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Expressions for correlation functions of classical non-isothermal two-component plasma are derived. In the limiting case of $\Theta_e\gg\Theta_i$ strong correlations arise due to the existence of weakly damping waves (ionic sound), whose phase velocity is between the thermal velocities of particles, $u_e\gg\omega/k\gg u_i$. Owing to these correlations, the additional term in the expression for pressure due to the Coulomb interaction changes its sign as compared to the case of thermodynamic equilibrium where such waves do not exist.

Preprint of a paper on spectroscopy of CO

Theoretical calculations are contributing a significantly higher proportion of data to contemporary spectroscopic databases, which have traditionally relied on experimental observations and semi-empirical models. It is now a common procedure to extend calculated line lists to include ro-vibrational transitions between all bound states of the ground electronic state up to the dissociation limit. Advanced ab initio methods are utilized to calculate the potential energy and dipole moment surfaces (PESs and DMSs), and semi-empirical PESs are then obtained by combining ab initio and experimental data. The objective is to reach high accuracy in the calculated transition intensities for all parts of spectrum, i.e. to increase the predictive power of the model. We show that in order to perform this task, one needs, in addition to the standard improvements of the PES and DMS in the spectroscopically accessible regions, to extend the ab initio calculations of the PES towards the united-atom limit along the stretching coordinates. The argument is based on the correlation between the intensities of high-overtone transitions and the repulsive potential wall that has previously been theoretically established for diatomic molecules and is empirically extended here to linear and nonlinear triatomic molecules. We generate partial line lists for water and ozone, and together with an already available line list for carbon dioxide, we derive the normal intensity distribution, which is a direct consequence of this correlation. The normal distribution is not an instrument to compute highly accurate intensities, rather it is a means to analyse the intensities computed by the traditional methods.

We compare the intensities of purely rotational and ro-vibrational transitions within the ground electronic state of CO calculated with two dipole moment functions (DMFs) of Li et al. (2015) and four potential energy functions (PEFs), a semi-empirical PEF of Meshkov et al. (doi: https://doi.org//10.5281/zenodo.1198744) and three empirical ones due to Coxon and Hajigeorgiou (2004, 2016, 2017). All these PEFs reproduce the experimental line positions with similar normalized standard deviations (NSDs), and the energy mismatch between the vibrational levels with v ⩽ 5 does not exceed 0.0002 cm−1 among all PEFs. Despite these similarities, we find that the rotational anomalies in the 0-0, 1-1, 2-2, 3-3, 4-4, and 5-0 bands shown in Figs. 3 and 4 of Medvedev et al. (2017) change their intensities by a factor of 2 to 250 among the above PEFs at a given DMF. Both the positions and intensities of the anomalies change between two DMFs at a given PEF.

We derive the expansion of the irregular physical solution over the spherical solutions at negative energies, which is necessary for obtaining the $S$ matrix of the process. The relation of this expansion to the theory developed by Giannakees et al., Phys. Rev. A 94, 013419 (2016), is analyzed. In particular, we show that the expansion of the irregular solution missing in Giannakees et al.'s theory can be derived from one of their main postulates. The expansion thus obtained turns out to be numerically equivalent to our expansion up to high angular momenta. Analytical expressions for the key matrix of both expansions are derived., 10 pages, 2 figures

Calculating intensities of ro-vibrational transitions is particularly challenging for transitions from a given vibrational state to all upper states up to the dissociation limit because their probabilities decrease exponentially with increasing Δ n , the change in the vibrational quantum number. The experimental intensities available for low- Δ n values are well reproduced by a variety of models but the models can greatly diverge in predicting the intensities of unobserved high-overtone transitions, the divergence rapidly increasing with the overtone number. In this paper, we investigate the impact of the dipole-moment function (DMF) representation on the high-overtone intensity simulation of the CO molecule. We tested various DMF forms including pointwise representation combined with cubic-spline interpolation, power and trigonometric expansions, and Pade approximants. Numerical calculations were performed with the highly accurate empirical potential-energy function (PEF) of Coxon and Hajigeorgiou (2004) using quadruple-precision arithmetic. Most calculated intensities fall off in the entire range of transitions according to the Normal Intensity Distribution Law (NIDL) (Medvedev, 2012). The slope of the NIDL trend line varies little between different analytical DMFs for a given PEF since the slope is basically associated with the PEF. Based on the NIDL, the limits within which the simulated intensities fall off up to the dissociation limit can be established. We claim that DMFs represented by analytical functions yield best results for all transitions. The pointwise functions (interpolated, in particular, by the conventional cubic splines) result in an unphysical flattening of the intensities at high- Δ n transitions, Δ n > 7 for CO.

