The reaction force constant: an indicator of the synchronicity in double proton transfer reactions

Earlier work, both experimental and computational, has drawn attention to the transition region in a chemical reaction, which includes the traditional transition state but extends along the intrinsic reaction coordinate ξ from perturbed forms of the reactants to perturbed forms of the products. The boundaries of this region are defined by the reaction force F(ξ), which is the negative gradient of the potential energy V(ξ) of the system along ξ. The reaction force constant κ(ξ), the second derivative of V(ξ), is negative throughout the transition region. We have now demonstrated, for a series of twelve double proton transfer processes, that the profile of κ(ξ) in the transition region is an indicator of the synchronicity of the two proton migrations in each case. When they are fully or nearly fully synchronous, κ(ξ) has a single minimum in the transition region. When the migrations are considerably nonsynchronous, κ(ξ) has two minima separated by a local maximum. Such an assessment of the degree of synchronicity cannot readily be made from an examination of the transition state alone, nor it is easily detected in the profiles of V(ξ) and F(ξ).     

Insights on the mechanism of proton transfer reactions in amino acids

In the present work, the joint use of the potential energy, the reaction electronic flux profiles and NBO analysis along the intrinsic reaction coordinate within the framework of the reaction force analysis allows us to gain insights into the mechanism of the proton transfer process in amino acids. The reaction was studied in alanine and phenylalanine in the presence of a continuum and with addition of one water molecule acting as a bridge, the results were compared to those of tryptophan. The bridging water molecule stabilizes the zwitterionic form and increases the reaction barriers by a factor of two. This result is interpreted in terms of the energy required to bring the amino acid and the water molecule closer to each other and to promote the proton transfer through the reordering of the electron density. Furthermore, the bridging water molecule induces a concerted asynchronous double proton transfer, where the transfer of the carboxyl hydrogen atom is followed by the second proton transfer to the ammonium group. In addition, a second not intervening water molecule was added, which changes the proton acceptor and donor properties of the reactive water molecule modulating the reaction mechanism. The aforementioned methods allow us to identify the order of the transferred protons and the asynchronicity, thereby, evolving as promising tools to not only characterize but also manipulate reaction mechanisms.     

Reaction force constant and projected force constants of vibrational modes along the path of an intramolecular proton transfer reaction

We have explored the relationships between the reaction force F(ξ), the reaction force constant κ(ξ) and the projected force constants of the intramolecular proton transfer HO−NS → ON−SH along the intrinsic reaction coordinate ξ. The structural changes and energetics associated with the reaction are analyzed in terms of the three regions defined by F(ξ): reactant, transition and product. The significance of the similarity between κ(ξ) and the variation of the force constant associated to the reaction coordinate mode, k_ξ(ξ), is discussed in detail.     

The reaction force: Three key points along an intrinsic reaction coordinate

The concept of the reaction force is presented and discussed in detail. For typical processes with energy barriers, it has a universal form which defines three key points along an intrinsic reaction coordinate: the force minimum, zero and maximum. We suggest that the resulting four zones be interpreted as involving preparation of reactants in the first, transition to products in the second and third, and relaxation in the fourth. This general picture is supported by the distinctive patterns of the variations in relevant electronic properties. Two important points that are brought out by the reaction force are that (a) the traditional activation energy comprises two separate contributions, and (b) the transition state corresponds to a balance between the driving and the retarding forces.     

A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates

We propose a generalization of the intrinsic reaction coordinate (IRC) for quantum many-body systems described in terms of the mass-weighted ring polymer centroids in the imaginary-time path integral theory. This novel kind of reaction coordinate, which may be called the "centroid IRC," corresponds to the minimum free energy path connecting reactant and product states with a least amount of reversible work applied to the center of masses of the quantum nuclei, i.e., the centroids. We provide a numerical procedure to obtain the centroid IRC based on first principles by combining ab initio path integral simulation with the string method. This approach is applied to NH(3) molecule and N(2)H(5) (-) ion as well as their deuterated isotopomers to study the importance of nuclear quantum effects in the intramolecular and intermolecular proton transfer reactions. We find that, in the intramolecular proton transfer (inversion) of NH(3), the free energy barrier for the centroid variables decreases with an amount of about 20% compared to the classical one at the room temperature. In the intermolecular proton transfer of N(2)H(5) (-), the centroid IRC is largely deviated from the "classical" IRC, and the free energy barrier is reduced by the quantum effects even more drastically.     

