Rate Constant Kf Research Articles

Effect of solvent polarity on the photophysical properties of coumarin-1 dye

Effects of solvent polarity on the photophysical properties of coumarin-1 (C1; 7-NEt2-4-CH3-1,2-benzopyrone) dye have been investigated using steady-state and time-resolved fluorescence measurements. In moderate to higher polarity solvents the properties like Stokes’ shifts (Δν̄), fluorescence quantum yields (Φf), fluorescence lifetimes (τf), radiative rate constants (kf), and nonradiative rate constants (knr) follow more or less linear correlation with the solvent polarity function Δf [={(D−1)/(2D+1)}−{(n2−1)/(2n2+1)}]. In nonpolar solvents, namely, hexane, cyclohexane, methylcyclohexane, 3-methylpentane, and decalin, however, all the above-mentioned properties show unusual deviation in comparison to the trend observed in moderate to higher polarity solvents. Thus, the Δν̄ and knr values are unusually lower and the Φf, τf, and kf values are unusually higher in nonpolar solvents. Comparing the results of C1 with those of its lower analogue, namely, coumarin-120 (C120; 7-NH2-4-CH3-1,2-benzopyrone), it has been inferred that like C120, the dye C1 also exists in different structural form in nonpolar solvents than in other solvents of moderate to higher polarities. It is proposed that in nonpolar solvents the dye exists in a nonpolar structure, where the 7-NEt2 group of the dye adopts a pyramidal configuration and consequently out of plane of the 1,2-benzopyrone moiety. In moderate to higher polarity solvents, the dye is supposed to exist in a polar intramolecular charge transfer structure with its 7-NEt2 group in resonance with the 1,2-benzopyrone moiety. The observed differences in some of the properties of C1 and C120 dyes in nonpolar solvents have been rationalized based on the relative rates of the flip-flop motions of the 7-amino groups of the two dyes. It is understood that where a very fast flip-flop motion of the 7-NH2 group in C120 introduces an activation-controlled nonradiative deexcitation channel for the dye excited state in nonpolar solvents, the very slow flip-flop motion of the 7-NEt2 group in C1 cannot introduce any such nonradiative deexcitation channel for the dye.

Kinetic Approach to the Nonlinear Curve of Bovine Serum Albumin Desorption from Stainless Steel Surfaces

The kinetics of the desorption of bovine serum albumin (BSA) from stainless steel particles at various surface coverage values (θ) or at various cleaning temperatures were studied in a plug-flow column fed by a 0.1 M NaOH solution.The desorption curves obtained by plotting the logarithm of the amount of residual BSA against cleaning time was analyzed by using an integrated model for two first-order processes occurring simultaneously.At each θ or temperature, the curve of BSA desorption could be successfully reduced to the sum of two independent and simultaneous first-order processes occurring at different rates.The desorption rate constant (kf) for the faster-desorbing BSA (BSAf) was influenced by θ, especially above 0.6.On the other hand, the rate constant (ks) for the slower-desorbing BSA (BSAs) was nearly constant when θ was above 0.6.The ks was approximately 10 to 20 times lower than kf.The Kf showed an Arrhenius-type temperature dependence.The apparent activation energy (Ea) of kf was estimated to be 33kJ/mol.The kf increased by approximately 1.4 times for every 10°C rise in temperature.The proportion of BSAs to the total amount of adsorbed BSA decreased with increasing cleaning temperatures.

Photophysical studies of mixed furan, pyrrole, and thiophene-containing oligomers with three and five rings

The photophysics of several oligomers containing mixed furan, pyrrole, and thiophene heterocyclic systems is reported. The mixed systems contain three rings and five rings of the heterocycles. Comprehensive spectroscopic and photophysical data were obtained and all of the rate constants kF, kIC, and kISC were evaluated. The lowest singlet excited state is of (1)B-like origin in any solvent. It is possible to have a reasonable understanding of the photophysics of the mixed ring systems compared to all the thiophene analogs if it is considered that some π–electron decoupling occurs at the site of the pyrrole or furan substitution, although this cannot be the total answer, as is discussed.