Recently, Euro et al. [Biochem. 47, 3185 (2008) ] have reported titration data for seven of nine FeS redox centers of complex I from Escherichiacoli. There is a significant uncertainty in the assignment of the titration data. Four of the titration curves were assigned to N1a, N1b, N6b, and N2 centers; one curve either to N3 or N7; one more either to N4 or N5; and the last one denoted Nx could not be assigned at all. In addition, the assignment of the titration data to the N6b/N6a pair is also uncertain. In this paper, using our calculated interaction energies [Couch et al. BBA 1787, 1266 (2009)], we perform statistical analysis of these data, considering a variety of possible assignments, find the best fit, and determine the intrinsic redox potentials of the centers. The intrinsic potentials could be determined with an uncertainty of less than ± 10 mV at a 95% confidence level for best fit assignments. We also find that the best agreement between theoretical and experimental titration curves is obtained with the N6b–N2 interaction equal to 71 ± 14 or 96 ± 26 mV depending on the N6b/N6a titration data assignment, which is stronger than was expected and may indicate a close distance of the N2 center to the membrane surface.

In the cycle of photosynthetic reaction centers, the initially oxidized special pair of bacteriochlorophyll molecules is subsequently reduced by an electron transferred over a chain of four hemes of the complex. Here, we examine the kinetics of electron transfer between the proximal heme c-559 of the chain and the oxidized special pair in the reaction center from Rps. sulfoviridis in the range of temperatures from 294 to 40 K. The experimental data were obtained for three redox states of the reaction center, in which one, two, or three nearest hemes of the chain are reduced prior to special pair oxidation. The experimental kinetic data are analyzed in terms of a Sumi–Marcus-type model developed in our previous paper,1 in which similar measurements were reported on the reaction centers from Rps. viridis. The model allows us to establish a connection between the observed nonexponential electron-transfer kinetics and the local structural relaxation dynamics of the reaction center protein on the microsecond time scale. The activation energy for relaxation dynamics of the protein medium has been found to be around 0.1 eV for all three redox states, which is in contrast to a value around 0.4–0.6 eV in Rps. viridis.1 The possible nature of the difference between the reaction centers from Rps. viridis and Rps. sulfoviridis, which are believed to be very similar, is discussed. The role of the protein glass transition at low temperatures and that of internal water molecules in the process are analyzed. España, Ministerio de Educación y Ciencia BFU2004-04914-C02-01/BMC Junta de Andalucía PAI CVI-261

In the recent work devoted to the calculation of the rovibrational line list of the CO molecule [G. Li et al., Astrophys. J., Suppl. Ser. 216, 15 (2015)], rigorous validation of the calculated parameters including intensities was carried out. In particular, the Normal Intensity Distribution Law (NIDL) [E. S. Medvedev, J. Chem. Phys. 137, 174307 (2012)] was employed for the validation purposes, and it was found that, in the original CO line list calculated for large changes of the vibrational quantum number up to Δn = 41, intensities with Δn > 11 were unphysical. Therefore, very high overtone transitions were removed from the published list in Li et al. Here, we show how this type of validation is carried out and prove that the quadruple precision is indispensably required to predict the reliable intensities using the conventional 32-bit computers. Based on these calculations, the NIDL is shown to hold up for the 0 → n transitions till the dissociation limit around n = 83, covering 45 orders of magnitude in the intensity. The low-intensity 0 → n transition predicted in the work of Medvedev [Determination of a new molecular constant for diatomic systems. Normal intensity distribution law for overtone spectra of diatomic and polyatomic molecules and anomalies in overtone absorption spectra of diatomic molecules, Institute of Chemical Physics, Russian Academy of Sciences, Chernogolovka, 1984] at n = 5 is confirmed, and two additional “abnormal” intensities are found at n = 14 and 23. Criteria for the appearance of such “anomalies” are formulated. The results could be useful to revise the high-overtone molecular transition probabilities provided in spectroscopic databases.