Characterizing the mechanism of the double proton transfer in the formamide dimer

The double proton transfer in the formamide dimer is characterized computationally by combining density functional theory and ab initio methods. The intrinsic reaction coordinate (IRC) is obtained at the B3LYP level of theory. Energies of several points along the IRC are treated by the more rigorous focal point method to test the validity of the B3LYP functional. The reaction mechanism is examined in terms of the energy profile, the reaction force, the chemical potential, and the reaction electronic flux. The energy profile for the activation process of the formamide dimer to the imino ether product obtained with the B3LYP functional is in agreement with the results of the focal point method. Together with the reaction force analysis and the reaction electronic flux a precise assignment of the structural and electronic contributions to the activation barrier becomes possible. The results show that the reaction starts with a structural rearrangement, where the two dimers approach each other, and is followed by electronic changes before the system reaches the transition state. This electronic contribution to the activation barrier steers the activation process. After the transition state is reached, deviations of the B3LYP functional from the more accurate focal point energies become apparent, where the errors may be rationalized in terms of the treatment of exchange. The inconsistency could be assigned to the incapacity of the functional to describe delocalization effects over the whole system.     

Ab initio molecular dynamics study of glycine intramolecular proton transfer in water

We use ab initio molecular-dynamics simulations to quantify structural and thermodynamic properties of a model proton transfer reaction that converts a neutral glycine molecule, stable in the gas phase, to the zwitterion that predominates in aqueous solution. We compute the potential of mean force associated with the direct intramolecular proton transfer event in glycine. Structural analyses show that the average hydration number (N(w)) of glycine is not constant along the reaction coordinate, but rather progresses from N(w) = 5 in the neutral molecule to N(w) = 8 for the zwitterion. We report the free-energy difference between the neutral and charged glycine molecules, and the free-energy barrier to proton transfer. Finally, we identify the approximations inherent in our method and estimate the corresponding corrections to our reported thermodynamic predictions.     

Analysis of the reaction force for a gas phase S(N)2 process: CH3Cl + H2O --> CH3OH + HCl

The "reaction force" F(R(c)) is the negative derivative of a system's potential energy V(R(c)) along the intrinsic reaction coordinate of a process. If V(R(c)) goes through a maximum, as is commonly the case, then F(R(c)) has a characteristic profile: a negative minimum followed by zero at the transition state and then a positive maximum. These features reflect four phases of the reaction: an initial one of reactant preparation, followed by two of transition to products, and then relaxation of the latter. In this study, we have analyzed, in these terms, a gas-phase S(N)2 substitution, selected to be CH3Cl + H2O --> CH3OH + HCl. We examine, at the B3LYP/6-31G level, the geometries, energetics, and molecular surface electrostatic potentials, local ionization energies, and internal charge separation.     

Mechanistic insights on how hydroquinone disarms OH and OOH radicals

Phenol derivatives are distinguished as successful free radical scavengers. We present a detailed analysis of hydroxyl hydrogen abstraction from hydroquinone by hydroxyl and hydroperoxyl radical with emphasis on changes that take place in the vicinity of the transition state. Quantum theory of atoms in molecules is employed to elucidate the sequence of positive and negative charge transfer by studying selected properties of the three key atoms (the transferring hydrogen, the donor atom, and the acceptor atom) along intrinsic reaction path. The presented results imply that in both reactions, which are examples of proton coupled electron transfer, proton, and electron get simultaneously transferred to the radical oxygen atom. The fact that the hydrogen's charge and volume do not monotonously change in the vicinity of the transition state in the product valley results from the adjacency of the proton and the electron to the donor and the acceptor oxygen atoms. Obtaining a detailed understanding of mechanisms by which free radicals are disarmed is of paramount importance given the effects of those highly reactive species on biological systems. A comprehensive analysis of hydroxyl hydrogen abstraction from hydroquinone by hydroxyl and hydroperoxyl radicals, based on changes of selected electronic properties of the three most relevant atoms (hydrogen donor, hydrogen acceptor, and the hydrogen itself), along the reaction coordinate, can be obtained by first‐principles calculations.     

