Cooperative interactions of hydrogen bonds in proton-transfer processes involving water molecules. Simulation of biochemical systems

Quantum-chemical calculations of molecular complexes simulating the proton channel of influenza A virus and the proton-transfer system of the active site of carboanhydrase enzyme were performed. These complexes comprise a proton-donor and a proton-acceptor groups bridged by a chain of water molecules. Calculations of the methylimidazole (H⁺)-H₂O-CH₃COO^? complex as a model of influenza M₂ virus revealed free translation motion of the water molecule between the donor and acceptor, as well as concerted proton transfer in both H bonds. The barrier for proton transfer is independent of the position of the bridging water molecule and varies linearly with the difference in the electrostatic potentials between the donor and acceptor. With elongation of the H-bond bridge between the donor and acceptor groups, the H-bond lengths and proton shifts in the chain links vary periodically. This process can be defined as an H-bond deformation wave (proton wave). It was shown that motion of one proton along the H bond is associated with vibrational motion of protons in other links, which results in wave propagation along the chain. The calculation results allowed the rate of the proton wave and the time of proton transfer from the donor to acceptor to be estimated.     

Proton transfer reactions and dynamics of sulfonic acid group in Nafion®

Proton transfer reactions and dynamics of the hydrophilic group (-SO(3)H) in Nafion? were studied at low hydration levels using the complexes formed from CF(3)SO(3)H, H(3)O(+) and nH(2)O, 1 ≤n≤ 3, as model systems. The equilibrium structures obtained from DFT calculations suggested at least two structural diffusion pathways at the -SO(3)H group namely, the "pass-through" and "pass-by" mechanisms. The former involves the protonation and deprotonation at the -SO(3)H group, whereas the latter the proton transfer in the adjacent Zundel complex. Analyses of the asymmetric O-H stretching frequencies (ν(OH)) of the hydrogen bond (H-bond) protons showed the threshold frequencies (ν(OH*)) of proton transfer in the range of 1700 to 2200 cm(-1). Born-Oppenheimer Molecular Dynamics (BOMD) simulations at 350 K anticipated slightly lower threshold frequencies (ν(A)(OH*,MD)), with two characteristic asymmetric O-H stretching frequencies being the spectral signatures of proton transfer in the H-bond complexes. The lower frequency (ν(A)(OH,MD))) is associated with the oscillatory shuttling motion and the higher frequency (ν(B)(OH,MD))) the structural diffusion motion. Comparison of the present results with BOMD simulations on protonated water clusters indicated that the -SO(3)H group facilitates proton transfer by reducing the vibrational energy for the interconversion between the two dynamic states (Δν), resulting in a higher population of the H-bonds with the structural diffusion motion. One could therefore conclude that the -SO(3)H groups in Nafion? act as active binding sites which provide appropriate structural, energetic and dynamic conditions for effective structural diffusion processes in a proton exchange membrane fuel cell (PEMFC). The present results suggested for the first time a possibility to discuss the tendency of proton transfer in H-bond using Δν(BA)(OH,MD)) and provided theoretical bases and guidelines for the investigations of proton transfer reactions in theory and experiment.     

The wave nature of the protonic conductivity mechanism in the active site of carboanhydrase

Quantum-chemical calculations were performed for the (NH₃)₃Zn²⁺...(H₂O)_n...NH₃ (n = 3–11) molecular complex to model the proton transfer system of the carboanhydrase enzyme. H-bond proton transfer along the chain connecting the donor and acceptor groups was shown to be concerted vibrational motion of all protons in the chain. A wave of H-bond deformations was related to the moving proton. The displacement of H-bond protons in the transition state of the proton transfer reaction with respect to their equilibrium positions corresponded to a structure that could be defined as a proton wave. The length of this wave found as the distance between H-bond contraction (O-H bond elongation) maxima was ～8 Å. Charge transfer from the donor to the acceptor occurred according to the mechanism of the concerted jump of H-bond protons as the wave reached the chain end. The barrier to transfer was independent of the number of chain links and equaled 10 kcal/mol.     

