. This structure is named reactant (R) and is actually a molecular complex within the supermolecular approach commonly used to calculate the kinetic properties. In addition, the activation energies were also calculated by considering the isolated reactant species, in which the reactants are initially infinitely separated. The rate constant (ks) was obtained from the Eyring−Polanyi eq 1 under normal conditions, where T = 298.15 K, p = 1 atm, and c° = 1 mol dm−3.

THEORETICAL METHODS

The complexes and the numbering sequence used in this work are represented in Scheme 1. To clarify the electronic nature of the ligand, we used the nomenclature ‘R-dien’ for all ligands alkylated or protonated at the N4 position (Scheme 1b) and ‘Rdien-H’ for the corresponding ligands deprotonated at N4 (Scheme 1a). Chloride substitution by water is considered to occur (Scheme 2) leading to evaluation of 16 hydration processes. For the complexes represented in Scheme 1a, experimental kinetic studies for hydration reactions were reported.9

ks = 11016

⎛ −ΔGa ⎞ kBT ⎟ exp⎜ ⎝ RT ⎠ hc°

(1)



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Table 1. Structural Parameters Calculated for the Reactive Species on the Hydration Pathway for [Au(R-dien-H)Cl]+ Complexes; Bond Length and Angles Are Given in Angstroms and Degrees, Respectively, and the Wiberg Bond Indexes Are Given in Parenthesesa Au−Cl dien-Hd

R TS R TS R TS R TS R TS

1 2 3 4

2.443 2.869 2.447 2.849 2.447 2.989 2.451 2.881 2.449 2.992

(0.49) (0.24) (0.48) (0.25) (0.47) (0.22) (0.48) (0.25) (0.47) (0.23)

Au−O 3.088 2.459 3.851 2.487 4.195 2.455 3.832 2.507 4.832 2.508

(0.005) (0.16) (0.008) (0.14) (0.011) (0.14) (0.011) (0.13) (0.006) (0.12)

Au−N7 2.112 2.108 2.107 2.119 2.154 2.174 2.109 2.121 2.164 2.185

(0.43) (0.42) (0.43) (0.39) (0.37) (0.35) (0.41) (0.38) (0.37) (0.34)

Au−N4 2.036 2.054 2.035 2.054 2.035 2.050 2.036 2.054 2.033 2.052

Au−N1

(0.66) (0.70) (0.64) (0.68) (0.62) (0.67) (0.63) (0.68) (0.60) (0.67)

2.098 2.106 2.148 2.144 2.155 2.175 2.147 2.149 2.165 2.186

(0.46) (0.43) (0.39) (0.37) (0.37) (0.35) (0.38) (0.38) (0.37) (0.34)

N4−Au−O

N4−Au−Cl

O−Au−Cl

τb

ΔΣc

149.6

141.3

69.1

0.26

−0.97

148.6

141.9

69.0

0.29

−0.94

148.1

146.1

65.6

0.29

−1.14

148.9

142.8

67.7

0.30

−0.86

149.4

146.1

64.3

0.28

−1.72

a

See Scheme 1a for the numbering sequence: 1, 1,1-Me2-dien-H; 2, 1,1,7,7-Me4-dien-H; 3, 1,1-Et2-dien-H; 4, 1,1,7,7-Et4-dien-H. bTrigonality degree calculated as |α − β|/60° with α and β being the two largest angles on the coordination sphere. For pentacoordinate compexes, when τ = 0, the geometry around the metal is a perfect square-planar, and when τ = 1, the structure is a trigonal-bipyramidal geometry. cMetal−ligand bond variation during the activation process. For ΔΣ0 the mechanism is of dissociative interchange type (Id). For ΔΣ=0 a concerted mechanism (I) operates. dStructural data from ref..10

Figure 1. Optimized geometries for the reactive species in the hydration process of [Au(R-dien-H)Cl]+ complexes: (a) 1, 1,1-Me2-dien-H; (b) 2, 1,1,7,7-Me4-dien-H. The intermolecular distances are in Angstroms.

Table 2. Kinetic Parameters for Hydration Reaction of [Au(R-dien-H)Cl]+ Complexes; the Energies Are in kcal mol−1 and the Rate Constant in M−1 s−1a b ΔGcalcd a

dien-H 1 2 3 4

e

18.04 18.47 20.06 19.14 21.23

[23.12] [23.51] [25.79] [24.46] [26.51]

b ΔHcalcd a

16.60 16.94 16.03 17.62 16.94

[12.51] [12.74] [14.88] [13.28] [16.06]

−TΔScalcd a 1.44 1.53 4.03 1.52 4.29

[10.61] [10.77] [10.91] [11.18] [10.45]

kcalcd a

c ΔGexptl a

d kexptl s

0.36 0.18 0.012 0.057 0.0017

17.75 18.40 19.09 19.68 22.79

0.6 0.2 0.062 0.023 0.00012

a

See Scheme 1a for the numbering sequence: 1, 1,1-Me2-dien-H; 2, 1,1,7,7-Me4-dien-H; 3, 1,1-Et2-dien-H; 4, 1,1,7,7-Et4-dien-H. bThe values in brackets are calculated assuming the isolated reactants. cEstimated through the experimental rate constant by using the Eyring−Polanyi eq 1 under normal conditions, namely, T = 298.15 K, p = 1 atm, and c° = 1 mol L−1. dFrom ref 9. eValues from ref 10.