Study and Application of Polarographic Catalytic Wave of Chlordiazepoxide in the Presence of Persulfate

AbstractPolarographic catalytic wave of chlordiazepoxide in the presence of K2S2O8 was studied in aqueous and DMF/H2O mixed solutions. The results showed that a single reduction wave in alkaline medium was the reduction of the N = C bond in 1,2‐position of chlordiazepoxide via an intermediate free radical in two one‐electron successive additions. When K2S2O8 was present, the free radical of the N = C bond was oxidized to regenerate the original, producing a parallel catalytic wave of chlordiazepoxide. It was determined that the apparent rate constant kf of the oxidation reaction was 3.2 × 103 mol−1·L·s−1. Using the catalytic wave the trace of chlordiazepoxide can be determined by linear‐potential scan polarography. In NH3/NH4Cl (pH 10.2 ± 0.1, 0.12 mol/L)/K2S2O8(0.016 mol/L) supporting electrolyte, the second‐order derivative peak current of the catalytic wave was rectilinear to chlordiazepoxide concentration in the range of 3.20 × 10−8‐1.60 × 10−7, 1.60 × 10−7‐1.44×10−6 and 1.44×10−6‐1.44x 10−5 mol/L, respectively. The limit of detection was 9.0×10−9 mol/L.

Activation parameters for three reactions interconverting isomeric 4- and 6-deuteriobicyclo[3.1.0]hex-2-enes.

Classic investigations of thermal equilibrations between 4,4-d2- and 6,6-d2-bicyclo[3.1.0]hex-2-enes (Doering, W. von E.; Roth, W. R. Angew. Chem., Int. Ed. Engl. 1963, 2, 115-122) and among deuterium-labeled and non-racemic 2-methyl-5-isopropylbicyclo[3.1.0]hex-2-enes (Delta3-thujenes) (Doering, W. von E.; Lambert, J. B. Tetrahedron 1963, 19, 1989-1994 and Doering, W. von E.; Schmidt, E. K. G. Tetrahedron 1971, 27, 2005-2030) and bicyclo[3.1.0]hex-2-enes (Cooke, R. S.; Andrews, U. H. J. Am. Chem. Soc. 1974, 96, 2974-2980) identified three different paths leading to distinct degenerate products. The equilibrations take place through [1,3]-carbon shifts with retention,suprafacial and inversion,antarafacial stereochemistry and a two-centered epimerization resulting in enantiomerization of the bicyclic skeleton through a "ring-flip" process. Activation parameters for the rate constants kr, kf, and ki associated with these paths have now been secured: Ea 43.8, 44.3, 44.8 kcal/mol and log A 14.1, 14.2, 14.1, respectively, nearly identical values, differing by less than probable error limits, consistent with a rate-determining formation followed by a rapid partitioning of a common diradical intermediate under dynamic control.

In situ FTIRS studies of kinetics of HCOOH oxidation on Pt(110) electrode modified with antimony adatoms

The electrochemical behavior of irreversibly adsorbed antimony on a Pt(110) electrode (Pt(110)/Sb) with various coverages was studied using cyclic voltammetry. The kinetics of HCOOH oxidation via reactive intermediates on Pt(110)/Sb were investigated quantitatively by employing the potential step technique and in situ FTIR spectroscopy. The results demonstrated that Sb adatoms were stable on Pt(110) when the electrode potential was below 0.45 V (SCE). It has been revealed that the dissociative adsorption of formic acid can be inhibited by the presence of Sbad on the Pt(110) surface. The electrocatalytic effects of Sbad towards HCOOH oxidation consist in a negative shift of the oxidation potential (about 350 mV) and the enhancement of the oxidation current. Based on the data processing method of integration transform developed in our previous papers, the kinetics of HCOOH oxidation on Pt(110)/Sb electrodes of different θSb have been investigated quantitatively, and both the rate constant kf and the transfer coefficient β were determined and reported.