Mixed Quantum Classical Reaction Rates based on the Phase Space Formulation of the Hierarchical Equations of Motion

In a previous work [J. Chem. Phys. 140 , 174105 (2014)], we have shown that a mixed quantum classical (MQC) rate theory can be derived to investigate the quantum tunneling effects in the proton transfer reactions. However, the method is based on the high temperature approximation of the hierarchical equation of motion (HEOM) with the Debye-Drude spectral density, and results in a multi-state Zusman type of equation. We now extend this theory to include quantum effects of the bath degrees of freedom. By writing the full HEOM into a multidimensional partial differential equation in phase space, we can define a new reaction coordinate, and the previous method can be generalized to the full quantum regime. The validity of the new method is demonstrated by using numerical examples, including the spin-Boson model, and the double well model for proton transfer reaction. The new method is found to resolve some key problems of the previous theory based on high temperature approximation, including possible numerical instability in long time simulation and wrong rate constant at low temperatures.     

Application of Schrödinger equation to study the tunnelling dynamics of proton transfer in the hydrogen bond of 2,5-dinitrobenzoic acid: proton T1 T1rho, and deuteron T1 relaxation methods

Temperature measurements of proton T1 (24.7 MHz), deuteron (deuterated hydroxyl group) T1 (55.2 MHz), and proton T1(rho) (B1 = 9 G) spin-lattice relaxation times of 2,5-dinitrobenzoic acid have been performed. An analysis of present experimental data together with previously published proton T1 (55.2 MHz) data has revealed the following molecular motions: proton/deuteron transfer in the hydrogen bond and two-site hopping of the whole dimer. It is shown that the proton-transfer dynamics are characterized by two correlation times tau(ov) and tau(tu), describing two fundamentally different motional processes, namely, thermally activated jumps over the barrier and tunneling through the barrier. The temperature dependence of 1/tau(tu) is the solution of Schr?dinger's equation, which also yields the temperature T(tun), where begins the tunnel pathway for proton transfer. A new equation for the spectral density function of complex motion consisting of the three motions is derived. The third motion (two-site hopping of the whole dimer characterized by tau(lib) correlation time) is responsible for a proton T1(rho) minimum in high temperatures, just below the melting point. Such a minimum is not reached by T1 temperature dependencies. The minimum of T1(rho) assigned to the classical hopping of a hydrogen-bonded proton occurs in the same low-temperature regime in which the flattening of the temperature dependencies of T1 points to the dominance of incoherent tunneling. This experimental fact denies the known theories predicting the intermediate temperature regime where a smooth transition between classical and quantum tunneling dynamics is expected. The fit of the derived theoretical equations to the experimental data T1(rho) and T1 is satisfactory. The correlation times obtained for deuterons indicate deuteron-transfer dynamics much slower than proton-transfer dynamics. It is concluded that the classical proton transfer takes place over the whole temperature regime, while the incoherent tunneling occurs below 46.5 (hydrogen) or 87.2 K (deuterium) only.     