N4, change insignificantly within 0.01 Å, although the bond order for Au−N4 (estimated by the Wiberg bond index) slightly decreases from 0.66 (dien-H) to 0.60 (4). The derivatives alkylated at both N1 and N7 (2 and 4) show the weakest Au−N1 and Au−N7 bonds within the series, with the bond order predicted to be 0.37. These structural data suggest that the chelating strength decreases upon alkylation, and the geometry of the metal tends to align linearly with the N4−Au− Cl axis, which is consistent to the expected geometry for the reduced form of Au(I) complexes. Some structural data for the reactant (R) and TS on the hydration pathways are given in Table 1. Although the reactant species are actually supermolecular complexes with one water molecule interacting with the gold complex, the discussion regarding the free base geometries still holds, as shown in Table 1. The optimized geometries for R and TS structures (complexes 1 and 2) are depicted in Figure 1. For the complexes 3 and 4, the R and TS

All calculations were carried out using the Gaussian09 package, revision A.02.21

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RESULTS AND DISCUSSION Hydration Reaction for [Au(R-dien-H)Cl]+ Complexes (1−4). Since experimental data for the dechlorination of complexes 1−4 (Scheme 1a) are available,9 they are discussed first to assess the level of theory used in this study. The rate constants were measured in pH 6.8 phosphate buffer where the R-dien is deprotonated at the N4 nitrogen (for labeling, see Scheme 1a) since pKa = 2.2 for 4 and 4.2 for 1, which yields the R-dien-H species. The alkylation of nitrogen positions N1 and N7 has some subtle effects on the structures of the free bases. From natural population analysis (NPA), we found that the effective positive charge at the gold atom decreases from 0.915e (dien-H) to 0.851e (4) and that the chelating bonds Au−N1 and Au−N7 expand from 2.103 (dien-H) to 2.162 Å (4). The other two bonds in the coordination sphere, Au−Cl and Au− 11017



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lesser extent (1.6 kcal mol−1 relative to TS-2), and therefore, the enthalpy barrier for 3 (ΔHa = 17.62 kcal mol−1) is higher than for 2 (ΔHa = 16.03 kcal mol−1). However, within the supermolecular approach, the entropy contribution (−TΔSa = 4.03 kcal mol−1 for complex 2 and −TΔSa = 1.52 kcal mol−1 for complex 3) leads to a higher free energy barrier for complex 2 (ΔGa = 20.1 kcal mol−1) than 3 (ΔGa = 19.1 kcal mol−1). The smaller absolute value of the activation entropy for 3 can be understood on the basis of the structure of R-3. The strong water−amine hydrogen bond significantly decreases the entropy of the reactant R-3, which is close to that predicted for TS-3, and therefore, the entropy difference throughout the activation process (R-3 → TS-3) is notably small. For the processes of the complex 3, [Au(1,1-Et2-dien-H)Cl]+ + H2O → R-3 and [Au(1,1-Et2-dien-H)Cl]+ + H2O → TS-3, the calculated −TΔS was 9.7 and 11.2 kcal mol−1, respectively. When complex 2 is considered, the corresponding values are 6.9 for R-2 and 10.9 kcal mol−1 for TS-2. Thus, it is clear that the higher activation free energy for complex 2 is due to the larger entropy of reactant R-2 relative to R-3. This trend can be generalized for all four complexes where smaller entropy change between R and TS structures was found for one substituted amine (1,1-R2-dien-H, 1 and 3) in comparison to complexes with fully substituted dien-H ligand (1,1,7,7-R4-dienH, 2 and 4) where more pronounced entropy change passing from R to TS structure is visible. The analysis of the activation processes using the isolated reactant species (values in brackets in Table 2) shows that the TS-2 is less stable than the TS-3 by 1.6 kcal mol−1 (enthalpy values), which is consistent with the predicted reactivity order. Moreover, both supermolecular and isolated reactant species approaches lead to the same rate constants order, dien-H > 1 > 3 > 2 > 4. Furthermore, it is interesting to compare complexes 1 and 3, which have the same substitution pattern, 1,1-R2-dien-H. The entropy changes are practically the same, with a slightly higher enthalpy barrier for 3 (Table 2). For complexes 1 and 3, the stability of the reactants R-1 and R-3 is similar, and the increase in the enthalpy of TS-3 relative to TS-1 plays a major role in the determination of the reactivity order. The reason is less clear in this case (probably higher orientational entropy for more bulky hydrophobic ligand), but some features can be discussed. The structural parameters for the reactant and transition states are given in Table 1. Focusing on the data for compounds 1 and 3, we note that the angle ∠O−Au−Cl in the TS structures (the reactivity angle), which defines the relative positions of the entering and leaving groups, is tighter for complex 3 (67.7°) than complex 1 (69.0°) due to the larger steric hindrance of ethyl than methyl groups. Correspondingly, the ΔΣ index is slightly less negative, which means that the bond formation is less important for TS-3 than for TS-1. Both features should be responsible for increasing the free energy barrier for complex 3. From the values in Tables 1 and 2, the relationship ΔGa × ∠O−Au−Cl can be established where ΔGa follows the trend dien-H < 1 < 3 < 2 < 4, which is inversely correlated with ∠O−Au−Cl angle, 69.1 > 69.0 > 67.7 > 65.6 > 64.3°, respectively (Figure 2). The activation free energies calculated from isolated reactant species are also given in Table 2 (values in brackets) and show a satisfactory correlation with the ∠O−Au−Cl angle as represented in Figure 2, establishing the reactivity order dien-H > 1 > 3 > 2 > 4 (although all of the values obtained overestimate the experimental data). Moreover, evaluation of the TS structures can help to design new sterically hindered ligands that can control substitution reaction rates. In

