The optimal tunneling path for the proton transfer in malonaldehyde

Chiral Recognition in Diaziridine Clusters and the Problem of Racemization Waves

Theoretical calculations (B3LYP/6-31+G**) of chiral clusters of diaziridines have been carried out. Five configurations of chiral and nonchiral clusters with up to eight monomers have been considered. The proton transfer within the neutral and protonated clusters has been studied as a possible source of racemization waves. The optical rotatory power (ORP) has been calculated for the neutral and protonated homochiral clusters. The results show that the clusters with alternated chiral molecules are the preferred ones and that the proton transfer proceeds with low energetic barriers in the protonated systems. The ORP results are very dependent on the shape of the clusters and the neutral or protonated state of them.

The ground state tunneling splitting and the zero point energy of malonaldehyde: A quantum Monte Carlo determination

Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7+/-0.3 cm-1 is obtained, and the vibrational ground state energy is found to be 15 122+/-4 cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21+/-0.09 cm-1 and the vibrational ground state energy to 14 385+/-2 cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface.

Double hydrogen tunneling revisited: the breakdown of experimental tunneling criteria

Formic acid dimer was chosen as a model system to investigate synchronous double proton transfer by means of variational transition state theory (VTST) for various isotopically modified hydrogen species. The electronic barrier for the double proton transfer was evaluated to be 7.9 kcal/mol, thus being significantly lower than it was determined in previous studies. The tunneling probabilities were evaluated at temperatures from 100 up to 400 K and typical Arrhenius behavior with enhancement by tunneling is observed. When comparing the transmission factors kappa in dependence of the mass of the tunneling hydrogen, it was found that there are two maxima, one at very low masses (e.g., 0.114 amu, corresponding to the muonium entity) and one maximum at around 2 amu (corresponding to deuterium). With the knowledge of the VTST-hydrogen transfer rates and the corresponding tunneling corrections, various tunneling criteria were tested (e.g., Swain-Schaad exponents) and were shown to fail in this reaction in predicting the extent of tunneling. This finding adds another aspect in the ongoing "Tunneling-Enhancement by Enzymes" discussion, as the used tunneling criteria based on experimental reaction rates may fail to predict tunneling behavior correctly.

Quantum Tunneling in the Midrange Vibrational Fundamentals of Tropolone

The Fourier transform infrared spectrum of tropolone(OH) vapor in the 1175-1700 cm(-1) region is reported at 0.0025 and 0.10 cm(-1) spectral resolutions. The 12 vibrational fundamentals in this region of rapidly rising vibrational state density are dominated by mixtures of the CC, CO, CCH, and COH internal coordinates. Estimates based on the measurement of sharp Q branch peaks are reported for 11 of the spectral doublet component separations DS(v) = |Delta(v) +/- Delta(0)|. Delta(0) = 0.974 cm(-1) is the known zero-point splitting, and three a(1) modes show tunneling splittings Delta(v) approximately Delta(0), four b(2) modes show splittings Delta(v) approximately 0.90Delta(0), and the remaining four modes show splittings Delta(v) falling 5-14% from Delta(0.) Significantly, the splitting for the nominal COH bending mode nu(8) (a(1)) is small, that is, 10% from Delta(0). Many of the vibrational excited states demonstrate strong anharmonic behavior, but there are only mild perturbations on the tautomerization mechanism driving Delta(0). The data suggest, especially for the higher frequency a(1) fundamentals, the onset of selective intramolecular vibrational energy redistribution processes that are fast on the time scale of the tautomerization process. These appear to delocalize and smooth out the topographical modifications of the zero-point potential energy surface that are anticipated to follow absorption of the nu(v) photon. Further, the spectra show the propensity for the Delta(v) splittings of b(2) and other complex vibrations to be damped relative to Delta(0).

