Jake Tan's Project in Kuo's group: Donor-Acceptor's Role

Why is the “donor-acceptor” coordinate a sine qua non in understanding the vibrational signatures of ionic hydrogen bond?

Our findings offer another counter-intuitive picture. If one looks into the Born-Oppenheimer (BO) paradigm, the IHB stretch has a higher stretching frequency than the “donor-acceptor” stretch. Hence, the former occurs faster than the latter, and they are expected to be decoupled. However, if one considers the vibration states, an interesting insight can be unraveled.

For instance, in proton-bound dimers of water, MeOH, and Me2O. That is H5O2+, (MeOH)2H+, and (Me2O)2H+. The “donor-acceptor” coordinate is the intermolecular O-O and belongs to an A irreducible representation. Meanwhile, the IHB stretch is expected to have a fundamental frequency around 1000 cm-1 and belongs to the B irreducible representation. Therefore, a coupling among their fundamental states is not expected, and the nodal planes of these fundamental states are not tilted as shown in Figure 5.

Figure 5: The contours (white) for the fundamental vibrational wave function of the O-O stretch (top row) and IHB stretch (bottom row) for H5O2+, (MeOH)2H+, and (Me2O)2H+. The colored contours correspond to the potential energy surface and the color bars are expressed in Hartree units. (Reproduced from publication 2)

The first combination tone, which is a simultaneous one quantum excitation in the O-O and IHB coordinates (|1,1>) is expected to occur around 1500 cm-1and belongs to the B irreducible representation. Hence, there is a non-zero coupling term between this combination tone with the fundamental IHB stretch. As a result, the initially dark combination tone (|1,1>) mixes with the bright proton stretch |0,1> leading to two important effects. 1) the red shifting of the IHB stretch and 2) the intensity borrowing of the |1,1> state from the |0,1> as shown in Figure 6a.

In addition to this, the next combination tone, which is a simultaneous two quanta excitation in the O-O coordinate and one quantum of excitation on the IHB stretch (|2,1>) also belongs to the B irreducible representation. Therefore, in a simplistic sense, the |2,1> state would also couple with the |1,1> state, leading to the redshifting of the |1,1> state and redistribution of intensities. This effect is shown in a three-level diagram in Figure 6b.

Figure 6: A vibrational state interaction diagram which accounts for the observed red shift of IHB stretch a) oversimplified two-state system and b) a more realistic model which accounts the interaction between |1,1> and |2,1>. The interaction between |0,1> and |1,1> leads to two coupled states |+> and |->, which both contains substantial |0,1> character. This accounts for the observed intensity of the combination band |1,1>. (Taken from publication 2)

The “donor-acceptor” coordinate is always present in Zundel structures. However, for polyatomic cases, there are flanking modes which could have vibrational frequencies close to 1000 cm-1. Provided that these modes possess the same symmetry with the IHB stretch, an intermode coupling among the fundamental states is possible. This speculation led to the design of the third project, where the proton-bound methanol dimer is examined.