Dynamics and mechanism of structural diffusion in linear hydrogen bond

Dynamics and mechanism of proton transfer in a protonated hydrogen bond (H-bond) chain were studied, using the CH(3)OH(2)(+)(CH(3)OH)(n) complexes, n = 1-4, as model systems. The present investigations used B3LYP/TZVP calculations and Born-Oppenheimer MD (BOMD) simulations at 350 K to obtain characteristic H-bond structures, energetic and IR spectra of the transferring protons in the gas phase and continuum liquid. The static and dynamic results were compared with the H(3)O(+)(H(2)O)(n) and CH(3)OH(2)(+)(H(2)O)(n) complexes, n = 1-4. It was found that the H-bond chains with n = 1 and 3 represent the most active intermediate states and the CH(3)OH(2)(+)(CH(3)OH)(n) complexes possess the lowest threshold frequency of proton transfer. The IR spectra obtained from BOMD simulations revealed that the thermal energy fluctuation and dynamics help promote proton transfer in the shared-proton structure with n = 3 by lowering the vibrational energy for the interconversion between the oscillatory shuttling and structural diffusion motions, leading to a higher population of the structural diffusion motion than in the shared-proton structure with n = 1. Additional explanation on the previously proposed mechanisms was introduced, with the emphases on the energetic of the transferring proton, the fluctuation of the number of the CH(3)OH molecules in the H-bond chain, and the quasi-dynamic equilibriums between the shared-proton structure (n = 3) and the close-contact structures (n ≥ 4). The latter prohibits proton transfer reaction in the H-bond chain from being concerted, since the rate of the structural diffusion depends upon the lifetime of the shared-proton intermediate state.     

Molecular geometry as a source of chemical information. 5. Substituent effect on proton transfer in para-substituted phenol complexes with fluoride--a B3LYP/6-311+G study

The simplified model system [p-X-PhO...H...F](-), where -X are -NO, -NO(2), -CHO, -H, -CH(3), -OCH(3), and -OH, with various O...F distance was used to simulate the wide range of the H-bond strength. Structural changes due to variation of the substituent as well as the H-bond strength are well monitored by the changes in the aromaticity index HOMA and by two empirical measures of the H-bond strength-the (1)H NMR chemical shift of proton involved and the C-O bond length. Changes in H-bonding strengths and the position of proton transfer while shortening the O...F distance are well described by the Hammett equation.     

Theoretical study on the excited-state intramolecular proton transfer in the aromatic schiff base salicylidene methylamine: an electronic structure and quantum dynamical approach

The proton-transfer dynamics in the aromatic Schiff base salicylidene methylamine has been theoretically analyzed in the ground and first singlet (pi,pi) excited electronic states by density functional theory calculations and quantum wave-packet dynamics. The potential energies obtained through electronic calculations that use the time-dependent density functional theory formalism, which predict a barrierless excited-state intramolecular proton transfer, are fitted to a reduced three-dimensional potential energy surface. The time evolution in this surface is solved by means of the multiconfiguration time-dependent Hartree algorithm applied to solve the time-dependent Schr?dinger equation. It is shown that the excited-state proton transfer occurs within 11 fs for hydrogen and 25 fs for deuterium, so that a large kinetic isotope effect is predicted. These results are compared to those of the only previous theoretical work published on this system [Zgierski, M. Z.; Grabowska, A. J. Chem. Phys. 2000, 113, 7845], reporting a configuration interaction singles barrier of 1.6 kcal mol(-1) and time reactions of 30 and 115 fs for the hydrogen and deuterium transfers, respectively, evaluated with the semiclassical instanton approach.     

Comparison between theoretical values and simulation results of viscosity for the dissipative particle dynamics method

In order to investigate the validity of the dissipative particle dynamics method, which is a mesoscopic simulation technique, we have derived an expression for viscosity from the equation of motion of dissipative particles. In the concrete, we have shown the Fokker-Planck equation in phase space, and macroscopic conservation equations such as the equation of continuity and the equation of momentum conservation. The basic equations of the single-particle and pair distribution functions have been derived using the Fokker-Planck equation. The solutions of these distribution functions have approximately been solved by the perturbation method under the assumption of molecular chaos. The expressions of the viscosity due to momentum and dissipative forces have been obtained using the approximate solutions of the distribution functions. Also, we have conducted nonequilibrium dynamics simulations to investigate the influence of the parameters, which have appeared in defining the equation of motion in the dissipative particle dynamics method. The theoretical values of the viscosity due to dissipative forces in the Hoogerbrugge-Koelman theory are in good agreement with the simulation results obtained by the nonequilibrium dynamics method, except in the range of small number densities. There are restriction conditions for taking appropriate values of the number density, number of particles, time interval, shear rate, etc., to obtain physically reasonable results by means of dissipative particle dynamics simulations.     

