3,745 research outputs found
Quantum chemical calculations show that the uranium molecule U2 has a quintuple bond
No full textCovalent bonding is commonly described by Lewis's theory(1), with an electron pair shared between two atoms constituting one full bond. Beginning with the valence bond description(2) for the hydrogen molecule, quantum chemists have further explored the fundamental nature of the chemical bond for atoms throughout the periodic table, confirming that most molecules are indeed held together by one electron pair for each bond. But more complex binding may occur when large numbers of atomic orbitals can participate in bond formation. Such behaviour is common with transition metals. When involving heavy actinide elements, metal-metal bonds might prove particularly complicated. To date, evidence for actinide-actinide bonds is restricted to the matrix-isolation(3) of uranium hydrides, including H2U-UH2, and the gas-phase detection(4) and preliminary theoretical study(5) of the uranium molecule, U-2. Here we report quantum chemical calculations on U-2, showing that, although the strength of the U-2 bond is comparable to that of other multiple bonds between transition metals, the bonding pattern is unique. We find that the molecule contains three electron-pair bonds and four one-electron bonds (that is, 10 bonding electrons, corresponding to a quintuple bond), and two ferromagnetically coupled electrons localized on one U atom each-so all known covalent bonding types are contributing
Large-Update Infeasible Interior-Point Methods for Linear Optimization
No full textRecently, C. Roos proposed a full-Newton step infeasible interior-point method (IIPM) for linear optimization (LO). Shortly afterwards, Mansouri and Roos presented a variant of this algorithm and Gu et al. a version with a simplified analysis. Roos' algorithm is a path-following method. It uses the so-called homotopy path as a guideline to an optimal solution. The algorithm has the advantage that it uses only full Newton steps (the step size is always 1, hence requires no computation), and its convergence rate is O(n), which coincides with the best known convergence rate for IIPMs. Apart from these nice features, the algorithm has the deficiency that it is a small-update method and hence it is too slow for practical purposes. In this thesis we design a large-update version of Roos' algorithm. We present a practically efficient implementation of (a variant of) the algorithm and compare its performance with that of the well- known LIPSOL package. The numerical results are promising as the iteration numbers of our algorithm are close to those of LIPSOL; in a few cases they outperform LIPSOL. Not surprisingly, as in large-update feasible interior-point methods (FIPMs), there is a gap between the practical and the theoretical behavior of our large-update IIPM. To be more precise, its theoretical convergence rate is O(n?n (log n)³) which is worse than the convergence rate of its full-Newton step variant. This phenomenon is well-known in the field of IPMs, and has been called the irony of IPMs: small-update methods have the best complexity results and are slow in practice, whereas large-update methods have worse complexity results and excellent performance in practice. For example, large-update FIPMs are by a factor worse than that of the full-Newton step FIPMs, i.e., O(?nlogn) versus O(?n). The thesis also contains a survey of IIPMs that have been presented by several authors in last two decades. It covers a wide range of methods, starting from Lustig's algorithm, to the infeasible potential-reduction methods of Mizuno, Kojima and Todd. We focus on convergence properties and polynomiality of the IIPMs presented in our survey.EWIElectrical Engineering, Mathematics and Computer Scienc
Counterexample to a Conjecture on an Infeasible Interior-Point Method
No full textIn [SIAM J. Optim., 16 (2006), pp. 1110–1136], Roos proved that the devised full-step infeasible algorithm has worst-case iteration complexity. This complexity bound depends linearly on a parameter , which is proved to be less than . Based on extensive computational evidence (hundreds of thousands of randomly generated problems), Roos conjectured that (Conjecture 5.1 in the above-mentioned paper), which would yield an iteration full-Newton step infeasible interior-point algorithm. In this paper we present an example showing that is in the order of , the same order as that proved in Roos's original paper. In other words, the conjecture is false.Software TechnologyElectrical Engineering, Mathematics and Computer Scienc
A THEORETICAL INVESTIGATION OF VALENCE AND RYDBERG ELECTRONIC STATES OF ACROLEIN,
No full textThe main features of the ultraviolet spectrum of acrolein have been studied by a multireference perturbative treatment and by a time dependent density functional approach. The valence and Rydberg transition energies have been calculated and the assignment of the experimental bands has been clarified. The different relaxation trends of the three lowest singlet and triplet excited states have been analyzed by unconstrained geometry optimizations. This has allowed, in particular, the characterization of a twisted 3(*) state, which is crucial for the interesting photophysics and photochemistry of the acrolein molecule and, more generally, of the ,-enones. Solvatochromic shifts in aqueous solution have been investigated using a combined discrete/continuum approach based on the so called polarizable continuum model. The experimental trends are well reproduced by this approach and a closer degeneracy in the triplet manifold has been detected in solution with respect to gas phase. ©2003 American Institute of Physics
On the electronic structure of the UO2 molecule
No full textThe structure and vibrational frequencies of the UO2 molecule have been determined using multiconfigurational wave functions (CASSCF/CASPT2), together with a newly developed method to treat spin-orbit coupling. The molecule has been found to have a (5f phi)(7s), (3)Phi (u), Omega = 2 ground state with a U-O bond distance of 1.77 Angstrom. The computed antisymmetric stretching a. frequency is 923 cm(-1) with a 16/18 isotope ratio of 1.0525 which compares with the experimental values of 915 cm(-1) and 1.0526, respectively. Calculations of the first adiabatic ionization energy gave the value 6.17 eV, which is 0.7 eV larger than the currently accepted experimental result. Reasons for this difference are suggested
The electronic spectrum of the UO2 molecule
No full textThe electronic spectrum of the UO2 Molecule has been determined using multiconfigurational wave functions together with the inclusion spin-orbit coupling. The molecule has been found to have a (5fphi)(7s), (3)Phi(2u), ground state. The lowest state of gerade symmetry, H-3(4g), corresponding to the electronic configuration (5f)(2) was found 3330 cm(-1) above the ground state. The computed energy levels and oscillator strengths were used for the assignment of the experimental spectrum in the energy range 17000-19000 and 27000-32000 cm(-1)
On Some Optimization Problems that Can Be Solved in O(n) Time
No full textWe consider nine elementary problems in optimization. We simply explore the conditions for optimality as known from the duality theory for convex optimization. This yields a quite straightforward solution method for each of these problems. The main contribution of this paper is that we show that even in the harder cases the solution needs only O(n) time.Accepted author manuscriptDiscrete Mathematics and Optimizatio
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