Thursday, September 8, 2011

Deconstructing quantum nuclear effects in hydrogen bonding

Most molecules and solids exhibit simple isotope effects associated with vibrational modes. In the harmonic limit the vibrational frequency scales with the inverse square root of the mass. Hence, replacing hydrogen with deuterium (D) should reduce the frequency by a factor of 1.414 = sqrt(2). However, significant anharmonicity or non-adiabatic (violations of Born-Oppenheimer?) effects can lead to very different effects. 
An important case is that of hydrogen bonding. The graph below shows gamma = the ratio of the O-H stretch stretch frequency to the O-D frequency as a function of the O-H frequency. The latter is a measure of the H-bond strength and is directly correlated with the donor-acceptor distance. The graph is taken from this paper.
One sees that as the mode softens [as the H-bond gets stronger] the isotope effect gets smaller. Playing around with the lowest energy eigenvalues for a Morse potential one can reproduce this effect. However, the physics behind the upward turn for lower frequencies [which presumably are in the domain where the D-H potential no longer has an energy barrier] is not clear to me. This reflects non-trivial quantum nuclear effects, as discussed in this recent PNAS paper.

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