structures are visually very similar to those represented in Figure 1. The experimental rate constants were obtained indirectly from a pseudofirst order reaction involving the displacement of chloride by bromide (kobs = ks + k2[Br−]).9 In this regime, ks represents the rate constant for the solvent-assisted displacement, where the rate-determining step is the water/chloride exchange and k2 is the rate constant for direct displacement of chloride by bromide. The computed ks values for dien-H and 1−4 complexes are given in Table 2 and compared to the experimental data.9 For the unsubstituted derivative, dien-H, the value of ks was used from our previous paper.10 Besides rate constants, the activation thermodynamic properties are also provided. The ΔGa and ΔHa values were calculated using the supermolecular and isolated reactant species (in brackets) approaches where the reagents are considered either as molecular complexes or infinitely separated molecules, respectively. In general, the experimental hydration rate trend (dien-H > 1,1-Me2-dien-H (1) > 1,1,7,7-Me4-dien-H (2) > 1,1Et2-dien-H (3) > 1,1,7,7-Et4-dien-H (4)) is reproduced satisfactorily, with the only exception compound 3 (1,1-Et2dien-H), for which the rate constant was higher than for compound 2 (1,1,7,7-Me4-dien-H) (see Table 2). According to the experimental data, two ethyl groups on the same nitrogen in compound 3 are expected to provide greater steric hindrance (and slower substitution rate) than four methyl groups in compound 2. This higher reaction rate calculated for complex 3 was experimentally observed for bromide/chloride substitution reaction.9 The suggested explanation in the case of these Br−/ Cl− reactions was based on a two-step mechanism passing through an open-ring structure for the 1,1-Et2-dien-H derivative (3). However, the different behavior for water and bromide nucleophiles were not discussed further in ref 9. From our previous discussion about geometries of the free bases, we concluded that the chelating bonds (Au−N1 and Au−N7) weaken upon alkylation, with a minor effect on the Au−N4 and Au−Cl bonds. Therefore, the ring-opening is expected to be faster for alkylated complexes than for the dien-H compound. For the dien-H complex, the ring-opening process was found to be notably slower (ΔGa = 32.3 kcal mol−1, k = 1.2 × 10−11 M−1 s−1) than the direct substitution reaction (ΔGa = 18.0 kcal mol−1, k = 0.4 M−1 s−1) when water was involved.10 To assess the contribution of the ring-opening pathways to the substitution kinetics of complex 3, as suggested in ref 9, the activation free energy for the ring-opening by water process was calculated. The activation free energy of 31.8 kcal mol−1 was obtained, which is ∼60% higher than the corresponding values for hydration (19.1 kcal mol−1, Table 2). Therefore, although slightly faster than the nonalkylated species, the ring-opening process should not be relevant for dechlorination of complex 3 by water and thus could not be the main reason for the relatively higher reactivity of complexe 3 over 2. An additional explanation of the reactivity order based on the molecular features of TS structures will be discussed below. When the ΔHa and −TΔSa activation energies are analyzed, we note that the activation enthalpy for compound 3 is higher than for 2 (Table 2, supermolecular approach) as a result of the more stable reactant R-3. In this complex, the water molecule is strongly hydrogen bonded to the primary amine (see Figure 1a as an example). Comparing compound 3 to compound 2 (Figure 1b), where water interacts with chloride, the stabilization enthalpy found for reactant R-3 was 3.2 kcal mol−1 lower. The TS-3 is also lower in enthalpy, however, to a 11018



