pK a Calculations of Aliphatic Amines, Diamines, and Aminoamides via Density Functional Theory with a Poisson-Boltzmann Continuum Solvent Model Vyacheslav S. Bryantsev, ² Mamadou S. Diallo,* ,²,‡ and William A. Goddard, III* ,² Materials and Process Simulation Center, Beckman Institute 139-74, California Institute of Technology, Pasadena, California 91125, and Department of CiVil Engineering, Howard UniVersity, Washington, DC 20059 ReceiVed: February 6, 2007; In Final Form: March 14, 2007 In order to make reliable predictions of the acid-base properties of macroligands with a large number of ionizable sites such as dendrimers, one needs to develop and validate computational methods that accurately estimate the acidity constants (pK a ) of their chemical building blocks. In this article, we couple density functional theory (B3LYP) with a Poisson-Boltzmann continuum solvent model to calculate the aqueous pK a of aliphatic amines, diamines, and aminoamides, which are building blocks for several classes of dendrimers. No empirical correction terms were employed in the calculations except for the free energy of solvation of the proton (H + ) adjusted to give the best match with experimental data. The use of solution-phase optimized geometries gives calculated pK a values in excellent agreement with experimental measurements. The mean absolute error is <0.5 pK a unit in all cases. Conversely, calculations for diamines and aminoamides based on gas-phase geometries lead to a mean absolute error >0.5 pK a unit compared to experimental measurements. We find that geometry optimization in solution is essential for making accurate pK a predictions for systems possessing intramolecular hydrogen bonds. 1. Introduction Amino and amido functionalized organic compounds are ubiquitous in nature. Their biological importance 1 has led to extensive studies of their structural and physicochemical proper- ties. In addition to their relevance in biochemistry and phar- maceutical chemistry, amines and amides are attractive building blocks in supramolecular chemistry. 2 Depending on solution pH, amine-based ligands can act as both cation and anion chelators. 3 Amide-containing receptors also exhibit dual cation/anion binding properties. They have emerged as attractive building blocks for a variety of anion receptors due to their relatively strong hydrogen bond donor N-H groups. 3 In addition, they contain oxygen and nitrogen heteroatoms that can coordinate with metal ions. 4 We are interested in the proton-, cation-, and anion-binding properties of diamines and aminoamides as building blocks for macroligands of well-defined molecular size, shape, and com- position such as dendrimers. 5 Examples of industrially important poly(propylenimine) (PPI) and poly(amidoamine) (PAMAM) dendrimers with amine and amidoamide functional groups are shown in Figure 1. The structures and anion/cation binding properties of PAMAM and PPI dendrimers in aqueous solutions and at solid-water interfaces strongly depend on solution pH, that is, their acid-base properties. A major focus of our current research program on dendrimer nanotechnology is to develop and validate a multiscale modeling approach for predicting proton, anion, and cation binding to dendrimers in aqueous solutions. A key step toward this goal is the ability to accurately calculate acidity constants (pK a ) for small fragments of a dendrimer. In this article, we address this issue in some detail. The effect of the macroligand field (i.e., dendrimer matrix) on the acid-base properties of dendrimer fragments will be the subject of future studies. Many reports have appeared in the literature describing computational methods of pK a calculations (see, for example, refs 6-10). The most commonly used schemes couple quantum chemical calculations of gas-phase deprotonation energy with * Authors to whom correspondence should be addressed. Beckman Institute MC 139-74, California Institute of Technology, Pasadena, CA 91125. Phone: 626 395 2730. Fax: 626 585 0918. E-mail addresses: wag@wag.caltech.edu (Goddard), and diallo@wag.caltech.edu (Diallo). ² California Institute of Technology. ‡ Howard University. Figure 1. 2-D structures of the first (G1) and second (G2) generation of PAMAM and PPI dendrimers with terminal NH2 groups. 4422 J. Phys. Chem. A 2007, 111, 4422-4430 10.1021/jp071040t CCC: $37.00 © 2007 American Chemical Society Published on Web 05/01/2007