A comparative ab initio study of intramolecular proton transfer in model alpha-hydroxyalkoxides

A comparative ab initio study was performed on the intramolecular proton-transfer reaction that occurs in alpha-hydroxyethanoxy, alpha-hydroxyphenoxide, and alpha-hydroxyethenoxy anions. The intramolecular proton transfer occurs in a five-member atom arrangement, between two oxygen atoms separated by a carbon-carbon bond. The chosen systems serve as models for alpha-hydroxyalkoxide molecules where the carbon-carbon bond varies from a single bond (the glycolate anion or alpha-hydroxyethanoxide anion) to a part of an aromatic ring (the alpha-hydroxyphenoxide anion), and finally to a double bond (the alpha-hydroxyethenoxide anion). Particular attention was given to the evolution along the intrinsic reaction coordinate of such properties as energies, relevant structural parameters, Mulliken charges, dipole moments, and 1H-NMR chemical shifts to reveal the similarities and differences for the proton transfer in the model systems.     

A Mixed Quantum-Classical Approach for Computing Effects of Intramolecular Motion on the Low-Barrier Hydrogen Bond

The fractionation factor is defined as the equilibrium constant for the reaction: R – H + DOH R – D + HOH. Of interest are values of fractionation factors for reactions where reactants and/or products form intramolecular low-barrier hydrogen bonds. Experimentally measured isotopic fractionation factors are usually interpreted via a one-dimensional potential energy surface along the intrinsic proton hydrogen bond coordinate. Such a one-dimensional picture cannot be completely correct. Intramolecular motions, such as vibrations and librations, can modulate the underlying potential energy surface along the hydrogen bond coordinate and thus affect the isotopic fractionation factor. We have recently generated a picture of the motion of the proton in a low-barrier hydrogen bond as taking place in an effective single-dimensional potential, which we term the potential of mean force (PMF). In this paper, we compute the PMF for a molecule with an intramolecular hydrogen bond in order to quantify the effect of intramolecular motions on the fractionation factor. The PMF and isotopic fractionation factor are computed with a combination of high-level density functional theory and molecular dynamics simulations.     

Concerted proton-electron transfers. Consistency between electrochemical kinetics and their homogeneous counterparts

The concerted proton-electron transfer (CPET) oxidation of phenol with water (in water) and hydrogen phosphate as proton acceptors provides a good example for testing the consistency of the electrochemical and homogeneous approaches to a reaction, the comprehension of which raises more mechanistic and kinetic challenges than that of a simple outer-sphere electron transfer. Comparison of the intrinsic kinetic characteristics (obtained at zero driving force of the CPET reaction) shows that consistency is indeed observed after a careful identification and quantitation of side factors (electrical work terms, image force effects). Water (in water) appears as a better intrinsic proton acceptor than hydrogen phosphate in both cases in terms of reorganization energy and pre-exponential factor, corroborating the mechanism by which electron transfer is concerted with Grotthus-type proton translocation in water. Detailed compared analysis of the approaches also revealed that modest but significant electric field effects may be at work in the electrochemical case. Comparison with phenoxide ion oxidation, taken as a reference outer-sphere electron transfer, points to a CPET precursor complex that possesses a precise spatial structure allowing the formation of one or several H-bonds as required by the occurrence of the CPET reaction, thus decreasing considerably the number of efficient collisions compared with those undergone by structureless spherical reactants.     

