In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro's, Nakatsuji's and Mazziotti's approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation.

In this work a new method to calculate anharmonic vibrational ground and excited state energies is proposed. The method relies on the auto-adjusting perturbation theory (APT) which has been successfully used to diagonalize square matrices. We use as zeroth order correction the self-consistent vibrational energies, and with the APT approach we calculate the vibrational anharmonic correlation correction to any desired order. In this paper we present the methodology and apply it to a model system and formaldehyde. Vibrational APT approach shows a robust convergent behavior even for the states where the standard (Rayleigh-Schrödinger) vibrational Møller-Plesset perturbation theory is clearly divergent.

SNB represents a helpful tool for detection of attention deficits, and RT indices represent the most significant variable in differentiation of both groups studied.

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A simple, three-dimensional, unstructured grid generation system is discussed and relevant results for turbomachinery and exhaust systems applications are presented. The method makes special emphasis in algorithm selection based in a small development effort to grid quality ratio. Engineering decisions based on state of the art grid technology knowledge have been adopted to balance fast development progress and turnover time. The system is based in the sequential execution of Advancing Front and a Delaunay algorithms to produced solution adapted meshes. In a first step a coarse background grid is created by the Advancing-Front method. During this phase boundaries are strictly preserved due to the nature of the approach. At this stage a Delaunay algorithm is employed and the boundary faces are blocked so that they cannot be destroyed in further triangulations. Since both techniques collaborate in the solution of the problem it is possible to write simplified versions of the algorithms that retain nearly all the benefits and eliminate most of the troubles while keeping still reasonable performances.