Tunneling formic acid dimers

A calculation of tunneling splitting in formic acid dimer has been undertaken by Makri and Miller [1989] for a model two-dimensional polynomial potential with antisymmetric coupling. The semiclassical approximation exploiting a version of the sudden approximation has given A = 0.9cm" while the numerically exact result is 1.8cm" Since this comparison was the main goal pursued by this model calculation, the asymmetry caused by the crystalline environment has not been taken into account. 

G. V. Mil nikov, O. Kuhn, and H. Nakamura, Ground state and vibrationally assisted tunneling in the formic acid dimer. J. Chem. Phys. 123, 074308 (2005). 

Figure 6.20. (a) Projection of a three-dimensional PES K(p,p2,p3) for two-proton transfer in formic acid dimer onto the (p, p,) and (p, p3) planes. In contrast with points A and B, in points C and D the potential along the p3 coordinate is a double well resulting in bifurcation of the reaction path [from Shida et al., 1991b]. (b) The contour lines correspond to equilibrium value of p3 and potential (6.37) when V(Q) = V0(Q4 - 2Q2), V0 = 21 kcal/ mol, C = 5.()9V0, A = 5.351/, Qn = 0.5. When Q > Qc, two-dimensional tunneling trajectories exist in the shaded region between curves 1 and 2. Curve 3 corresponds to synchronous transfer. 

The most recent calculations on the tunneling dynamics of double proton transfer in formic acid dimer and benzoic acid dimers have been reported by Smedar-china et al. [20]. They used direct dynamics calculations to predict the tunneling splittings of both carboxylic dimers. 

According to Refs. [35, 56] the mechanism of proton tunneling assisted by the excitation of low-frequency modes in molecular crystals with moderate H-bonds differs strongly from that in the gas phase [62]. In the isolated formic acid dimer the tunneling splitting increases monotonically with the 0---0 excitation, while in crystals the dependence of the probability of proton tunneling on the excitation low-frequency modes is non-monotonic. 

With one exception, these results are based solely on quantum-chemical calculations of the potential energy surface. Theoretical evaluation of the transfer dynamics has been attempted only for the formic acid dimer, for which two general level splittings have been observed and assigned to synchronous double proton tunneling in the ground state and a vibrational excited state, respectively. 

The instanton theory of tunneling splittings in hydrogen-bonded systems and decay of metastable states in polyatomic molecules was studied by Nakamura et al. [182, 192, 195, 201-204, 216] They formulated a rigorous solution of the multidimensional Hamiltonian-Jacobi and transport equations, developed numerical methods to construct a multidimensional tunneling instanton path, and applied this method to HO [201], malonaldehyde [192, 195], vinyl radical [203], and formic acid dimer [202]. Coupled electron and proton transfer reactions were recently reviewed by Hammes-Schiffer and Stuchebrukhov [209]. 

A similar behavior is found in the 1 2 inclusion of 26 with formic acid 71 (Fig. 20, type II). We notire a H-bonded dimer of 26 and one of the formic acid molecules binding the host dimer in a pseudo-dimeric arrangement via the free —COOH groups of the host dimer. The second guest molecule is also placed into an interstitial tunnel of the dimeric host/bound-guest matrix. Here the 1 2 stoichiometry is due to the small size of the guest partner. 

The structures of the acetic acidS0) and of the propionic acid71 inclusions of 26 (Fig. 20, type III) are isomorphous to each other. The increased guest volume with respect to formic acid yields 1 1 stoichiometry, with no H-bonds between host and guest molecules in either case. The tunnel where the dimers of guests are situated (see Fig. 32 a) is functionally the same as in the case of the self-dimerized pairs of the formic acid guests. 

Daly, A.M., Bunker, P.R., and Kukolich, S.G. (2010) Evidence for proton tunneling from the microwave spectrum of the formic acid-propriolic acid dimer./. Chem. Phys., 132,... 

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