Pt(II) Uptake by Dendrimer Outer Pockets - American Chemical Society

Nov 8, 2007 - Francisco Tarazona-Vasquez and Perla B. Balbuena*. Department of Chemical Engineering, Texas A&M UniVersity, College Station, Texas ...
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J. Phys. Chem. B 2008, 112, 4172-4181

Pt(II) Uptake by Dendrimer Outer Pockets: 1. Solventless Ligand Exchange Reaction Francisco Tarazona-Vasquez and Perla B. Balbuena* Department of Chemical Engineering, Texas A&M UniVersity, College Station, Texas 77843 ReceiVed: August 1, 2007; In Final Form: NoVember 8, 2007

Density functional theory is used to elucidate molecular-level details of the complexation of Pt(II) metal compounds with PAMAM dendrimers. Particular attention is given to the ligand exchange reaction (LER). Binding of Pt(II) complexes to one dendrimer atom site (monodentate binding) is found to be thermodynamically feasible. Tertiary amine nitrogen (N3) is found to be the most favorable binding site in agreement with previous experimental work. Comparing the binding of Pt(II) species to atom sites in simple molecules with those to similar sites in dendrimer outer pockets allowed us to assess the impact of dendrimer branches on the binding. The impact of branches is manifested in more complex reaction profiles for complexation of Pt(II) species, because of the numerous ways in which a single molecule could be hosted by an outer dendrimer pocket. It is found that branches slightly improve the binding strength to all sites, particularly to N3. However, they could also be responsible for the increase of the activation energy for direct LER of PtCl42- and PtCl3(H2O)at the N3 site. Considering the thermodynamics of both complexation steps, namely noncovalent binding (NCB) and LER, it is found that to have a PtCl3- moiety bound to N3, as a result of NCB + LER operating on PtCl42-, is more likely than to have any other ion hosted in the outer pockets. However, the activation energy for direct LER of PtCl42- at the N3 site is found to be the largest among all Pt(II) metal complexes and even larger than the barrier to its own aquation yielding PtCl3(H2O)-.

1. Introduction Platinum is currently used in a wide range of industrial catalytic applications. Traditional catalyst preparation techniques like wet-impregnation have long sought to maximize BET surface areas, by minimizing the metal particle size, in order to optimize the conversion of reactants into products of the relevant chemical reactions, consequently reducing the impact of the expensiveness of the metal in the economy of the process. However, an increasingly smaller size of the metal particle makes it more susceptible to sintering and related phenomena;1,2 therefore, new synthesis methods have been developed and reported in the literature3 that tend to alleviate these problems. Dendrimer-templated synthesis is one such promising novel technique and purports the manufacture of stable metal nanoparticles with uniform size distribution.4 The resulting nanoparticles produced with this technique are being investigated as potential catalysts not only as encapsulated nanoparticles5,6 but also by depositing the nanocomposite on a support and removing the template.7 It is expected that understanding the complexation of metal precursors with the PAMAM template would be relevant for further studies of nanoparticle formation. Templated synthesis techniques involve the dendrimer as template (T), metal precursor (C-P; C, counterion and P, precursor), and water as solvent (S). Usually, two solutions are prepared, one where the PAMAM dendrimer is dissolved (T-S interactions are established) and another where a metal precursor is dissolved (P-S and C-S interactions are established). Upon mixing of these solutions, the possibility of having P-T and C-T interactions opens up. Therefore, metal precursor (P) as well as counterion (C) start to compete for displacing the solvent (S) out of the pockets. For a successful complexation, the P-T interactions need to be not only stronger than P-S and T-S * Corresponding author. E-mail: [email protected].

but also stronger than C-T. Potassium tetrachloroplatinate (K2PtCl4) has been by and large the metal precursor salt of choice in polyamidoamine (PAMAM) dendrimer-templated synthesis.8-10 This complexation has been observed to be relatively slow.11 We can suggest a priori at least three factors that would explain why PtCl42- is slow for complexation with PAMAM dendrimers: first, slow diffusion of PtCl42- compared with low molecular weight anions, for instance, Cl- can diffuse three times faster than PtCl42-,12,13 second, the similar affinity of PtCl42- and competing ions proceeding from salt dissolution (K+, Cl-) for the dendrimer pockets,14 and third, configurational changes in the dendrimer associated with the uptake of PtCl42and other ions, for instance, species residing in the outer pocket determine the pocket amide O orientation.14 Most of the experimental work to date has been mainly devoted to elucidating a few aspects of the ligand substitution reaction, also called ligand exchange reaction (LER). For instance, XPS experiments determined a Pt/Cl ratio of 1:3 after complexation of K2PtCl4 with the PAMAM dendrimer, suggesting then that the LER occurred.15 Later NMR experiments not only suggested a monodentate binding but also bi- and tridentate binding of Pt(II) to nitrogen atom sites in the dendrimer.11 Finally, recent EXAFS experiments suggested the presence not only of nitrogen atoms but also oxygen atoms in the first coordination shell of the Pt(II) ion.7 As it is important to understand how the complexation of PtCl42- takes place, we focus our attention on studying the thermodynamic and kinetic aspects of the LER. Particularly, we analyze the solventless LER of the tetrachloroplatinate anion and its mono- and diaquated Pt metal species (II). We expect our computational approach to be a helpful contribution to the understanding of the binding of Pt(II) species to dendrimer sites, thus providing molecular-level insights into the complexation of such species that are not readily accessible to experimental

10.1021/jp0761517 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/15/2008

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SCHEME 1: Model Fragments of Pamam Dendrimer Regions Used in This Worka

a (A) Tri-methylamine; (B) methyl acetamide; (C) methanol; (D) DF27: single branch; (E) DF41: outer pocket. DF stands for dendrimer fragment and the two-digit number indicates the number of atoms that composes the fragment.

