Excluded volume effect for large and small solutes in water

The cavitation effect, i.e., the process of the creation of a void of excluded volume in bulk solvent (a cavity), is considered. The cavitation free energy is treated in terms of the information theory (IT) approach [Hummer, G.; Garde, S.; Garcia, A. E.; Paulaitis, M. E.; Pratt, L. R. J. Phys. Chem. B 1998, 102, 10469]. The binomial cell model suggested earlier is applied as the IT default distribution p(m) for the number m of solute (water) particles occupying a cavity of given size and shape. In the present work, this model is extended to cover the entire range of cavity size between small ordinary molecular solutes and bulky biomolecular structures. The resulting distribution consists of two binomial peaks responsible for producing the free energy contributions, which are proportional respectively to the volume and to the surface area of a cavity. The surface peak dominates in the large cavity limit, when the two peaks are well separated. The volume effects become decisive in the opposite limit of small cavities, when the two peaks reduce to a single-peak distribution as considered in our earlier work. With a proper interpolation procedure connecting these two regimes, the MC simulation results for model spherical solutes with radii increasing up to R = 10 A [Huang, D. H.; Geissler, P. L.; Chandler, D. J. Phys. Chem. B 2001, 105, 6704] are well reproduced. The large cavity limit conforms to macroscopic properties of bulk water solvent, such as surface tension, isothermal compressibility and Tolman length. The computations are extended to include nonspherical solutes (hydrocarbons C1-C6).     

Reorganization free energies for long-range electron transfer in a porphyrin-binding four-helix bundle protein

To explore the possibility of electron transport in a recently designed four-helix bundle protein (Cochran, F. V.; et al. J. Am. Chem. Soc. 2005, 127, 1346), we have computed the reorganization free energy for (i) oxidation of a single Ru-porphyrin cofactor and (ii) electron self-exchange between two Ru-porphyrin cofactors binding to the solvated protein. Sampling the classical electrostatic energy gap for 20 ns, we find that the fluctuations are well described by Gaussian statistics and obtain reorganization free energies of 0.90 +/- 0.04 eV for oxidation and 1.36 +/- 0.08 eV for self-exchange. The latter is 0.1-0.2 eV higher than the experimental estimate for interprotein electron self-exchange in cytochrome b5. As in natural electron carriers, inner-sphere reorganization is very small, 88 meV for self-exchange between two model cofactors computed at the density functional level of theory. Decomposing the outer-sphere reorganization free energy, we find that the solvent (aqueous ionic solution) is the primary outer-sphere medium for oxidation, contributing 0.60 eV (69%). The protein contributes only 0.27 eV (31%). For self-exchange, the solvent contribution, 0.68 eV (54%), and the protein contribution, 0.59 eV (46%), are almost equally important. The large solvent contribution is due to the slow decay of dipole reorientation of the solvent as a function of distance to the cofactor, implying that the change in the electric field upon electron transfer is not as effectively screened by the four-helix bundle protein. However, ranking the residues according to their free energy contributions, it is suggested that the reorganization free energy can be decreased by about 0.2 eV if two glutamine residues in the vicinity of the cofactor are mutated into less polar amino acids.     

Theoretical study of electron, proton, and proton-coupled electron transfer in iron bi-imidazoline complexes.

A comparative theoretical investigation of single electron transfer (ET), single proton transfer (PT), and proton-coupled electron transfer (PCET) reactions in iron bi-imidazoline complexes is presented. These calculations are motivated by experimental studies showing that the rates of ET and PCET are similar and are both slower than the rate of PT for these systems (Roth, J. P.; Lovel, S.; Mayer, J. M. J. Am. Chem. Soc. 2000, 122, 5486). The theoretical calculations are based on a multistate continuum theory, in which the solute is described by a multistate valence bond model, the transferring hydrogen nucleus is treated quantum mechanically, and the solvent is represented as a dielectric continuum. For electronically nonadiabatic electron transfer, the rate expressions for ET and PCET depend on the inner-sphere (solute) and outer-sphere (solvent) reorganization energies and on the electronic coupling, which is averaged over the reactant and product proton vibrational wave functions for PCET. The small overlap of the proton vibrational wave functions localized on opposite sides of the proton transfer interface decreases the coupling for PCET relative to ET. The theory accurately reproduces the experimentally measured rates and deuterium kinetic isotope effects for ET and PCET. The calculations indicate that the similarity of the rates for ET and PCET is due mainly to the compensation of the smaller outer-sphere solvent reorganization energy for PCET by the larger coupling for ET. The moderate kinetic isotope effect for PCET arises from the relatively short proton transfer distance. The PT reaction is found to be dominated by solute reorganization (with very small solvent reorganization energy) and to be electronically adiabatic, leading to a fundamentally different mechanism that accounts for the faster rate.     

