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.     

Nonlinear whispering-gallery modes in a microellipse cavity

We study theoretically the effect of deformed microelliptical cavities on lasing characteristics. We show that the transition of stationary lasing states from unidirectional rotational waves to a mixture of clockwise and anticlockwise rotational waves occurs when the shape of a disk is deformed to that of an ellipse.     

Quasi-stadium laser diodes with an unstable resonator condition

We have observed lasing in a complicated eigenmode of a quasi-stadium laser diode with an unstable resonator consisting of two curved end mirrors obeying an unstable resonator condition and two straight sidewall mirrors. The laser was fabricated by application of a reactive-ion-etching technique to a molecular beam epitaxy-grown graded-index separate-confinement heterostructure single-quantum-well GaAs/AlGaAs structure. The far-field pattern shows that the lasing mode corresponds to the complicated lowest-loss mode obtained numerically by an extended Fox-Li method.     

Fresnel filtering of Gaussian beams in microcavities

We study the output from the modes described by the superposition of Gaussian beams confined in the quasi-stadium microcavities. We experimentally observe the deviation from Snell's law in the output when the incident angle of the Gaussian beam at the cavity interface is near the critical angle for total internal reflection, providing direct experimental evidence on the Fresnel filtering. The theory of the Fresnel filtering for a planar interface qualitatively reproduces experimental data, and a discussion is given on small deviation between the measured data and the theory.     

LR test for random-effects covariance structure in a parallel profile model

We consider a parallel profile model which is useful in analyzing parallel growth curves of several groups. The likelihood ratio criterion for a hypothesis concerning the adequacy of a random-effects covariance structure is obtained under the parallel profile model. The likelihood ratio criterion for the hypothesis in the general one-way MANOVA model is also obtained. Asymptotic null distributions of the criteria are derived when the sample size is large. We give a numerical example of these asymptotic results.     

Synthesis of poly(ester amide)s by the melt polycondensation of semiaromatic polyesters with ethanolamine and their characterization

Semiaromatic poly(ester amide)s (PEAs) were synthesized by the melt polycondensation of ethanolamine (EA) derivatives with dimethyl terephthalate and ethylene glycol in the presence of tetrabutyl titanate as a catalyst, and their crystallization and thermal properties were investigated. The introduction of an amide group into a semiaromatic polyester such as poly(ethylene terephthalate) (PET) produced PEAs (EA-modified PET polymers) with an increase in the melting point. However, these PEAs were found to decompose at a lower temperature than PET on the basis of TGA. Moreover, direct pyrolysis/mass spectrometry measurements suggested that an initial step of the thermal decomposition was a β-CH hydrogen-transfer reaction via asix-member ring transition state at the ester–ethylene–amide unit, at which carbon–oxygen bond scission took place to yield carboxyl and N-vinylamide end groups. Furthermore, molecular orbital calculations using trimer models bis[2-[[4-(methoxycarbonyl)benzoyl]oxy]ethyl]terephthalate, N-[2-[[4-(methoxycarbonyl)benzoyl]oxy]ethyl]-4-[2-[[4-(methoxycarbonyl)benzoyl]oxy]ethyloxycarbonyl]benzamide, and N,N′-bis[2-[[4-(methoxycarbonyl)benzoyl]oxy]ethyl]terephthalamide strongly supported the idea that the β-CH hydrogen-transfer reaction in the thermal decomposition of PEAs might occur more easily at the methylene group next to the amide group in an ester–ethylene–amide unit rather than at the methylene group next to the ester group in an ester–ethylene–ester unit. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2184–2193, 2007     

An experimental investigation on isoclinic parameters in viscoelastoplastic materials under cyclic stresses

Photovisco-elastoplasticity has been developed and applied to various problems in nonlinear stress analysis as an extension of photoelasticity into nonlinear photomechanics. In photoelasticity, because stress is simply related to strain, isochromatics are proportional to either the principal stress difference or the principal strain difference and isoclinics indicate the directions of either principal stresses or principal strains separately. However, in photovisco-elastoplasticity, these optical responses are nonlinearly related to both stress and strain state simultaneously. Thus isochromatics are related nonlinearly with both the principal stress and strain differences. Isoclinics depend on the direction of principal strain as well as that of principal stress. Concerning now isoclinic parameter: according to the results of experiments performed by us for the deformation state where the directions of principal stress and strain do not coincide with one another, it has been found that isoclinic parameter moves gradually from the direction of principal stress to that of principal strain with increasing viscous deformation under constant stress. In the present research, extending our previous investigations, the behavior of isoclinic parameter has been examined experimentally under cyclic stressing, where the direction of principal stress changes alternately. In the course of an experiment, the variation of isoclinic parameter in relation to the number of cycles was measured together with the corresponding strain state on the thin-walled tubular specimen of celluloid softened by heating, subjected to combined loading conditions consisting of constant axial tension and cyclic torsion. The results obtained may be summarized as follows.