S–T conversion induced by external magnetic field in gaseous oxalylfluoride excited to the 7151-level of the à 1Au state

Fluorescence decay of gaseous oxalylfluoride (COF)2 excited to the à 1Au(7151) level was measured as a function of gas pressure in absence and in presence of magnetic field, B=0.3 T. On excitation to this level, the dynamics in both zero and nonzero fields may be described in the intermediate-molecule limit, with the fluorescence exhibiting biexponential and triexponential decay, respectively. The fast component decay rate constant kf=(5.31±0.22)⋅107 s−1 is independent on the (COF)2 gas pressure or magnetic field strength, while that of the first slow component depends on both. The second slow component lifetime is independent of the field strength, while dependent on the gas pressure. The Stern–Volmer dependence, measured with a field in the 0.3–12 mTorr pressure range, is nonlinear. The results obtained were explained by the indirect (electronic- and nuclear-spin-decoupling) mechanism, proposed earlier.

Adsorption-parallel catalytic waves of cinnamic acid in hydrogen peroxide-tetra-n-butylammonium bromide-acetate system

The mechanism of the adsorption-parallel catalytic wave of cinnamic acid (C6H5-CH = CH-COOH) in acetate buffer (pH = 4.0)-H2O2-tetra-n-butylammonium bromide (Bu4N · Br) solution was studied by the linear-sweep polarography, cyclic voltammetry and digital simulation approach. Experimental results indicate that the reduction mechanism of cinnamic acid isECdimE’ process, in which the C = C double bond of cinnamic acid first undergoes 1e, 1H+ reduction to produce an intermediate free radical C6H5-CH-CH2-COOH(E), then the further reduction of the free radical in 1e, 1H+ addition (E’) occurs simultaneously with a dimerization reaction between two free radicals (Cdim). Bu4N· Br enhances the polarographic current of cinnamic acid and shifts the peak potential to positive direction. The enhancement action of Bu4N· Br is due to the adsorption of cinnamic acid induced by Bu4N+ species. In addition, H2O2 causes the parallel catalytic wave of cinnamic acid. The mechanism of the catalytic wave isEC’ process because H2O2 oxidizes the free radical of cinnamic acid to regenerate the original C =C bond(C’), preventing both the further reduction and the dimerization of the free radicals. The apparent rate constantkf of the oxidation reaction is 1.35×102 mol· L-1· s-1. A new class of catalytic waves for organic compounds, the adsorption-parallel catalytic waves upon the dual enhancement action of both the surfactant and oxidant, has been presented.

“N-Fused Porphyrin”: A New Tetrapyrrolic Porphyrinoid with a Fused Tri-pentacyclic Ring

The syntheses and X-ray structures of novel porphyrinoids, “N-fused porphyrins (NFPs)”, and their reactivity were described. NFP was spontaneously produced from the bromo-substituted N-confused tetraarylporphyrin in a pyridine solution at room temperature. X-ray diffraction analyses revealed that the porphyrinoid core containing a fused tri-pentacyclic ring is almost planar. The deviation from the mean plane of 4e‘, for example, was within 0.30 Å. The peripheral aryl substituents were tilted 50.4, 53.5, 64.4, and 12.4° relative to the porphyrin mean plane, respectively. The occurrence of a three-centered hydrogen bonding in the NFP core was inferred by the downfield shift of the inner NH signal (e.g., 8.48 ppm for 4e‘) in 1H NMR and the short distances (within 2.4−2.9 Å) among the inner core nitrogens, N2, N3, and N4. The optical absorption spectra of NFPs exhibit Soret-like transitions around 360, 500, and 550 nm and weak Q-like bands around 650, 700, 850, and 940 nm in CH2Cl2. The electrode process of 4e‘ showed the first oxidation at 0.08 V and reduction at −1.37 V (vs Fc/Fc+), which suggested the small energy gap attributed to the unusual long-wavelength absorption was mainly due to the rising of the HOMO energy level. The first-order rate constants (kf) for the transformation from NCPs to NFPs were largely affected by the substituents at the meso position, showing a good correlation with Hammet σ+ parameters. Moreover, the reverse reaction from NFPs to NCPs was observed in the CH2Cl2 solution by treating with a base. Dynamic ring inversion in the tetrapyrrolic porphyrin core is discussed.