Ligand reorganization and activation energies in nonadiabatic electron transfer reactions

The activation energy and ligand reorganization energy for nonadiabatic electron transfer reactions in chemical and biological systems are investigated in this paper. The free energy surfaces and the activation energy are derived exactly in the general case in which the ligand vibration frequencies are not equal. The activation energy is derived by free energy minimization at the transition state. Our formulation leads to the Marcus-Hush [J. Chem. Phys. 24, 979 (1956); 98, 7170 (1994); 28, 962 (1958)] results in the equal-frequency limit and also generalizes the Marcus-Sumi [J. Chem. Phys. 84, 4894 (1986)] model in the context of studying the solvent dynamic effect on electron transfer reactions. It is found that when the ligand vibration frequencies are different, the activation energy derived from the Marcus-Hush formula deviates by 5%-10% from the exact value. If the reduced reorganization energy approximation is introduced in the Marcus-Hush formula, the result is almost exact.     

Simulations of time-dependent fluorescence in nano-confined solvents

The time-dependent fluorescence of a model diatomic molecule with a charge-transfer electronic transition in confined solvents has been simulated. The effect of confining the solvent is examined by comparing results for solutions contained within hydrophobic spherical cavities of varying size (radii of 10-20 angstroms). In previous work [J. Chem. Phys. 118, 6618 (2002)] it was found that the solute position in the cavity critically affects the absorption and fluorescence spectra and their dependence on cavity size. Here we examine the effect of cavity size on the time-dependent fluorescence, a common experimental probe of solvent dynamics. The present results confirm a prediction that motion of the solute in the cavity after excitation can be important in the time-dependent fluorescence. The effects of solvent density are also considered. The results are discussed in the context of interpreting time-dependent fluorescence measurements of confined solvent systems.     

A classical point charge model study of system size dependence of oxidation and reorganization free energies in aqueous solution

The response of water to a change of charge of a solvated ion is, to a good approximation, linear for the type of iron-like ions frequently used as a model system in classical force field studies of electron transfer. Free energies for such systems can be directly calculated from average vertical energy gaps. Exploiting this feature, we have computed the free energy and the reorganization energy of the M2+/M3+ and M1+/M2+ oxidations in a series of model systems all containing a single Mn+ ion and an increasing number of simple point charge water molecules. Long-range interactions are taken into account by Ewald summation methods. Our calculations confirm the observation made by Hummer, Pratt, and Garcia (J. Phys. Chem. 1996, 100, 1206) that the finite size correction to the estimate of solvation energy (and hence oxidation free energy) in such a setup is effectively proportional to the inverse third power (1/L3) of the length L of the periodic cell. The finite size correction to the reorganization energy is found to scale with 1/L. These simulation results are analyzed using a periodic generalization of the Born cavity model for solvation, yielding three different estimates of the cavity radius, namely, from the infinite system size extrapolation of oxidation free energy and reorganization energy, and from the slope of the linear dependence of oxidation free energy on 1/L3. The cavity radius for the reorganization energy is found to be significantly larger compared to the radius for the oxidation (solvation) free energy. The radius controlling the 1/L3 dependence of oxidation free energy is found to be comparable to the radius for reorganization. The implication of these results for density functional theory-based ab initio molecular dynamics calculation of redox potentials is discussed.     

