Jake Tan's Research in Kuo's Group: Proton-Bound Amines

A counter-intuitive picture on proton quantum confinement

A series of proton-bound amines namely: (NH3)2H+, (MeNH2)2H+, (Me2NH)2H+ and (Me3N)2H+ were studied. At present, only (NH3)2H+ has an experimentally accessible spectrum. We decided to perform a computational study on it with the purpose of offering a simple picture that experimentalist can verify. We have used Density Functional Theory (DFT) at the B3LYP/6-311+G(d,p) level of theory and basis set. Intuitively, as we enhanced the degree of methylation, the proton affinity of the amines would increase. If that is the case, then we expect that the excess proton will be tightly held in one of the amines causing the force constant to increase. This cascade of effects will lead to increasing νIPB from (NH3)2H+ to (Me3N)2H+. Such picture from chemical intuition was captured by frequency calculations under static nuclei –calculations conducted at the harmonic approximation. However, we have found that upon incorporation of the nuclear motion, the trend is completely reversed. Instead of a blue shift in νIPB, a red shift was observed upon enhancement of methylation (Figure 2).

                                Figure 2: Counter-intuitive picture arising from nuclear quantum effects

for νIPB on symmetric dimers of ammonia and lower amine homologs.

The cause of the counter-intuitive result lies in the potential energy surface along the proton coordinate (z-coordinate in the figure) as shown in Figure 3. It turns out that the proton transfer barrier gets higher upon methylation. This pushes the ground vibrational state to higher energy. Meanwhile, as we move from (NH3)2H+ to (Me3N)2H+, the width of the potential energy curve widens. This, in turn, leads to the lowering of the excited states. The combination of these effects induces the fundamental (|0> to |1>) transition for the proton stretch to red-shift from (NH3)2H+ to (Me3N)2H+ as shown in Figure 4. All of these results demonstrate that a proton is a quantum object.

Figure 3: Potential energy curve along the N-H+-N coordinate (z-coordinate). Upon methylation enhancement, the proton barrier and potential width increases. This combination of effects is responsible for the counter-intuitive picture for IPB stretch wavenumber (νIPB). (Reproduced from publication 7)

Figure 4: The probability densities corresponding to the four lowest vibrational states of the proton-bound dimers of amines. It is evident that the proton quantum confinement effect is clearly understood by a blue-shift on the ground state energy and red shift in the first excited state across the series. (Reproduced from publication 7)

Our works on this family of amines were presented in the XVIIIth International Workshop on Quantum Systems in Chemistry, Physics, and Biology. Later on, it became part of the conference proceedings entitled: Frontiers in Quantum Methods and Applications in Chemistry and Physics: Selected and Edited Proceedings of QSCP-XVIII (Paraty, Brazil, December 2013).

The picture that we offer in this work is a very simple model that is accessible to any spectroscopist. However, we knew that a polyatomic system has several vibrational degrees of freedom. There are 3N-5 for linear and 3N-6 for non-linear molecules, where N is the number of atoms. In the next project, we considered the effect of the “donor-acceptor” stretching coordinate.