Kinetics and thermodynamics of ionization of 4,4′-dimethoxytrityl alcohol in acetonitrile–aqueous acids: determination of enthalpies and entropies of activation and of reaction

We have studied the equilibration shown in eqn. (2) of 4,4′-dimethoxytrityl alcohol in aqueous perchloric, nitric, and hydrochloric acids containing 20% acetonitrile at different temperatures using stopped-flow kinetics techniques. The observed overall pseudo first-order rate constant for equilibration, kobs, decreases with increasing electrolyte concentrations at constant hydronium ion concentration; kobs, has been resolved into forward and reverse components using the equilibrium UV absorbance and the temperature-independent molar absorptivity of the 4,4′-dimethoxytrityl carbenium ion. The forward reaction (rate constant kf) is first order in both the alcohol and the acid; the reverse reaction (rate constant kr) is pseudo first order with respect to the carbocation. At constant hydronium ion concentration, the forward rate constant increases with the concentration of electrolyte whereas the reverse rate constant decreases. Quantitative effects for perchlorate, nitrate, and chloride are different. Results are accommodated by a mechanism which involves pre-equilibrium protonation of the alcohol, heterolysis of the protonated alcohol to give a 4,4′-dimethoxytrityl carbenium ion–water ion–molecule pair, then conversion of this into the dissociated carbenium ion in equilibrium with ion pairs. There are additional parallel reaction channels from the protonated alcohol and electrolyte anions. Some of the elementary rate constants have been evaluated, and enthalpies and entropies of activation have been determined. Correspondingly, some equilibrium constants of the proposed mechanism have been evaluated, and associated enthalpies and entropies of reaction have been determined.

Properties of the Intramolecular Excited Charge-Transfer States of Carbazol-9-yl Derivatives of Aromatic Ketones

Photoinduced intramolecular charge transfer (ICT) in a series of a newly synthesized N-bonded donor−acceptor derivatives of 3,6-di-tert-butylcarbazole containing benzophenone and acetophenone as an electron acceptor has been studied in solutions. In solvents more polar than butyl ether, excitation leads to an emissive singlet state. Solvatochromic effects on the spectral position and profile of the stationary fluorescence spectra clearly indicate the CT character of the emitting singlet states of all the compounds studied. An analysis of the CT fluorescence and absorption band shapes leads to the quantities relevant for the electron transfer in the Marcus inverted region. The analysis of the fluorescence rate constants (kf) and corresponding transition dipole moments (M) indicate that Marcus theory can be applied for the quantitative description of the radiationless charge recombination processes in such cases, when an intersystem crossing to the excited triplet states may be neglected (i.e., in the polar...

The 4,4'-dimethoxytrityl carbenium ion by ionization of 4,4'-dimethoxytrityl alcohol in acetonitrile - aqueous perchloric and nitric acids containing electrolytes: kinetics, equilibria, and ion-pair formation

We have studied the equilibration shown in eq. [3] of 4,4prime-dimethoxytrityl alcohol in aqueous perchloric and nitric acids containing low proportions of acetonitrile using stopped-flow kinetics techniques. The rate constants for the overall progress to equilibrium, kobs, have been resolved into forward and reverse components using the equilibrium UV absorbance and a value for the molar absorptivity of the 4,4prime-dimethoxytrityl carbenium ion determined in concentrated aqueous perchloric acid. The forward reaction (rate constant kf) is first order in both the alcohol and the acid concentrations; the reverse reaction (rate constant kr) is pseudo first order with respect to the carbocation. At constant hydronium ion concentration, the forward rate constant increases linearly with the concentration of electrolyte, whereas the reverse rate constant decreases. These effects depend upon the nature of the anion, but not the cation, and are not ionic strength effects. At constant anion concentrations, kf in both acids, and kr in perchloric acid, are independent of hydronium ion concentration; however, kr decreases with increasing hydronium ion concentration at constant nitrate concentration. At nonconstant ionic strength, changes in kf and kr observed in increasing concentrations of perchloric acid are attributable wholly to changes in perchlorate concentration. A mechanism is proposed which involves pre-equilibrium protonation of the alcohol, heterolysis of the protonated alcohol to give a 4,4prime-dimethoxytrityl carbenium ion - water ion-molecule pair, then conversion of this into a dissociated carbenium ion in equilibrium with ion pairs. To account for the strong effects of perchlorate and nitrate upon the forward rate constants, it is proposed that these anions provide additional reaction channels from the ion-molecule pair. However, we find no evidence of acid catalysis in the reaction of the ion-molecule pair (in contrast to our finding for the reaction of the corresponding ion-molecule pair formed from dimethoxytritylamine in acidic media). Some of the elementary rate and equilibrium constants of the proposed mechanism have been evaluated.Key words: trityl, carbenium ion, stopped-flow, ion pair, ion-molecule pair.