1. The cyclic-variation phase of isoclinic parameter lags behind the cyclic-variation phase of the direction of principal stress. The phase difference between these cyclic variations remains constant regardless of the number of cycles.
2. Isoclinic parameter has a value close to the direction of the principal stress within a range of a small number of cycles and decreases with an increase in the number of cycles. However, it does not approach the direction of principal strain but a value between the direction of the principal stress and that of the principal strain, with a certain constant ratio to them.

     

UV luminescent organic-capped ZnO quantum dots synthesized by alkoxide hydrolysis with dilute water

A novel synthesis route to organic-capped and colloidal ZnO quantum dots (QDs) has been developed. Specifically, zinc-di-t-butoxide and zinc-di-n-butoxide are hydrolyzed by very dilute water (400-600 mass ppm) in hydrophilic benzylamine and polymerized to ZnO by dehydration and/or a butanol elimination reaction. Growth of the ZnO QDs and exchange of the surface capping ligand from the hydroxyl groups and/or benzylamine to the oleylamine occur by heating the colloidal solution after addition of the oleylamine at 100-180°C. The final ZnO QDs with diameters in the range of 3-7 nm are highly dispersible in various organic solvents. The ZnO QDs exhibit the quantum size effect upon UV emission; it was controlled between 3.39 and 3.54 eV in the present study. The defect-related Vis emission decreased and the UV emission becomes dominant when zinc-di-n-butoxide with a 99.99% zinc purity is used as the starting material. The intensity of the photoluminescence UV emission is 1.5 times higher than that of the Vis emission.     

Benzoannelation stabilizes the d(xy)1 state of low-spin iron(III) porphyrinates

A series of low-spin, six-coordinate complexes [Fe(TBzTArP)L(2)]X (1) and [Fe(TBuTArP)L(2)]X (2) (X = Cl(-), BF(4)(-), or Bu(4)N(+)), where the axial ligands (L) are HIm, 1-MeIm, DMAP, 4-MeOPy, 4-MePy, Py, and CN(-), were prepared. The electronic structures of these complexes were examined by (1)H NMR and electron paramagnetic resonance (EPR) spectroscopy as well as density functional theory (DFT) calculations. In spite of the fact that almost all of the bis(HIm), bis(1-MeIm), and bis(DMAP) complexes reported previously (including 2) adopt the (d(xy))(2)(d(xz), d(yz))(3) ground state, the corresponding complexes of 1 show the (d(xz), d(yz))(4)(d(xy))(1) ground state at ambient temperature. At lower temperature, the electronic ground state of the HIm, 1-MeIm, and DMAP complexes of 1 changes to the common (d(xy))(2)(d(xz), d(yz))(3) ground state. All of the other complexes of 1 and 2 carrying 4-MeOPy, 4-MePy, Py, and CN(-) maintain the (d(xz), d(yz))(4)(d(xy))(1) ground state in the NMR temperature range, i.e., 298-173 K. The EPR spectra taken at 4.2 K are fully consistent with the NMR results because the HIm and 1-MeIm complexes of 1 and 2 adopt the (d(xy))(2)(d(xz), d(yz))(3) ground state, as revealed by the rhombic-type spectra. The DMAP complex of 1 exists as a mixture of two electron-configurational isomers. All of the other complexes adopt the (d(xz), d(yz))(4)(d(xy))(1) ground state, as revealed by the axial-type spectra. Among the complexes adopting the (d(xz), d(yz))(4)(d(xy))(1) ground state, the energy gap between the d(xy) and d(π) orbitals in 1 is always larger than that of the corresponding complex of 2. Thus, it is clear that the benzoannelation of the porphyrin ring stabilizes the (d(xz), d(yz))(4)(d(xy))(1) ground state. The DFT calculation of the bis(Py) complex of analogous iron(III) porphyrinate, [Fe(TPTBzP)(Py)(2)](+), suggests that the (d(xz), d(yz))(4)(d(xy))(1) state is more stable than the (d(xy))(2)(d(xz), d(yz))(3) state in both ruffled and saddled conformations. The lowest-energy states in the two conformers are so close in energy that their ordering is reversed depending on the calculation methods applied. On the basis of the spectroscopic and theoretical results, we concluded that 1, having 4-MeOPy, 4-MePy, and Py as axial ligands, exists as an equilibrium mixture of saddled and ruffled isomers both of which adopt the (d(xz), d(yz))(4)(d(xy))(1) ground state. The stability of the (d(xz), d(yz))(4)(d(xy))(1) ground state is ascribed to the strong bonding interaction between the iron d(xy) and porphyrin a(1u) orbitals in the saddled conformer caused by the high energy of the a(1u) highest occupied molecular orbital in TBzTArP. Similarly, a bonding interaction occurs between the d(xy) and a(2u) orbitals in the ruffled conformer. In addition, the bonding interaction of the d(π) orbitals with the low-lying lowest unoccupied molecular orbital, which is an inherent characteristic of TBzTArP, can also contribute to stabilization of the (d(xz), d(yz))(4)(d(xy))(1) ground state.