Recent experimental data by Mizoguchi and Ohta are analyzed under the assumption of fast equilibrium between the locally excited (LE), radical-ion-pair (RIP), and exciplex states. In the absence of the equilibrium, no magnetic field effect on the LE fluorescence would be observed. Owing to the equilibrium, the relative electric-field-induced changes of the quantum yields of the LE and exciplex emissions as functions of the magnetic field are linearly connected to each other. The electric field shifts the equilibrium from the LE state toward the RIP state. Predictions are made for the magnetic field effect on the fluorescence kinetics.

Some proton pumps, such as cytochrome c oxidase (CcO), translocate protons across biological membranes at a rate that considerably exceeds the rate of proton transport to the entrance of the proton-conducting channel via bulk diffusion. This effect is usually ascribed to a proton-collecting antenna surrounding the channel entrance. In this paper, we consider a realistic phenomenological model of such an antenna. In our model, a homogeneous membrane surface, which can mediate proton diffusion toward the channel entrance, is populated with protolytic groups that are in dynamic equilibrium with the solution. Equations that describe coupled surface-bulk proton diffusion are derived and analyzed. A general expression for the rate constant of proton transport via such a coupled surface-bulk diffusion mechanism is obtained. A rigorous criterion is formulated of when proton diffusion along the surface enhances the transport. The enhancement factor is found to depend on the ratio of the surface and bulk diffusional constants, pKa values of surface protolytic groups, and their concentration. A capture radius for a proton on the surface and an effective size of the antenna are found. The theory also predicts the effective distance that a proton can migrate on the membrane surface between a source (such as CcO) and a sink (such as ATP synthase) without fully equilibrating with the bulk. In pure aqueous solutions, protons can travel over long distances (microns). In buffered solutions, the travel distance is much shorter (nanometers); still the enhancement effect of the surface diffusion on the proton flow to a target on the surface can be tens to hundreds at physiological buffer concentrations. These results are discussed in a general context of chemiosmotic theory.

A simple practical way to account for the effect of quantum modes on electron transfer (ET) is to use the Jortner expression for ET rate. The expression includes two quantum parameters which describe the properties of high-frequency modes in the system. In our recent paper (J. Chem. Phys. 2000, 112, 9015), we developed a method to calculate these parameters for redox cofactors from ab initio data on their potential energy surfaces. In this paper, we extend our method to include the solvent, which is treated as a continuous dielectric medium. As an example, two reactions describing photoreduction of the flavin cofactor in DNA photolyase (an enzyme that repairs thymine dimers in DNA) are investigated. We calculated the quantum parameters for each cofactor (flavin radical, tryptophan, tryptophan cation radical, and tyrosine), as well as for water, which was used as a model medium, and then obtained the dependence of ET rates kET on the driving force ΔG0 in a wide range of ΔG0. As expected, the quantum modes ...

A general expression for the rate of bridge mediated electron transfer reaction is derived which takes into account effects of nuclear dynamics of donor and acceptor complexes as well as those of the bridge. The theory includes treatment of a non-Born-Oppenheimer effect specific for a long distance electron transfer. The derived expression for the rate is designed for applications in numerical studies of long range electron transfer reactions in proteins. Recent experimental measurements of the rates of long-range electron transfer (ET) reactions in proteins by Dutton and Gray and co-workers [1]-[4] and their debate of the role of the protein medium in biological electron transfer have prompted an active development of general theory and computer simulations of such reactions [5]. In this paper we continue our analysis [6], [7] of the role of the dynamics of the protein medium and other nuclear dynamic effects in biological electron transfer reactions. Usually, long-range electron transfer reactions are discussed within the framework of general non-adiabatic theory developed originally for "short-range'' reactions [8], [9]. In this theory the reaction rate is described by the well known semi-classical expression: Here X and AGO are the standard reorganization energy and driving force of the reaction, and TDA is the coupling of the initial and final electronic states. When applied to long-range reactions this coupling is treated as an effective one, arising due to the presence of the atoms of the protein medium in between the redox centers. These atoms, or the bridge, provide intermediate virtual states for superexchange coupling which make a long-range electronic communication between redox centers possible [lo], [ll]. The above expression assumes that electron transfer occurs as a single thermally assisted tunneling jump, when the two electronic states on the donor (D) and acceptor (A) complexes become resonant in the course of thermal fluctuations. The factor lT~~l/fi in the above expression can be interpreted as the transfer rate at the transition state, and the rest of the expression gives simply the fraction of the molecules at the transition state. (The distribution of the energy difference between D and A states is Gaussian, and the transition state in this formulation is a state in which the two levels are within ~T~TDAI from each other).

