Deep proton tunneling in the electronically adiabatic and non-adiabatic limits: comparison of the quantum and classical treatment of donor-acceptor motion in a protein environment

Cell Phone Radiation Exposure Limits and Engineering Solutions

In the 1990s, the Institute of Electrical and Electronics Engineers (IEEE) restricted its risk assessment for human exposure to radiofrequency radiation (RFR) in seven ways: (1) Inappropriate focus on heat, ignoring sub-thermal effects. (2) Reliance on exposure experiments performed over very short times. (3) Overlooking time/amplitude characteristics of RFR signals. (4) Ignoring carcinogenicity, hypersensitivity, and other health conditions connected with RFR. (5) Measuring cellphone Specific Absorption Rates (SAR) at arbitrary distances from the head. (6) Averaging SAR doses at volumetric/mass scales irrelevant to health. (7) Using unrealistic simulations for cell phone SAR estimations. Low-cost software and hardware modifications are proposed here for cellular phone RFR exposure mitigation: (1) inhibiting RFR emissions in contact with the body, (2) use of antenna patterns reducing the Percent of Power absorbed in the Head (PPHead) and body and increasing the Percent of Power Radiated for communications (PPR), and (3) automated protocol-based reductions of the number of RFR emissions, their duration, or integrated dose. These inexpensive measures do not fundamentally alter cell phone functions or communications quality. A health threat is scientifically documented at many levels and acknowledged by industries. Yet mitigation of RFR exposures to users does not appear as a priority with most cell phone manufacturers.

πσ*-Mediated Nonadiabatic Tunneling Dynamics of Thiophenols in S1: The Semiclassical Approaches

The S-H bond tunneling predissociation dynamics of thiophenol and its ortho-substituted derivatives (2-fluorothiophenol, 2-methoxythiophenol, and 2-chlorothiphenol) in S₁ (ππ*) where the H atom tunneling is mediated by the nearby S₂ (πσ*) state (which is repulsive along the S-H bond extension coordinate) have been investigated in a state-specific way using the picosecond time-resolved pump-probe spectroscopy for the jet-cooled molecules. The effects of the specific vibrational mode excitations and the SH/SD substitutions on the S-H(D) bond rupture tunneling dynamics have been interrogated, giving deep insights into the multidimensional aspects of the S₁/S₂ conical intersection, which also shapes the underlying adiabatic tunneling potential energy surfaces (PESs). The semiclassical tunneling rate calculations based on the Wentzel-Kramers-Brillouin (WKB) approximation or Zhu-Nakamura (ZN) theory have been carried out based on the ab initio PESs calculated in the (one, two, or three) reduced dimensions to be compared with the experiment. Though the quantitative experimental results could not be reproduced satisfactorily by the present calculations, the qualitative trends among different molecules in terms of the behavior of the tunneling rate versus the (adiabatic) barrier height or the number of PES dimensions could be rationalized. Most interestingly, the H/D kinetic isotope effect observed in the tunneling rate could be much better explained by the ZN theory compared to the WKB approximation, indicating that the nonadiabatic coupling matrix elements should be invoked for understanding the tunneling dynamics taking place in the proximity of the conical intersection.

Nonadiabatic quantum dynamics of the coherent excited state intramolecular proton transfer of 10-hydroxybenzo[h]quinoline

The photoinduced nonadiabatic dynamics of the enol-keto isomerization of 10-hydroxybenzo[h]quinoline (HBQ) are studied computationally using high-dimensional quantum dynamics. The simulations are based on a diabatic vibronic coupling Hamiltonian, which includes the two lowest [Formula: see text] excited states and a [Formula: see text] state, which has high energy in the Franck-Condon zone, but significantly stabilizes upon excited state intramolecular proton transfer. A procedure, applicable to large classes of excited state proton transfer reactions, is presented to parametrize this model using potential energies, forces and force constants, which, in this case, are obtained by time-dependent density functional theory. The wave packet calculations predict a time scale of 10-15 fs for the photoreaction, and reproduce the time constants and the coherent oscillations observed in time-resolved spectroscopic studies performed on HBQ. In contrast to the interpretation given to the most recent experiments, it is found that the reaction initiated by [Formula: see text] photoexcitation proceeds essentially on a single potential energy surface, and the observed coherences bear signatures of Duschinsky mode-mixing along the reaction path. The dynamics after the [Formula: see text] excitation are instead nonadiabatic, and the [Formula: see text] state plays a major role in the relaxation process. The simulations suggest a mainly active role of the proton in the isomerization, rather than a passive migration assisted by the vibrations of the benzoquinoline backbone.

