Within the framework of an adequate spectral representation, the geometrical description of an N-atom molecular system by n=N−1 Jacobi relative position vectors is shown to be particularly advantageous with regard to the criterion of prediagonalization of the matrix representing the kinetic energy operator.

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Articles you may be interested inA multidimensional pseudospectral method for optimal control of quantum ensembles A classical determination of vibrationally adiabatic barriers and wells of a collinear potential energy surfaceWe describe a new algorithm for computing eigenvalues, spectral intensities, and selected eigenvectors of multidimensional vibrational potential surfaces. The method involves a synthesis of pseudospectral and sequential adiabatic reduction methods and merges the storage and computational advantages of the former with the improved basis set generated by the latter. The recursive residue generation method, which utilizes a Lanczos-based diagonalization procedure, is employed to calculate the observables. As a test case, we apply the method to computation of the infrared and stimulated emission pumping spectra for the HCN molecule and demonstrate a very large (one to three orders of magnitude) reduction in computational effort (for comparable accuracy) as compared to discrete variable representation (DVR)/adiabatic reduction or standard collocation approaches. We expect that this advantage will be increased considerably for larger (e.g., tetra-atomic) systems and will permit accurate basis set calculations on such systems to be carried out in a straightforward fashion.324

Within the framework of adapted coupled-angular-momentum spectral representations, the geometrical description of a four-atom molecular system by three Jacobi relative position vectors is shown to result in matrices representing the kinetic energy operator, prediagonalized to a very large extent. A fully diagonal representation is built for the angular ͑internal and rotational͒ part of the problem.

A methodology for the calculation of high energy vibrational eigenstates of S0 acetylene is described. Acetylene is modeled as a 5D planar molecule. The discrete variable representation (DVR) is employed for radial coordinates with a finite basis representation (FBR) for the angular coordinates. Symmetry adaptation of the primitive basis (dimension 2.7 × 106) coupled with a two level diagonalization/truncation scheme maintains relatively small basis sets (< 2500 functions) in all diagonalizations. Eigenvalues up to nearly 3700 cm−1 above the ground state are reported.

Even though there has been a proliferation of e-society measures in recent years, analyses of the metrics of the "information society" are still far from responsive to the needs of many stakeholders and continue to suffer from a number of serious limitations. Issues in eight critical areas are briefly presented. They include: definition of the universe to be measured; definition of the objects and phenomena to include in the universe; need to establish measurements based upon solid theories; units of measurements; data sources and collection; methods of analysis and construction of indicators; target audiences; and purpose and utilization of measurements. An organized collective effort, which could provide the impetus for the development of a coherent academic field of study, is called for to address this "grand challenge."

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