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two other molecular features are addressed: the alkylation of the secondary amine at N4 and the leaving group effect for complexes 7 (1,4,7-Me3-dien) and 9 (1,4,7-Et3-dien), where only one side of the molecular plane is shielded by the alkyl groups, which allows two distinct substitution pathways. Molecular properties calculated in aqueous solution for the free bases are depicted in Figure 3, including the net charge on the gold atom (qAu), dipole moment (μ), and molecular volume (Vm), estimated from a 0.001 e/bohr3 density envelope. For the methyl derivatives, the effective positive charge on metal varies in a narrow range from 0.982e (10) to 0.999e (7) and is close to that for the dien complex (0.985e). The electron-donor effect of the ethyl analogues is much more pronounced, with the positive charge on the gold atom decreasing systematically from 0.975e for 1,1-Et2-dien (6) to 0.902e for 1,1,4,7,7-Et5-dien analogue (12), Figure 3a. The dipole moment is approximately 11.5 D for the N4 protonated species (dien, 5, 6, 13, and 14) and decreases below 11 D for the other complexes. The less polar compounds are those with an ethyl group at N4 (8 and 12) where the dipole moment is smaller than 10 D (Figure 3b). The molecular volume increases with the number of alkyl groups, except for the derivatives of the fully alkylated primary amine 13 and 14 with estimated volumes smaller and larger than expected, respectively (Figure 3c). For complexes 6 (1,1-Et2-dien) and 13 (1,1,7,7-Me4-dien), the molecular volume is similar, and thus, steric hindrance and reactivity could be expected similar, as shown previously for the R-dien-H corresponding compounds. The kinetics for the hydration of R-dien complexes (Scheme 1b) are described in the next paragraphs and correlated with the molecular properties of the reactive species. The N4 protonated complexes 5 (1,1-Me2-dien), 6 (1,1-Et2dien), 13 (1,1,7,7-Me4-dien), and 14 (1,1,7,7-Et4-dien) are considered first. These compounds are analogues to 1, 3, 2, and 4, respectively, and are likely to be present in acidic solution. For the complexes protonated at N4, the minimum region on the PES for interaction of water with the gold complex is notably flat, and several structures are probable (the conformer obtained from the IRC is labeled the IRC minimum onward). For the dien parent molecule, the IRC minimum has the water

Figure 2. Activation free energy for hydration process of [Au(R-dienH)Cl]+ complexes as a function of the ∠O−Au−Cl angle of the TS geometries. The values were calculated using the supermolecular and isolated reactant species approaches. The linear fitting for activation = (59 ± 4) − (0.60 ± 0.06) (∠O−Au−Cl) (r free energy was ΔGcalcd a = (70 = 0.987; σ = 0.2; N = 5) (supermolecular approach) and ΔGcalcd a ± 3) − (0.68 ± 0.04) (∠O−Au−Cl) (r = 0.994; σ = 0.2; N = 5) (isolated reactant species approach).

the next section, the hydration processes for a series of [Au(Rdien)Cl]2+ complexes (5−14) are analyzed, and the analogous relationship is assessed. Hydration Reaction for [Au(R-dien)Cl]2+ Complexes (5−14). Experimental data for the reactivity of the Au(III) complexes with the R-dien series of ligands (Scheme 1b) are not available; however, for Pd(II) analogues, the hydration rate constants are provided in the literature for most of the derivatives studied here, and a reactivity order is proposed.2 These will be used as the reference in the present part, although Pd(II) complexes are much more reactive than Au(III) ones. To illustrate, the dechlorination rate constant is approximately 10−7 s−1 for the [Au(dien)Cl]2+ complex10 and 40 s−1 for the [Pd(dien)Cl]+ analogue.2 For the R-dien series, in addition to the substitution pattern discussed for the R-dien-H complexes,

Figure 3. Molecular properties calculated for [Au(R-dien)Cl]2+ complexes in aqueous solution. (a) Charge on the Au atom (qAu) calculated from natural population analysis (NPA); (b) electric dipole moment (μ) and (c) molecular volume (Vm) estimated from a 0.001 e/bohr3 density envelope. 11019



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Figure 4. Optimized geometries for the reactant species found from hydration IRC (IRC minima): 5, 1,1-Me2-dien; 13, 1,1,7,7-Me4-dien; 6, 1,1-Et2dien; 14, 1,1,7,7-Et4-dien.

Figure 5. Molecular electrostatic potential (MEP) calculated for complexes dien, 5, 6, 13, and 14. The isodensity was set to 0.001 e/bohr.3

Table 3. Structural Parameters Calculated for the Reactive Species on the Hydration Pathway of [Au(R-dien)Cl]2+ Complexes; Bond Length and Angles Are Given in Angstroms and Degrees, Respectivelya dien 5 6 7 7-a 8 9 9-a 10 11 12 13 14

d

R TS R TS R TS R TS R TS R TS R TS R TS R TS R TS R TS R TS R TS

Au−Cl

Au−O

Au−N7

Au−N4

Au−N1

2.338 2.808 2.349 2.785 2.346 2.804 2.352 2.804 2.348 2.807 2.346 2.834 2.352 2.792 2.348 2.927 2.351 2.919 2.354 3.053 2.356 3.016 2.354 2.902 2.349 2.991

4.105 2.258 3.847 2.297 4.548 2.299 4.214 2.273 3.981 2.279 4.015 2.314 4.633 2.284 3.866 2.255 3.118 2.285 4.585 2.280 4.612 2.313 3.982 2.264 4.834 2.274

2.095 2.085 2.103 2.103 2.103 2.108 2.117 2.113 2.102 2.117 2.095 2.109 2.128 2.125 2.111 2.133 2.151 2.184 2.159 2.200 2.161 2.196 2.142 2.185 2.158 2.196

2.079 2.077 2.074 2.082 2.078 2.081 2.102 2.101 2.102 2.100 2.107 2.112 2.111 2.113 2.109 2.109 2.110 2.105 2.105 2.112 2.114 2.122 2.072 2.071 2.073 2.072