techniques. After a brief discussion of models and computational procedures in section 2, we present our results and discuss them in section 3. This section starts with a discussion on the feasibility of binding PtCl42- to a number of dendrimer atom sites (section 3.1). Then the analysis is extended to mono- and diaquated complexes of PtCl42- as they bind to the most favorable dendrimer atom binding site (section 3.2). Conclusions are given in section 4. 2. Models and Computational Procedure As the precursor molecule diffuses through the solvent toward the dendrimer, it is reasonable to assume that it will first reach and interact with the dendrimer outer regions. It is also reasonable to assume that the larger the dendrimer, the more spherical it will become, particularly for generations greater or equal than 4,16,17 and therefore the more likely for the outer regions to look similar to their adjacent ones. If the dendrimer is large and spherical, then the dendrimer-precursor interactions are most likely to be local, at least in their initial stages, because the intersection of a sphere and a plane (of the square planar complex) is at least a point and because of the relatively small size of the precursor molecules when compared to the dendrimer size. Thus, the localized nature of the interactions would render unnecessary the modeling of a complete dendrimer justifying the use of fragments to study such interactions. The interaction between large generation dendrimers and water can be modeled by classical molecular dynamics simulations.18,19 However due to the extensive sampling required, classical MD simulations cannot be used to accurately model the binding of multiple ions/anions/water.20 Moreover, if the goal is to model chemical reactions, such as the ligand exchange reaction, force field allowing bond breaking and forming would be needed. On the other hand, QM methods allow for modeling of chemical reactions but cannot handle large systems, and this is another reason why fragment models were used in this work. Molecules such as trimethylamine, n-methyl acetamide, and methanol (Scheme 1) are used to model the binding sites in its simplest way in a branchless environment. We also modeled a dendrimer branch with a 27-atom fragment (DF27) and an outer pocket with a 41-atom dendrimer fragment (DF41). The outer pocket fragment (DF41) consists of two dendrimer branches stemming out from a tertiary amine nitrogen (N3) and terminated

in -OH group. One of those branches including the tertiary amine nitrogen site makes up the single branch model (DF27). Although we have used both single branches as well as single molecule models in sections 3.1 and 3.2.2, in the subsequent sections, we used 41-atom two-branch models to describe dendrimer outer regions (“pockets” hereafter) and to calculate the strength of their interactions with metal precursors, solvent, and counterions, extending our previous work.14 There are at least two facts that underscore the inadequacy of the choice of adding a continuum medium to the systems in Scheme 1. First, the outer pocket is not an independent entity but is rather surrounded by other branches and pockets; and second, the outer pocket is able to accept water through the space permitted by the relative distance between its -OH groups. Putting both facts together, it is reasonable to assume that outer pockets locate in the middle of an environment of heterogeneous rather than homogeneous dielectric constant, thus discouraging the use of a continuum to treat the solvent effect. Density functional theory (DFT) was used to optimize minimum energy as well as transition state (TS) structures relevant to the systems studied in the present work with no symmetry constraints. TS structures were located by either running the Berny optimization21 to a saddle point, traditional TS search, or using the synchronous transit-guided quasi Newton (STQN) TS optimization method22 or both. The activation energy (Ea) is defined as the difference in entalphy of the relevant states. The calculations were done with Gaussian 0323 suite of programs. The B3LYP hybrid flavor of DFT along with Hay and Wadt pseudopotentials24 for Pt and 6-31+g(d) basis set for all other atoms were chosen. Validation of the method and basis set has been reported previously.20 The optimization of the geometries was followed by second derivative matrix calculations and the resulting vibrational analysis provided estimates for the zero point energy and temperature corrections to the entalphy and Gibbs free energy at 298 K within the harmonic approximation. 3. Results 3.1. Search for the Most Favorable Binding Site for Complexation of Tetrachloroplatinate Anion (PtCl42-). Binding of Pt(II) to both tertiary amine N (N3) and secondary amide N (N2) in PAMAM dendrimers11 and to secondary amide O25

4174 J. Phys. Chem. B, Vol. 112, No. 14, 2008 SCHEME 2: Profile for the Reaction of Fragment and PtCl42- According to eq 1a

Tarazona-Vasquez and Balbuena TABLE 1: ∆G of Reaction for the Overall Complexation of PtCl42- with Molecular Fragments According to eq 1a model

site

fragment

∆G

single site molecule

N3 N2 OH O N3 N2 OH O N3 N2 OH O

N(CH3)3 CH3-CO-NH-CH3 CH3OH CH3-CO-NH-CH3 DF27 DF27 DF27 DF27 DF41 DF41 DF41 DF41

-51.1 -48.4 -48.0 -40.7 -56.3 -48.8 -49.0 -39.4 -60.0 -53.9 -54.8 -48.9

single branch

outer pocket a (A) Fragment + PtCl42- are separated; (B) fragment and PtCl42interact through NCB resulting in fragment-PtCl42- (structure I1); (C) transition state structure for fragment-PtCl42- (structure TS1); (D) fragment-PtCl3-Cl- (structure I2); (E) fragment-PtCl3- + Cl- are separated either endotermically or exotermically.