Scaled particle theory study of the length scale dependence of cavity thermodynamics in different liquids

It has been noted that the work of cavity creation in water exhibits a crossover behavior, in that its cavity size dependence changes from volume dependence for small cavities to area dependence for larger cavities [Lum, K.; Chandler, D.; Weeks, J. D. J. Phys. Chem. B 1999, 103, 4570]. It is shown here that this behavior can be reproduced using the scaled particle theory in a straightforward manner for six different liquids (water, methanol, ethanol, benzene, cyclohexane, and carbon tetrachloride). It has also been suggested that the crossover is due to a change in the physical mechanism of the process, from one entropy-dominated to another enthalpy-dominated. However, the crossover behavior can be produced using the scaled particle theory without invoking any change in any physical mechanism. Also, the crossover occurs at a length scale of the size of the liquid molecules, as has been pointed out by others. This is the length regime where the work of cavity creation bears little relation to the bulk liquid surface tension. In addition, it is pointed out that cavity creation can always be considered as a purely entropy-driven process, which is usually accompanied by another process with compensating enthalpy and entropy changes.     

Cyclopropylcarbinyl --> homoallyl-type ring opening of ketyl radical anions. Structure/reactivity relationships and the contribution of solvent/counterion reorganization to the intrinsic barrier

[reaction: see text] Following a protocol developed by Mathivanan, Johnston, and Wayner (J. Phys. Chem. 1995, 99, 8190-8195), the radical anions of several cyclopropyl- and oxiranyl-containing carbonyl compounds were generated in an effort to measure the rate constants for their ring opening (k(o)) by laser flash photolysis. The results of these experiments are compared to those obtained from earlier electrochemical studies, and the combined data set is used to rationalize the kinetics of radical anion ring opening in a general context by using Saveant's theory pertaining to stepwise dissociative electron transfer (Acc. Chem. Res. 1993, 26, 455-461). Compared to cyclopropylcarbinyl --> homoallyl rearrangements of neutral free radicals, at comparable driving force, the radical anion ring openings are slightly slower. The small difference in rate is attributed to the contribution of an additional, approximately 2 kcal/mol, solvent reorganization component for the radical anion rearrangements. The solvent reorganization energy for ring opening of these radical anions is believed to be small because the negative charge does not move appreciably in the progression reactant --> transition state --> product.     

The complex of apomyoglobin with the fluorescent dye coumarin 153

Understanding a protein's dielectric response requires both a theoretical model and a well-defined experimental system. The former has already been proposed by Song (J. Chem. Phys. 116, 9359 [2002]). We suggest that the latter is provided by the complex of coumarin 153 (C153) with apomyoglobin (ApoMb). C153 has been exhaustively studied and has proven to be an excellent probe of the solvation dynamics of polar solvents. Myoglobin is one of the most thoroughly studied proteins. Myoglobins from a wide range of species have been subject to X-ray structural analysis and site-directed mutagenesis. Here, we demonstrate the existence of a robust C153-apomyglobin system by means of molecular dynamics simulations, equilibrium binding studies using a Job's plot and capillary electrophoresis, circular dichroism and time-resolved fluorescence. The reorganization energy of C153 bound to ApoMb is compared with that of C153 in bulk solvent using the method of Jordanides et al. (J. Phys. Chem. B 103, 7995 [1999]).     

Steric guided change of electron transfer mechanism in benzene

In fluorescence quenching study via electron transfer (ET), the quenching rate constant (k(q)) values generally decrease with lowering of quencher concentration, since smaller concentration of quencher always leads to a red shift in the donor-acceptor (D-A) distance in ET [M. Tachiya, S. Murata, J. Phys. Chem. 96 (1992) 8441; S. Murata, M. Tachiya, J. Phys. Chem. 100 (1996) 4064; L. Burel, M. Mastafavi, S. Murata, M. Tachiya, J. Phys. Chem. A 103 (1999) 5882]. However, while doing a comparative study with different carbazole (CZ) derivatives-1,4-dicyanobenzene (DCB) systems in benzene (BZ), we observed a deviation from that normal behaviour. It was found that for all of them with lower quencher (DCB) concentration, k(q) values actually increase instead of the expected reduction. Exceptionally, for simple CZ (C12H9N) with decrease in concentration of DCB, k(q) values can even reach the order of energy transfer (10(11) s(-1)). Interestingly, it is not observed when toluene (TL) or xylene (XY) is used as solvent. To explain this unique observation, a sandwich type of molecular structure is predicted, where BZ sliding in between CZ and DCB brings them closer enough, imparting more through bond character to CZ-DCB interaction and hence a higher rate of ET (k(q)) is observed [L. Burel, M. Mastafavi, S. Murata, M. Tachiya, J. Phys. Chem. A. 103 (1999) 5882].     

