Treating molecules in arbitrary spin states using the parametric two-electron reduced-density-matrix method

Minimizing the electronic energy with respect to a parameterized two-electron reduced density matrix (2-RDM) is known as a parametric variational 2-RDM method. The parametric 2-RDM method with the M 2-RDM parametrization [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)] is extended to treat molecules in arbitrary spin states. Like its singlet counterpart, the M parametric 2-RDM method for arbitrary spin states is derived using approximate N-representability conditions, which allow it to capture more correlation energy than coupled cluster with single and double excitations at a lower computational cost. We present energies, optimized bond lengths, potential energy curves, and occupation numbers for a set of molecules in a variety of spin states using the M and K parametric 2-RDM methods as well as several wavefunction methods. We show that the M parametric 2-RDM method can describe bond breaking of open-shell molecules like triplet B(2) and singlet and triplet OH(+) even in the presence of strong correlation. Finally, the computed 2-RDMs are shown to be nearly N-representable at both equilibrium and non-equilibrium geometries.     

Strongly correlated barriers to rotation from parametric two-electron reduced-density-matrix methods in application to the isomerization of diazene

Recently, parameterization of the two-electron reduced density matrix (2-RDM) has made possible the determination of electronic energies with greater accuracy and lower cost than traditional electron-pair theories including coupled cluster with single and double excitations [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. We examine the method's performance for strongly correlated barriers to rotation; in particular, we study two distinct pathways in the isomerization of diazene (N(2)H(2)) from cis to trans: (i) a strongly correlated rotational pathway and (ii) a moderately correlated inversion pathway. While single reference wavefunction methods predict that the rotational barrier is higher than the inversional barrier, the parametric 2-RDM method predicts that the rotational barrier is lower than the inversional barrier by 3.1 kcal/mol in the extrapolated basis set limit. The parametric 2-RDM results are in agreement with those from multireference methods including multireference perturbation theory and the solution to the anti-Hermitian contracted Schro?dinger equation. We report energies, optimized structures, and natural orbital occupation numbers for three diazene minima and two transition states.     

Parametric two-electron reduced-density-matrix method applied to computing molecular energies and properties at nonequilibrium geometries

A parametric approach to the variational calculation of the two-electron reduced density matrix (2-RDM) for many-electron atoms and molecules has recently been developed in which the 2-RDM is parametrized to be both size consistent and nearly N-representable [C. Kollmar, J. Chem. Phys. 125, 084108 (2006); A. E. DePrince and D. A. Mazziotti, Phys. Rev. A 76, 049903 (2007)]. The parametric variational 2-RDM method is applied to computing ground-state molecular energies and properties at nonequilibrium geometries in significantly larger basis sets than previously employed. We study hydrogen abstraction from the hydroxide groups of H(2)O, NH(3)OH, and CH(3)OH. The 2-RDM method, parametrized by single and double excitations, shows significant improvement over coupled-cluster methods with similar excitations in predicting the shape of potential energy curves and bond-dissociation energies. Previous work completes the parametrization of the energy and 2-RDM by a system of n(2)h(2) normalization constraints, where n and h are the number of occupied and unoccupied orbitals, respectively. In the present paper, however, we show that the constraints can be eliminated by incorporating them into the energy and 2-RDM functions and, hence, the constrained optimization of the ground-state energy can be reformulated as an unconstrained optimization. The 2-RDMs from the parametric method are very nearly N-representable, and as measured by an l(2) norm, they are more accurate than the 2-RDMs from configuration interaction truncated at single and double excitations by an order of magnitude.     

Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method

The variational two-electron reduced-density-matrix (2-RDM) method allows for the computation of accurate ground-state energies and 2-RDMs of atoms and molecules without the explicit construction of an N-electron wave function. While previous work on variational 2-RDM theory has focused on calculating full configuration-interaction energies, this work presents the first application toward approximating multiconfiguration self-consistent-field (MCSCF) energies via low-rank restrictions on the 1- and 2-RDMs. The 2-RDM method with two- or three-particle N-representability conditions reduces the exponential active-space scaling of MCSCF methods to a polynomial scaling. Because the first-order algorithm [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] represents each form of the 1- and 2-RDMs by a matrix factorization, the RDMs are readily defined to have a low rank rather than a full rank by setting the matrix factors to be rectangular rather than square. Results for the potential energy surfaces of hydrogen fluoride, water, and the nitrogen molecule show that the low-rank 2-RDM method yields accurate approximations to the MCSCF energies. We also compute the energies along the symmetric stretch of a 20-atom hydrogen chain where traditional MCSCF calculations, requiring more than 17x10(9) determinants in the active space, could not be performed.     

