A quadrupolar expansion for r

An expansion is given for the inverse interelectronic distance in terms of the coordinates of the two electrons. The terms in the expansion contain the coordinates of the first electron with respect to two centers A, B and those of the second electron with respect to two centers C, D.     

Evaluation of integrals over STOs on different centers and the complementary convergence characteristics of ellipsoidal‐coordinate and zeta‐function expansions

One‐electron integrals over three centers and two‐electron integrals over two centers, involving Slater‐type orbitals (STOs), can be evaluated using either an infinite expansion for 1/r₁₂ within an ellipsoidal‐coordinate system or by employing a one‐center expansion in spherical‐harmonic and zeta‐function products. It is shown that the convergence characteristics of both methods are complimentary and that they must both be used if STOs are to be used as basis functions in ab initio calculations. To date, reports dealing with STO integration strategies have dealt exclusively with one method or the other. While the ellipsoidal method is faster, it does not always converge to a satisfactory degree of precision. The zeta‐function method, however, offers reliability at the expense of speed. Both procedures are described and the results of some sample calculation presented. Possible applications for the procedures are also discussed. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 1–13, 1999     

Active Intermediates in Copper Nitrite Reductase Reactions Probed by a Cryotrapping‐Electron Paramagnetic Resonance Approach

Redox active metalloenzymes catalyse a range of biochemical processes essential for life. However, due to their complex reaction mechanisms, and often, their poor optical signals, detailed mechanistic understandings of them are limited. Here, we develop a cryoreduction approach coupled to electron paramagnetic resonance measurements to study electron transfer between the copper centers in the copper nitrite reductase (CuNiR) family of enzymes. Unlike alternative methods used to study electron transfer reactions, the cryoreduction approach presented here allows observation of the redox state of both metal centers, a direct read‐out of electron transfer, determines the presence of the substrate/product in the active site and shows the importance of protein motion in inter‐copper electron transfer catalyzed by CuNiRs. Cryoreduction‐EPR is broadly applicable for the study of electron transfer in other redox enzymes and paves the way to explore transient states in multiple redox‐center containing proteins (homo and hetero metal ions).     

Bidirectional electron transfer in photosystem I: direct evidence from high-frequency time-resolved EPR spectroscopy

Efficient charge separation occurring within membrane-bound reaction center proteins is the most important step of photosynthetic solar energy conversion. All reaction centers are classified into two types, I and II. X-ray crystal structures reveal that both types bind two symmetric membrane-spanning branches of potential electron-transfer cofactors. Determination of the functional roles of these pairs of branches is of fundamental importance. While it is established that in type II reaction centers only one branch functions in electron transfer, we present the first direct spectroscopic evidence that both cofactor branches are active in the type I reaction center, photosystem I.     

Molecular symmetry and ab initio calculations: IV. Symmetry-matrix and symmetry-supermatrix in calculations of two-electron repulsion integrals

The product of two Gaussians having different centers is itself a one-center Gaussian, thus multicenter integrals with a Cartesian Gaussian basis can be reduced to one-center integrals. Recurrence relations for overlap integrals and electron repulsion integrals (ERIs) are derived at these centers. The calculations of overlap integrals and ERIs are carried out step by step from the highest symmetry case (one center) to required cases (different centers) by using the translation of Cartesian Gaussians. Full exploitation of symmetry in calculation processes can result in optimal use of these recurrence relations. Compared with the recently published algorithms, based on the recurrence relations derived by Obara and Saika [J. Chem. Phys., 84 , 3963 (1986)], the floating point operations (FLOPs) for ERI calculations (having four different centers) can be reduced by a factor of ca. 2. A significant extra saving in calculations and storage can be obtained if atoms, linear, or planar molecules are discussed. © 1997 John Wiley & Sons, Inc.     

