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A b initio averaged relativistic effective core potentials (AREP) and spin–orbit (SO) operators are reported for the elements Cs through Rn. Two sets have been calculated for certain elements to provide AREPs with varying core/valence space definitions thereby permitting the treatment of core–valence correlation interactions. The AREPs and SO operators are tabulated as expansions in Gaussian-type functions (GTF). GTF valence basis sets for the lowest energy state of each atom are tabulated. The reliability of the AREPs and SO operators is gauged by comparing calculated atomic excitation energies and SO splitting energies with all-electron relativistic values. Calculated atomic excitation energies are found to agree to 0.12 eV and SO energies to 3.4%.

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Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and

This work addresses the construction of slow manifolds for chemically reactive flows. This construction relies on the same decomposition of a local eigensystem that is used in formation of what are known as Intrinsic Low Dimensional Manifolds ͑ILDMs͒. We first clarify the accuracy of the standard ILDM approximation to the set of ordinary differential equations which model spatially homogeneous reactive systems. It is shown that the ILDM is actually only an approximation of the more fundamental Slow Invariant Manifold ͑SIM͒ for the same system. Subsequently, we give an improved extension of the standard ILDM method to systems where reaction couples with convection and diffusion. Reduced model equations are obtained by equilibrating the fast dynamics of a closely coupled reaction/convection/diffusion system and resolving only the slow dynamics of the same system in order to reduce computational costs, while maintaining a desired level of accuracy. The improvement is realized through formulation of an elliptic system of partial differential equations which describe the infinite-dimensional Approximate Slow Invariant Manifold ͑ASIM͒ for the reactive flow system. This is demonstrated on a simple reaction-diffusion system, where we show that the error incurred when using the ASIM is less than that incurred by use of the Maas-Pope Projection ͑MPP͒ of the diffusion effects onto the ILDM. This comparison is further done for ozone decomposition in a premixed laminar flame where an error analysis shows a similar trend.