(O) and to hydroxyl O26 (OH) in other compounds has been suggested by experimental work. Therefore several structures (for selected geometric parameters, see Table A, Supporting Information) of the form fragment-PtCl3- where a Cl- ligand has been replaced by a dendrimer atom site (N3, N2, O, and OH) were calculated. Solventless complexation of PtCl42- leading to the LER product structures (D in Scheme 2) follows three steps. First step is a NCB reaction (process A f B), the second step is a LER (process B f D), and the third step can be the release of Cl- (process D f E) which can be either endo- or exotermic. The overall complexation process represented by eq 1 is A f E (Scheme 2)

fragment + PtCl42- w fragment-[PtCl3-] + Cl- (1) The reference needed to understand how the dendrimer branches affect binding between metal precursor (P) and template (T) is provided by simple molecules such as N(CH3)3, n-methylacetamide, and methanol (Scheme 1) used as single site models to test binding to sites N3, N2, and OT, respectively, in the absence of branches. Although Scheme 2 depicts a TS structure between I1 and I2, no TS search was performed and neither was the solvent effect considered in this section, but the scheme is presented here to illustrate the general procedure followed in other sections. This thermodynamic analysis approach ought to be understood as a test to find out the most favorable site for the complexation of PtCl42- and is meant to be qualitative rather than quantitative. ∆G values for the overall complexation of PtCl42- described by eq 1 are presented in Table 1. The order of binding is not consistent across a variety of fragments. From Table 1 it can be seen that N3 > N2 > OH > O for single sites whereas that order changes to N3 > OH > N2 > O when the larger fragments (DF27 and DF41) are used. Nonetheless, the difference between the ∆G for the binding to N2 and binding to OH is not significant (less than 1 kcal/mol), thus it can be affirmed that binding to N2 is as feasible as binding to OH. From all four sites tested, it is clear that complexation of Pt(II) to amide O is the least likely type of binding. These calculations point out that monodentate binding of Pt(II) to the dendrimer is feasible, in accord with experimental work,11,15,27 and that it is more likely to have Pt(II) binding preferentially to N3, also in agreement with experimental results.11,27 Our results also suggest that branches enhance the binding of PtCl42- to all sites and to tertiary amine N (N3) in particular.

a Dendrimer atom sites: tertiary amine N (N3), secondary amide N (N2), amide O (O), hydroxyl O (OH). Values in kcal/mol.

TABLE 2: ∆G of Reaction and Activation Energies (Ea), in kcal/mol, for the LER between Pt(II) Complexes and the Tertiary Amine Site (N3) of N(CH3)3 According to eq 2a species 2-b

PtCl4 PtCl3(H2O)cis-PtCl2(H2O)2 trans-PtCl2(H2O)2 b

Ea (∆H)

∆GI2-I1

20.5 16.6 21.6 25.6

-55.3 -5.9 -8.0 -6.4

a Ea) ∆HTS-I1 (see Scheme 2 for nomenclature: I1, TS, and I2). ∆EI2-I1 ) E(N(CH3)3-PtCl3-) + E(Cl-) - E(N(CH3)3-PtCl42-).

For instance, binding to N3 is improved in -9.0 kcal/mol (for details, see Supporting information, Table B) when switching from a single molecule (single site model) to an outer pocket environment (modeled with the DF41 fragment). 3.2. Search for the Most Likely Precursor when N3 Is the Binding Site. Having observed that the tertiary amine site (N3) is the most favorable site for binding, we extend the thermodynamical analysis of section 3.1 to mono- and diaquated complexes of PtCl42-. Calculated TS structures and activation energies are analyzed to assess the kinetic effect. The N3 site is modeled with a single site (N(CH3)3) in section 3.2.1 and with a DF41 fragment in section 3.2.2, enabling us to evaluate the effect of branches on the activation energies. 3.2.1. LER of Pt(II) Complexes with N(CH3)3. The LER step of the complexation of Pt(II) complexes to N(CH3)3 is given by the following equation:

[N(CH3)3-PtCx′Dy′] (I1) f TS f [N(CH3)3PtCx-1′Dy′-C′] (I2) (2) where PtCx′Dy′ represents PtCl42- and its mono- and di-aquated complexes and C′ is the leaving ligand. The free energy change involved with the release of Cl- is included in the ∆G value of -55.3 kcal/mol (Table 2) because a LER structure (I2) for PtCl42- could not be found (for selected geometric parameters see Table C, Supporting Information). For the other three complexes, their calculated free energies of reaction are not significantly different. Therefore, regarding only these three species, it can be said that complexation is most likely to be kinetically rather than thermodynamically controlled. The lowest activation energy (Ea) found for PtCl3(H2O)suggests that the reaction (eq 2) will be easier to perform with PtCl3(H2O)-. 3.2.2. LER of Pt(II) Complexes with DF41. Modeling the tertiary amine site (N3) with DF41 is more challenging than modeling a single site molecule like N(CH3)3, because of the larger number of atoms resulting in a number of isomeric

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SCHEME 3: Reaction Profile for the Reaction of Dendrimer Fragment and PtCx′Dy′ According to eqs 3 and 4a

a (A) DF41-H2O + PtCx′Dy′ are separated; (B) DF41-H2O and PtCx′Dy′ interact in various ways resulting in an array of DF41-PtCx′Dy′ configurations. The configuration of lowest energy is termed LECRs whereas the configuration that leads to the transition state structure (TS1) is termed I1. These two structures may or may not be the same; (C) TS structure for DF41-PtCx′Dy′ (structure TS1); (D) DF40-N3PtCx-1′Dy′-C’. The configuration of lowest energy is termed LECPs whereas the configuration following from the transition state structure (TS1) is termed I2. These two structures may or may not be the same; (E) DF40-N3-PtCx-1′Dy′ + C′ are separated. Note: this is a simplified and generic representation of a reaction profile when DF41 is involved. See text and next schemes for specific reaction profiles.

configurations on both the reactants (for a collection of snapshots of DF41-PtCx′Dy′ structures, see Tables D-G, Supporting Information) and in the products side (see Scheme 3), thus making difficult the tracing of the reaction profile. We also calculated ∆GLER(overall) defined as the difference in free energy in passing from LECRs to LECPs (lowest energy configurations of reactants and products) which differs from the ∆GLER (∆GI2-I1) previously used (see caption to Scheme 3). The relevant equations for this process are