Intermolecular electron-transfer reactions in soluble methane monooxygenase: a role for hysteresis in protein function

Electron transfer from reduced nicotinamide adenine dinucleotide (NADH) to the hydroxylase component (MMOH) of soluble methane monooxygenase (sMMO) primes its non-heme diiron centers for reaction with dioxygen to generate high-valent iron intermediates that convert methane to methanol. This intermolecular electron-transfer step is facilitated by a reductase (MMOR), which contains [2Fe-2S] and flavin adenine dinucleotide (FAD) prosthetic groups. To investigate interprotein electron transfer, chemically reduced MMOR was mixed rapidly with oxidized MMOH in a stopped-flow apparatus, and optical changes associated with reductase oxidation were recorded. The reaction proceeds via four discrete kinetic phases corresponding to the transfer of four electrons into the two dinuclear iron sites of MMOH. Pre-equilibrating the hydroxylase with sMMO auxiliary proteins MMOB or MMOD severely diminishes electron-transfer throughput from MMOR, primarily by shifting the bulk of electron transfer to the slowest pathway. The biphasic reactions for electron transfer to MMOH from several MMOR ferredoxin analogues are also inhibited by MMOB and MMOD. These results, in conjunction with the previous finding that MMOB enhances electron-transfer rates from MMOR to MMOH when preformed MMOR-MMOH-MMOB complexes are allowed to react with NADH [Gassner, G. T.; Lippard, S. J. Biochemistry 1999, 38, 12768-12785], suggest that isomerization of the initial ternary complex is required for maximal electron-transfer rates. To account for the slow electron transfer observed for the ternary precomplex in this work, a model is proposed in which conformational changes imparted to the hydroxylase by MMOR are retained throughout the catalytic cycle. Several electron-transfer schemes are discussed with emphasis on those that invoke multiple interconverting MMOH populations.     

Molecular simulation of solvent-induced stokes shift in absorption/emission spectra of organic chromophores

The values of steady-state solvatochromic Stokes shifts (SS) in absorption/emission electronic spectra of organic chromophores are studied theoretically in the framework of the Hush-Marcus model. Charge distributions for chromophore solutes in their S0 and S1 states are found by means of conventional quantum-chemical methods combined with the continuum PCM approach for treating solvation effects. The solvent reorganization energies, which are expected to correlate with the solvent-induced part of 1/2 SS, are found in a molecular dynamics (MD) simulation which invokes a novel method for separation of the inertial piece of the electrostatic response (Vener, et al. J. Phys. Chem. B 2006, 110, 14950). Computations, performed in two solvents (acetonitrile and benzene), consider three organic dyes: coumarin 153 as a benchmark system and two other chromophores, for which experimental spectra are also reported. The results are found to be in reasonable agreement with the experiment. A consistent treatment of nonlinear effect in the solvent response, promoted by the polarizability of solutes and contributing to the solvent reorganization energies (Ingrosso, et al. J. Phys. Chem. B 2005, 109, 3553), improves the results of computations.     

Towards an understanding of many-particle effects in hydrophobic association in methane solutions

This paper applies the multiscale coarse-graining method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] to analyze many-body effects in concentrated methane solutions. Pairwise decompositions of N-particle solute-solute potentials of mean force (PMFs), and the respective solvent cavity potentials, enthalpic, entropic, and heat capacity of hydrophobic association, are calculated directly from unconstrained molecular-dynamics simulations of methane solutions at different molar fractions, with the highest being 0.055. The many-body effects in hydrophobic hydration are further studied using N-methane PMFs, which are explicitly dependent on solvent coordinates.     

