Z. T. Chu

Quantum corrections for rate constants of diabatic and adiabatic reactions in solutions

A method for the calculation of quantized rate constants of chemical reactions in condensed phases is presented. The method focuses on the evaluation of nuclear tunneling corrections for classical activation free energies of diabatic and adiabatic reactions. The diabatic problem is treated by the quasiharmonic dispersed polaron model, using both a second order quantum mechanical rate constant, which is exact for quasiharmonic systems, and a semiclassical approximation based on an analytical density matrix formulation. The adiabatic free energy functionals are obtained by using the corresponding diabatic system as a reference state. A path integral formulation is also used both as a guide for the derivation of the adiabatic correction and as an alternative method for problems of limited dimensionality. The close relationship between the free energy functionals of the present approach and those developed in our earlier studies of electron transfer and proton transfer reactions is pointed out. The method is ...

The dynamics of the primary event in rhodopsins revisited

Abstract The conclusions obtained from an early simulation study of the primary event in the vision process are reexamined by simulating the dynamics of the primary photoisomerization reaction in bacteriorhodopsin using a detailed molecular model for the protein-chromophore complex. The calculated photoisomerization time is of the same order of magnitude as that predicted by the early simulation and found in recent experimental studies. Several simulations with different conditions indicate that the isomerization process involves an efficient transfer of energy from the reaction coordinate to other degrees of freedom and is better described by a damped-motion model than by an inertial model. The damped motion is expected to give a significant quantum yield for both the cis→trans and trans→cis cases only if the minimum of the excited state potential surface is located above the ground state maximum (unless the excited state surface is extremely shallow or if the inertial effects associated with the surface crossing process are very large). The present study suggests that the observed quantum yield should not be analyzed by one-dimensional models but by multidimensional microscopic simulations that consider the surface crossing process and the subsequent ground state relaxation processes.

On the energetics of the primary electron-transfer process in bacterial reaction centers

Abstract The energetics of the initial electron-transfer steps in photosynthetic bacterial reaction centers are evaluated by free-energy perturbation calculations using several different treatments of the ionizable amino acid residues and of solvent molecules in and around the protein. The calculation illustrate the problems with incomplete treatments of dielectric effects. Calculations that do not include mobile solvent lead to large overestimates of the effects of ionized amino acid side-chains, and can give errors of up to 20 kcal mol −1 in the free-energy difference between the ion-pair states P + B − and P + H − . When mobile solvent molecules are included, these two states are calculated to be relatively close together in free energy.

Electrostatic Effects on the Speed and Directionality of Electron Transfer in Bacterial Reaction Centers: The Special Role of Tyrosine M-208

The solution of the crystal structures of purple bacterial reaction centers has raised several puzzling questions: First, considering the symmetry of the crystal structure, why does the special pair of bacteriochlorophylls (P) transfer an electron to the bacteriopheophytin on the “L” side of the complex (HL) so much more rapidly than it does to the bacteriopheophytin on the “M” side (HM)? And what roles do the accessory bacteriochlorophylls (BL and BM) play in the electron-transfer reaction? The answers to these questions are likely to be intertwined. One possibility is that favorable electrostatic interactions with the protein lower the energy of the P+BL- radical-pair so that this state lies close to or below the excited dimer (P*), whereas the corresponding radical-pair on the M side (P+BM-) lies at a significantly higher energy. This would allow BL to act as an intermediate electron carrier betwen P* and HL as suggested by the recent work of Holzapfel et al. [1,2]. The competing route through P+BM- to P+HM- would be blocked by the need for thermal activation, particularly at low temperatures. A difference between the electrostatic interactions of the protein with the two radical-pairs might suffice to explain the directionality even if P+BL- lies above P* and facilitates the reaction only by mixing quantum-mechanically with P* and P+HL- (superexchange) [3–8]. If P+BM- is at a higher energy than P+BL-, its mixing with P* would be weaker.

Macroscopic and Microscopic Estimates of the Energetics of Charge Separation in Bacterial Reaction Centers

Two approaches for calculating the free energies of transient radical-pair states in bacterial reaction centers are discussed. Although macroscopic models that assign a homogenous dielectric constant to the protein and solvent are major oversimplifications, they help to clarify the importance of considering the self-energies of the charged species, and to put limits on the energetics of the charge-separation processes. The microscopic Protein-Dipoles-Langevin-Dipoles (PDLD) approach provides a much more realistic treatment of dielectric effects, but requires lengthy calculations that depend on numerous interrelated factors. Calculations by both approaches indicate that, in Rhodopseudomonas viridis reaction centers, the state P+B- generated by movement of an electron from the primary electron donor (P) to a neighboring bacteriochlorophyll (B) lies close to the excited state P* in energy, where it possibly could serve as an intermediate in electron transfer to the bacteriopheophytin (H). This conclusion agrees with previous free-energy-perturbation calculations and indicates that any model (macroscopic or microscopic) that includes all the relevant contributions and reproduces the energy of the relaxed P+H- should find the relaxed P+B- state near P*. In addition, the macroscopic model shows that electron transfer from P* to H is likely to be exothermic even in the absence of a strong field from the atomic charges of the protein.

Two-dimensional free energy surfaces for primary electron transfer in a photosynthetic reaction center

Abstract Fushiki and Tachiya [Chem. Phys. Lett. 255 (1996) 83] recently analyzed the free energy surfaces of the initial electron-transfer processes in photosynthetic bacterial reaction centers. The authors state that when the results from simulations described by Warshel, Chu and Parson [Photochem. Photobiol. A: Chem. 82 (1994) 123] are analyzed using their formulation, the calculated energy of a key ion-pair state is inconsistent with experiment. They also state that previous analyses of the photosynthetic electron-transfer reactions had been limited to one-dimensional free energy surfaces. We show here that both these assertions are incorrect.

Free Energy Functions for Charge Separation in Wild-Type and Mutant Bacterial Reaction Centers

We have used molecular-dynamics simulations to examine the time-dependent energy gap between P* and P+BL- in purple bacterial reaction centers (RCs). Here P is the primary electron donor and BL(BA) is the neighboring “accessory” bacteriochlorophyll (BChl) that probably accepts an electron in the initial step of charge separation. From the fluctuations of the energy gap during molecular-dynamics trajectories in the reactant and product states one can obtain the Marcus free-energy curves that determine the activation energy of the initial charge-separation reaction. Effects of mutations on the activation energy can be explored, and protein motions that are coupled to the reaction can be characterized.

Primary Electron Transfer Mechanisms in Bacterial Reaction Centers

The solution of the crystal structure of reaction centers from purple photosynthetic bacteria (1–4) has raised a challenge: Can we account for the directionality, speed and efficiency of the primary photochemical electron transfer reactions on the basis of the crystal structure?