NCB: [DF41-H2O] + PtCx′Dy′ f [DF41-PtCx′Dy′] + H2O (3) LER: [DF41-PtCx′Dy′] + H2O f [DF41-PtCx-1′Dy′] + [C′-H2O] (4) where PtCx′Dy′ represents the Pt(II) complexes and C′ the leaving ligand. The NCB reaction energies according to eq 3 as well as the geometric parameters of DF41-PtCx′Dy′ structures (LECRs, I1, and others) are provided as Supporting Information (for selected geometric parameters, see Table H, Supporting Information). What follows is a description of the LER part of the complexation between DF41 and each of the four Pt(II) complexes studied here. Although numerous reaction profiles could be traced, we have attempted to describe at least one starting from the lowest energy configuration of DF41-PtCx′Dy′ (LECRs) all the way down to the lowest energy configuration in the LER products side (LECPs). Yet the calculation of the full reaction profile (all the intermediates and TS structures) has not been possible for some Pt(II) complexes due to its complexity. Nonetheless, the TS between I1 and I2 was calculated for all cases (for selected geometric parameters, see Table 1, Supporting Information). 3.2.2.1. LER Profile when the Pt(II) Complex is PtCl42-. A TS structure was calculated with Berny optimization of a trigonal-bipyramidal-like TS structure.28 I1 and I2 structures were obtained by optimization of initial configurations set up by subtracting or adding a fraction of the imaginary frequency

Figure 1. DF41-fragment-[PtCl3-] structures corresponding to products of eq 1. Upper left: DF40-N3-PtCl3-; Upper right: DF40N2-PtCl3-. Although these structures are thermodynamically viable according to our calculations, they are only a first approximation of what the real case in outer pockets look like, where solvent is likely to interact with the pocket and the Pt(II) complex.

displacement vector from the TS atomic coordinates, respectively. Also, we noticed first that I1 but not I2 was derived directly from TS because no displacement leading to a branch rotation is found in the TS displacement vector in the forward direction and, second, that no stable intermediates could be found either between I1 and TS or between TS and I2. Therefore, Ea and ∆GI2-I1 were calculated to be +27.5 and -4.7 kcal/mol, respectively. Also, a few insights are gained. First, that the rotation of a branch is necessary to minimize the repulsion between PtCl3- and Cl- in the product structure (I2), and elsewhere we show that such repulsion could require the presence of explicit solvent in order to be minimized. 3.2.2.2. LER Profile when the Pt(II) Complex is PtCl3(H2O)-. PtCl3(H2O)- reacts through a number of steps described by the following equations starting with the NCB product DF41-PtCl3(H2O)- (I1B) that is obtained, according to eq 3, with a ∆GNCB ) -7.7 kcal/mol. Step 1: Accommodation of PtCl3(H2O)- inside the pocket. The reactant (I1B) and product (I1F) are represented in Scheme 4.

DF41-PtCl3(H2O)- (I1B) w DF41-PtCl3(H2O)- (I1F) Ea and ∆GI1F-I1B are 12.1 and 3.8 kcal/mol, respectively. During this step a N3-H2O-Pt hydrogen bond (length ) 1.67 Å) is broken and another ∼CdOsH2OsPt hydrogen bond (length ) 1.73 Å) is formed. The orientation of the amide O atoms in the pocket changes from outward-outward (I1B) to outwardinward (I1F). Step 2: LER: Pt(II) binds to N3. The reactant (I1F) and product (I2) are represented in Scheme 4.

DF41-PtCl3(H2O)- (I1F) w DF40-N3-PtCl3-(H2O) (I2) Ea and ∆GI2-I1F are +20.5 and -3.3 kcal/mol, respectively. Once this step is complete, the leaving ligand (H2O) forms a ∼CdOsHOH hydrogen-bond of length 1.91 Å. The orientation of the amide O atoms in the pocket changes back to outwardoutward. Step 3: Re-accommodation of water inside pocket (leading to LECPs). The reactant (I2) and product (LECPs) are represented in Scheme 4.

DF40-N3-PtCl3--(H2O) (I2) w DF40-N3-PtCl3-(H2O) (LECPs)

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Tarazona-Vasquez and Balbuena

Figure 2. Binding to tertiary amine (N3): Left: I1; middle: TS; right: I2: The leaving ligand, Cl-, interacts with the secondary amide hydrogen (N2-H-Cl: 2.29 Å) and with the hydroxyl hydrogen (∼O-H-Cl: 2.14 Å) of the open branch.

Figure 3. Reaction profile for solventless reaction: DF41-H2O + PtCl3(H2O)- w DF40-N-PtCl3- + (H2O)2.

Figure 5. Reaction profile for the solventless reaction: DF41-H2O + cis-PtCl2(H2O)2 w DF40-N3-cis-PtCl2(H2O) + (H2O)2.

next step (not shown), ligand release, is not thermodynamically favorable (∆G ) 2.5 kcal/mol). However LERoverall + ligand release is still favorable (∆G ) -1.0 kcal/mol). Figures 3 and 4 illustrate the reaction energy profile and the evolution of the main distances of this process. 3.2.2.3. LER Profile when the Pt(II) Complex is cis-PtCl2(H2O)2. Solventless LER of cis-PtCl2(H2O)2 takes place according to the following steps starting with the NCB product DF41- cis-PtCl2(H2O)2 (I1) that is obtained, according to eq 3, with a ∆GNCB ) -5.2 kcal/mol. Step 1: LER: Pt(II) binds to N3. The reactant (I1) and product (I2) are represented in Scheme 5.

Figure 4. Evolution of bond distances Pt-N(entering ligand) and Pt-O (leaving ligand) along the course of the solventless LER: DF41-PtCl3(H2O)- w DF40-N3-PtCl3--(H2O).

