Modeling -Terminated Polypropylene Imine Dendrimer Fragmentation with DFT

Eric W. Martin, Jacob T. Kilgore and William D. Price

Marshall University Department of Chemistry Huntington, WV 25755


Dendrimers are regularly branched polymers with a treelike structure that can be tuned for size, shape, and functionality. This relatively new class of compound has shown potential for useful host-guest chemistries including site-specific drug delivery via molecular recognition, catalysis, and nonlinear optics. Gas-phase dissociation studies have been initiated to probe the structure and stability of the half and first generation polypropylene dendrimer complexes and to develop an analytical framework for their characterization. These dissociation studies result in fragmentation products of mass-to-charge ratios that can be assigned to multiple possible isomers formed by potentially competing mechanisms.

Since these reactions are under kinetic control we will present density functional results for modeling the dissociation mechanisms for the most abundantly produced fragments from the protonated dendrimers. The BMK functional in conjunction with a moderately-sized basis has been chosen for its utility in determining transition state energies and kinetic parameters.


Dendrimers have several promising and exciting possibilities ranging from use as chelating agents1 to site-specific host-guest chemistry and controlled gene2 and drug delivery systems3. Distinct properties of dendrimers, such as well-defined architecture and a high ratio of moieties to molecular volume, make these materials highly interesting for the development of nanomaterials and medicines4. The compact, nanometer- scale structure of the hyperbranched polymer results in high solubility and low solution viscosity5, while the dense arrangement of functional groups allows pharmaceutical agents and magnetic resonance imaging contrast dyes to be chemically grafted to the dendrimer in concentrated amounts6. Additionally, these “molecular containers” could also be applied in waste remediation and resource recovery, in fuel storage for new sources of energy, or in the development of highly sensitive, highly selective chemical detectors for use in homeland security, chemical process quality control, environmental monitoring, etc.

Increasing interest in the design and use of these dendrimer systems has created a need for new methods of physical and chemical characterization. Electrospray ionization mass spectrometry (ESI-MS) has not been used extensively for characterizing dendrimers, however, it has been successfully applied in the characterization of the structure and stability of biopolymers, classical polymers, and non-covalent and organometallic complexes. Additionally, understanding the gas-phase chemistry of the dendrimer may play a critical role in understanding the stability of the polymer by providing insight into the fundamental organic chemistry properties and reactions that dominate these particular molecules.7 The collision-induced dissociation (CID) ESI-MS data is most effectively used to elucidate structure and mechanistic pathways if it is augmented by computational methods; both classical molecular dynamics (MD) and DFT/ab initio approaches are employed. Methods

A molecular analog – protonated N,N-dimethyl-3-aminopropanontirle – was used to model the loss of acetonitrile from the G1 protonated nitrile-terminated PPI dendrimer. All calculations were conducted using the Gaussian 03 program. Initial scans of the energy surface used the B3LYP/6-31G* level of theory. Stationary points were then geometry optimized with the B3LYP/6-311G**, M05-2X/6-311G**, and BMK/6-311G** methods. Unrestricted calculations were utilized for transition and intermediate states that may display some radical character, otherwise restricted methods were employed. The zero point energies were calculated at the B3LYP/6-311G** level and scaled by factor of 0.9678 prior to computing thermodynamic quantities. Transition state structures were determined using the Synchronous Transit-Guided Quasi- Newton (STQN) method and were verified by frequency analysis. All optimized transition state structures resulted in one negative frequency indicating the appropriate concavity. Intrinsic Reaction Coordinate calculations verified that the located transition states connect the associated minima. It has been established that both the BMK9 and M05-2X10 functionals have an 8kJ/mol range accuracy for transition state barriers.

a) MS/MS H2N

NH NH2 Product Ion? H2N N


b) MS/MS N

NH N Product Ions? N N

Why Two? N

Figure 1– Comparison of electrospray ionization, collision-induced dissociation (CID) ms/ms spectra for protonated (a) -terminated polypropylene Imine (PPI) dendrimer and (b) nitrile-terminated polypropylene Imine (PPI) dendrimer. CID data of the generation 1 protonated form of the amine- terminated polypropylene (PPI) dendrimer (317 amu), indicates only a single fragmentation pathway resulting in the loss of a neutral product with a molecular mass of 131 amu. Several possible mechanisms leading to these fragment ions are shown in Figure 2. The CID spectrum of the generation 1 nitrile- terminated dendrimer (301 amu) shows two competing pathways leading to neutral loss fragments of 123 and 41 amu. The CID conditions obtained in the quadrupole ion trap used in these experiments are multiple low- energy collisions are not expected to develop an effective internal ion temperature (Teff) greater than 600 K.


