Complete Gas-Phase Proton Microaffinity Analysis of Two Bulky Polyamine Molecules Sadegh Salehzadeh,* Mehdi Bayat, and Mehdi Hashemi Faculty of Chemistry, Bu-Ali Sina UniVersity, Hamedan, Iran ReceiVed: April 13, 2007; In Final Form: June 7, 2007 Density functional theory (DFT) and ab initio (Hartree-Fock) calculations employing the 6-31G* basis set are used to determine gas-phase proton microaffinities (PA n,i ) of two bulky symmetrical tripodal tetraamine ligands N[(CH 2 ) 4 NH 2 ] 3 , trbn, and N[(CH 2 ) 5 NH 2 ] 3 , trpa. The corresponding proton macroaffinities ( PA n ) are calculated not only according to our recently established method but also considering two alternative formulas based on a Boltzmann distribution. The successive protonation macroconstants in aqueous solution for these bulky amines are predicted from the well-defined correlation between the calculated proton macroaffinities, without considering Boltzmann distribution, and the corresponding log K n for these amines. The overall protonation constants are also predicted by two different methods. 1. Introduction It is now well-established that electronic structure calculations provide accurate gas-phase proton affinities as well as valuable information on the structure of a base and its conjugate acid. 1 The proton affinity of a monobasic neutral ligand at 0 K is defined as the negative of the electronic energy difference between HL + and L together with a correction for difference in zero point energies. To convert the 0 K value to 298 K, one has to include thermal corrections for the translational, rotational, and vibrational energies and a correction for the change in the number of molecules assuming ideal gas behavior. 2 Obviously for each polybasic molecule there may be several ways for protonation depending on which site is protonated. Protonation of different sites will release different amounts of energy. Therefore the incorrect term “proton affinity” for protonation of a special site on a polybasic molecule can be replaced by “proton microaffinity”, which we recently used for gas-phase protonation of polybasic molecules. 3 We also applied two other types of defined gas-phase proton affinities for such molecules: proton macroaffinity and proton overall affinity. The proton macroaffinity of a polybasic molecule corresponds to its protonation macroconstant in solution. We established an equation, eq 1, for calculation of proton macroaffinities, PA n , of polyamine molecules with any type of symmetry. 3 where This formula shows that PA n not only depends on the proton microaffinities, PA n,i , and the relative abundance of the species which is related to them, R n,j , but also on the available identical sites that undergo protonation, S n,i . Obviously the relative abundance of the initial neutral molecule, R 1,1 , is 1, and that of any other species depends on both the relative abundance of previous species, R n-1,j , and the available identical sites on them, S n-1,j , which are involved in its formation. The proton overall affinity, PA ov , is also defined as the negative of the electronic energy difference between L and its fully protonated form (herein H 4 L 4+ ) together with a correction for difference in zero point energies. According to Hess’s law the summation of the calculated proton macroaffinities for one polybasic molecule ( PA ov ; see eq 2) must be the same as or very close to its PA ov . For first time, we have shown that there is a good correlation between the calculated gas-phase proton macroaffinities and the corresponding solution-protonation macroconstants (K n ; see eqs 3 and 4) for a number of tripodal tetraamines (see Figure 1; tren, pee, ppe, tpt, and ppb) that in recent years have been interesting to us. 3-8 Furthermore the correlation between the calculated log PA ov and measured log  4 (see eq 5) was really excellent for the latter tetraamines. * Corresponding author. Fax: +98(811)8257407. E-mail: saleh@basu.ac.ir. PA n ) ∑ j)1 l ∑ i)1 m PA n,i R n,j S n,i ∑ j)1 l ∑ i)1 m R n,j S n,i (1) R n,j ) ∑ j)1 K R n-1,j S n-1,j Figure 1. Structures of the tripodal tetraamine ligands investigated here along with their common abbreviations. PA ov ) ∑ n)1 m PA n (2) H n-1 L (n-1)+ + H + h H n L n+ (3) K n ) [H n L n+ ] [H n-1 L (n-1)+ ][H + ] (4)  n ) K 1 K 2 ...K n (5) 8188 J. Phys. Chem. A 2007, 111, 8188-8192 10.1021/jp072882v CCC: $37.00 © 2007 American Chemical Society Published on Web 08/02/2007