Semiclassical calculations of tunneling splitting in malonaldehyde

Abstract

We have devised a semiclassical procedure based on the Makri–Miller [J. Chem. Phys. 91, 4026 (1989)] model for calculating the eigenvalue splitting in many-atom systems and have used it to calculate the ground-state splitting in several isotopomers of malonaldehyde. A potential-energy surface that includes all twenty-one vibrational degrees of freedom was constructed based on the available theoretical and experimental information. The results for calculations in which all atoms are allowed full three-dimensional motion are in good agreement with the experimentally measured values. Restricting the molecular motion to a plane leads to an increase in the splitting due to a decrease in the average height and width of the barrier to tunneling when the molecule is not allowed to vibrate transverse to the molecular plane. Low energy mode-specific excitations were used to study the sensitivity of the splitting to the motions of heavy atoms. The results show that the heavy atom motions have significant influence on the tunneling. This study demonstrates that simple semiclassical methods can be used to treat proton tunneling in large systems.

The ground state tunneling splitting of malonaldehyde: Accurate full dimensional quantum dynamics calculations

“…Since then the determination of the ground state tunneling splitting of MA has been the focus of several studies ranging from reduced dimensionality quantum calculations 7,8 to elaborate full-dimensional semiclassical treatments. [9][10][11][12][13][14][15][16][17] Most of these studies employed MA as a test case for method development measuring the accuracy of the calculation by comparing the computed value of the ground state splitting with the experimental one.…”

Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Malonaldehyde and Tropolone

“…[15,19]. Indeterminate e Sewell et al [62]. Vibrations from the utilized PES correlate poorly with the observed midrange vibrations.…”

“…In column 4 the D V /D 0 ratios are listed next to theoretical ratios [61][62][63][64] discussed below. Of the nine experimental values only the four lower frequency skeletal displacements -two in-plane and two out-ofplane -appear to significantly impact the tunneling process.…”

“…Vibrations from the utilized PES correlate poorly with the observed midrange vibrations. [62]. The utilized PES is based on the 1983 valence force field, and early vibrational assignments of Smith et al [15] -some of which differ from later work [59,60].…”

Some New Classical and Semiclassical Models for Describing Tunneling Processes with Real-Valued Classical Trajectories

“…Several examples of such approaches exist; for example, a model used by Miller and co-workers 10,11 (which is patterned after Tully and Preston's surface-hopping models for treating electronically nonadiabatic processes 12 ) is a fairly primitive way of describing tunneling processes with only real-valued trajectories, but it has found some utility. [13][14][15][16][17][18][19] Within the semiclassical (SC) initial value representation (IVR), it has also been shown that purely real-valued classical trajectories can describe tunneling processes to a very useful extent. [20][21][22] (The very reason the IVR was first introduced, 23 in fact, was to be able to describe classically forbidden vibrationally inelastic scattering with realvalued trajectories.…”