An Experimental and ab Initio CI Study for Charge Transfer Excited States and Their Relaxation in Pyrroloborane Derivatives

The fluorescence of dimesityl-pyrroloboranes with different ground state twist angles is investigated by absorption, steady state, and time-resolved fluorescence spectroscopies. Only one strongly Stokes shifted charge transfer fluorescence band is found, characterized by monoexponential decays. This fluorescence is connected with extremely low fluorescence rate constants (kf = (1−2) × 106 s-1) which are nearly solvent and temperature independent and indicate the forbidden character of the emission. The pretwisted compound shows reduced kf values and only a lengthening of the lifetimes with decreasing temperature whereas the planar compound shows a lifetime maximum (increase followed by decrease) upon cooling. This is interpreted as evidence that the planar compound relaxes to a more twisted structure in the excited state. Large-scale ab initio CI calculations on a smaller model system confirm the nearly full charge-transfer character present for all twist angles and the energy minimum in the excited state...

Studies of kinetics of HCOOH oxidation on Pt(100), Pt(110), Pt(111), Pt(510) and Pt(911) single crystal electrodes

The kinetics of HCOOH oxidation via a reactive intermediate on Pt(100), Pt(110), Pt(111), Pt(510) and Pt(911) single crystal electrodes were studied quantitatively. The difficulty due to the self-poisoning involved in HCOOH oxidation has been overcome successfully by designing a programmed potential step procedure, which is based on results of kinetic studies of dissociative adsorption of HCOOH. The data processing method of integration transform of j∼t transient data was developed for extracting kinetic parameters. The rate constant (kf), the apparent activation energy (ΔH≠°) and the transfer coefficient (β) for HCOOH oxidation on different Pt single crystal electrodes have been evaluated. The values of ΔH≠° obtained on the 5 Pt single crystal electrodes vary from 10.1±0.1 to 32.7±0.2 kJ mol−1. The results demonstrated that the well-defined Pt(110) electrode possesses the lowest value of ΔH≠° amongst the 5 Pt single crystal electrodes studied, signifying a higher electrocatalytic activity for HCOOH oxidation. According to the values of ΔH≠°, the electrocatalytic activity of the three basal planes of Pt single crystals can be arranged in the ascending order of Pt(110)>Pt(111)>Pt(100). The values of ΔH≠° of the two stepped surface are close to that of Pt(100) (32.2±0.5 kJ mol−1), which is in good accord with the configuration of surface structure of the two stepped surfaces since the majority surface sites are of (100) symmetry. It has been found that the transfer coefficient β does not vary with the reaction temperature, and manifests a similar variation as that of ΔH≠° versus the orientation of the Pt single crystal electrode. The small values of β (ranging from 0.102±0.004 to 0.251±0.008) may suggest a stepwise transfer of two electrons and imply the unavoidable interaction of HCOOH with surfaces of the Pt single crystal electrodes. The variation of ΔH≠° and β versus the orientation of Pt single crystal electrode demonstrated, from a kinetic point of view and for the first time, the effects of surface atomic arrangement towards HCOOH oxidation.

High pressure studies of the Kramers turnover behavior for the excited-state isomerization of 2-alkenylanthracene in alkane

The isomerization rate of 2-(2-propenyl)anthracene (22PA) in the lowest excited singlet (S1) state was investigated in supercritical fluids (SCF); ethane and CO2, as well as in a series of liquid n-alkanes at high pressures. Combining the present results with our preceding ones which had been examined in compressed liquid n-alkane solvents [J. Phys. Chem. A 101, 2240 (1997)] we completed the curve of forward isomerization rate constant (kf) against solvent viscosity (η) over the entire friction range. We also discuss the dependence of kf on the inverse of solvent self-diffusion coefficient (D−1), which is used as a measure of solvent collisional frequency. The Kramers turnover behavior of 22PA thus observed was compared with our previous result of 2-vinylanthracene [J. Chem. Phys. 103, 5548 (1995)]. The kf values of both isomerization reactions around the turnover viscosity region never attains those which are predicted by transition state theory.