Simple and accurate method to evaluate tunneling splitting in polyatomic molecules

A practical and accurate semiclassical method for calculating the tunneling splitting of the ground state in polyatomic molecules is presented based on a recent version of the instanton theory [J. Chem. Phys. 115, 6881 (2001)]. The method uses ab initio quantum chemical data for the potential energy surface without any concomitant extrapolation and requires only a small number of ab initio data points to get convergence even for large molecules. This enables one to use an advanced level of electronic structure theory and achieve a high accuracy of the result. The method is applied to the 9-atomic malonaldehyde molecule by making use of the potential energy surface at the level of CCSD(T) with the hybrid basis set of aug-cc-pVTZ (for oxygen atoms and the transferred hydrogen atom) and cc-pVTZ (for other atoms).

An exploration of electronic structure and nuclear dynamics in tropolone. I. The X̃A11 ground state

The ground electronic state (X 1A1) of tropolone has been examined theoretically by exploiting extensive sets of basis functions [e.g., 6-311++G(d,p) and aug-cc-pVDZ] in conjunction with the high levels of electron correlation made possible by density functional (DFT/B3LYP), Moller-Plesset perturbation (MP2), and coupled-cluster [CCSD and CCSD(T)] methods. Unconstrained MP2 and CCSD optimization procedures performed with the reference 6-311++G(d,p) basis predict a slightly nonplanar equilibrium structure characterized by a small barrier to skeletal inversion (< or =10 cm(-1) magnitude). Complementary harmonic frequency analyses have shown this nonplanarity to be a computational artifact arising from adversely tuned carbon d-orbital exponents embodied in the standard definitions of several Pople-type basis sets. Correlation-consistent bases such as Dunning's aug-cc-pVDZ are less susceptible to these effects and were employed to confirm that the X 1A1 hypersurface supports a rigorously planar global minimum. The fully optimized geometries and vibrational force fields obtained by applying potent coupled-cluster schemes to the relaxed-equilibrium (Cs) and transition-state (C2v) conformers of tropolone afford a trenchant glimpse of the key features that mediate intramolecular hydron exchange in this model system. By incorporating perturbative triples corrections at the substantial CCSD(T) level of theory, an interoxygen distance of r(O...O)=2.528 A was determined for the minimum-energy configuration, with the accompanying proton-transfer reaction being hindered by a barrier of 2557.0 cm(-1) height. The potential energy landscape in tropolone, as well as the nature of the attendant hydron migration process, is discussed within the framework of the encompassing G4 molecular symmetry group.

Time-resolved photoelectron spectroscopy of proton transfer in the ground state of chloromalonaldehyde: Wave-packet dynamics on effective potential surfaces of reduced dimensionality

We report on a simple but widely useful method for obtaining time-independent potential surfaces of reduced dimensionality wherein the coupling between reaction and substrate modes is embedded by averaging over an ensemble of classical trajectories. While these classically averaged potentials with their reduced dimensionality should be useful whenever a separation between reaction and substrate modes is meaningful, their use brings about significant simplification in studies of time-resolved photoelectron spectra in polyatomic systems where full-dimensional studies of skeletal and photoelectron dynamics can be prohibitive. Here we report on the use of these effective potentials in the studies of dump-probe photoelectron spectra of intramolecular proton transfer in chloromalonaldehyde. In these applications the effective potentials should provide a more realistic description of proton-substrate couplings than the sudden or adiabatic approximations commonly employed in studies of proton transfer. The resulting time-dependent photoelectron signals, obtained here assuming a constant value of the photoelectron matrix element for ionization of the wave packet, are seen to track the proton transfer.

Tunneling dynamics of double proton transfer in formic acid and benzoic acid dimers

Direct dynamics calculations based on instanton techniques are reported of tunneling splittings due to double proton transfer in formic and benzoic acid dimers. The results are used to assign the observed splittings to levels for which the authors of the high-resolution spectra could not provide a definitive assignment. In both cases the splitting is shown to be due mainly to the zero-point level rather than to the vibrationally or electronically excited level whose spectrum was investigated. This leads to zero-point splittings of 375 MHz for (DCOOH)(2) and 1107 MHz for the benzoic acid dimer. Thus, contrary to earlier calculations, it is found that the splitting is considerably larger in the benzoic than in the formic acid dimer. The calculations are extended to solid benzoic acid where the asymmetry of the proton-transfer potential induced by the crystal can be overcome by suitable doping. This has allowed direct measurement of the interactions responsible for double proton transfer, which were found to be much larger than those in the isolated dimer. To account for this observation both static and dynamic effects of the crystal forces on the intradimer hydrogen bonds are included in the calculations. The same methodology, extended to higher temperatures, is used to calculate rate constants for HH, HD, and DD transfers in neat benzoic acid crystals. The results are in good agreement with reported experimental rate constants measured by NMR relaxometry and, if allowance is made for small structural changes induced by doping, with the transfer matrix elements observed in doped crystals. Hence the method used allows a unified description of tunneling splittings in the gas phase and in doped crystals as well as of transfer rates in neat crystals.