TABLE 3: Difference in Electronic Energy with Zero-Point Energy Correction (∆E0), Enthalpy (∆H), and Gibbs Free Energy (∆G) Relative to Energetics of DF41-H2O + PtCl3(H2O)- (E(DF41-H2O) + E(PtCl3(H2O)-) ) 0.0 kcal/mol) for Stationary Points along the Reaction Profile of the Solventless Complexation: DF41-H2O + PtCl3(H2O)- w DF40-N3-PtCl3- + (H2O)2a stationary point

∆E0

∆H

∆G

I1B (LECRs) TSA I1F TS1 I2 LECPs I3 (separated products)

-11.7 0.1 -6.9 13.9 -11.8 -15.6 -9.7

-10.9 1.3 -5.9 14.7 -11.0 -14.5 -8.8

-7.7 1.8 -3.8 19.1 -7.2 -11.2 -8.7

a

Values in kcal/mol.

∆G for this step is -4.0 kcal/mol. No TS structure was calculated in between stationary points and taking the three first steps above together yield a ∆GLER(overall) ) -3.5 kcal/mol. The

DF41-cis-PtCl2(H2O)2 (I1) w DF40-N3-cis-PtCl2(H2O)-(H2O) (I2) Ea and ∆GI2-I1 are +21.1 and -9.9 kcal/mol, respectively. Three hydrogen bonds keep cis-PtCl2(H2O)2 bound to the dendrimer pocket. But once the reaction is complete, the ∼N3-HOH hydrogen bond of length 1.61 Å is broken. The leaving ligand H2O forms another (∼NH-OH2) hydrogen bond of length 1.89 Å. The next two steps involve accommodation of the cis-PtCl2(H2O) moiety inside the pocket. Step 2: Breaking of ∼Pt-OH2-(OH)∼ hydrogen bond. The reactant (I2) and product (I3) are represented in Scheme 5. One of the two original hydrogen bonds (∼Pt-OH2-(OH)∼ of bond length ) 1.67 Å) in configuration I1 is broken but a weaker hydrogen bond (∼PtsOH2sOdC∼ of bond length 1.83 Å) is formed. This may explain why ∆GI3-I2 is 3.6 kcal/mol and Ea is 5.1 kcal/mol. Step 3: Breaking of ∼OHsOdC∼ hydrogen bond. The reactant (I3) and product (I4) are represented in Scheme 5. Upon reaction, the hydrogen bond ∼OHsOdC∼ (bond length ) 1.88 Å) is broken. Then, the hydroxyl terminal group (OH) binds to the cis-PtCl2(H2O) moiety (∼OH-Cl bond

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SCHEME 4: Stable Points along the Solventless LER: DF41-PtCl3(H2O)- w DF40-N3-PtCl3--(H2O)

SCHEME 5: Stable Points along the Solventless LER: DF41-cis-PtCl2(H2O)2 w DF40-N3-cis-PtCl2(H2O)-(H2O)

distance ) 2.31 Å). Ea and ∆GI4-I3 are +1.3 and -0.47 kcal/ mol, respectively. Without considering the last two steps in the reaction profile, ∆GLER ) -9.9 kcal/mol. The next step, ligand release (∆GI5-I4 summed up with ∆GI3-I2 and ∆GI4-I3) is not thermodynamically favorable (∆G ) 5.7 kcal/mol). However LERoverall + ligand release is still favorable (∆G ) -4.2 kcal/mol). Figures 5 and 6 illustrate the reaction energy profile and the evolution of the main distances of this process.

3.2.2.4. LER profile when the Pt(II) complex is trans-PtCl2(H2O)2. Solventless LER of trans-PtCl2(H2O)2 takes place according to the following steps starting with the NCB product DF41-trans-PtCl2(H2O)2 (I1) that is obtained with a ∆GNCB ) -7.7 kcal/mol. Step 1: Accommodation of trans-PtCl2(H2O)2 inside pocket. The reactant (B) and product (Z) are represented in Scheme 6. Ea and ∆GZ-B are 2.5 and 4.6 kcal/mol, respectively. During this step, a branch rotates to better accommodate trans-PtCl2-

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Tarazona-Vasquez and Balbuena TABLE 4: Difference in Electronic Energy with Zero-Point Energy Correction (∆E0), Enthalpy (∆H), and Gibbs Free Energy (∆G) Relative to Energetics of DF41-H2O + cis-PtCl2(H2O)2 (E(DF41-H2O) + E(cis-PtCl2(H2O)2) ) 0.0 kcal/mol) for Stationary Points along the Reaction Profile of the Solventless Complexation: DF41-H2O + cis-PtCl2(H2O)2 w DF40-N3-cis-PtCl2(H2O) + (H2O)2a

Figure 6. Evolution of bond distances Pt-N(entering ligand) and Pt-O (leaving ligand) along the course of the solventless LER: DF41-cisPtCl2(H2O)2 w DF40-N3-cis-PtCl2(H2O)-(H2O).

stationary point

∆E0

∆H

∆G

I1 TS1 I2 TS2 I3 TS3 I4 I5 (separated products)

-10.1 10.8 -20.9 -15.6 -16.7 -15.2 -17.7 -12.1

-10.1 11.0 -20.8 -15.7 -16.4 -15.1 -17.3 -11.8

-5.2 15.4 -15.1 -9.2 -11.5 -9.1 -12.0 -9.4

a

Values in kcal/mol.