The inhomogeneous electron liquid in some bioinorganic assemblies studied by density functional methods

The review starts with a discussion of some recent advances related to the foundations of density functional theory (DFT). Some emphasis is placed on methods which should have special relevance to bioinorganic assemblies. In particular, the inhomogeneous electron liquid in the ground state of such systems is a specific focal point. After a brief summary concerning the possible variational validity of some popular energy functionals, the future value of the important Dirac idempotent density matrix is emphasised, both from first principles and semiempirically by making use of X-ray diffraction experiments. The review concludes with two topical examples of bioinorganic assemblies. The first concerns our own work on an anticancer drug based on a Ru complex, while as a second example a recent DFT study of a molecular biosensor by K. Salazar-Salinas, L.A. Jauregui, C. Kubli-Garfias, J.M. Seminario [J. Chem. Phys. 130, 105101 (2009)] involving an Fe complex is briefly summarised.     

The oxidation of tyrosine and tryptophan studied by a molecular dynamics normal hydrogen electrode

The thermochemical constants for the oxidation of tyrosine and tryptophan through proton coupled electron transfer in aqueous solution have been computed applying a recently developed density functional theory (DFT) based molecular dynamics method for reversible elimination of protons and electrons. This method enables us to estimate the solvation free energy of a proton (H(+)) in a periodic model system from the free energy for the deprotonation of an aqueous hydronium ion (H(3)O(+)). Using the computed solvation free energy of H(+) as reference, the deprotonation and oxidation free energies of an aqueous species can be converted to pK(a) and normal hydrogen electrode (NHE) potentials. This conversion requires certain thermochemical corrections which were first presented in a similar study of the oxidation of hydrobenzoquinone [J. Cheng, M. Sulpizi, and M. Sprik, J. Chem. Phys. 131, 154504 (2009)]. Taking a different view of the thermodynamic status of the hydronium ion, these thermochemical corrections are revised in the present work. The key difference with the previous scheme is that the hydronium is now treated as an intermediate in the transfer of the proton from solution to the gas-phase. The accuracy of the method is assessed by a detailed comparison of the computed pK(a), NHE potentials and dehydrogenation free energies to experiment. As a further application of the technique, we have analyzed the role of the solvent in the oxidation of tyrosine by the tryptophan radical. The free energy change computed for this hydrogen atom transfer reaction is very similar to the gas-phase value, in agreement with experiment. The molecular dynamics results however, show that the minimal solvent effect on the reaction free energy is accompanied by a significant reorganization of the solvent.     

Effective generation of molecular cavities in polarizable continuum model by DefPol procedure

A new computational strategy for the building of molecular cavities (named DefPol) has been linked to the most recent implementation of the polarizable continuum model (PCM) for the representation of solvent effects on physicochemical properties of large molecules. Free energies, analytical gradients, and Hessians can be computed in this framework in the rigid cavity approximation. Coupling DefPol cavities with a number of other recent improvements of the standard algorithm (e.g., effective use of symmetry, iterative procedures with linear scaling) significantly enlarges the dimensions of systems amenable to refined computations and strongly reduces the gap between computations for isolated molecules and in solution. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1693–1701, 1999     

Ruthenium-manganese complexes for artificial photosynthesis: factors controlling intramolecular electron transfer and excited-state quenching reactions

Continuing our work toward a system mimicking the electron-transfer steps from manganese to P(680)(+) in photosystem II (PS II), we report a series of ruthenium(II)-manganese(II) complexes that display intramolecular electron transfer from manganese(II) to photooxidized ruthenium(III). The electron-transfer rate constant (k(ET)) values span a large range, 1 x 10(5)-2 x 10(7) s(-1), and we have investigated different factors that are responsible for the variation. The reorganization energies determined experimentally (lambda = 1.5-2.0 eV) are larger than expected for solvent reorganization in complexes of similar size in polar solvents (typically lambda approximately 1.0 eV). This result indicates that the inner reorganization energy is relatively large and, consequently, that at moderate driving force values manganese complexes are not fast donors. Both the type of manganese ligand and the link between the two metals are shown to be of great importance to the electron-transfer rate. In contrast, we show that the quenching of the excited state of the ruthenium(II) moiety by manganese(II) in this series of complexes mainly depends on the distance between the metals. However, by synthetically modifying the sensitizer so that the lowest metal-to-ligand charge transfer state was localized on the nonbridging ruthenium(II) ligands, we could reduce the quenching rate constant in one complex by a factor of 700 without changing the bridging ligand. Still, the manganese(II)-ruthenium(III) electron-transfer rate constant was not reduced. Consequently, the modification resulted in a complex with very favorable properties.