Probing irradiation induced DNA damage mechanisms using excited state Car-Parrinello molecular dynamics

Photoinduced proton transfer in the Watson-Crick guanine (G)-cytosine (C) base pair has been studied using Car-Parrinello molecular dynamics (CP-MD). A flexible mechanical constraint acting on all three hydrogen bonds in an unbiased fashion has been devised to explore the free energy profile along the proton transfer coordinate. The lowest barrier has been found for proton transfer from G to C along the central hydrogen bond. The resulting charge transfer excited state lies energetically close to the electronic ground state suggesting the possibility of efficient radiationless decay. It is found that dynamic, finite temperature fluctuations significantly reduce the energy gap between the ground and excited states for this charge transfer product, promoting the internal conversion process. A detailed analysis of the internal degrees of freedom reveals that the energy gap is considerably reduced by out-of-plane molecular vibrations, in particular. Consequently, it appears that considering only the minimum energy path provides an upper-bound estimate of the associated energy gap compared to the full-dimension dynamical reaction coordinate. Furthermore, the first CP-MD simulations of the G-C base pair in liquid water are presented, and the effects of solvation on its electronic structure are analyzed.     

Proton transfer in a polar solvent from ring polymer reaction rate theory

We have used the ring polymer molecular dynamics method to study the Azzouz-Borgis model for proton transfer between phenol (AH) and trimethylamine (B) in liquid methyl chloride. When the A-H distance is used as the reaction coordinate, the ring polymer trajectories are found to exhibit multiple recrossings of the transition state dividing surface and to give a rate coefficient that is smaller than the quantum transition state theory value by an order of magnitude. This is to be expected on kinematic grounds for a heavy-light-heavy reaction when the light atom transfer coordinate is used as the reaction coordinate, and it clearly precludes the use of transition state theory with this reaction coordinate. As has been shown previously for this problem, a solvent polarization coordinate defined in terms of the expectation value of the proton transfer distance in the ground adiabatic quantum state provides a better reaction coordinate with less recrossing. These results are discussed in light of the wide body of earlier theoretical work on the Azzouz-Borgis model and the considerable range of previously reported values for its proton and deuteron transfer rate coefficients.     

The mechanism of double proton transfer in dimers of uracil and 2-thiouracil--the reaction force perspective

The intermolecular double proton transfer in dimers of uracil and 2-thiouracil is studied through density functional theory calculations. The reaction force framework provides the basis for characterizing the mechanism that in all cases has been associated to a dynamic balance between polarization and charge transfer effects. It has been found that the barriers for proton transfer depend upon the nature of the acceptor atoms and its position within the seminal monomer. Actually, the change in the nature of the hydrogen bonds connecting the two monomers along the reaction coordinate may favor or disfavor the double-proton transfer.     

Understanding the physics and chemistry of reaction mechanisms from atomic contributions: a reaction force perspective

Studying chemical reactions involves the knowledge of the reaction mechanism. Despite activation barriers describing the kinetics or reaction energies reflecting thermodynamic aspects, identifying the underlying physics and chemistry along the reaction path contributes essentially to the overall understanding of reaction mechanisms, especially for catalysis. In the past years the reaction force has evolved as a valuable tool to discern between structural changes and electrons' rearrangement in chemical reactions. It provides a framework to analyze chemical reactions and additionally a rational partition of activation and reaction energies. Here, we propose to separate these energies further in atomic contributions, which will shed new insights in the underlying reaction mechanism. As first case studies we analyze two intramolecular proton transfer reactions. Despite the atom based separation of activation barriers and reaction energies, we also assign the participation of each atom in structural changes or electrons' rearrangement along the intrinsic reaction coordinate. These participations allow us to identify the role of each atom in the two reactions and therfore the underlying chemistry. The knowledge of the reaction chemistry immediately leads us to suggest replacements with other atom types that would facilitate certain processes in the reaction. The characterization of the contribution of each atom to the reaction energetics, additionally, identifies the reactive center of a molecular system that unites the main atoms contributing to the potential energy change along the reaction path.     