TABLE 5: Difference in Electronic Energy with Zero-Point Energy Correction (∆E0), Enthalpy (∆H), and Gibbs Free Energy (∆G) Relative to Energetics of DF41-H2O + trans-PtCl2(H2O)2 (E(DF41-H2O) + E(trans-PtCl2(H2O)2) ) 0.0 kcal/mol) for Stationary Points along the Reaction Profile of the Solventless Complexation: DF41-H2O + trans-PtCl2(H2O)2 w DF40-N3-trans-PtCl2(H2O) + (H2O)2a

Figure 7. Reaction profile for the solventless reaction: DF41-H2O + trans-PtCl2(H2O)2 w DF40-N3-trans-PtCl2(H2O) + (H2O)2.

stationary point

∆E0

∆H

∆G

B TSA Z TSB I1 TS I2 I3 I4 I5 I6 (separated products)

-11.8 -9.3 -6.4 2.5 -1.1 17.7 -9.8 -11.6 -13.0 -15.5 -13.4

-11.1 -8.6 -5.7 3.3 0.0 18.3 -8.4 -10.5 -12.1 -14.8 -13.5

-7.7 -6.1 -3.1 5.3 1.0 23.3 -6.7 -7.2 -8.9 -10.7 -9.2

a

Values in kcal/mol.

The reactant (I1) and product (I2) are represented in Scheme 6.

DF41-trans-PtCl2(H2O)2 w DF40-N3-trans-PtCl2(H2O)-(H2O)

Figure 8. Evolution of bond distances Pt-N(entering ligand) and Pt-O (leaving ligand) along the course of the solventless LER: DF41-transPtCl2(H2O)2 w DF40-N3-trans-PtCl2(H2O)-(H2O). Evolution of PtO(DF41) is also followed. Note: Pt-O(DF41) is the distance between Pt atom and an amide O. See text for details.

(H2O)2. This is achieved by forming a PtsOH2sOdC∼ hydrogen bond (bond length ) 1.75 Å) in addition to the existent PtsOH2s(OH)∼ (bond length ) 2.13 Å). It should be noticed also that in the product the tertiary amine site (N3) is no longer protonated. Step 2: Breaking of N3-H2O-Pt hydrogen-bond. The reactant (Z) and product (I1) are represented in Scheme 6. Ea and ∆GI1-Z are 9.0 and 4.1 kcal/mol, respectively. During this step, the water bound to N3 rotates, thus breaking the N3H2O-Pt hydrogen bond (bond length ) 1.56 Å). Step 3: LER. Pt(II) binds to N3.

Ea and ∆GI2-I1 are +18.3 and -7.7 kcal/mol. The PtsOH2s OdC∼ hydrogen bond formed in step 1 is broken. Step 4: Accommodation of water inside the pocket. The reactant (I2) and product (I3) are represented in Scheme 6. No TS structure was sought. ∆GI3-I2 is -0.54 kcal/mol. A ∼NH-OH2 hydrogen bond is formed (bond length ) 2.03 Å). Step 5: Accommodation of water inside the pocket. The reactant (I3) and product (I4) are represented in Scheme 6. No TS structure was sought. ∆GI3-I2 is -1.7 kcal/mol. The ∼NH-OH2 hydrogen bond formed in step 4 shortens a bit (bond length ) 1.96 Å). Step 6: Accommodation of water inside the pocket. The reactant (I4) and product (I5) are represented in Scheme 6. No TS structure was sought. ∆GI3-I2 is -1.8 kcal/mol. The ∼NH-OH2 hydrogen bond formed in step 4 shortens a bit further (bond length ) 1.92 Å). One of the dendrimer pocket branches rotate forming an internal ∼CdOsOH∼ bond of 1.86 Å. Considering all of the steps (from LECRs to LECPs), ∆GLER(overall) ) -3.0 kcal/mol. The next step, ligand release, is not thermodynamically favorable (∆G ) 1.5 kcal/mol). However LERoverall + ligand release is still favorable (∆G ) -1.5 kcal/

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J. Phys. Chem. B, Vol. 112, No. 14, 2008 4179

SCHEME 6: Stable Points along the Solventless LER: DF41-trans-PtCl2(H2O)2 w DF40-N3-trans-PtCl2(H2O)-(H2O)

mol). Figures 7 and 8 illustrate the reaction energy profile and the evolution of the main distances of this process. The NCB order of binding (PtCl42- > PtCl3(H2O)- ∼ transPtCl2(H2O)2 > cis-PtCl2(H2O)2 follows somewhat the trend in electrostatic charge of the Pt(II) complexes. Cl- is released upon LER of PtCl42-, whereas when its mono- and diaquated complexes undergo LER, H2O is released. The ∆GLER (∆GI2-I1) order of binding (cis-PtCl2(H2O)2 > trans-PtCl2(H2O)2 > PtCl42- > PtCl3(H2O)-) seems to suggest that diaquated Pt(II) species (uncharged molecules) are more ready to exchange their ligand (water) for N3, although there is no favorable tendency to let it go away in the pocket (as ligand release energies are positive). The ∆GLER(overall) order of binding coincides with ∆GLER only when I1 is the LECRs. This is not the case for

PtCl3(H2O)- or for trans-PtCl2(H2O)2. Therefore it should be easier in principle for cis-PtCl2(H2O)2 and PtCl42- to undergo LER. However, other factors should be considered too. For instance, Table 7 shows that the activation energies increase due to the presence of branches when either PtCl42- or PtCl3(H2O)- react directly with the N3 site. This seems to cast doubts on whether PtCl42- really binds directly to N3 or not, especially because the barrier for its aquation to PtCl3(H2O)(23.7 kcal/mol) is lower than the barrier for direct LER (27.5 kcal/mol). Table 7 also shows that the activation energy remains high toward binding to N3 in the presence of branches for cis-PtCl2(H2O)2 (from 21.6 to 21.1 kcal/mol). This fact together with its

4180 J. Phys. Chem. B, Vol. 112, No. 14, 2008

Tarazona-Vasquez and Balbuena

TABLE 6: ∆G of Reaction for the Individual Processes of the Complexation between Pt(II) Compounds and the Tertiary Amine Site (N3) of DF41 According to DF41-PtCx′Dy′ w DF40-N-PtCx-1′Dy′-Cx′a species (PtCx′Dy′) process