On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals I. Single‐center expansion method

The multicenter charge‐density expansion coefficients [I. I. Guseinov, J Mol Struct (Theochem) 417 , 117 (1997)] appearing in the molecular integrals with an arbitrary multielectron operator were calculated for extremely large quantum numbers of Slater‐type orbitals (STOs). As an example, using computer programs written for these coefficients, with the help of single‐center expansion method, some of two‐electron two‐center Coulomb and four‐center exchange electron repulsion integrals of Hartree–Fock–Roothaan (HFR) equations for molecules were also calculated. Accuracy of the results is quite high for the quantum numbers, screening constants, and location of STOs. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 146–152, 2000     

The femtosecond dynamics of electron transfer in a modified photosynthesis reaction center: Quantum, classical, and kinetic analyses

The dynamics of electron transfer in a modified photosynthesis reaction center in which electron transfer from the bridge to the acceptor is blocked is considered. A microscopic model of the process is suggested. Within this model, the diabatic electronic states of the donor and bridge are described by one-dimensional displaced harmonic oscillators. The dynamics of the population of electronic states is calculated by the quantum method of wave packets and classical and kinetic modeling. The suggested model is used to study the qualitative dependence of the dynamics of electron transfer on the nonadiabatic interaction potential. The parameters of the model are determined by comparing the experimental and calculated absorption spectra of the product of electron transfer. It is shown that kinetic models can be used to approximately describe the dynamics of electron transfer in reaction centers. The boundaries of the applicability of the kinetic method are considered.     

Conformationally constrained macrocyclic diporphyrin-fullerene artificial photosynthetic reaction center

Photosynthetic reaction centers convert excitation energy from absorbed sunlight into chemical potential energy in the form of a charge-separated state. The rates of the electron transfer reactions necessary to achieve long-lived, high-energy charge-separated states with high quantum yields are determined in part by precise control of the electronic coupling among the chromophores, donors, and acceptors and of the reaction energetics. Successful artificial photosynthetic reaction centers for solar energy conversion have similar requirements. Control of electronic coupling in particular necessitates chemical linkages between active component moieties that both mediate coupling and restrict conformational mobility so that only spatial arrangements that promote favorable coupling are populated. Toward this end, we report the synthesis, structure, and photochemical properties of an artificial reaction center containing two porphyrin electron donor moieties and a fullerene electron acceptor in a macrocyclic arrangement involving a ring of 42 atoms. The two porphyrins are closely spaced, in an arrangement reminiscent of that of the special pair in bacterial reaction centers. The molecule is produced by an unusual cyclization reaction that yields mainly a product with C(2) symmetry and trans-2 disubstitution at the fullerene. The macrocycle maintains a rigid, highly constrained structure that was determined by UV-vis spectroscopy, NMR, mass spectrometry, and molecular modeling at the semiempirical PM6 and DFT (B3LYP/6-31G**) levels. Transient absorption results for the macrocycle in 2-methyltetrahydrofuran reveal photoinduced electron transfer from the porphyrin first excited singlet state to the fullerene to form a P(?+)-C(60)(?-)-P charge separated state with a time constant of 1.1 ps. Photoinduced electron transfer to the fullerene excited singlet state to form the same charge-separated state has a time constant of 15 ps. The charge-separated state is formed with a quantum yield of essentially unity and has a lifetime of 2.7 ns. The ultrafast charge separation coupled with charge recombination that is over 2000 times slower is consistent with a very rigid molecular structure having a small reorganization energy for electron transfer, relative to related porphyrin-fullerene molecules.     

Studies on Ziegler-Natta catalysts. Part V. Stereospecificity of the active center

Experimental results on Ziegler-Natta catalysts, based on observations made with the electron microscope, and a qualitative comparison of the stereospecificity of various catalyst combinations are given. The polymerization of olefin in these experiments is performed in the gas phase on dry catalysts in the absence of solvent or excess aluminium alkyl. The crystallographic structure of the lateral faces of α-TiCl₃ is established by electron microscopy and electron diffraction. The electron micrographs of α-TiCl₃–AlMe₃ catalysts show that the active centers, which are revealed by the dotwise formation of polymer, are located along the growth spirals, on lateral faces, and on surface defects. These regions of the surface are the only regions in which the surface titanium atoms are incompletely coordinated. The presence of chlorine vacancies and exposed titanium atoms is therefore an essential condition for the formation of active centers. However, the number of active centers is small in comparison to the number of incompletely coordinated titanium atoms, and hence it is concluded that the normally occurring α-TiCl₃ sites with one vacancy do not yield active centers on reaction with aluminum alkyl. It is proposed that the reaction with aluminum alkyl on such sites leads ultimately to a bimetallic complex which fills the original vacancy on the titanium atom. That the complexation is reversible and that the deblocked alkylated site, which is of the type proposed by Cossee, is an active center is not excluded. Such a center would, however, give atactic polymer. Similar complex formation on a TiCl₃ site having originally two vacancies would leave one vacancy on the titanium atom. This is believed to be the center of stereospecific polymerization. A model of this active center and a mechanism of polymer growth on it are proposed.     