2.078 2.083 2.127 2.135 2.132 2.136 2.118 2.114 2.121 2.136 2.135 2.133 2.130 2.121 2.128 2.158 2.151 2.177 2.164 2.193 2.160 2.189 2.144 2.174 2.163 2.190

N4−Au−O

N4−Au−Cl

O−Au−Cl

τb

ΔΣc

162.1

125.6

71.7

0.07

−1.38

159.5

128.8

71.6

0.12

−1.10

159.2

130.3

70.4

0.14

−1.78

163.7

124.2

71.6

0.05

−1.49

160.2

127.4

70.9

0.07

−1.22

158.5

131.9

69.5

0.16

−1.20

163.2

124.6

71.6

0.02

−1.92

159.9

131.6

67.1

0.05

−0.98

158.7

133.6

67.1

0.16

−0.21

154.7

141.3

63.4

0.20

−1.53

155.2

140.2

63.8

0.21

−1.57

159.9

131.5

67.7

0.11

−1.10

156.6

138.0

64.8

0.17

−1.85

a

See Scheme 1b for numbering sequence: 5, 1,1-Me2-dien; 6, 1,1-Et2-dien; 7, 1,4,7-Me3-dien; 8, 1,1,4-Et3-dien; 9, 1,4,7-Et3-dien; 10, 1,1,4,7,7-Me5dien; 11, 4-Me-1,1,7,7-Et4-dien; 12, 1,1,4,7,7-Et5-dien; 13, 1,1,7,7-Me4-dien; 14, 1,1,7,7-Et4-dien. bTrigonality degree calculated as |α − β|/60° with α and β being the two largest angles on the coordination sphere. For pentacoordinate compexes, when τ = 0, the geometry around metal is a perfect square-planar, and when τ = 1, the structure is a trigonal-bipyramidal geometry. cMetal−ligand bond variation during the activation process. For ΔΣ < 0, the mechanism is assigned as associative interchange (Ia), and for ΔΣ > 0, the mechanism is of dissociative interchange type (Id). For ΔΣ = 0, a concerted mechanism (I) operates. dStructural data from ref 10.

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molecule close to the primary amine (N1/7) (Figure 4); even though the second minimum with the water close to the secondary amine (N4) has been found 1.5 kcal mol−1 lower in energy. The IRC for the methylated compounds (5 and 13) led to molecular complexes with the water interacting with secondary amine at N4 (Figure 4), and the structure where water is hydrogen bonded to N7 was found 0.4 kcal mol−1 higher in energy than the IRC minimum in complex 5. When the alkyl groups are ethyl (complexes 6 and 14), the water molecule is predicted to act as a hydrogen bond donor to chloride ligand (Figure 4). Two other minima where water acts as a hydrogen bond acceptor were explored for complex 6 and found lower in energy than the IRC minimum by 2.3 kcal mol−1 (the N4 and N7 structures are degenerate). The energy difference between the reactants discussed above can be partially understood on the basis of the molecular electrostatic potential (MEP) calculated for the corresponding free bases, Figure 5. In addition to the color scale, the minimum/ maximum points on the MEP surface are located in the vicinity of chloride and amine groups. The numerical values in extremes are included in Figure 5. The decrease of MEP at N4 region from dien to 1,1,7,7-Et4-dien complex (14) is apparent from Figure 5. This follows the preference order of N4 minimum relative to the N1/7 one: dien > 5 > 6. The MEP may also be used to get insight into the reaction pathway followed for each complex from the IRC. For dien, the MEP is relatively high over the N1−Au−N7 axis and then, the water molecule follows this direction from the TS structure. This is not the case for complex 5 where the positive MEP drives the water over the N4···N7 direction, favoring the higher potential region at N4. For complex 13, the positive MEP is over the N4−Au bond and drives the water toward N4 amine likewise. For complexes 6 and 14, besides the smaller potential on the amine moieties (Figure 5), steric hindrance over the molecular plane (mainly on the gold metal center) operates pushing the water molecule closer to the chloride ligand and forming a weaker Cl···H(aqua) bond. These distinct structures of reactants, which are a result of the flat PES in the minimum region, will lead to different energy barriers calculated using the supermolecular approach. Nonetheless, to be consistent with the methodology, the IRC minima (Figure 4) were considered for determination of the rate constants of all complexes. The main structural parameters for the R and TS reactive species are given in Table 3. In the TS structure, the Au−Cl and Au−O bonds are approximately 2.80 and 2.30 Å for 5 and 6 and 2.90 and 2.26 Å for 13 and 14, which are shorter than the corresponding bonds in the R-dien-H analogues (Table 1). This is due to the reduced donating activity of N4 in the presence of an N4−H bond, which leads to higher effective positive charge on the central gold atom for R-dien complexes. The ΔΣ values in Tables 1 and 3 are more negative for R-dien than the R-dien-H complexes. The reactivity angle (∠O−Au− Cl) is in the range of 64.8−71.6° and follows the same order established for the R-dien-H complexes: 5 > 6 > 13 > 14, although it is slightly wider for the dien series due to the shorter Au−Cl and Au−O bonds. The kinetic parameters are given in Table 4, calculated according to the supermolecular and isolated reactant species approaches (values in brackets). As shown in our previous paper,10 the substitution reactions for the dien complexes are much slower than for dien-H analogues (cf., Tables 2 and 4). From the supermolecular approach, which leads to good agreement with the experimental data for the Rdien-H series (Table 2), the rate constants are in the order of