An improved methyltrioxorhenium-catalyzed epoxidation of alkenes with hydrogen peroxide

Methyltrioxorhenium (MTO)-catalyzed epoxidation of alkenes with H(2)O(2) has been significantly improved by using 3-methylpyrazole as an additive. A system consisting of 35% H(2)O(2) and MTO-3-methylpyrazole in CH(2)Cl(2) catalyzes the epoxidation of various alkenes in excellent yields. The catalytic activity of MTO-3-methylpyrazole surpasses MTO-pyrazole and MTO-pyridine catalysts. Quantitative yields of epoxides from cyclic and internal alkenes were obtained with only 0.05-0.1 mol% of MTO in the presence of 10 mol% of 3-methylpyrazole.     

An improved method for direct conversion of heteroaryl-aldehydes to heteroaryl-acetonitriles

Treatment of heteroaryl-aldehydes with diethyl cyanophosphonate in the presence of a catalytic amount of LiCN affords phosphorylated cyanohydrins which are reduced in situ with SmI₂ to give heteroaryl-acetonitriles in generally good overall yields (50-100%). The generality of the process is demonstrated.     

Reagent-injection flow analysis: application to the determination of nanomolar levels of hydrogen peroxide in seawater

A reagent-injection flow technique, which allows automatic control of the volume of reagent to be injected, is described. The sensitivity of the measurements can be adjusted over a wide range by changing the injection volume. This technique also eliminates problems in photometric determinations arising from refractive index effects and from light scattering by suspended particles in the sample. Consequently, absorbances as small as 0.00004 can be measured. The capabilities of this reagent-injection flow technique were tested by using it to determine hydrogen peroxide in seawater at nanomolar levels with photometric detection. The concentration of hydrogen peroxide was determined as the colored condensation product of N-ethyl-N-(sulfopropyl)aniline and 4-aminoantipyrene; the detection limit was 12 nM.     

Reactions of hydrogen atom with hydrogen peroxide

Rate coefficients are calculated using canonical variational transition state theory with multidimensional tunneling (CVT/SCT) for the reactions H + H2O2 --> H2O + OH (1a) and H + H2O2 --> HO2 + H2 (1b). Reaction barrier heights are determined using two theoretical approaches: (i) comparison of parametrized rate coefficient calculations employing CVT/SCT to experiment and (ii) high-level ab initio methods. The evaluated experimental data reveal considerable variations of the barrier height for the first reaction: although the zero-point-exclusive barrier for (1a) derived from the data by Klemm et al. (First Int. Chem. Kinet. Symposium 1975, 61) is 4.6 kcal/mol, other available measurements result in a higher barrier of 6.2 kcal/mol. The empirically derived zero-point-exclusive barrier for (1b) is 10.4 kcal/mol. The electronic structure of the system at transition state geometries in both reactions was found to have "multireference" character; therefore special care was taken when analyzing electronic structure calculations. Transition state geometries are optimized by multireference perturbation theory (MRMP2) with a variety of one-electron basis sets, and by a multireference coupled cluster (MR-AQCCSD) method. A variety of single-reference benchmark-level calculations have also been carried out; included among them are BMC-CCSD, G3SX(MP3), G3SX, G3, G2, MCG3, CBS-APNO, CBS-Q, CBS-QB3, and CCSD(T). Our data obtained at the MRMP2 level are the most complete; the barrier height for (1a) using MRMP2 at the infinite basis set limit is 4.8 kcal/mol. Results are also obtained with midlevel single-reference multicoefficient correlation methods, such as MC3BB, MC3MPW, MC-QCISD/3, and MC-QCISD-MPWB, and with a variety of hybrid density functional methods, which are compared with high-level theory. On the basis of the evaluated experimental values and the benchmark calculations, two possible recommended values are given for the rate coefficients.     

