Library

Notes: A theoretical investigation on the rates of electron-transfer processes Q-I + QII → Q-I + Q-II and Q-I + Q-II → QI + Q2-II was carried out by using the Marcus theory of long-range electron transfer in solution. The molecular reorganizational parameter λ, the free-energy change ΔG0 for the overall reaction, and the electronic matrix element HDA for these two processes were calculated from the INDO-optimized geometries of molecules QI, QII, and histidine. QI and QII are plastoquinones (PQ) which are hydrogen-bonded to a histidine each, and the two histidines may or may not be coordinated to a Fe2+ ion. The plastoquinone representing QI is additionally flanked by two peptide fragments. Each of the species (Pep)2QI · His and His · QII has been considered to be immersed in a dielectric continuum that represents the surrounding molecules and protein folds. INDO calculations confirm the standard reduction potential for the first process (calculated 0.127 V; observed 0.13 V) and predict a midpoint potential of 0.174 V for the second process at 300 K at pH 7 (experimental value remains uncertain but is known to be close to 0.13 V). The plastoquinone fragment carries almost all the net charge (about 95.7%) in [PQ · His]- and the net charge in [PQH · His]-. The electron is transferred effectively from the plastoquinone part of [(Pep)2QI · His]- to the plastoquinone moiety of QII · His in the first step and to the plastoquinone fragment of HisH+ · Q-II in the second step. Therefore, we made use of the formula for the rate of through-space electron transfer from QI to QII (and to Q-II). The plastoquinones are, of course, electronically coupled to histidines, and the transfer is, in reality, through the molecular bridge consisting of histidines and also Fe2+. The through-bridge effect is inherent in our calculation of ΔG0, HDA, and the reorganization parameter λ. We investigated the correlation between half-times for the transfer and (D-1op- D-1s), where Dop and Ds are, respectively, optical and static dielectric constants of the condensed phase in the vicinity of the plastoquinones. We found that with reasonable values of Dop (2.6) and Ds (8.5) the experimental rates are adequately explained in terms of transfers from the plastoquinone moiety of QI to that of QII. The t1/2 values calculated for the two processes are 247 and 472 μs in the absence of Fe2+ and 134 and 181 μs in the presence of Fe2+. These are in good agreement with the observed values which are ≈ 100 and ≈ 200 μs when Fe2+ is present in the matrix and which are known to be almost twice as large when the Fe2+ is evicted from the matrix. The present work also shows that the Marcus-Hush theory of long-range electron transfers can be successfully applied to the investigation of processes occurring in a semirigid condensed phase like the thylakoid membrane region. © 1997 John Wiley & Sons, Inc.

Notes: The problem of excitons in interaction with phonons in a molecular crystal has been reinvestigated as a continuation of our earlier work. The exciton-phonon interaction has been taken to be linear in lattice displacements. The external medium, the phonon assembly, has been considered to be in thermal equilibrium. Following Simons, we have incorporated the effects of the medium on the exciton dynamics into a time-dependent effective potential that contains the equilibrium average exciton-phonon interaction as well as terms arising from the fluctuations in the medium's coordinates about their equilibrium values. A correlation function that represents the probability of exciton transfer has been given in the interaction picture. The time evolution of this correlation function has been determined by following Kubo's technique of cumulant expansion. The zeroth-, second-, and fourth-order contributions to the correlation function have been calculated in this way. The second- and fourth-order contributions have been diagrammatically represented. The second-order contribution has been explicitly calculated in different physical limits, namely, the slow exciton and the slow phonon limits at high and low temperatures and for very large and very small time. A few simple formulas for the transfer probability of a bare exciton in a molecular crystal of cubic symmetry have been derived from the Debye approximation for the dispersion of phonons. It has been specifically shown that the sum over phonon modes in the large time dynamics leads to a fully destructive interference in second order at a very low temperature and gives rise to a diffusive transport at a high enough temperature. A natural way of clothing the excitons has been considered and the clothed exciton has been represented diagrammatically. The dressing requires the correlation function to be redefined in terms of the clothed states and the clothed operators. The clothed exciton correlation function that represents the probability of transfer of excitons fully clothed by the phonons in thermal equilibrium turns out to be identical with the bare exciton correlation function. This attaches a novel interpretation to the correlation function which was originally defined by Simons. Transfer probabilities for a clothed exciton in a cubic crystal has been explicitly worked out for different physical limits under the Debye model of phonon dispersion. From these results a few expressions for the macroscopic diffusion coefficient of the clothed exciton have been obtained. A few critical comments have been incorporated. © 1996 John Wiley & Sons, Inc.

