In this paper, we have computed the rovibrational spectrum of the H(3) (+) molecule using a new global potential energy surface, invariant under all permutations of the nuclei, that includes the long range electrostatic interactions analytically. The energy levels are obtained by a variational calculation using hyperspherical coordinates. From the comparison with available experimental results for low lying levels, we conclude that our accuracy is of the order of 0.1 cm(-1) for states localized in the vicinity of equilateral triangular configurations of the nuclei, and changes to the order of 1 cm(-1) when the system is distorted away from equilateral configurations. Full rovibrational spectra up to the H(+)+H(2) dissociation energy limit have been computed. The statistical properties of this spectrum (nearest neighbor distribution and spectral rigidity) show the quantum signature of classical chaos and are consistent with random matrix theory. On the other hand, the correlation function, even when convoluted with a smoothing function, exhibits oscillations which are not described by random matrix theory. We discuss a possible similarity between these oscillations and the ones observed experimentally.
ABSTRACT:The convergence behavior of the total energy with the increase of the basis set is analyzed in two-electron systems, H 2 and H + 3 , where the source of error is the basis set truncation. Extrapolation of total energy to the complete basis set limit is carried out with the exponential and inverse cubic power (or higher order) functional forms, as a function of the cardinal number X that describes the correlation consistent basis sets, used in this work. The ability of the different extrapolation schemes to generate accurate potential energy curves or surfaces, over a wide range of geometries, is examined, following the criteria outlined by Halkier et al. (Chem Phys Lett, 1999, 310, 385). Comparison with the most accurate potential energy curve and surface for the ground electronic state of H 2 (X 1 + g ) and H + 3 ( 1 A ), respectively, shows that a simple two point extrapolation with the quintuple and sextuple zeta correlation-consistent basis sets results yields to practically "spectroscopic accuracy." To assess the precision of the extrapolated potential energy surfaces, several properties are compared with the most accurate ones. As an example, the vibrational energies obtained with the extrapolated energies have an error of only a few tenths of a cm −1 .
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