New interpretation of proton and deuteron tunneling in 2'-methylacetophenone

This is the accepted manuscript of the following article: Fernández-Ramos, A., Siebrand, W., & Smedarchina, Z. (2013). New interpretation of proton and deuteron tunneling in 2'-methylacetophenone. Chemical Physics Letters, 586, 61-66. doi: 10.1016/j.cplett.2013.09.020The enol–keto transition rate constants in 2′-methylacetophenone observed by Grellmann et al. are calculated from first principles. The results reinterpret the proposed mechanism and show that proton tunneling is preceded by dissociation of a substrate-solvent complex rather than by rotamer interconversionS

The rainbow instanton method: A new approach to tunneling splitting in polyatomics

The following article appeared in The Journal of Chemical Physics 137, 224105 (2012) and may be found at https://doi.org/10.1063/1.4769198A new instanton approach is reported to tunneling at zero-temperature in multidimensional (MD) systems in which a “light particle” is transferred between two equivalent “heavy” sites. The method is based on two concepts. The first is that an adequate MD potential energy surface can be generated from input of the stationary configurations only, by choosing as a basis the normal modes of the transition state. It takes the form of a double-minimum potential along the mode with imaginary frequency and coupling terms to the remaining (harmonic) oscillators. Standard integrating out of the oscillators gives rise to an effective 1D instanton problem for the adiabatic potential, but requires evaluation of a nonlocal term in the Euclidean action, governed by exponential (memory) kernels. The second concept is that this nonlocal action can be treated as a “perturbation,” for which a new approximate instanton solution is derived, termed the “rainbow” solution. Key to the approach is avoidance of approximations to the exponential kernels, which is made possible by a remarkable conversion property of the rainbow solution. This leads to a new approximation scheme for direct evaluation of the Euclidean action, which avoids the time-consuming search of the exact instanton trajectory. This “rainbow approximation” can handle coupling to modes that cover a wide range of frequencies and bridge the gap between the adiabatic and sudden approximations. It suffers far fewer restrictions than these conventional approximations and is proving particularly effective for systems with strong coupling, such as proton transfer in hydrogen bonds. Comparison with the known exact instanton action in two-dimensional models and application to zero-level tunneling splittings in two isotopomers of malonaldehyde are presented to show the accuracy and efficiency of the approachS

Multidimensional Hamiltonian for tunneling with position-dependent mass

A multidimensional Hamiltonian for tunneling is formulated, based on the mode with imaginary frequency of the transition state as a reaction coordinate. To prepare it for diagonalization, it is transformed into a lower-dimension Hamiltonian by incorporating modes that move faster than the tunneling into a coordinate-dependent kinetic energy operator, for which a Hermitian form is chosen and tested for stability of the eigenvalues. After transformation to a three-dimensional form, which includes two normal modes strongly coupled to the tunneling mode, this Hamiltonian is diagonalized in terms of a basis set of harmonic oscillator functions centered at the transition state. This involves a sparse matrix which is easily partially diagonalized to yield tunneling splittings for the zero-point level and the two fundamental levels of the coupled modes. The method is tested on the well-known benchmark molecule malonaldehyde and a deuterium isotopomer, for which these splittings have been measured. Satisfactory agreement with experiment results is obtainedS

Methanol dimer formation drastically enhances hydrogen abstraction from methanol by OH at low temperature

The kinetics of the reaction of methanol with hydroxyl radicals is revisited in light of the reported new kinetic data, measured in cold expansion beams. The rate constants exhibit an approximately 102-fold increase when the temperature decreases from 200 to 50 K, a result that cannot be fully explained by tunneling, as we confirm by new calculations. These calculations also show that methanol dimers are much more reactive to hydroxyl than monomers and imply that a dimer concentration of about 30% of the equilibrium concentration can account quantitatively for the observed rates. The assumed presence of dimers is supported by the observation of cluster formation in these and other cold beams of molecules subject to hydrogen bonding. The calculations imply an important caveat with respect to the use of cold expansion beams for the study of interstellar chemistryA. F. R. and E. M. N. acknowledge funding from Ministerio de Economia y Competitividad of Spain (Research Grant No CTQ2014-58617-R). E. M. N. acknowledges financial support from Xunta de Galicia (Research Grant No GRC2014/032)S

