Theoretical studies on proton affinities of H 2 N–(CH 2 ) n –NH 2 (n =2À10) diamines at gas phase. Good correlation with protonation constants in solution Sadegh Salehzadeh * , Mehdi Bayat, Fereshteh Yaghoobi Faculty of Chemistry, Bu-Ali Sina University, Mahdieh, Hamedan, Iran article info Article history: Received 12 January 2009 Received in revised form 3 April 2009 Accepted 3 April 2009 Available online 14 April 2009 Keywords: Theoretical studies Proton affinity Protonation constants Diamines Hydrogen bonding abstract A theoretical study on complete protonation of a series of diamine molecules with general formula H 2 N– (CH 2 ) n –NH 2 (n =2À10, L2ÀL10) has been reported. The gas-phase protonation energies were computed using density functional theory (DFT) calculations. The standard 6-31G * and 6-311++G ** basis sets were used in all calculations. Three species, L, HL + and H 2 L 2+ can be considered in protonation steps of diamine molecules. Among these, the HL + is involved in both the first, L + H + ? HL + , and second, HL + +H + ? H 2 L 2+ , steps. Two different structures were considered for latter species: (I) a linear-like structure (II) a cyclic structure due to intramolecular hydrogen bonding. The trends for variations of calculated PA 1 in the ser- ies of these molecules, is very similar to that of their measured protonation constants when we consider the linear structure for all species. Furthermore, for latter structures there are good correlations between the calculated proton macroaffinities in the gas-phase with corresponding protonation constants in solu- tion. The latter observation has led us to predict the stepwise protonation constants for L7 and L9. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction Recently, according to a theoretical study on proton affinity of some tripodal tetraamines, we introduced three new defined gas- phase proton affinities for polybasic molecules: proton microaffin- ity, proton macroaffinity and proton overallaffinity [1]. The proton microaffinity corresponds to protonation of a special site on a pol- ybasic molecule [1–4]. The number of proton microaffinities, sim- ilar to number of protonation microconstants, depends not only upon the number of basic sites but also upon the symmetry of the molecule [5]. The proton macroaffinity corresponds to a weighted mean of various proton microaffinities in each step of the protonation of a polybasic molecule. The number of proton macroaffinities for one polybasic molecule depends on the number of basic sites. The proton overallaffinty is also corresponds to full protonation of a polybasic molecule. The proton overallaffinity can be calculated in two different ways. It can be defined as the negative of the electronic energy difference between L (a polybasic molecule) and its fully protonated form, H 2 L 2+ , together with a cor- rection for difference in zero point energies. In latter case, we show the proton overallaffinity as PA ov . In second way, it can be defined as summation of the calculated proton macroaffinities for the pol- ybasic molecule. In this case, we show it as PA ov . Obviously, as a consequence of Hess’s law, for one polybasic molecule the PA ov must be the same as or very close to PA ov , if the proton macroaffin- ities, PA n , are calculated in a correct way. In this work, we report the results of our theoretical studies on full protonation of a series of diamine molecules with general for- mula H 2 N–(CH 2 ) n –NH 2 (n =2À10). The first protonation step of a number of latter compounds at gas phase have been already inves- tigated [6–12]. Herein, for first time, we report a theoretical study on both protonation steps of all above molecules at gas phase. The diamines with 2À10 methylene groups are selected because their protonation constants, except for n = 7 and 9, at different ionic strengths are available. Thus, we can study the correlation of our gas-phase proton affinities with corresponding protonation con- stants in solution. The chain like structure of the aliphatic diamines permits us to easily consider or ignore the intramolecular hydro- gen-bond formation in the monoprotonated species (HL + ). Hence, we can consider a cyclic structure and/or a linear-like structure for latter species. A literature review shows that in all previous studies on gas-phase proton affinities of aliphatic diamines the intramolecular hydrogen-bonding is considered in HL + species [6–10]. In present study, we consider both the cyclic and the linear structures for HL + species. Obviously, the amount of proton affinity depends on the stability of the structures considered for species in- volved in porotonation process. The different structures are corre- spond to different proton affinities. Thus, according to study on the correlation of our different calculated proton affinities with corre- sponding protonation constants in solution we can guess whether the cyclic or the linear-like structure must be considered for dia- mine molecules in solution. 0166-1280/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2009.04.003 * Corresponding author. Fax: +98 811 8257407. E-mail address: saleh@basu.ac.ir (S. Salehzadeh). Journal of Molecular Structure: THEOCHEM 906 (2009) 68–71 Contents lists available at ScienceDirect Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem