Interference, fluctuation, and alternation of electron tunneling in protein media. 2. Non-condon theory for the energy gap dependence of electron transfer rate

Developing the quantum transition rate theory of Prezhdo and Rossky (J. Chem. Phys. 1997, 107, 5863), we produced a new non-Condon theory of the rate of electron transfer (ET) which happens through a protein medium with conformational fluctuation. The new theory is expressed by a convolution form of the power spectrum for the autocorrelation function of the electronic tunneling matrix element T(DA)(t) with quantum correction and the ordinary Franck-Condon factor. The new theory satisfies the detailed balance condition for the forward and backward ET rates. The ET rate formula is divided into two terms of elastic and inelastic tunneling mechanisms on the mathematical basis. The present theory is applied to the ET from Bph(-) to Q(A) in the reaction center of Rhodobacter sphaeroides. Numerical calculations of T(DA)(t) were made by a combined method of molecular dynamics simulations and quantum chemistry calculations. We showed that the normalized autocorrelation function of T(DA)(t) is almost expressed by exponential forms. The calculated energy gap law of the ET rate is nearly Marcus' parabola in most of the normal region and around the maximum region, but it does not decay substantially in the inverted region, which is called the anomalous inverted region. We also showed that the energy gap law at the high uphill energy gap in the normal region is elevated considerably from the Marcus' parabola, which is called the anomalous normal region. Those anomalous energy gap laws are due to the inelastic tunneling mechanism which works actively at the energy gap far from zero. We presented an empirical formula for easily calculating the non-Condon ET rate, which is usable by many researchers. We provided experimental evidence for the anomalous inverted region which was basically reproduced by the present theory. The present theory was extensively compared with the previous non-Condon theories.     

High throughput continuous titration based on a flow ratiometry controlled with feedback-based variable triangular waves and subsequent fixed triangular waves

We propose a new approach for high-throughput continuous titration based on a flow ratiometry. The method was applied to potentiometric titrations of acids and bases. A base solution, the flow rate F_B of which was varied in response to controller output voltage V_c, was merged with an acid solution under constant total (acid + base) flow rate. Downstream, the pH of the mixed solution was measured with a flow-through glass electrode. Initially, V_c, and thus F_B was increased linearly. At the instant the equivalence point (EP) was sensed, the ramp direction of V_c was reversed from upward to downward. The direction was reversed to upward when EP was sensed again. Such the feedback-based operation gives a triangular waveform of V_c, because there is a delay corresponding mainly to the transit time of merged solutions to reach the sensor. The value of V_c that gives EP composition, V_E, was estimated by averaging the most recent maximum and minimum values of V_c. Next, fixed triangular waves of V_c was used to control F_B. The amplitude and the scan rate of the waves were fixed narrower and faster, respectively, than those in the feedback-based operation in order to improve the throughput rate. The EP can be located as long as the scan range covers V_E. These automated processes limited the titration to just the narrow range around EP, and thus realized extremely high throughput rate of maximally 17.6 titrations per minute (=3.4 s per titration) at R.S.D. = 0.35%.     

Mechanistic approaches to asymmetric synthesis of aziridines from guanidinium ylides and aryl aldehydes

To approach more realistic mechanisms for asymmetric aziridine synthesis from guanidinium ylides and aryl aldehydes, reactions were systematically carried out by using a variety of p-substituted benzaldehydes under modified conditions. Two kinds of reaction mechanisms controlled by the nature of the p-substituents of aryl aldehydes is proposed for the two-steps aziridine synthesis composed of a C-C bond formation by nucleophilic addition of guanidinium ylides to aryl aldehydes (step 1) and the fragmentation of intermediate adducts to aziridine products by intramolecular nucleophilic substitution (step 2). A S_Ni-like mechanism via cationic-like transition state is proposed for step 2 in the asymmetric synthesis using EDG-substituted benzaldehydes, whereas with EWG-substituted benzaldehydes, a S_N2-like mechanism is proposed. Hammett analysis, based on the diastereomeric ratio in the aziridine products, is consistent with the proposed rate-determining steps in these two mechanisms. A second Hammett analysis, based on the enantiomeric ratio of the aziridine products, clearly reveals the difference in the susceptibilities to the electronic substituents effect between step 1 and step 2.     

Symmetry or asymmetry in cheletropic additions forming cyclopropanes

Cheletropic additions forming cyclopropane rings were studied theoretically. Ten addition paths were traced by means of density-functional-theory calculations. Two 1,4-dienes, 1,4-pentadiene, and tricyclo[5.3.1.0^4,9]undeca-2,5-diene were adopted as substrates. CO, SO₂, C₂H₅PCl₂, CCl₂ and SiCl₂ were employed as cheletropic reagents (Xs). An orbital correlation diagram of the Woodward–Hoffmann (W–H) rule and frontier molecular orbital (FMO) interactions between them were investigated in detail. The FMO interactions, HOMO (1,4-diene)lumo (X) and homo (X)LUMO (diene), work reasonably for the progress of the reactions. Those cause the formation of two C–X bonds and a cyclopropane ring, and alternation of double bonds to single bonds. All the additions are concerted. The easiness of the ring formation depends upon the energy gap between HOMO and lumo and that between homo and LUMO, and the spatial directions of HOMO and LUMO extensions. Symmetry conservation of the W–H rule does not hold necessarily for those addition paths. The symmetry-breaking was discussed in terms of FMO interactions.Acknowledgement This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan and by Nishida Memorial Foundation for Fundamental Chemical Research.     

Ultrasonic effects on electroorganic processes: Part 16. Stereoselectivity control of hydrodimers formed in cathodic reduction of acetophenones

Stereoselectivity (meso/dl ratio) of the hydrodimers (HDs) formed in cathodic reduction of acetophenones was greatly affected by ultrasonic irradiation with power higher than an ultrasonic cavitation threshold in weakly acidic solutions, while such an ultrasonic effect on stereocontrol was not observed in either strongly acidic or alkaline solutions.     

PHOTOOXYGENATION OF METHYL LINOLEATE SENSITIZED BY PORPHYRINS AND DYES IN ACETONITRILE SOLUTION AND AQUEOUS EMULSION SYSTEMS

Photooxygenation reaction of an unsaturated fatty acid ester, methyl linoleate (methyl 9- cis. 12- cis -octadecadienoate, ML-H), sensitized by porphyrins and several types of dyes has been studied in aqueous emulsion and acetonitrile solution under air at 40°C. The oxygen (O₂) uptake proceeded slowly in the absence of sensitizers upon irradiation of an aqueous emulsion and an acetonitrile solution of ML-H (20 m M ) at ℷ_ex > 290 nm (11.4 and 6.1 μmol h^-1, respectively). The rate of O₂ uptake was enhanced by a catalytic amount (0.1 m M ) of porphyrins and dyes; hematoporphyrin (HP), zinc tetrakis(N-methyl-4-pyridiniumyi)porphyrin (ZnTMPyP), methylene blue (MB), rose bengal (RB), acridine orange (AO), and acriflavine (AF). In both systems, the sensitized photooxidation of ML-H by O₂ proceeded equimolarly to produce isomeric mixture of C9 and C13 hydroperoxides having the trans,cis and trans,trans conjugated diene configurations, independent of the types of the sensitizers used. The yield ratio of trans,trans/ trans,cis products in the MB-sensitized photooxygenation in acetonitrile and aqueous emulsion were almost equal (0.32 and 0.35. respectively). The sensitizing activity of the sensitizers, as measured by the quantum yield of O₂ uptake, increased in the order: MB (≃ 0) < ZnTMPyP < RB < HP < AF < AO in the aqueous emulsion and AO < AF < HP < RB = MB in the acetonitrile solution. The order in homogeneous acetonitrile solution was interpreted by the sensitizing ability of the dyes to produce singlet oxygen, while that in heterogeneous aqueous emulsion was correlated to the lipophilicity of dyes as well as the singlet-oxygen-producing ability.