Iodine as a catalyst for efficient conversion of ketones to gem-dihydroperoxides by aqueous hydrogen peroxide

Iodine has been shown to be an efficient catalyst for the selective dihydroperoxidation of ketones with aqueous hydrogen peroxide. Ketones were directly converted to their corresponding gem-dihydroperoxides using a "green" oxidant (30% aq H(2)O(2)) and a simple catalyst (iodine) under neutral conditions in acetonitrile. The yield of hydroperoxidation of various cyclic ketones was 60-98% including androstane-3,17-dione, and acyclic ketones were converted with a similar efficiency. [reaction: see text]     

The determination of hydrazobenzene by the die method with hydrogen peroxide catalyzed with vanadium

Hydrazobenzene cannot be oxidized to azobenzene with hydrogen peroxide in ethanol-containing medium. Vanadium(V) ions catalyze the oxidation; in their presence the reaction takes place rapidly. A thermometric (DIE) method was developed for the determination of hydrazobenzene, based on the oxidation reaction with hydrogen peroxide catalyzed by vanadium(V). The reaction is initiated by the addition of the solution of the catalyst, which is applied in small amount (100l). Thus, the application of the immersion pipette is not necessary. The standard deviation of the determination is ±0.42 mg hydrazobenzene in 50 ml ethanol.

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Zusammenfassung Hydrazobenzol kann in Äthanolhaltigem Medium mit Wasserstoffperoxid nicht zu Azobenzol oxidiert werden. Vanadium(V)-ionen katalysierten die Oxidation, in ihrer Gegenwart vollzieht sich die Reaktion rasch. Der Autor entwickelt eine thermometrische (DIE) Methode zur Bestimmung von Hydrazobenzol, die auf der durch Vanadium(V)-katalysierten Oxidationsreaktion mit Wasserstoffperoxid beruht. Die Reaktion wird durch Zugabe der in kleinen Mengen (1001) angewandten Katalysatorlösung ausgelöst. Dadurch erübrigt sich der Einsatz von Immersionspipetten. Die Standardabweichung betrÄgt ± 0.42 mg Hydrazobenzol in 50 ml Äthanol.

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Résumé L'hydrazobenzène ne peut pas Être oxydé par l'eau oxygénée dans un milieu contenant de l'éthanol. Les ions vanadium(V) catalysent l'oxydation et la réaction a Heu à grande vitesse en leur présence. Les auteurs ont développé une méthode thermométrique (DIE) afin d'effectuer le dosage de l'hydrazobenzène. Cette méthode repose sur la réaction d'oxydation par l'eau oxygénée en présence de vanadium(V) comme catalyseur. La réaction est initiée par addition de la solution du catalyseur utilisée en faible quantité (100l). Ainsi, l'emploi d'une pipette d'immersion n'est pas nécessaire. L'écart-type du dosage est ±0.42 mg d'hydrazobenzène dans 50 ml d'éthanol.

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. (V) . () , , (V). (100l) . . ±0.42 50 .

     

Electrocatalytic reduction of hydrogen peroxide on modified graphite electrodes: application to the development of glucose biosensors

The electrocatalytic activities of a series of compact graphites modified with microquantities of platinum metals (Pd or Pt+Pd) towards the electrochemical reduction of hydrogen peroxide were characterised. Operational parameters such as the optimal working potential, the influence of temperature and the resulting electrode characteristics were examined. The benefits of using graphite modified with Pt+Pd (mixture ratio 30%:70%) as the basic transducer in a glucose biosensor with improved sensitivity were demonstrated. It was proven that, under the working conditions chosen, the selected electrode (whether bare or covered with an enzyme layer) did not respond to any glutathione, uric acid or ascorbic acid (which all normally occur in biological fluids) present.     

