Diagonalization of large matrices: a new parallel algorithm.

On the basis of a dressed matrices formalism, a new algorithm has been devised for obtaining the lowest eigenvalue and the corresponding eigenvector of large real symmetric matrices. Given an N × N matrix, the proposed algorithm consists in the diagonalization of (N - 1)2 × 2 dressed matrices. Both sequential and parallel versions of the proposed algorithm have been implemented. Tests have been performed on a Hilbert matrix, and the results show that this algorithm is up 340 times faster than the corresponding LAPACK routine for N = 10(4) and about 10% faster than the Davidson method. The parallel MPI version has been tested using up to 512 nodes. The speed-up for a N = 10(6) matrix is fairly lineal until 64 cores. The time necessary to obtain the lowest eigenvalue and eigenvector is nearly 5.5 min with 512 cores. For an N = 10(7) matrix, the speed-up is nearly linear to 256 cores and the calculation time is 5.2 h with 512 nodes. Finally, in order to test the new algorithm on MRCI matrices, we have calculated the ground state and the π → π* excited state of the butadiene molecule, starting from both SCF and CASSCF wave functions. In all the cases considered, correlation energies and wave functions are the same as obtained with the Davidson algorithm.

Methyl vinyl ketone+OH and methacrolein+OH oxidation reactions: a master equation analysis of the pressure- and temperature-dependent rate constants.

High-level electronic structure calculations and master equation analyses were carried out to obtain the pressure- and temperature-dependent rate constants of the methyl vinyl ketone+OH and methacrolein+OH reactions. The balance between the OH addition reactions at the high-pressure limit, the OH addition reactions in the fall-off region, and the pressure-independent hydrogen abstractions involved in these multiwell and multichannel systems, has been shown to be crucial to understand the pressure and temperature dependence of each global reaction. In particular, the fall-off region of the OH addition reactions contributes to the inverse temperature dependence of the rate constants in the Arrhenius plots, leading to pressure-dependent negative activation energies. The pressure dependence of the methyl vinyl ketone+OH reaction is clearly more important than in the case of the methacrolein+OH reaction owing to the weight of the hydrogen abstraction process in this second system. Comparison of the theoretical rate constants and the experimental measurements shows quite good agreement.

Pressure dependence in the methyl vinyl ketone + OH and methacrolein + OH oxidation reactions: an electronic structure study.

High-level electronic structure calculations were carried out for the study of the reaction pathways in the OH-initiated oxidations of methyl vinyl ketone (MVK) and methacrolein (MACR). For the two conformers of MVK (called synperiplanar and antiperiplanar), the addition channels of OH to the terminal and central carbon atom of the double bond dominate the overall rate constant, whereas the abstraction of the methyl hydrogen atoms has no significant kinetic role. In the case of MACR, only the antiperiplanar conformer is important in its reactivity. In addition, the lower Gibbs free energy barrier for MACR corresponds to the aldehydic hydrogen abstraction reaction, which will be somewhat more favorable than the addition processes. The subtle balance between the different pathways (additions versus abstractions) serves to give an understanding of the pressure dependence of the rate constants of these tropospheric oxidation processes.

Ab initio study on the mechanism of the atmospheric reaction OH + O3-->HO2 + O2.

The atmospheric reaction (1) OH + O3-->HO2 + O2 was investigated theoretically by using MP2, QCISD, QCISD(T), and CCSD(T) methods with various basis sets. At the highest level of theory, namely, QCISD, the reaction is direct, with only one transition state between reactants and products. However, at the MP2 level, the reaction proceeds through a two-step mechanism and shows two transition states, TS1 and TS2, separated by an intermediate, Int. The different methodologies employed in this paper consistently predict the barrier height of reaction (1) to be within the range 2.16-5.11 kcal mol-1, somewhat higher than the experimental value of 2.0 kcal mol-1.