N+H N +N + HN



N+H H N+H N N + H



H N+H N +N + HN


FIGURE 2. – Proposed mechanisms for core cleavage of amine-terminated first-generation PPI dendrimer: (a) internal nucleophilic substitution on alpha to protonation site forming a quaternary amine, (b) elimination at non-protonated tertiary carbon and formation of or (c) hydride transfer to carbon alpha to protonation site and formation of imine. BMK/6-311G** Free Energy Diagram of Competing Dissociation Mechanisms for Model PPI Dendrimer




200 Alternate Charged Products

G (kJ/mol)

! b) Ene 160

120 311G** Relative


BMK/6 80 c) a)


Imine 0 N-Methyl Model Reactant Figure 3 – Thermochemistry of proposed fragmentation mechanisms calculated at the BMK/6- 311G** model chemistry. Vibrational frequencies calculated at the B3LYP/6-311G** level (scaled by 0.967). These data indicate that the nucleophilic substitution mechanism should dominate the fragmentation pathway for the protonated amine-terminated dendrimer and account for the analogous dissociation leading to the 178 amu product ion for the protonated nitrile-terminated dendrimer. Note: in both cases the reactant must twist to obtain the proper geometry for dissociation.

BMK/6-311G** Free Energy Diagram of Competing Dissociation Channels for Model Nitrile-terminated PPI Dendrimer





G (kJ/mol)


180 Proton-Shift Products Complex

120 311G** Relative -

BMK/6 60

0 Hydride-Shift Products Model Reactant Complex Substitution Products -60 Complex

Figure 4 – Thermochemistry of proposed fragmentation mechanisms of nitrile-terminated dendrimer calculated at the BMK/6-311G** model chemistry. Vibrational frequencies calculated at the B3LYP/6-311G** level (scaled by 0.967). These data indicate that the nucleophilic substitution mechanism should dominate the fragmentation pathway for the protonated nitrile- terminated dendrimer and account for the 178 amu product ion. The proposed mechanisms for the neutral loss of 41 amu are not viable under the experimental conditions of Figure 1. Even potential proton tunneling for the proton-shift mechanism would not result in any observable product.

Substitution Proton Shift Hydride Shift Reactant TS TS TS ΔG (kJ/mol) ΔG (kJ/mol) ΔG (kJ/mol) ΔG (kJ/mol) B3LYP 0.00 101.48 212.43 410.26 6-31G* B3LYP 0.00 98.92 205.98 393.66 6-311G** M05-2X 0.00 120.37 238.50 427.06 6-311G** BMK 0.00 120.36 225.31 419.94 6-311G**

Table 1. Comparison of the activation Gibb’s Free Energy relative to the lowest energy reactant conformation for the three transition states located in this study. Evaluating transition energies has proven to be a challenge for DFT methods. Here, the B3LYP (the most commonly used), BMK and M05-2X (both developed for reproducing experimental transition energies) functionals are compared using a common basis set. The B3LYP method systematically produces values that are considerably lower than the other two. However, the agreement between the BMK and M05-2X ranges between 0.0 (the internal nucleophilic substitution) and 13.2 (proton shift mechanism) kJ/mol.


The proposed mechanisms and associated activation free energies must agree with the experimental data. Unimolecular dissociation rates (and rate constants) for the nitrile-terminated dendrimer were determined using seven different collision energies. There is no simple quantitative relationship between these collision energies and Teff for these ions eliminating the use of an Eyring analysis to obtain the ΔG‡ for these ‡ reactions. Comparing the ratio of k260 and k178 while using the ΔΔG for these dissociations will yield Teff.

 −ΔG260

 kBT  RTeff   e −(ΔG178 −ΔG260 )       k260  h  RTeff ΔG260 − ΔG178 k178 =  = e ⇒ Teff = ln  k −ΔG178 R k (1) 178  k T  RT  260   B e eff  h 

For the proton-shift mechanism a Teff of 18000 K would have to be reached to duplicate€ the mass spectra in Figure 1b. A mechanism with this BMK or M05-2X ΔΔG‡ would not be observed under the experimental conditions described here. Combining the experimental rate constants and the BMK or M05-2X ΔG‡ with an Eyring analysis for the nucleophilic substitution mechanism, the Teff range for these experiments is estimated to be 400 – 465 K (a ‡ reasonable value). With these values for Teff the estimated range for ΔΔG of possible competing pathways for the neutral loss of 41 amu can be determined to be 6.3 kJ/mol. This suggests that some other low transition energy mechanism exists for this neutral loss.


• The internal nucleophilic substitution mechanism is favored over both the hydride shift mechanisms for the neutral loss of 131 and 123 amu for the amine- and nitrile-terminated dendrimer, respectively.

• The calculated ΔG‡ for the nucleophilic substitution mechanism with both the BMK and M05-2X functionals are in excellent agreement

and yield a Teff that lies in the reasonable range for the experimental conditions.

• The agreement in the calculated ΔG‡ for the hydride and proton- shift mechanisms between the BMK and M05-2X functionals is within the reported error associated with the methods, however the B3LYP functional yields a much lower ΔG‡.

• Neither the hydride nor proton-shift mechanisms are viable competing mechanisms for the internal nucleophilic substitution within the kinetic window of this CID experiment.


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