New translation method for STOs and its application to calculation of two-center two-electron integrals

The new translation method for Slater-type orbitals (STOs) previously tested in the case of the overlap integral is extended to the calculation of two-center two-electron molecular integrals. The method is based on the exact translation of the regular solid harmonic part of the orbital followed by the series expansion of the residual spherical part in powers of the radial variable. Fair uniform convergence and stability under wide changes in molecular parameters are obtained for all studied two-center hybrid, Coulomb, and exchange repulsion integrals. Ten-digit accuracy in the final numerical results is achieved through multiple precision arithmetic calculation of common angular coefficients and Gaussian numerical integration of some of the analytical formulas resulting for the radial integrals. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 91–100, 2000     

Transition metal substituted polyoxometalates and their application in the direct hydroxylation of benzene to phenol with hydrogen peroxide

A series of transition metal substituted polyoxometalates with a Keggin structure were prepared and utilized for the hydroxylation of benzene to phenol. Among the compounds tested, [(CH₃)₄N]₄PMo₁₁VO₄₀ exhibits the highest phenol yield (13.0%) and selectivity (90.6%) in acetic acid/acetonitrile. Vanadium peroxo is the active site of the reaction, and ammonium also plays an important role. The influence of various reaction parameters, such as solvent, reaction time, reaction temperature, and amount of hydrogen peroxide used were investigated to obtain the optimal reaction conditions.     

A versatile method for preparation of O-alkylperoxycarbonic acids: epoxidation with alkyloxycarbonylimidazoles and hydrogen peroxide

A variety of O-alkylperoxycarbonic acids ($\text{2}$) were conveniently prepared $\text{in}$$\text{situ}$ by utilizing alkyloxycarbonylimidazoles ($\text{1}$) as their precursors. Epoxidation of alkenes with such peroxy-acids was studied and their reactivities were compared with those of peroxycarboxylic acids.     

3-Glycidoxypropyltrimethoxysilane mediated in situ synthesis of noble metal nanoparticles: application to hydrogen peroxide sensing

The in situ synthesis is reported of noble metal nanoparticles via 3-glycidoxypropyltrimethoxysilane mediated reduction of 3-aminopropyltrimethoxysilane treated metal salts during sol-gel processing. The method described involves the synthesis of uniform spherical nanoparticles of gold, silver and palladium with controlled size that can be directly utilized for thin film preparation. A detailed study of the synthesis and application of gold nanoparticles to the electrochemical detection of hydrogen peroxide was carried out and reveals that the amplification of hydrogen peroxide sensing is size-dependent. In addition, these nanoparticles exhibit excellent compatibility towards composite preparation. As an example, a nanocomposite with Prussian Blue (PB) is synthesized and found to be useful for the fabrication of chemically modified electrodes (CME). The resulting CME shows dramatic improvement in the electrochemistry of PB with gradual enhancement in electrocatalytic efficiency towards hydrogen peroxide sensing. The nanocomposite is used to study the direct and horseradish peroxidase (HRP)-catalyzed reduction of hydrogen peroxide. The results recorded for hydrogen peroxide analysis show an improvement in sensitivity and limit of detection on decreasing the size of gold nanoparticles in all cases.     

Testing performance of the improved pinhole collimator and its application to small animals

Testing performance of the improved pinhole collimator of 1.5 mm aperture attached to the gamma camera was carried out with three kinds of radionuclides, 99mTc, 67Ga and 131I, using a hand-made phantom. The results obtained in this experiment were compared to those obtained with a human pinhole collimator of 4 mm aperture. Those were nearly understood by taking account of the effective aperture of a pinhole collimator for each effective photon energy. And all scintigrams obtained from rats with various scintigraphy showed high resolution images.     

Reaction of hydrogen peroxide with perchlorates

Conclusions Silver perchlorate catalyzes the decomposition of aqueous hydrogen peroxide solutions and, contrary to the literature data, does not form the salt AgClO₅ in either ethanol medium or in diethyl ether medium. Silver perchlorate, the same as other perchlorates, does not form molecular compounds with hydrogen peroxide at 0°C.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2640–2641, November, 1974.     

TMSCl-promoted selective oxidation of sulfides to sulfoxides with hydrogen peroxide

Selective oxidation of sulfides to sulfoxides is achieved using H₂O₂ and TMSCl as the promotor. Aromatic and aliphatic sulfides are oxidized to sulfoxides in excellent yields and in short reaction times. Different functional groups including ketone, alkene, ester, and alcohol are tolerated.     

Palladium-catalyzed oxidation of vinyl ether to acetate with hydrogen peroxide

The selective hydrogen peroxide oxidation of vinyl ethers to give acetates was developed using triphenylphosphine palladium and triethyl amine catalysts under mild reaction conditions.