Hydrogen motion in proton sponge cations: a theoretical study.

This work presents a study of intramolecular NHN hydrogen bonds in cations of the following proton sponges: 2,7-bis(trimethylsilyl)-1,8-bis(dimethylamino)naphthalene (1), 1,6-diazabicyclo[4.4.4.]tetradecane (2), 1,9-bis(dimethylamino)dibenzoselenophene (3), 1,9-bis(dimethylamino)dibenzothiophene (4), 4,5-bis(dimethylamino)fluorene (5), quino[7,8-h]quinoline (6) 1,2-bis(dimethylamino)benzene (7), and 1,12-bis(dimethylamino)benzo[c]phenantrene (8). Three different patterns were found for proton motion: systems with a single-well potential (cations 1-2), systems with a double-well potential and low proton transfer barrier, ΔEe (cations 3-5), and those with a double-well potential and a high barrier (cations 6-8). Tests of several density functionals indicate that the PBEPBE functional reproduces the potential-energy surface (PES) obtained at the MP2 level well, whereas the B3LYP, MPWB1K, and MPW1B95 functionals overestimate the barrier. Three-dimensional PESs were constructed and the vibrational Schrödinger equation was solved for selected cases of cation 1 (with a single-well potential), cation 4 (with a ΔEe value of 0.1 kcal mol(-1) at the MP2 level), and cations 6 (ΔEe = 2.4 kcal mol(-1)) and 7 (ΔEe=3.4 kcal mol(-1)). The PES is highly anharmonic in all of these cases. The analysis of the three-dimensional ground-state vibrational wave function shows that the proton is delocalized in cations 1 and 4, but is rather localized around the energy minima for cation 7. Cation 6 is an intermediate case, with two weakly pronounced maxima and substantial tunneling. This allows for classification of proton sponge cations into those with localized and those with delocalized proton behavior, with the borderline between them at ΔEe values of about 1.5 kcal mol(-1). The excited vibrational states of proton sponge cations with a low barrier can be described within the framework of a simple particle-in-a-box model. Each cation can be assigned an effective box width.