The Soybean Lipoxygenase-Substrate Complex: Correlation between the Properties of Tunneling-Ready States and ENDOR-Detected Structures of Ground States

Hydrogen tunneling in enzymatic C-H activation requires a dynamical sampling among ground-state enzyme-substrate (E-S) conformations, which transiently generates a tunneling-ready state (TRS). The TRS is characterized by a hydrogen donor-acceptor distance (DAD) of 2.7 Å, ∼0.5 Å shorter than the dominant DAD of optimized ground states. Recently, a high-resolution, 13C electron-nuclear double-resonance (ENDOR) approach was developed to characterize the ground-state structure of the complex of the linoleic acid (LA) substrate with soybean lipoxygenase (SLO). The resulting enzyme-substrate model revealed two ground-state conformers with different distances between the target C11 of LA and the catalytically active cofactor [Fe(III)-OH]: the active conformer "a", with a van der Waals DAD of 3.1 Å between C11 and metal-bound hydroxide, and an inactive conformer "b", with a distance that is almost 1 Å longer. Herein, the structure of the E-S complex is examined for a series of six variants in which subtle structural modifications of SLO have been introduced either at a hydrophobic side chain near the bound substrate or at a remote residue within a protein network whose flexibility influences hydrogen transfer. A remarkable correlation is found between the ENDOR-derived population of the active ground-state conformer a and the kinetically derived differential enthalpic barrier for D versus H transfer, ΔEa, with the latter increasing as the fraction of conformer a decreases. As proposed, ΔEa provides a "ruler" for the DAD within the TRS. ENDOR measurements further corroborate the previous identification of a dynamical network coupling the buried active site of SLO to the surface. This study shows that subtle imperfections within the initial ground-state structures of E-S complexes are accompanied by compromised geometries at the TRS.

Proton-coupled electron transfer reactions: analytical rate constants and case study of kinetic isotope effects in lipoxygenase

A general theory has been developed for proton-coupled electron transfer (PCET), which is vital to a wide range of chemical and biological processes. This theory describes PCET reactions in terms of nonadiabatic transitions between reactant and product electron-proton vibronic states and includes the effects of thermal fluctuations of the solvent or protein environment, as well as the proton donor-acceptor motion. Within the framework of this general PCET theory, a series of analytical rate constant expressions has been derived for PCET reactions in well-defined regimes. Herein, the application of this theory to PCET in the enzyme soybean lipoxygenase illustrates the regimes of validity for the various rate constant expressions and elucidates the fundamental physical principles dictating PCET reactions. Such theoretical studies provide significant physical insights that guide the interpretation of experimental data and lead to experimentally testable predictions. A combination of theoretical treatments with atomic-level simulations is essential to understanding PCET.

Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion

Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton transfer and proton-coupled electron transfer in chemical and biological processes.

Wide-dynamic-range kinetic investigations of deep proton tunnelling in proteins

Directional proton transport along 'wires' that feed biochemical reactions in proteins is poorly understood. Amino-acid residues with high pKa are seldom considered as active transport elements in such wires because of their large classical barrier for proton dissociation. Here, we use the light-triggered proton wire of the green fluorescent protein to study its ground-electronic-state proton-transport kinetics, revealing a large temperature-dependent kinetic isotope effect. We show that 'deep' proton tunnelling between hydrogen-bonded oxygen atoms with a typical donor-acceptor distance of 2.7-2.8 Å fully accounts for the rates at all temperatures, including the unexpectedly large value (2.5 × 10(9) s(-1)) found at room temperature. The rate-limiting step in green fluorescent protein is assigned to tunnelling of the ionization-resistant serine hydroxyl proton. This suggests how high-pKa residues within a proton wire can act as a 'tunnel diode' to kinetically trap protons and control the direction of proton flow.