Recent experiments suggest that protons can travel along biological membranes up to tens of micrometers, but the mechanism of transport is unknown. To explain such a long-range proton translocation we describe a model that takes into account the coupled bulk diffusion that accompanies the migration of protons on the surface. We show that protons diffusing at or near the surface before equilibrating with the bulk desorb and re-adsorb at the surface thousands of times, giving rise to a power-law desorption kinetics. As a result, the decay of the surface protons occurs very slowly, allowing for establishing local gradient and local exchange, as was envisioned in the early local models of biological energy transduction.

Extensive rovibrational line lists were computed for nine isotopologues of the CO molecule, namely, {sup 12}C{sup 16}O, {sup 12}C{sup 17}O, {sup 12}C{sup 18}O, {sup 13}C{sup 16}O, {sup 13}C{sup 17}O, {sup 13}C{sup 18}O, {sup 14}C{sup 16}O, {sup 14}C{sup 17}O, and {sup 14}C{sup 18}O in the ground electronic state with v ≤ 41, Δv ≤ 11, and J ≤ 150. The line intensity and position calculations were carried out using a newly determined piece-wise dipole moment function (DMF) in conjunction with the wavefunctions calculated from an experimentally determined potential energy function from Coxon and Hajigeorgiou. A direct-fit method that simultaneously fits all the reliable experimental rovibrational matrix elements has been used to construct the dipole moment function near equilibrium internuclear distance. In order to extend the amount and quality of input experimental parameters, new Cavity Ring Down Spectroscopy experiments were carried out to enable measurements of the lines in the 4-0 band with low uncertainty as well as the first measurements of lines in the 6-0 band. A new high-level ab initio DMF, derived from a finite field approach has been calculated to cover internuclear distances far from equilibrium. Accurate partition sums have been derived for temperatures up to 9000 K. In additionmore » to air- and self-induced broadening and shift parameters, those induced by CO{sub 2} and H{sub 2} are now provided for planetary applications. A complete set of broadening and shift parameters was calculated based on sophisticated extrapolation of high-quality measured data. The line lists, which follow HITRAN formalism, are provided as supplementary material.« less

In a recent work from this group (Popovic, D. M.; Stuchebrukhov A. A. FEBS Lett. 2004, 566, 126), a model of proton pumping by cytochrome c oxidase (CcO) was proposed. The key element of the model is His291 (bovine notation), a histidine ligand to enzyme's CuB redox center, which plays the role of the pump element. The model assumes that upon electron transfer between heme a and the binuclear catalytic center of the enzyme, two sequential proton transfers occur: First, a proton from Glu242 is transferred to an unprotonated His291, then a second proton, after reprotonation of Glu242 from the negative side of the membrane, is transferred to a hydroxyl group in the binuclear center, a water molecule is formed, and the first proton, due to proton–proton repulsion, is expelled from His291 to the positive side of the membrane, resulting in a pumping event. In the process the free energy of water formation (i.e., reduction of oxygen) is transformed into a proton gradient across the membrane. The model possesses specific kinetic features. It assumes, for example, that upon electron transfer the first proton is transferred to the proton-loading site of the pump, His291, and not to the catalytic center of the enzyme. Here, we analyze the kinetic properties of the proposed model, and calculate the time dependence of the membrane potential generated by CcO upon a single electron injection into the enzyme. These data are directly compared with recent experimental measurements of the membrane potential generated by CcO. Specifically, F to O, and O to E transitions will be discussed. Several enzymes from different organisms (bovine, two bacterial enzymes, and several mutants) are compared and discussed in detail. The kinetic description, however, is phenomenological, and does not include explicitly the nature of the groups involved in proton translocation, except in terms of their position depth within the membrane; thus, the kinetic equations developed here are in fact describe a generic model, similar, e.g., to that proposed earlier by Peter Rich (P.R. Rich, Towards an understanding of the chemistry of oxygen reduction and proton translocation in the iron-copper respiratory oxidases. Aust. J. Plant Physiol. 22 (1995) 479–486), and which is based on the idea of displacement of the pumped protons by the chemical ones.