Table 4. Kinetic Parameters for Hydration Reaction of [Au(R-dien)Cl]2+ Complexes; the Energies Are in kcal mol−1 and the Rate Constant in M−1 s−1a b ΔGcalcd a

dien 5 6 7 7-a 8 9 9-a 10 11 12d 13 14

c

26.50 26.64 25.03 20.33 27.92 26.98 20.60 31.49 26.58 29.25 31.99 31.73 27.79

[30.66] [30.21] [30.14] [27.99] [31.07] [30.52] [29.72] [34.46] [37.13] [35.64] [38.68] [33.45] [34.37]

b ΔHcalcd a

24.05 24.77 19.42 17.43 24.49 24.03 18.50 27.16 24.38 25.27 27.37 28.37 24.93

[19.22] [19.06] [19.15] [17.50] [19.81] [18.98] [18.16] [22.00] [25.00] [25.45] [26.53] [22.25] [24.32]

−TΔScalcd a 2.44 1.87 5.61 2.90 3.43 2.95 2.10 4.33 2.20 3.98 4.62 3.35 2.86

[11.44] [11.15] [10.98] [10.49] [11.26] [11.54] [11.56] [12.46] [12.13] [10.19] [12.15] [11.20] [10.05]

kcalcd × 105 s 0.0228 0.0180 0.273 763 0.00207 0.0101 483.8 0.00000499 0.0199 0.000219 0.00000214 0.00000332 0.00258

a See Scheme 1b for numbering sequence: 5, 1,1-Me2-dien; 6, 1,1-Et2dien; 7, 1,4,7-Me3-dien; 8, 1,1,4-Et3-dien; 9, 1,4,7-Et3-dien; 10, 1,1,4,7,7-Me5-dien; 11, 4-Me-1,1,7,7-Et4-dien; 12, 1,1,4,7,7-Et5-dien; 13, 1,1,7,7-Me4-dien; 14, 1,1,7,7-Et4-dien. bThe values in brackets are calculated assuming the isolated reactant species. cValues from ref 10. d The convergence was not complete for geometry optimization (rms gradient norm = 0.00033779 a.u.).

10−1−10−3 M−1 s−1 for dien-H and complexes 1−4 and 10−7− 10−11 M−1 s−1 for dien and complexes 5, 6, 13, and 14. As discussed above, the activation barriers predicted from the supermolecular approach are strongly dependent on the structure and stability of the reactants for the N4 protonated complexes. From values in Table 4, the free energy barrier follows the order 6 < dien < 5 < 14 < 13 (supermolecular approach), which are not completely correlated with the ∠O− Au−Cl angle: dien > 5 > 6 > 13 > 14. For the three former complexes, a similar trend is predicted from the isolated reactant species (values in brackets) where the 1,1-R2-dien derivatives are found more reactive than the unsubstituted dien compound. This is due to a weak, but effective, electrostatic interaction of the chloride leaving group with the N−H primary amine in the TS geometry (for example, the Cl···HN distance is 2.64 Å for TS-5 and 2.80 Å for TS-dien). The higher reactivity of complex 14 than 13 in the supermolecular approach is due the low stability of the reactant R-14 where the water is bound to chloride (Figure 4). To complete the previous discussion, the reactivity of complex 8 (1,1,4-Et3-dien) is compared to complex 6 (1,1Et2-dien). As shown in Figure 3c, the molecular volume of 8 is approximately 30% larger than 6 as a result of the insertion of the ethyl group at N4. As a consequence, the ∠O−Au−Cl angle decreases from 70.4 to 69.5°. Despite the narrowing of the reactivity angle upon alkylation of N4, the activation enthalpy is lower for 8 than for 6 (values in brackets) as a result of the more effective Cl···HN interaction in the former TS structure, where the distance is 2.5 Å. The activation free energy difference is only 0.4 kcal mol−1, which favors the process for 6 in the isolated reactant species approach. Within the supermolecular approach, the hydration of complex 6 is also faster than 8, but the activation free energy difference is larger (∼2 kcal mol−1) as a result of the high stability of R-8 where the water molecule is hydrogen bonded to the primary amine at N7. Nevertheless, the alkylation of N4 has only a secondary effect compared to the substitution of the N1 and N7 positions. 11021



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Figure 6. Optimized geometries for the reactive species in the two distinct hydration pathways of [Au(1,4,7-dien)Cl]2+ complex named 7 and 7-a. The distances inset are in Angstroms.

Figure 7. Activation energies for the hydration process of [Au(R-dien)Cl]+ complexes as a function of the ∠O−Au−Cl angle of the TS geometries. The values were calculated using the supermolecular approach (a) and considering the isolated reactants (b). The linear fitting for activation free = (82 ± 18) − (0.8 ± 0.2) (∠O−Au−Cl) (r = 0.670; σ = 2; N = 13) and (b) ΔGcalcd = (96 ± 9) − (0.9 ± 0.1) (∠O−Au−Cl) energy was (a) ΔGcalcd a a (r = 0.891; σ = 1.5; N = 13).