PtCl42-

PtCl3(H2O)-

cis-PtCl2(H2O)2

trans-PtCl2(H2O)2

LECRs to I1 I1 to I2 (LER) I2 to LECPs LECRs to LECPs (LERoverall) ligand release (lr) LERoverall + lr total (NCB + LERoverall + lr)

-33.2 0.0 -4.7 0.0 -4.7 -31.0 -35.7 -68.9

-7.7 3.8 -3.3 -4.0 -3.5 2.5 -1.0 -11.2c

-5.2 0.0 -9.9 0.0 -9.9 5.7 -4.2 -15.1c

-7.7 8.7 -7.7 -4.0 -3.0 1.5 -1.5 -10.7c

NCBb

a See Schemes 4-6 for nomenclature. Values in kcal/mol. b NCB yields DF41-X, product of the following reaction: DF41-H2O + X f DF41-X + H2O. c These values do not include the ligand release (lr) energy.

TABLE 7: Activation Energies (Ea) Given as ∆HTS-I1 in Absence and Presence of Branches

species

Ea no branches N(CH3)3

Ea branches (DF41)

Ea PtCl42aquation

PtCl42PtCl3(H2O)cis-PtCl2(H2O)2 trans-PtCl2(H2O)2

20.5 16.6 21.6 25.6

27.5 20.5 21.1 18.3

23.7a 16.6/29.9

a

Experimental value: 21.0 kcal/mol.29

weak NCB energy (-5.2 kcal/mol) suggest that this Pt(II) complex may not be able to directly bind to N3. Table 7 also shows a reduction of about 7.3 kcal/mol in the activation energy when trans-PtCl2(H2O)2 binds to N3 in outer pocket environments with respect to N(CH3)3. However there are other factors to weigh here. First, its NCB free energy is weak (-7.7 kcal/mol); second, trans-PtCl2(H2O)2 is not as readily available as other Pt(II) complexes would be because it can only appear once the large activation energy (29.9 kcal/ mol) for the second aquation of PtCl42- toward trans-PtCl2(H2O)2 is overcome; third, its I1 structure can only be reached once the two kinetic barriers (Section 3.2.2.4) of thermodynamically unfeasible elementary reactions are overcome. From Table 7 it is observed also that when Pt(II) complexes bind to the N3 site of an outer pocket (DF41) Ea follows the trend -from greater to least: PtCl42- > cis-PtCl2(H2O)2 > PtCl3(H2O)- > trans-PtCl2(H2O)2. From this trend, we realize that PtCl3(H2O)- has the second lowest Ea. On the other hand, we noticed that PtCl3(H2O)- can be obtained from the first aquation of PtCl42-, a process with lower Ea than direct LER of PtCl42- to N3 in DF41 as annotated before. In fact, geometry analysis shows that the Pt-N3 distance in I1 is 3.93 Å for PtCl3(H2O)- (5.60 Å when facing PtCl42-) when binding to N(CH3)3. (Values taken from Table C, Supporting Information.) However there is no significant difference in the Pt-N3 distance between PtCl42- (5.72 Å) and PtCl3(H2O)- (5.70 Å) when binding to DF41 occurs. (Values taken from Table 1, Supporting Information.) Other factors are a barrier of 12.1 kcal/mol needs to be overcome in order to arrive at the I1 structure and the barrier to aquate PtCl3(H2O)- to cis-PtCl2(H2O)2 is lower (16.6 kcal/mol) than that needed to overcome for binding of Pt(II) to N3 (20.5 kcal/mol) making depletion of PtCl3(H2O)- to form cis-PtCl2(H2O)2 more likely. Finally, we have to account for the presence of counterions. Unlike PtCl42- and its aquated complexes, they will not undergo LER. However they can occupy the dendrimer pockets and compete with the Pt(II) complexes as reported in a previous study.14 It is observed that the highest NCB free energy of a counterion binding a DF41 pocket (∆G ) -62.3 kcal/mol; see

Appendix) is lower than the NCB + LER free energy to bind PtCl42- to N3 site (∆G ) -68.9 kcal/mol). This is true only for PtCl42- and not for the mono- and diaquated complexes. Therefore, thermodynamics suggests that the free energy made available by direct LER of mono- and diaquated complexes of PtCl42- preceded by NCB binding is not enough to overcome the competition of other ions for the outer pockets (DF41). Besides, as mentioned before, we do not know whether PtCl42reacts directly with the N3 site or not. But if PtCl42- is aquated inside the pockets, then its aquated species can react with N3. 4. Conclusions Given that a LER between a dendrimer pocket and a given Pt(II) species is preceded by uptake of such species into the outer pockets,14 in this work we have explored the feasibility of LER in these systems and provided some insights into the corresponding structures and reactions. We found that Pt(II) is most likely to bind to tertiary amine N (N3) than to alternative binding sites (N2, OH, amide O). This is in agreement with experimental results.11,15,27 Our study also indicates that it is more likely to observe PtCl42- bound to a tertiary amine N (N3) than to observe competitor counterions encapsulated within pockets. However, it is more likely to have counterions encapsulated within a pocket than to have mono- and diaquated Pt(II) species formed outside outer pockets, bound to a tertiary amine N (N3) site. Yet, it is not clear whether PtCl42- is the precursor species because the energy barrier for the direct ligand exchange reaction (LER) of PtCl42- to N3 is higher than that for its aquation to PtCl3(H2O)-. We also found that the energy barrier for the direct LER of PtCl3(H2O)- is lower than that of the aquation of PtCl42-, and as mentioned above, PtCl3(H2O)- is not likely to bind to N3 when it forms outside pockets. However aquation of PtCl42may take place inside the pocket instead, thus a pathway of less resistance could be aided by the solvent suggesting further studies of the solvent effect to assess its impact on the LER. Our findings parallel somewhat what has been found in recent experimental work27 regarding complexation of Pt(II) and Pd(II) to dendrimers, where it was found that Pd(II) coordinates to the N3 dendrimer site and suggested PdCl3(H2O)- to be the precursor species. No similar findings were reported for Pt(II)dendrimer systems to the best of our knowledge. Finally, comparison of Pt(II) species complexation to N3 in both a single site molecule and an unprotonated outer pocket indicates that the branches of outer pockets improve slightly the thermodynamic stability of binding Pt(II) to all sites particularly in N3 but at the expense of increasing the kinetic barrier toward LER for some Pt(II) complexes like PtCl42- and PtCl3(H2O)-.