Entanglement and co-tunneling of two equivalent protons in hydrogen bond pairs

The following article appeared in The Journal of Chemical Physics 148, 102307 (2018) and may be found at https://doi.org/10.1063/1.5000681A theoretical study is reported of a system of two identical symmetric hydrogen bonds, weakly coupled such that the two mobile protons can move either separately (stepwise) or together (concerted). It is modeled by two equivalent quartic potentials interacting through dipolar and quadrupolar coupling terms. The tunneling Hamiltonian has two imaginary modes (reaction coordinates) and a potential with a single maximum that may turn into a saddle-point of second order and two sets of (inequivalent) minima. Diagonalization is achieved via a modified Jacobi-Davidson algorithm. From this Hamiltonian the mechanism of proton transfer is derived. To find out whether the two protons move stepwise or concerted, a new tool is introduced, based on the distribution of the probability flux in the dividing plane of the transfer mode. While stepwise transfer dominates for very weak coupling, it is found that concerted transfer (co-tunneling) always occurs, even when the coupling vanishes since the symmetry of the Hamiltonian imposes permanent entanglement on the motions of the two protons. We quantify this entanglement and show that, for a wide range of parameters of interest, the lowest pair of states of the Hamiltonian represents a perfect example of highly entangled quantum states in continuous variables. The method is applied to the molecule porphycene for which the observed tunneling splitting is calculated in satisfactory agreement with experiment, and the mechanism of double-proton tunneling is found to be predominantly concerted. We show that, under normal conditions, when they are in the ground state, the two porphycene protons are highly entangled, which may have interesting applications. The treatment also identifies the conditions under which such a system can be handled by conventional one-instanton techniquesFinancial support from Ministerio de Economia y Competitividad of Spain (Research Grant No. CTQ2014-58617-R), the Consellería de Cultura, Educación e Ordenación Universitaria (Centro singular de investigacion de Galicia acreditación 2016-2019, No. ED431G/09), and the European Regional Development Fund (ERDF) is gratefully acknowledgedS

Model for the analysis of enzymatic proton-transfer reactions with an application to soybean lipoxygenase-1 and six mutants

A general analytical model is introduced for the analysis of temperature-dependent rate constants in enzymatic hydrogen and deuterium transfer reactions. It exploits the relationship between kinetic isotope effects (KIEs) and their temperature dependence in tunneling reaction to derive criteria that indicate whether a data set can be assigned to one rate-determining tunneling step in the enzymatic reaction sequence. If so, the model evaluates the relative contributions of the tunneling mode and supporting skeletal modes to transfer and provides information on these modes. Recently reported kinetic data on proton transfer in linoleic acid catalyzed by soybean lipoxygenase-1 (SLO1) and six mutants are analyzed by the model, which includes two oscillators, one representing proton motion relative to the skeletal framework and the other the supporting framework motions. It is concluded that most but not all components of this data set can be assigned to a single tunneling step, possible exceptions being associated with the highest observed rates, in agreement with evolutionary expectations. This still allows a complete analysis, namely in terms of the deuteron rate constants. The analysis evaluates how the contributions to proton transfer of the two modes and the electronic term depend on transfer distances in the enzyme and its mutants. It also provides rationalizations for several apparent anomalies, such as the vanishing of the activation energy for some mutants and the observed invariance of the KIE among mutants with very different activity.Peer reviewed: YesNRC publication: Ye

Kinetic Isotope Effects in Multiple Proton Transfer

NRC publication: Ye

Analysis of kinetic isotope effects in enzymatic carbon-hydrogen cleavage reactions

The instanton approach, as previously applied to proton tunneling in molecular systems, is adapted to carbon\u2013hydrogen bond cleavage catalyzed by enzymes. To compensate for the complexity of enzymatic reactions, simplifications are introduced based on the observation in numerous X-ray measurements that enzymes tend to form compact structures, which is assumed to have led toward optimization of specific parameters that govern the tunneling rate in the instanton formalism. On this basis, semiempirical equations are derived that link observed kinetic data directly to these parameters. These equations provide an analytical relation between the kinetic isotope effect and its temperature dependence for each hydrogen isotope, from which mechanistic and structural information can be extracted, including the nature of the hydrogen acceptor, the magnitude of the hydrogen transfer distance, the presence of endothermicity, and the contribution and frequency of skeletal vibrations that assist the tunneling. The method is used to analyze kinetic data reported for eight enzymatic CH-cleavage reactions; the enzymes or models thereof studied include methylmalonyl-coenzyme A mutase (coenzyme B12), galactose oxidase, lipoxygenase-1 with six mutants, methylamine dehydrogenase, an oxoiron(IV)porphyrin radical cation, phenylalanine hydroxylase, a bis(\u3bc-oxo)dicopper complex, and rice \u3b1-oxygenase.Peer reviewed: YesNRC publication: Ye

Mechanisms of CH-bond cleavage catalyzed by enzymes

NRC publication: Ye