10 research outputs found
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
Multiple solutions of coupled-cluster equations for PPP model of [10]annulene
Multiple (real) solutions of the CC equations (corresponding to the CCD, ACP
and ACPQ methods) are studied for the PPP model of [10]annulene, C_{10}H_{10}.
The long-range electrostatic interactions are represented either by the
Mataga--Nishimoto potential, or Pople's R^{-1} potential. The multiple
solutions are obtained in a quasi-random manner, by generating a pool of
starting amplitudes and applying a standard CC iterative procedure combined
with Pulay's DIIS method. Several unexpected features of these solutions are
uncovered, including the switching between two CCD solutions when moving
between the weakly and strongly correlated regime of the PPP model with Pople's
potential.Comment: 5 pages, 4 figures, RevTeX
Prediction Properties of Aitken's Iterated Delta^2 Process, of Wynn's Epsilon Algorithm, and of Brezinski's Iterated Theta Algorithm
The prediction properties of Aitken's iterated Delta^2 process, Wynn's
epsilon algorithm, and Brezinski's iterated theta algorithm for (formal) power
series are analyzed. As a first step, the defining recursive schemes of these
transformations are suitably rearranged in order to permit the derivation of
accuracy-through-order relationships. On the basis of these relationships, the
rational approximants can be rewritten as a partial sum plus an appropriate
transformation term. A Taylor expansion of such a transformation term, which is
a rational function and which can be computed recursively, produces the
predictions for those coefficients of the (formal) power series which were not
used for the computation of the corresponding rational approximant.Comment: 34 pages, LaTe
Scalar Levin-Type Sequence Transformations
Sequence transformations are important tools for the convergence acceleration
of slowly convergent scalar sequences or series and for the summation of
divergent series. Transformations that depend not only on the sequence elements
or partial sums but also on an auxiliary sequence of so-called remainder
estimates are of Levin-type if they are linear in the , and
nonlinear in the . Known Levin-type sequence transformations are
reviewed and put into a common theoretical framework. It is discussed how such
transformations may be constructed by either a model sequence approach or by
iteration of simple transformations. As illustration, two new sequence
transformations are derived. Common properties and results on convergence
acceleration and stability are given. For important special cases, extensions
of the general results are presented. Also, guidelines for the application of
Levin-type sequence transformations are discussed, and a few numerical examples
are given.Comment: 59 pages, LaTeX, invited review for J. Comput. Applied Math.,
abstract shortene
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 of partial sums, but also explicit estimates
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
Fast and robust registration of PET and MR images of human brain
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