Near-dissociation states and coupled potential curves for the HeN+ complex

The near-dissociation microwave rovibronic spectra of HeN+ [Carrington et al., Chem. Phys. Lett. 262, 598 (1996)] are used to obtain coupled potential energy curves for the six electronic states correlating with He+N+ 3P0, 3P1, and 3P2. High-quality ab initio calculations are carried out, using a spin-restricted open-shell coupled-cluster method with an augmented correlation-consistent quintuple-zeta basis set (aug-cc-pV5Z). Fully coupled calculations of bound and quasibound states are performed, including all six electronic states, and suggest two possible assignments of the observed transitions. The potentials are then morphed (scaled) to reproduce the experimental frequencies. One of the two assignments, designated SH1, is preferred because it gives a more satisfactory explanation of the observed hyperfine splittings. The corresponding morphed potential has well depths of 1954 cm−1 and 192 cm−1 for the spin-free 3Σ− and 3Π curves, respectively

Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory

\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation which uses as input data not only the elements of a sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates $\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit incorporation of the information contained in the truncation error estimates makes this and related transformations potentially much more powerful than for instance Pad\'{e} approximants. Special cases of the new transformation are sequence transformations introduced by Levin [Int. J. Comput. Math. B \textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189 - 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A \textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations - explicit expressions, recurrence formulas, explicit expressions in the case of special remainder estimates, and asymptotic order estimates satisfied by rational approximants to power series - is formulated in terms of hitherto unknown mathematical properties of the new transformation introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of Mathematical Physic

The intermolecular potential energy surface of the He·NO+ cationic complex

Close-coupling calculations of bound rotational and vibrational states are carried out on a new intermolecular potential energy function based on 200 energies of the He·NO+ cationic complex calculated at the coupled-cluster single double (triple)/aug-cc-pV5Z ab initio level of theory at a range of geometries and point-by-point corrected for basis set superposition error. The potential energy function is constructed by combining the reciprocal power reproducing kernel Hilbert space interpolation with Gauss–Legendre quadrature. The best estimate of the intermolecular dissociation energy, De, is 198±4 cm–1, obtained by extrapolations to the complete basis set limit, and calculating estimates for relativistic effects and core and core-valence correlation effects