Instanton theory for the tunneling splitting of low vibrationally excited states

We develop the instanton theory for calculating the tunneling splitting of excited states. For the case of low vibrational quantum states we derive a canonically invariant formula which is applicable to a multidimensional system of arbitrary Riemannian metric. The effect of multidimensionality in relation to the vibrational excitation is explained in terms of the effective frequencies along the instanton trajectory. The theory is demonstrated to work well by taking HO2 molecule as an example.

The ground-state tunneling splitting of various carboxylic acid dimers

Carboxylic acid dimers in gas phase reveal ground-state tunneling splittings due to a double proton transfer between the two subunits. In this study we apply a recently developed accurate semiclassical method to determine the ground-state tunneling splittings of eight different carboxylic acid derivative dimers (formic acid, benzoic acid, carbamic acid, fluoro formic acid, carbonic acid, glyoxylic acid, acrylic acid, and N,N-dimethyl carbamic acid) and their fully deuterated analogs. The calculated splittings range from 5.3e-4 to 0.13 cm(-1) (for the deuterated species from 2.8e-7 to 3.3e-4 cm(-1)), thus indicating a strong substituent dependence of the splitting, which varies by more than two orders of magnitude. One reason for differences in the splittings could be addressed to different barriers heights, which vary from 6.3 to 8.8 kcal/mol, due to different mesomeric stabilization of the various transition states. The calculated splittings were compared to available experimental data and good agreement was found. A correlation could be found between the tunneling splitting and the energy barrier of the double proton transfer, as the splitting increases with increased strength of the hydrogen bonds. From this correlation an empirical formula was derived, which allows the prediction of the ground-state tunneling splitting of carboxylic acid dimers at a very low cost and the tunneling splittings for parahalogen substituted benzoic acid dimers is predicted.

About the stability of sulfurous acid (H2SO3) and its dimer

The characterization and isolation of sulfurous acid (H2SO3) have never been accomplished and thus still remain one of the greatest open challenges of inorganic chemistry. It is known that H2SO3 is thermodynamically unstable. In this study, however, we show that a Ci-symmetric dimer of sulfurous acid (H2SO3)2 is 3.5 kcal mol-1 more stable than its dissociation products SO2 and H2O at 77 K. Additionally, we have investigated the kinetic stability of the sulfurous acid monomer with respect to dissociation into SO2 and H2O and the kinetic isotope effect (KIE) on this reaction by transition-state theory. At 77 K, the half-life of H2SO3 is 15 x 10(9) years, but for the deuterated molecule (D2SO3) it increases to 7.9 x 10(26) years. At room temperature, the half-life of sulfurous acid is only 24 hours; however, a KIE of 3.2 x 10(4) increases it to a remarkable 90 years. Water is an efficient catalyst for the dissociation reaction since it reduces the reaction barrier tremendously. With the aid of two water molecules, one can observe a change in the reaction mechanism for sulfurous acid decomposition with increasing temperature. The most likely mechanism below 170 K is via an eight-membered transition-state ring; yet, above 170 K, a mechanism with a six-membered transition state ring becomes the predominant one. For deuterated sulfurous acid, this change in reaction mechanism can be observed at 120 K. Consequently, between 120 and 170 K, different predominant reaction mechanisms occur for the decomposition of normal and deuterated sulfurous acid when assisted by two water molecules. However, the much longer half-life of deuterated sulfurous acid and the stability of the sulfurous acid dimer at 77 K are encouraging for future synthesis and characterization under laboratory conditions.