The derivatives 7 and 9 (all-cis-1,4,7-alkyl-dien) are compared in order to assess the effect of the leaving group, when these compounds allow nucleophile attack from both sides of the molecular plane. In the complexes 7 and 9, the water approaches through the sterically hindered side, and in 7a and 9-a, the water attacks the opposite side of the molecule, interacting with free N−H bonds in reactant supermolecule. From Table 3, the TS geometries are almost a perfect square pyramid (τ ≈ 0) with water occupying the square base. This is also the case for the parent molecule dien, where both molecular sides are unsubstituted. The ∠O−Au−Cl angle is smaller when the leaving chloride is on the bulky side, and the confinement effect is more pronounced for the ethyl analogue. In TS-9-a, the Au−Cl bond is quite long, 2.927 Å, increasing the bond breaking relevance, and the overall mechanism is less associative (ΔΣ = −0.98 Å). The optimized geometries for R and TS are shown in Figure 6 for complexes 7 and 7-a. It is obvious that the stability of R-7-a is greater than R-7 due the strong water···amine hydrogen bond, which accounts for 4.8 kcal mol−1 in favor of R-7-a (enthalpy difference). Conversely, the TS-7-a is higher in enthalpy by 2.3 kcal mol−1 than TS-7 due to the smaller ∠O−Au−Cl angle. Therefore, the activation enthalpy is predicted to be 7.1 kcal mol−1 higher for 7-a within the supermolecular approach. The enthalpy barrier for the ethyl analogue 9 is even lower than 9-a by 8.7 kcal mol−1 (Table 4). For both isomers, the leaving group pathway drives the overall process and is more likely to occur through the unsubstituted side (7 and 9). The lower activation barrier for 7 and 9 is not only a result of the lower stability of the R species but also the

more stable TS structures as follows from comparison of the corresponding values in brackets in Table 4. If the activation energies of 7-a and 9-a are compared to the dien compound, where water approaches through the unsubstituted side of the molecule, the alkyl effect on the chloride leaving group is apparent from the decreasing ∠O−Au−Cl angle, 71.7, 70.9, and 67.1°, and the increasing free energy barrier 26.50, 27.92, and 31.49 kcal mol−1 for dien, 7-a, and 9-a, respectively. Also, the fully alkylated, penta-alkylated derivatives 10, 11, and 12, can be compared and analyzed. The complexes 10 (1,1,4,7,7-Me5-dien) and 13 (1,1,7,7-Me4-dien) differ by the alkyl group at position N4, which is also the case for the pair 12 (1,1,4,7,7-Et5-dien) and 14 (1,1,7,7-Et4-dien). As stated above, the exchange of hydrogen by the alkyl at the secondary amine should play a minor role in the structure and reactivity of the complexes. Indeed, from Table 3, the Au−Cl and Au−O bonds in the TS geometries are within narrow ranges of 2.92−2.90 and 2.29−2.26 Å, respectively, for 10 and 13 analogues, and 3.02−2.99 and 2.31−2.27 Å for the 12 and 14 derivatives. Similar narrow ranges are observed for the reactivity angle, 67.1−67.7° and 63.8−64.8°, respectively. For the hybrid compound with methyl at N4 and ethyl at N1 and N7 (11), the TS geometry is closer to TS-12, showing the smaller effect of the substitution at the position N4. From the values in Table 4, it is clear that the free energy barrier increases in the order 10 < 11 < 12 that is controlled mainly by the activation enthalpy. Comparing the free energy barrier for the pairs 10/13 and 12/ 14 in the model of isolated reactant species (values in brackets in Table 4), it reveals a sizable increase in the values upon 11022



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trend. In addition to the qualitative trend, quantitative structure/reactivity relationship (QSRR) is established using the ∠O−Au−Cl angle from the TS structure (the reactivity angle) as a molecular descriptor. For [Au(R-dien-H)Cl]+ complexes, the QSRR models are ΔGcalcd = (59 ± 4) − a (0.60 ± 0.06)(∠O−Au−Cl) (r = 0.987; σ = 0.2; N = 5) (supermolecular approach) and ΔGcalcd = (70 ± 3) − (0.68 ± a 0.04) (∠O−Au−Cl) (r = 0.994; σ = 0.2; N = 5) (isolated reactant species approach), with the former leading to better agreement with experiment (the angle values are in degrees). New molecular features are evaluated for the broad series of R-dien complexes, including the alkylation of the secondary amines and the leaving group effect for the analogues with three alkyl substituents on the same side of the molecular plane. For those complexes, the chloride can leave the molecule through two distinct pathways and is more likely to occur through the unsubstituted side. Moreover, instead of the approach of water, the leaving group pathway drives the overall process. The alkylation of the secondary amine has basically a minor effect on the reactivity compared to the corresponding disubstituted analogue. To illustrate, the free energy barrier for the R = 1,1,4Et3 ligand is only 0.4 kcal mol−1 higher than that predicted for R = 1,1-Et2. However, when bulky ligands (R = 1,1,7,7-alkyl) are considered, the exchange of H by the alkyl group at the secondary amine leads to a sizable increase in the activation energy, approximately 4 kcal mol−1. Lastly, as for the few Rdien-H complexes, QSRR models are also proposed for the Rdien derivatives: ΔGcalcd = (82 ± 18) − (0.8 ± 0.2) (∠O−Au− a Cl) (r = 0.670; σ = 2; N = 13) (supermolecular approach) ΔGcalcd = (96 ± 9) − (0.9 ± 0.1) (∠O−Au−Cl) (r = 0.891; σ = a 1.5; N = 13) (isolated reactant species approach). The latter is more robust from a statistical point of view, although it is expected to overestimate the activation free energy, as shown for R-dien-H complexes. From these models, three distinct regions are identified, accounting for low reactivity complexes with at least four ethyl groups (∠O−Au−Cl < 65°), intermediate reactivity complexes with four methyl groups (65° < ∠O−Au−Cl < 69°), and high reactivity complexes with two or three alkyl groups (∠O−Au−Cl > 69°). Regardless of the predictive power of the QSRR proposed here, the reactivity angle proved to be a suitable molecular descriptor and can be used to design new ligands based on transition state structure.