The 4,4'-dimethoxytrityl carbenium ion by ionization of 4,4'-dimethoxytrityl alcohol in acetonitrile - aqueous perchloric and nitric acids containing electrolytes: kinetics, equilibria, and ion-pair formation

We have studied the equilibration shown in eq. [3] of 4,4prime-dimethoxytrityl alcohol in aqueous perchloric and nitric acids containing low proportions of acetonitrile using stopped-flow kinetics techniques. The rate constants for the overall progress to equilibrium, kobs, have been resolved into forward and reverse components using the equilibrium UV absorbance and a value for the molar absorptivity of the 4,4prime-dimethoxytrityl carbenium ion determined in concentrated aqueous perchloric acid. The forward reaction (rate constant kf) is first order in both the alcohol and the acid concentrations; the reverse reaction (rate constant kr) is pseudo first order with respect to the carbocation. At constant hydronium ion concentration, the forward rate constant increases linearly with the concentration of electrolyte, whereas the reverse rate constant decreases. These effects depend upon the nature of the anion, but not the cation, and are not ionic strength effects. At constant anion concentrations, kf in both acids, and kr in perchloric acid, are independent of hydronium ion concentration; however, kr decreases with increasing hydronium ion concentration at constant nitrate concentration. At nonconstant ionic strength, changes in kf and kr observed in increasing concentrations of perchloric acid are attributable wholly to changes in perchlorate concentration. A mechanism is proposed which involves pre-equilibrium protonation of the alcohol, heterolysis of the protonated alcohol to give a 4,4prime-dimethoxytrityl carbenium ion - water ion-molecule pair, then conversion of this into a dissociated carbenium ion in equilibrium with ion pairs. To account for the strong effects of perchlorate and nitrate upon the forward rate constants, it is proposed that these anions provide additional reaction channels from the ion-molecule pair. However, we find no evidence of acid catalysis in the reaction of the ion-molecule pair (in contrast to our finding for the reaction of the corresponding ion-molecule pair formed from dimethoxytritylamine in acidic media). Some of the elementary rate and equilibrium constants of the proposed mechanism have been evaluated.Key words: trityl, carbenium ion, stopped-flow, ion pair, ion-molecule pair.

Application of Non-Steady-State Kinetics to Resolve the Kinetics of Proton-Transfer Reactions between Methylarene Radical Cations and Pyridine Bases

Apparent deuterium kinetic isotope effects (KIEapp) of four different methylarene radical cation−pyridine base reactions in dichloromethane (0.2 M tetrabutylammonium hexafluorophosphate) were observed to increase toward a constant value with increasing extent of reaction. The reactions were studied by derivative cyclic voltammetry (DCV), and rate constants were assigned by comparing the experimental with the theoretical DCV data. The kinetic results rule out a simple second-order proton-transfer reaction and implicate a mechanism in which a complex is first formed that then undergoes proton transfer, followed by separation of the products. That KIEapp are extent of reaction-dependent is observed before steady-state is reached. The concurrent analysis of kinetic data for the reactions of both ArCH3•+ and ArCD3•+ with bases under non-steady-state conditions facilitates the resolution of the apparent rate constant [kapp = kfkp/(kb + kp)] into the microscopic rate constants (kf, kb, and kp) for the individual...

COS-Forming Reaction between CO and Sulfur: A High-Temperature Intrinsic Kinetics Study

Carbonyl sulfide is formed in the front end (i.e., the reaction furnace and the waste heat boiler) of Claus plants which are commonly used to recover sulfur from acid gases. Moreover, COS along with CS2, are recognized as the problematic sulfur compounds that contribute significantly to plant sulfur emissions. Further, there is limited kinetic information on the important reaction for the formation of these two compounds. Now, it is well-known that one of the important COS-forming reactions is that between CO and sulfur. In our laboratory, we conducted an experimental study to measure the intrinsic kinetics of this homogeneous gas-phase reaction in the temperature range of 600−1150 °C and over a residence time of 0.5−2.0 s. The overall reaction was found to be second order with a reaction rate constant kf = (3.18 ± 0.36) × 105 exp[−(6700 ± 108 K)/T] m3/(kmol·s). In addition, a kinetic model was developed to account for both the COS formation and the COS decomposition reactions. And, finally, for the rever...