Notes: The stepwise acid dissociation constants for p-benzohydroquinone (QH2) in aqueous media have been explicitly calculated for the first time, with the INDO parametrized SCF-MO method. We have optimized the geometries of QH2, QH-, and Q2- and of the QH2 · 6H2O, QH- · (H3O+) · 5H2O, and Q2- · (H3O+)2 · 4H2O systems that model the solvated species. The presence of the associated water molecules (and hydronium ions) account for the stabilization due to hydrogen bonding as well as for a part of the effect of interaction of these molecules with the respective reaction fields in an aqueous medium. To simulate the first solvation shell in a more complete manner, four more water molecules have been considered to be placed above and below the quinonoid ring and the optimized geometries of the resulting hydrated species, QH2 · 10H2O, QH- · (H3O+) · 9H2O, and QH- · (H3O+) · 8H2O, have been determined. The standard free-energy changes calculated for the dissociation of QH2 into QH- and H+ is 0.0251 Hartree (65.9 kJ mol-1) and that of QH- into Q2- and H+ is 0.0285 Hartree (74.8 kJ mol-1). Experimentally observed dissociation constants for these two steps correspond to free-energy changes of 0.0214 Hartree (56.2 kJ mol-1) and 0.0248 Hartree (65.1 kJ mol-1), respectively. © 1995 John Wiley & Sons, Inc.

Notes: The standard electrode potential for the quinone (Q)-hydroquinone (QH2) couple in aqueous acidic media has been explicitly calculated. Molecular geometries of Q and QH2 have been optimized. Protonation of Q, i.e., the formation of QH+ and QH22+, have been considered. Molecular geometries of these species have been thoroughly optimized. The energy of complexation of these molecules with water have been calculated by optimizing the structures of the hydrated complexes Q · 6H2O, QH2 · 6H2O, QH+ · 6H2O. and QH22+ · 6H2O. The ion-solvent interaction energy of QH+ · 6H2O, in turn, has been calculated by considering the complex QH+ · 6H2O… 2H2O, where the two extra water molecules approach the charge center of the complex QH+ · 6H2O vertically from top and bottom of the quinonoid ring. The standard reduction potential calculated by the CNDO method, 0.8548 V, is somewhat larger than the experimental potential, 0.6998 V, at 25°C. But the INDO value, 0.7085 V, is in excellent agreement with the observed potential. The electrode potential for the plastoquinone (PQ)-plastohydroquinone (PQH2) couple present in the aqueous pool in chloroplast has been calculated by the INDO method. The basic geometries of PQ, PQH+, and PQH2/sb have been synthesized by adopting the optimized geometries of Q, QH+, and QH2 and considering methyl substituents as well as an isoprenoid side chain containing up to 3 isoprene units with possible geometrical isomerism. The hydrated species PQ · 6H2O, PQH+ · 6H2O, and PQH2 · 6H2O are unstable compared to the isolated species PQ, PQH+, and PQH2, respectively. In fact, we have found that the hydration of PQH+ and PQH2 is much less extensive, and stability arises only when the hydroxyl groups in these two molecules are hydrogen-bonded to water molecules. But PQH+ is also stabilized through the association of two more water molecules in the vertical direction. For this reason, we have calculated the reduction potential of the PQ/PQH2 system from the energies of the isolated molecules PQH2 and the hydrated species PQH+ · 2H2O. The computed standard reduction potential is 0.2785 V and it yields a potential of 0.07V at pH 7 at 25°C, which is in good agreement with the reduction potential 0.11 V observed for plastoquinone in the aqueous pool in chloroplast. © 1994 John Wiley & Sons, Inc.