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J. Phys. Chem. B, Vol. 112, No. 14, 2008 4181

Acknowledgment. This work was partially supported by the National Science Foundation Grant CTS-0103135 and by the Department of Energy Grant DE-FG02-05ER15729. Supercomputer time granted by the National Energy Research Scientific Computing Center (NERSC) and by the DoD Major Shared Resource Centers (ARL MSRC and ASC MSRC) is gratefully acknowledged. Appendix A Electronic energy with zero point energy correction (∆E0), enthalpy (∆H), and Gibbs free energy (∆G) for NCB reaction: DF41-(H2O) + B f DF41-B + H2O

species B

∆E0

∆H

∆G

K+ K-(H2O)+ K-(H2O)2+ ClOHPtCl42PtCl3(H2O)cis-PtCl2(H2O)2 trans-PtCl2(H2O)2

-36.1 -39.9 -34.6 -31.6 -62.8 -36.1 -11.6 -10.1 -11.8

-34.1 -39.4 -34.4 -30.6 -63.2 -34.9 -10.8 -10.1 -11.1

-40.5 -37.4 -31.0 -36.2 -62.3 -33.2 -7.7 -5.2 -7.7

Supporting Information Available: Tables of stabilization energy due to branches, tables of calculated DF41-PtCxDy structures, and tables of selected bonds and angles for reactant, transition state, and product structures for both single site and outer pocket models. References to this material are included in the text. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Campbell, C. T.; Parker, S. C.; Starr, D. E. Science 2002, 298, 811. (2) Schalow, T.; Brandt, B.; Starr, D. E.; Laurin, M.; Schauermann, S.; Shaikhutdinov, S. K.; Libuda, J.; Freund, H.-J. Catal. Lett. 2006, 107, 189. (3) Cushing, B. L.; Kolesnichenko, V. L.; O’Connor, C. J. Chem. ReV. 2004, 104, 3893. (4) Niu, Y.; Crooks, R. M. C. R. Chimie 2003, 6, 1049. (5) Esumi, K.; Isono, R.; Yoshimura, T. Langmuir 2004, 20, 237.

(6) Crooks, R. M.; Zhao, M.; Sun, L.; Chechik, V.; Yeung, L. K. Acc. Chem. Res. 2001, 34, 181. (7) Alexeev, O. S.; Siani, A.; Lafaye, G.; Williams, C. T.; Ploehn, H. J.; Amiridis, M. D. J. Phys. Chem. B 2006, 110, 24903. (8) Scott, R. W. J.; Datye, A. K.; Crooks, R. M. J. Am. Chem. Soc. 2003, 125, 3708. (9) Lang, H.; May, R. A.; Iversen, B. L.; Chandler, B. D. J. Am. Chem. Soc. 2003, 125, 14832. (10) Xie, H.; Gu, Y. L.; Ploehn, H. J. Nanotechnology 2005, 16, S492. (11) Pellechia, P. J.; Gao, J.; Murphy, C. J. Inorg. Chem. 2004, 43, 1421. (12) Torrico, F.; Pappalardo, R. R.; Sanchez, Marcos, E.; Martinez, J. M. Theor. Chem. Acc. 2006, 115, 196. (13) Li, Y.-H.; Gregory, S. Geochim. Cosmo. Acta 1974, 38, 703. (14) Tarazona-Vasquez, F.; Balbuena, P. B. J. Phys. Chem. A 2007, 111, 945. (15) Zhao, M.; Crooks, R. M. AdV. Mater. 1999, 11, 217. (16) Vohs, J. K.; Fahlman, B. D. New J. Chem 2007, 31, 1041. (17) Frechet, J. M. J.; Tomalia, D. A. Dendrimers and Other Dendritic Polymers; Wiley: New York, 2001. (18) Maiti, P. K.; Cagin, T.; Wang, G.; Goddard, W. A. Macromolecules 2004, 37, 6236. (19) Maiti, P. K.; Cagin, T.; Lin, S.-T.; Goddard, W. A. Macromolecules 2005, 38, 979. (20) Tarazona-Vasquez, F.; Balbuena, P. B. J. Phys. Chem. A 2007, 111, 932. (21) Schlegel, H. B. J. Comp. Chem. 1982, 3, 214. (22) Peng, C.; Ayala, P. Y.; Schlegel, H. B.; Frisch, M. J. J. Comp. Chem. 1996, 17, 49. (23) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople., J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (24) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270. (25) Kaminskaia, N. V.; Kostic, N. M. Inorg. Chem. 2001, 40, 2368. (26) Steinborn, D.; Junicke, H.; Bruhn, C. Angew. Chem., Int. Ed. Engl. 1997, 36, 2686. (27) Ye, H. C.; Scott, R. W. J.; Crooks, R. M. Langmuir 2004, 20, 2915. (28) Deeth, R. J.; Elding, L. I. Inorg. Chem. 1996, 35, 5019. (29) Grantham, L. F.; Elleman, T. S.; Martin, D. S. J. J. Am. Chem. Soc. 1955, 77, 2965.