Numerical analysis of kinetic rate constants derived from stochastic computer simulation

AbstractA numerical approach has been developed to determine the individual rate constants (kf − s and ks − f), as well as the equilibrium constant from the ratio of the rate constants (kf − s/ks − f), by using stochastic simulation. This approach is illustrated for simulations of the absorption (partition) process between homogeneous fluid and surface phases under diffusion‐limited conditions. A pair of regression methods is derived from the chemical system with the initial distribution of molecules entirely in either the fluid or surface phase. These two methods are complementary in determining the rate constants for distribution coefficients that are lower or higher than unity, respectively. A standard exponential (two‐parameter) regression equation is compared with a biexponential (four‐parameter) equation, which provides for inherent correction of numerical error. The effects of the number of molecules, as well as the time increment and range, are examined in detail. This provides guidance to optimize the computational parameters of the simulation. The proposed approach has been successfully applied for distribution coefficients ranging from 0.01 to 100.0, yielding individual rate constants kf − s and ks − f with ± 0.84% and ± 0.57% average relative standard deviation, and the ratio of the rate constants with ± 1.04% average relative standard deviation and ± 1.14% average relative error.

Effects of single and double mutations in plastocyanin on the rate constant and activation parameters for the rearrangement gating the electron-transfer reaction between the triplet state of zinc cytochrome c and cupriplastocyanin.

The unimolecular rate constant for the photoinduced electron-transfer reaction 3Zncyt/pc(II) --> Zncyt+/pc(I) within the electrostatic complex of zinc cytochrome c and spinach cupriplastocyanin is kF. We report the effects on kF of the following factors, all at pH 7.0: 12 single mutations on the plastocyanin surface (Leu12Asn, Leu12Glu, Leu12Lys, Asp42Asn, Asp42Lys, Glu43Asn, Glu59Gln, Glu59Lys, Glu60Gln, Glu60Lys, Gln88Glu, and Gln88Lys), the double mutation Glu59Lys/Glu60Gln, temperature (in the range 273.3-302.9 K), and solution viscosity (in the range 1. 00-116.0 cP) at 283.2 and 293.2 K. We also report the effects of the plastocyanin mutations on the association constant (Ka) and the corresponding free energy of association (DeltaGa) with zinc cytochrome c at 298.2 K. Dependence of kF on temperature yielded the activation parameters DeltaH, DeltaS, and DeltaG. Dependence of kF on solution viscosity yielded the protein friction and confirmed the DeltaG values determined from the temperature dependence. The aforementioned intracomplex reaction is not a simple electron-transfer reaction because donor-acceptor electronic coupling (HAB) and reorganizational energy (lambda), obtained by fitting of the temperature dependence of kF to the Marcus equation, deviate from the expectations based on precedents and because kF greatly depends on viscosity. This last dependence and the fact that certain mutations affect Ka but not kF are two lines of evidence against the mechanism in which the electron-transfer step is coupled with the faster, but thermodynamically unfavorable, rearrangement step. The electron-transfer reaction is gated by the slower, and thus rate determining, structural rearrangement of the diprotein complex; the rate constant kF corresponds to this rearrangement. Isokinetic correlation of DeltaH and DeltaS parameters and Coulombic energies of the various configurations of the Zncyt/pc(II) complex consistently show that the rearrangement is a facile configurational fluctuation of the associated proteins, qualitatively the same process regardless of the mutations in plastocyanin. Correlation of kF with the orientation of the cupriplastocyanin dipole moment indicates that the reactive configuration of the diprotein complex involves the area near the residue 59, between the upper acidic cluster and the hydrophobic patch. Kinetic effects and noneffects of plastocyanin mutations show that the rearrangement from the initial (docking) configuration, which involves both acidic clusters, to the reactive configuration does not involve the lower acidic cluster and the hydrophobic patch but involves the upper acidic cluster and the area near the residue 88.