Constitutive equations for the flow behavior of entangled polymeric systems: application to star polymers

A semimicroscopic derivation is presented of equations of motion for the density and the flow velocity of concentrated systems of entangled polymers. The essential ingredient is the transient force that results from perturbations of overlapping polymers due to flow. A Smoluchowski equation is derived that includes these transient forces. From this, an equation of motion for the polymer number density is obtained, in which body forces couple the evolution of the polymer density to the local velocity field. Using a semimicroscopic Ansatz for the dynamics of the number of entanglements between overlapping polymers, and for the perturbations of the pair-correlation function due to flow, body forces are calculated for nonuniform systems where the density as well as the shear rate varies with position. Explicit expressions are derived for the shear viscosity and normal forces, as well as for nonlocal contributions to the body force, such as the shear-curvature viscosity. A contribution to the equation of motion for the density is found that describes mass transport due to spatial variation of the shear rate. The two coupled equations of motion for the density and flow velocity predict flow instabilities that will be discussed in more detail in a forthcoming publication.     

Faster proton transfer dynamics of water on SnO2 compared to TiO2

Proton jump processes in the hydration layer on the iso-structural TiO(2) rutile (110) and SnO(2) cassiterite (110) surfaces were studied with density functional theory molecular dynamics. We find that the proton jump rate is more than three times faster on cassiterite compared with rutile. A local analysis based on the correlation between the stretching band of the O-H vibrations and the strength of H-bonds indicates that the faster proton jump activity on cassiterite is produced by a stronger H-bond formation between the surface and the hydration layer above the surface. The origin of the increased H-bond strength on cassiterite is a combined effect of stronger covalent bonding and stronger electrostatic interactions due to differences of its electronic structure. The bridging oxygens form the strongest H-bonds between the surface and the hydration layer. This higher proton jump rate is likely to affect reactivity and catalytic activity on the surface. A better understanding of its origins will enable methods to control these rates.     

Structure, stability and spectral signatures of monoprotic carborane acid-water clusters (CBW(n), where n = 1-6)

The gas phase structure, stability, spectra, and proton transfer properties of monoprotic carborane acid-water clusters [CB(11)F(m)H(11-m)(OH(2))(1)]-(H(2)O)(n) (where m = 0, 5, and 10; n = 1-6) have been calculated using density functional theory (DFT) with the Becke's three-parameter hybrid exchange functional and Lee-Yang-Parr correlation functional (B3LYP) using 6-31+G* basis set. Results reveal that Eigen cation defects are found in CBW(n) (where n = 2-6) clusters and these clusters are significantly more stable than the non-Eigen geometry. In addition to the conventional hydrogen bond (H-bond) the role of dihydrogen bond (DHB) and halogen bond (XB) in the stabilization of these clusters can be observed from the molecular graphs derived from the atoms in molecules (AIM) analysis. Spectral information shows the features of Eigen cation and proton oscillation involved in the proton transfer process. The dissociation of proton from the perfluoro derivatives with two water molecules is more favorable when compared to the other derivatives.     

The role of the alien proton acceptor on the formation of LC structure in H-bonded monomeric and polymeric derivatives of alkoxybenzoic acids

The formation of the complex between 4-cyanopyridine and 4-(6-acryloyloxy-hexyloxy) benzoic acid and its polymeric analog proceeds due to the proton transfer with the H-bond formation. The presence of two proton acceptor groups within one molecule provides a strong shift of the electron density along the complex molecule due to the conjugation within the proton acceptor molecule. The dielectric relaxation process in a symmetric associate experimentally observed is explained as a kinetic effect related to the formation and destruction of the associate.

