Formic Acid Dimer DCOOH

The double hydrogen bond in principle facilitates two mechanisms of double proton transfer stepwise and concerted. Studying the transfer rates within the semi-classical tunneling approximation of the variational transition state theory, Kim found that the two protons are transferred synchronously across the transition state with D2h symmetry [194], The actual proton-tunneling distance is considerably reduced due to the contraction of the hydrogen bonds, i.e., heavy atom motion promotes the proton transfer. On the other hand, the ab initio path-integral Car-Parinello calculations predict that the motion of the two protons in the vicinity of the potential minima is 

Unfortunately, the reliable final accurate value of Aq cannot be obtained, since the highest possible quantum chemical calculations are not yet satisfactory enough 

FIG U RE 7.15 Potential energy along the instanton trajectory based on interpolation of a small number of ab initio points in the case of formic acid dimer. Dotted line DFT/6-31+G(d) Solid line DFT/aug-cc-pVTZ Dashed line DFT/6-311++G(3df,3pd) Dash-dotted line CCSD(T) correction to DFT/aug-cc-pVTZ instanton. (Taken from Reference [184] with permission.) 

It is very instructive to compare the exact expression of the pre-exponential factor B with the approximation used by Tautermann and co-workers [42,200]. In their calculations the pre-exponential factor was taken from the one-dimensional theory by Garg [199], 

Tunneling Splitting and Instanton Parameters for the Ground State in (DC00H)2. All DFT Calculations Have Been Performed with the B3LYP Functional. The 1D Approximation Refers to the Approximate Treatment of the Pre-Exponential Factor with and without Inclusion of the Zero-Point Energy (ZPE) 

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Early theoretical work on FAD was concerned with the dimer equilibrium geometry and the electronic structure (see for example Refs. [32-36]). Ah initio molecular orbital studies on the structure of formic acid dimer in 1984 agreed very well with the experimental structures as determined by electron diffraction [37]. Due to the importance of the double proton transfer of FAD as a key prototype for multiple proton transfer reactions several theoretical studies have been reviewed in the literature [38]. Rotational constants for formic acid dimer were obtained by high resolution spectroscopy of (DCOOH)2 [39] and by femtosecond degenerate four wave mixing experiments in the gas cell at room temperature and under supersonic jet experiments by Matylisky et al. [40]. 

The microwave spectrum of the normal argon-acetaldehyde and of the Ar-CHsCDO van der Waals dimer has been used to determine their structure646 which was found to be a non-planar skew, with the Ar binding on top of the C—C—O triangle. The planar or nearly so structure of the Ar-formic acid van der Waals dimer has also been determined647 from assigning the rotation spectrum of normal, Ar, DCOOH and HCOOH isotopomers. 

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