Ab initio study of the mechanism of the atmospheric reaction: NO2 + O3 --> NO3 + O2.

The atmospheric reaction NO2 + O3 --> NO3 + O2 (1) has been investigated theoretically by using the MP2, G2, G2Q, QCISD, QCISD(T), CCSD(T), CASSCF, and CASPT2 methods with various basis sets. The results show that the reaction pathway can be divided in two different parts at the MP2 level of theory. At this level, the mechanism proceeds along two transition states (TS1 and TS2) separated by an intermediate, designated as A. However, when the single-reference higher correlated QCISD methodology has been employed, the minimum A and the transition state TS2 are not found on the hypersurface of potential energy, which confirms a direct reaction mechanism. Single-reference high correlated and multiconfigurational methods consistently predict the barrier height of reaction (1) to be within the range 2.5-6.1 kcal mol(-1), in reasonable agreement with experimental data. The calculated reaction enthalpy is -24.6 kcal mol(-1) and the reaction rate calculated at the highest CASPT2 level, of k = 6.9 x 10(-18) cm(3) molecule(-1) s(-1). Both results can be regarded also as accurate predictions of the methodology employed in this article.

A theoretical ab initio study on the H(2)NO + O(3) reaction.

The deviation of the NH(2) pseudo-first-order decay Arrhenius plots of the NH(2) + O(3) reaction at high ozone pressures measured by experimentalists, has been attributed to the regeneration of NH(2) radicals due to the subsequent reactions of the products of this reaction with ozone. Although these products have not yet been characterized experimentally, the radical H(2)NO has been postulated, because it can regenerate NH(2) radicals through the reactions: H(2)NO + O(3) --> NH(2) + O(2) and H(2)NO + O(3) --> HNO + OH + O(2). With the purpose of providing a reasonable explanation from a theoretical point of view to the kinetic observed behaviour of the NH(2) + O(3) system, we have carried ab initio electronic structure calculations on both H(2)NO + O(3) possible reactions. The results obtained in this article, however, predict that of both reactions proposed, only the H(2)NO + O(3) --> NH(2) + O(2) reaction would regenerate indeed NH(2) radicals, explaining thus the deviation of the NH(2) pseudo-first-order decay observed experimentally.

An Ab initio study on the mechanism of the atmospheric reaction NH2 + O3-->H2NO + O2.

The atmospheric reaction NH2 + O3-->H2NO + O2 has been investigated theoretically by using MP2, QCISD, QCISD(T), CCSD(T), CASSCF, and CASPT2 methods with various basis sets. At the MP2 level of theory, the hypersurface of the potential energy (HPES) shows a two step reaction mechanism. Therefore, the mechanism proceeds along two transition states (TS1 and TS2), separated by an intermediate designated as Int. However, when the single-reference higher correlated QCISD and the multiconfigurational CASSCF methodologies have been employed, the minimum structure Int and TS2 are not found on the HPES, which thus confirms a direct reaction mechanism. Single-reference high correlated and multiconfigurational methods consistently predict the barrier height of the reaction to be within the range of 3.9 to 6.6 kcal mol-1, which is somewhat higher than the experimental value. The calculated reaction enthalpy is -67.7 kcal mol-1.

Ab Initio Study on the Mechanism of Tropospheric Reactions of the Nitrate Radical with Alkenes: Ethene.

A mechanism for the reaction of the NO(3) radical with the simplest alkene, ethene, is proposed. The mechanism involves three paths leading to three main different products: oxirane, ethanal, and nitric acid. The three paths start from the same initial intermediate, an NO(3)-ethene adduct. The calculated energy barriers show that the oxirane is the product kinetically more favored. Initial analysis of the potential energy surface was made at AM1 level. Then, the geometries and characterization of the found stationary points on the surface were refined at ROHF level with a 6-31G basis set. Further refinement was carried out at CASSCF level with the same basis set, and an active space was built with five active electrons in six active orbitals.