Computer simulations of the effect of protein dynamics on the long distance tunneling mediated by the protein matrix have been carried out for a Ru-modified (His 126) azurin molecule. We find that the tunneling matrix element is a sensitive function of the atomic configuration of the part of the protein matrix in which tunneling currents (pathways) are localized. Molecular dynamics simulations show that fluctuations of the matrix element can occur on a time scale as short as 10 fs. These short time fluctuations are an indication of a strong dynamic coupling of a tunneling electron to vibrational motions of the protein nuclear coordinates. The latter results in a modification of the conventional Marcus picture of electron transfer in proteins. The new element in the modified theory is that the tunneling electron is capable of emitting or absorbing vibrational energy (phonons) from the medium. As a result, some biological reactions may occur in an activationless fashion. An analytical theoretical model is proposed to account for thermal fluctuations of the medium in long distance electron transfer reactions. The model shows that, at long distances, the phonon-modified inelastic tunneling always dominates over the conventional elastic tunneling.

The quasiclassical Landau-Lifshitz formula is applied to higher overtone vibrational transitions. The transition probabilities are expressed in terms of the repulsive branch of the molecular potential, which can be characterized by a constant β describing its rapid rise in the region of strong interatomic repulsion. Values of β are calculated from the higher overtone band intensities for both diatomic molecules and the local vibrations in polyatomic molecules.

We have developed theory and the computational scheme for the analysis of the kinetics of the membrane potential generated by cytochrome c oxidase upon single electron injection into the enzyme. The theory allows one to connect the charge motions inside the enzyme to the membrane potential observed in the experiments by using data from the “dielectric topography” map of the enzyme that we have created. The developed theory is applied for the analysis of the potentiometric data recently reported by the Wikstrom group [I. Belevich, D.A. Bloch, N. Belevich, M. Wikstrom and M.I. Verkhovsky, Exploring the proton pump mechanism of cytochrome c oxidase in real time, Proc. Natl. Acad. Sci. U. S. A. 104 (2007) 2685–2690] on the O to E transition in Paracoccus denitrificans oxidase. Our analysis suggests, that the electron transfer to the binuclear center is coupled to a proton transfer (proton loading) to a group just “above” the binuclear center of the enzyme, from which the pumped proton is subsequently expelled by the chemical proton arriving to the binuclear center. The identity of the pump site could not be determined with certainty, but could be localized to the group of residues His326 (His291 in bovine), propionates of heme a 3 , Arg 473/474, and Trp164. The analysis also suggests that the dielectric distance from the P-side to Fe a is 0.4 or larger. The difficulties and pitfalls of quantitative interpretation of potentiometric data are discussed.

Respiratory complex I couples the transfer of electrons from NADH to ubiquinone and the translocation of protons across the mitochondrial membrane. A detailed understanding of the midpoint reduction potentials (Em) of each redox center and the factors which influence those potentials are critical in the elucidation of the mechanism of electron transfer in this enzyme. We present accurate electrostatic interaction energies for the iron–sulfur (FeS) clusters of complex I to facilitate the development of models and the interpretation of experiments in connection to electron transfer (ET) in this enzyme. To calculate redox titration curves for the FeS clusters it is necessary to include interactions between clusters, which in turn can be used to refine Em values and validate spectroscopic assignments of each cluster. Calculated titration curves for clusters N4, N5, and N6a are discussed. Furthermore, we present some initial findings on the electrostatics of the redox centers of complex I under the influence of externally applied membrane potentials. A means of determining the location of the FeS cofactors within the holo-complex based on electrostatic arguments is proposed. A simple electrostatic model of the protein/membrane system is examined to illustrate the viability of our hypothesis.