石英的顺磁中心在电子自旋共振测年中的特性及应用

沉积物的电子自旋共振测年是利用石英矿物中的顺磁中心浓度确定总辐射能量,进而推定石英矿物的埋藏年代。石英中可用于测年的顺磁中心包括E′心、Al心、Ti心和Ge心。E′心需要经过热活化后才能测年。Al心是一种电子空穴心,在低温下可观测到较强的信号值。光照可以使Al心漂白,但有残留值存在。Ti心、Ge心都是电子中心,Ti心在低温测试中可见,信号微弱。Ge心光晒退最敏感,在常温观测中可见。不同顺磁中心的形成机理不同,导致它们具有不同的特性,适用于不同沉积环境中的样品测年,在冰碛物中Ge心测年更具有可行性。电子自旋共振测试时降低温度可使信号增强,Ti心在10 K和15 K时信号强度最大;Al心在20 K时信号最强;Ge心在200 K时信号明显增强。在电子自旋共振测年中可根据不同顺磁中心信号强度的变化调整测试温度获得信号的最优值。在以后的电子自旋共振(ESR)测试中可以选取信号最强时的测试温度进行测试,以增强微弱信号的信噪比,有利于对复杂的信号形态的分辨确定,提高对信号强度定量的准确性。     

Space hybrids

The theory of defining localized functions as simultaneous eigenfunctions of commuting matrices representing the variables x, y, and z is developed further to include r, the radial variable. The appropriate complete basis set for use when the weight function in the scalar product is an exponential is described. Hybrid functions that are each strongly localized around a center are defined as eigenfunctions and can be used to describe the electron density of an atom. The hybrid centers lie at the vertices of regular polyhedra centered on the nucleus. The hybrids have the important property of vanishing at the centers of all the other hybrids. Two simple examples are given to illustrate the theory and the methods of calculation. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Synthetic studies towards lagunamide C: Polyketide assembly investigations

Lagunamide C is a depsipeptide natural product with low nM cytotoxicity towards numerous cancer cell lines. Synthetically, it is disconnected to a pentapeptide backbone and polyketide unit that possesses four stereogenic centers, of which two of centers are in question (C38 & 40). Our model system highlights a high-selective aldol addition via a Crimmin’s auxiliary setting the C40 ester linkage, and a non-facially selective cyclopropanation with subsequent ring opening for the installation of the C38 methyl center.     

Calculation of the molecular electrostatic potential from a multipole expansion based on localized orbitals

A multicenter multipole expansion of molecular electron density is described with centers chosen as the centroids of localized molecular orbitals. This simple expansion yields good molecular electrostatic potentials and is computationally inexpensive to use.     

Unified treatment for the evaluation of arbitrary multielectron multicenter molecular integrals over Slater‐type orbitals with noninteger principal quantum numbers

The expansion formula has been presented for Slater‐type orbitals with noninteger principal quantum numbers (noninteger n‐STOs), which involves conventional STOs (integer n‐STOs) with the same center. By the use of this expansion formula, arbitrary multielectron multicenter molecular integrals over noninteger n‐STOs are expressed in terms of counterpart integrals over integer n‐STOs with a combined infinite series formula. The convergence of the method is tested for two‐center overlap, nuclear attraction, and two‐electron one‐center integrals, due to the scarcity of the literature, and fair uniform convergence and great numerical stability under wide changes in molecular parameters is achieved. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Protein dynamics control of electron transfer in photosynthetic reaction centers from Rps. sulfoviridis

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.     

