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In this paper we propose a new quadrature scheme for computing vibrational spectra and apply it, using a Lanczos algorithm, to CH3CN. All 12 coordinates are treated explicitly. We need only 157'419'523 quadrature points. It would not be possible to use a product Gauss grid because 33 853 318 889 472 product Gauss points would be required. The nonproduct quadrature we use is based on ideas of Smolyak, but they are extended so that they can be applied when one retains basis functions θn1(r1)...θnD(rD) that satisfy the condition α1n1 + ··· + αDnD <= b, where the αk are integers. We demonstrate that it is possible to exploit the structure of the grid to efficiently evaluate the matrix-vector products required to use the Lanczos algorithm. [ABSTRACT FROM AUTHOR]

Properties of ferrofluid bilayer (modeled as a system of two planar layers separated by a h and each layer carrying a soft sphere dipolar liquid) are calculated in the framework of inhomogeneous Ornstein-Zernike equations with reference hypernetted chain closure (RHNC). The bridge functions are taken from a soft sphere (1/r12) reference system in the pressure-consistent closure approximation. In order to make the RHNC problem tractable, the angular dependence of the correlation functions is expanded into special orthogonal polynomials according to Lado. The resulting equations are solved using the Newton-GRMES algorithm as implemented in the publicdomain solver NITSOL. Orientational densities and pair distribution functions of dipoles are compared with Monte Carlo simulation results. A numerical algorithm for the Fourier-Hankel transform of any positive integer order on a uniform grid is presented. [ABSTRACT FROM AUTHOR]