Simulation of proton transport in the gramicidin A channel

The free energy profiles for proton transfer along the oriented water file inside the gramicidin A channel were calculated. An original implementation of the rigid-body molecular dynamics method was used for describing the peptide groups of the channel and outer water molecules. The inner water wire was simulated using the PM6 force field parameters, which adequately describe the formation and cleavage of chemical and hydrogen bonds in water molecules. Different mechanisms of proton transfer through the gramicidin A channel were considered, namely, proton H⁺ translocation, transfer of the anion defect OH^?, and reorientation of the water file inside the channel. To facilitate parallel calculations of trajectories, the reaction coordinate was divided into segments, and the results were combined by the weighted histogram analysis method. The first two processes, H⁺ and OH^? transfers, were shown to be barrierless. Only the stage of reorientation of the water file inside the channel has an energy barrier.     

DOIT: a program to calculate thermal rate constants and mode‐specific tunneling splittings directly from quantum‐chemical calculations

In this contribution we discuss computational aspects of a recently introduced method for the calculation of proton tunneling rate constants, and tunneling splittings, which has been applied to molecules and complexes, and should apply equally well to bulk materials. The method is based on instanton theory, adapted so as to permit a direct link to the output of quantum‐chemical codes. It is implemented in the DOIT (dynamics of instanton tunneling) code, which calculates temperature‐dependent tunneling rate constants and mode‐specific tunneling splittings. As input, it uses the structure, energy, and vibrational force field of the stationary configurations along the reaction coordinate, computed by conventional quantum‐chemical programs. The method avoids the difficult problem of calculating the exact least‐action trajectory, known as the instanton path, and instead focusses on the corresponding instanton action, because it governs the dynamic properties. To approximate this action for a multidimensional system, the program starts from the one‐dimensional instanton action along the reaction coordinate, which can be obtained without difficulty. It then applies correction terms for the coupling to the other vibrational degrees of freedom, which are treated as harmonic oscillators (transverse normal modes). The couplings are assumed linear in these modes. Depending on the frequency and the character of the transverse modes, they may either decrease or increase the action, i.e., help or hinder the transfer. A number of tests have shown that the program is at least as accurate as alternative programs based on transition‐state theory with tunneling corrections, and is also much less demanding in computer time, thus allowing application to much larger systems. An outline of the instanton formalism is presented, some new developments are introduced, and special attention is paid to the connection with quantum‐chemical codes. Possible sources of error are investigated. To show the program in action, calculations are presented of tunneling rates and splittings associated with triple proton transfer in the chiral water trimer. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 787–801, 2001     

Ultrafast deactivation of an excited cytosine-guanine base pair in DNA

Multiconfigurational ab initio calculations and QM/MM molecular dynamics simulations of a photoexcited cytosine-guanine base pair in both gas phase and embedded in the DNA provide detailed structural and dynamical insights into the ultrafast radiationless deactivation mechanism. Photon absorption promotes transfer of a proton from the guanine to the cytosine. This proton transfer is followed by an efficient radiationless decay of the excited state via an extended conical intersection seam. The optimization of the conical intersection revealed that it has an unusual topology, in that there is only one degeneracy-lifting coordinate. This is the central mechanistic feature for the decay both in vacuo and in the DNA. Radiationless decay occurs along an extended hyperline nearly parallel to the proton-transfer coordinate, indicating the proton transfer itself is not directly responsible for the deactivation. The seam is displaced from the minimum energy proton-transfer path along a skeletal deformation of the bases. Decay can thus occur anywhere along the single proton-transfer coordinate, accounting for the remarkably short excited-state lifetime of the Watson-Crick base pair. In vacuo, decay occurs after a complete proton transfer, whereas in DNA, decay can also occur much earlier. The origin of this effect lies in the temporal electrostatic stabilization of dipole in the charge-transfer state in DNA.