Transition from a monomer to a polymer proton donor leads to the formation of the characteristic 1:1 complex with SmC layered structure different from that of a polymer itself.     

A theoretical model for electron and proton coupling at quinone-binding site of photosystem II of higher plants

In this work we consider the coupling of electron and proton transfer near Q(B) in the reaction center (RC) of photosystem II (PS2). We have carried out the calculations of the energy levels and proton density in the system Q(B)(-) Histidine L190. It is shown that the proton of the histidine forms the H-bond with twice-reduced Q(B)(2-). Based on these calculations, we propose a new explanation of the coupling between the electron and proton transfer.     

气相水杨酸激发态分子内质子转移特性分析

采用密度泛函理论(DFT)和含时密度泛函理论(TD-DFT)研究了气相水杨酸(SA)分子的激发态氢键动力学过程。通过对水杨酸分子基态和激发态结构的优化,以及对其稳态吸收和发射光谱特性、前线分子轨道、红外振动光谱和势能曲线的计算分析,阐明水杨酸分子内质子转移可在激发态下自发地发生,导致其激发态可存在烯醇式和酮式两种异构体结构,并揭示了这种质子转移源于分子内电荷转移的激发态氢键的加强机制。     

Protonic Quantum Correlations in the H-Bond Dynamics of Nucleic Acids. Part 1. Conformational comparison of G-C with Benner's κ-π

A new base pair (called κ-π) of Watson-Crick type, with an H-bond pattern different from that in A-T and G-C base pairs, has been recently synthesized by Benner and coworkers and shown to be stable and incorporable into duplex DNA and RNA by polymerases. This new base pair, which contains three H-bonds, is compared with G-C, in the framework of modern dynamical theory of quantum nonlocality and quantum correlations (also called Einstein-Podolsky-Rosen correlations). Connection with the traditional treatment of proton transfer in DNA base pairs, which uses the adiabatic approximation (thus considering the protons as classical particles), is explicitly made. As a result, the dynamics of the H-bond pattern of G-C is shown to exhibit a specific quantum-mechanical phase stability (or: rigidity, stiffness), which is clearly missing in the case of κ-π. This finding is discussed and illustrated, also in connection with recent quantum chemical calculations of proton transfers in DNA base pairs. Additionally, certain speculations concerning a probable ‘evolutionary advantage’ of G-C with respect to κ-π are shortly considered.     

The effect of hydrogen bonding on the excited-state proton transfer in 2-(2'-hydroxyphenyl)benzothiazole: a TDDFT molecular dynamics study

The dynamics of the excited-state proton transfer (ESPT) in a cluster of 2-(2'-hydroxyphenyl)benzothiazole (HBT) and hydrogen-bonded water molecules was investigated by means of quantum chemical simulations. Two different enol ground-state structures of HBT interacting with the water cluster were chosen as initial structures for the excited-state dynamics: (i) an intramolecular hydrogen-bonded structure of HBT and (ii) a cluster where the intramolecular hydrogen bond in HBT is broken by intermolecular interactions with water molecules. On-the-fly dynamics simulations using time-dependent density functional theory show that after photoexcitation to the S(1) state the ESPT pathway leading to the keto form strongly depends on the initial ground state structure of the HBT-water cluster. In the intramolecular hydrogen-bonded structures direct excited-state proton transfer is observed within 18 fs, which is a factor two faster than proton transfer in HBT computed for the gas phase. Intermolecular bonded HBT complexes show a complex pattern of excited-state proton transfer involving several distinct mechanisms. In the main process the tautomerization proceeds via a triple proton transfer through the water network with an average proton transfer time of approximately 120 fs. Due to the lack of the stabilizing hydrogen bond, intermolecular hydrogen-bonded structures have a significant degree of interring twisting already in the ground state. During the excited state dynamics, the twist tends to quickly increase indicating that internal conversion to the electronic ground state should take place at the sub-picosecond scale.