insertion of an alkyl group at N4, which is approximately 4 kcal mol−1. This is much more pronounced than the increase observed for the pair 6/8 (0.4 kcal mol−1), suggesting that, for fully alkylated amines at the N1 and N7 positions, the substitution of a secondary amine at N4 might play a more important role on the reactivity of the complex. Finally, the structure/reactivity relationships are addressed for the whole series of the R-dien-gold complexes. The reactivity angle, ∠O−Au−Cl, is used as a molecular descriptor, which closely correlates with the activation enthalpy and free energy barrier. The results are plotted in Figure 7 for the supermolecular and isolated reactant species approaches, although the data are strongly dependent on the reactant complex in the former model. As discussed for the R-dien-H complexes (Figure 2), the overall reactivity of the R-dien compounds is also described by the reactivity angle, with activation free energy decreasing linearly with the ∠O−Au−Cl angle. The fitted lines in Figure 7 have similar slopes as also found for R-dien-H complexes (Figure 2), although the free energy barrier is slightly more sensitive (higher slopes) for the R-dien series of compounds. In Figure 7, it is clear that the three blocks of compounds are grouped according to their substitution pattern. In group 1, the less reactive complexes with four ethyl groups at N1 and N7 positions are included, where ∠O−Au−Cl < 65°. Group 2 contains the complexes with intermediate reactivity substituted by four methyl groups at N1 and N7 (65° < ∠O−Au−Cl < 69°), and group 3 includes those complexes with two or three alkyl groups, where the ∠O−Au−Cl angle is larger than 69°. For [Pd(R-dien)Cl]+ complexes, the experimental data for the hydration reaction are reported2 with the following reactivity order: dien > 7 > 9 > 13 ≈ 8 ≈ 10 > 14 > 12 ≈ 11, which differs from the predictions for gold complexes in the present study: 7 > 9 > 6 > dien ≈ 10−5 ≈ 8 > 14 > 11 > 13−12 (supermolecular approach) and 7 > 9 > 6 ≈ 5 > 8 ≈ dien > 13 > 14 > 11 > 10 > 12 (isolated reactant species approach). In spite of the these differences in reactivity ordering observed for [Pd(R-dien)Cl]+ and predicted for [Au(R-dien)Cl]2+ complexes, the overall trend is somehow maintained with the more reactive derivatives dien, 7, and 9 (group 3), intermediate reactive complexes 8, 10, and 13 (group 2) and less reactive compounds 11, 12 and 14 (group 1). Therefore, the results reported in this study can be used as a guide to design new ligands based on dien and dien-H parent ligands with bulky alkyl substituents. The relationships included in the present study for Au(III) complexes can be used as a predictive model for the activation free energy, mainly from the supermolecular approach, which values satisfactorily agree with experimental data for dien-H series of complexes.

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AUTHOR INFORMATION

Corresponding Author

*Fax: +553232293314. E-mail: [email protected]. Notes

■

The authors declare no competing financial interest.

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CONCLUSIONS The reactivity of 14 gold(III) complexes with the general formulas [Au(R-dien-H)Cl]+ and [Au(R-dien)Cl]2+, where R = ethyl and/or methyl, is predicted by modeling their hydration pathways. Experimental data are available for [Au(R-dienH)Cl]+ derivatives; these data are used to assess the computational models. For these complexes and the unsubstituted parent compound, [Au(dien-H)Cl]+, the absolute deviation in the Gibbs free energy barrier is less than 1 kcal mol−1, with the largest relative error found to be 7% for the bulkiest complex [Au(1,1,7,7-Et4-dien-H)Cl]+. For the R-dienH series, the activation free energy follows this order: 1,1,7,7Et4-dien-H (4) > 1,1,7,7-Me4-dien-H (2) > 1,1-Et2-dien-H (3) > 1,1-Me2-dien-H (1), which is consistent with the observed

ACKNOWLEDGMENTS H.D.S. and D.P. would like to thank the Brazilian agencies CNPq, CAPES, and FAPEMIG (ETC-00001-12) for financial support. J.V.B. is grateful to GACR project No P205/10/0228 and MSMT grant No. ME 10149 for supporting this project.

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REFERENCES

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