Type 1 reaction center of photosynthetic heliobacteria

The reaction center (RC) of heliobacteria contains iron-sulfur centers as terminal electron acceptors, analogous to those of green sulfur bacteria as well as photosystem I in cyanobacteria and higher plants. Therefore, they all belong to the so-called type 1 RCs, in contrast to the type 2 RCs of purple bacteria and photosystem II containing quinone molecules. Although the architecture of the heliobacterial RC as a protein complex is still unknown, it forms a homodimer made up of two identical PshA core proteins, where two symmetrical electron transfer pathways along the C2 axis are assumed to be equally functional. Electrons are considered to be transferred from membrane-bound cytochrome c (PetJ) to a special pair P800, a chlorophyll a-like molecule A0, (a quinone molecule A1) and a [4Fe-4S] center Fx and, finally, to 2[4Fe-4S] centers FA/FB. No definite evidence has been obtained for the presence of functional quinone acceptor A1. An additional interesting point is that the electron transfer reaction from cytochrome c to P800 proceeds in a collisional mode. It is highly dependent on the temperature, ion strength and/or viscosity in a reaction medium, suggesting that a heme-binding moiety fluctuates in an aqueous phase with its amino-terminus anchored to membranes.     

Heterocyclization of Amidophenacylation Products of Uracil

When uracil is reacted with benzoylamino(chloro)acetophenone, we obtain two amidophenacylation products depending on the condensation conditions. The first product contains an amidophenacyl moiety at the N¹ center, and in the second product two such moieties are located at the N¹ and N³ centers of the uracil. Treatment of these accessible uracil derivatives with phosphorus oxychloride, thionyl chloride, or phosphorus pentasulfide leads to cyclization of the amidophenacyl side group, which is used to synthesize a number of modified pyrimidine bases with 2,5-diphenyloxazole or 2,5-diphenylthiazole residues.     

草酸根桥联双核铜(Ⅱ)体系的磁耦合机理

应用密度泛函理论,采用对称性破损方法分析了草酸根桥联双核铜(Ⅱ)体系的磁耦合机理。在该双核体系中,两铜(Ⅱ)原子的自旋布居大小相等,符号相反,磁中心间的作用为反铁磁耦合。草酸根桥配体向磁中心的电子转移使得铜(Ⅱ)原子的自旋显著离域,这种离域有利于反铁磁耦合,草酸根桥配体中的碳原子上出现自旋极化。当铜(Ⅱ)原子的配位环境由平面四方形向四面体或四方锥变化时,反铁磁耦合的强度减弱。体系的沿前轨道主要由铜(Ⅱ)原子d轨道和配体原子p轨道构成,这种构成利于草酸根桥配体与磁中心之间的电子转移。     

TiCl_4/MgCl_2负载型烯烃聚合催化剂活性中心性质的研究

用乙酰氯淬灭法测定了TiCl_4/MgCl_2-AlR_3催化1-辛烯聚合体系的活性中心数,确定了不同助催化剂、外加给电子体等条件下聚合速率、活性中心数、增长速率常数等随聚合时间的变化。结合对产物分子量分布的分峰拟合研究,确定了催化剂上存在多种活性中心及其聚合特性的差别,并发现有机给电子体对某些活性中心有选择性作用,使其失活或改变性质。     

Temperature-dependent coordination in E. coli manganese superoxide dismutase

Two different temperature dependences of the manganese(II) high-field electron paramagnetic resonance spectrum of manganese superoxide dismutase from E. coli were observed. In the 25-200 K range, the zero-field interaction steadily decreased with increasing temperature. This was likely due to the thermal expansion of the protein. From these results, it was possible to deduce an approximately r(-)(2.5) dependence of Mn(II) zero-field interaction on ligand-metal distance. At temperatures above 240 K, a distinct six-line component was detected, the amplitude of which decreased with increasing temperature. On the basis of similarities to the six-line spectrum observed for the azide-complexed E. coli manganese superoxide dismutase, the newly detected six-line spectrum was assigned to a hexacoordinate Mn(II) center resulting from the coordination of a nearby water molecule to the normally five-coordinate center. The changes in enthalpy and entropy characterizing the hexacoordinate-pentacoordinate equilibrium in the 240-268 K range were -5 kcal/mol and -24 cal/mol.K, respectively. The structural implications of the zero-field parameters of the newly found hexacoordinate form in comparison to those of the Mn(II) centers in concanavalin-A and manganese-containing R. spheroides photosynthetic reaction centers and the values predicted by the superposition model are discussed.