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Large-amplitude quantum mechanics in polyatomic hydrides. II. A particle-on-a-sphere model for
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Image of FIG. 1.
FIG. 1.

Convergence behavior for a POS model of (, ) as a function of . The POS ground-state energy is within of DMC predictions (dotted lines) by .

Image of FIG. 2.
FIG. 2.

POS convergence behavior for energies as a function of . The POS ground-state energy is compared against DMC predictions (dotted line).

Image of FIG. 3.
FIG. 3.

(a) rotational energies of levels with as a function of potential stiffness scale factor . (b) At higher resolution, centrifugal induced splittings of the nominally degenerate symmetric top levels for are shown for , which are considerably larger but match the qualitative patterns experimentally observed.

Image of FIG. 4.
FIG. 4.

Bending energies of as a function of the potential scale factor .

Image of FIG. 5.
FIG. 5.

Minimum energy paths for through the and transition states, separating the minima. Note the remarkable agreement between critical points for the 10D relaxed potential and the pairwise fit.

Image of FIG. 6.
FIG. 6.

Pair correlation functions for for from DMC calculations for a series of potential models: (a) 15D full potential, (b) the 10D relaxed potential, and (c) the pairwise-additive least-squares fit.

Image of FIG. 7.
FIG. 7.

Convergence of results for a POS potential as a function of . Though convergence in is clearly indicated, the POS ground state is still appreciably higher than the DMC predictions (dotted lines). CPU times for each of the values are also listed.

Image of FIG. 8.
FIG. 8.

Ground-state energies of as a function of the potential stiffness , calculated by DMC and POS with both the 10D (DMC, open squares) and pairwise (POS, dashed line) potentials. The inset demonstrates level of convergence of POS and DMC (pairwise) calculations as a function of . Note the excellent agreement between 10D and pairwise DMC calculations, further highlighting the surprising accuracy of the pairwise-additive potential approximation.

Image of FIG. 9.
FIG. 9.

The lowest eigenenergies (with respect to the ground state) as a function of potential stiffness ( to ) for each nuclear-spin symmetry with nonzero statistical weight [results for all symmetries available on EPAPS (Ref. 81)]. The trends in the POS energy-level patterns indicate a noteworthy absence of tunneling splitting behavior with increasing . This differs from rotation-contortion model results of Bunker and co-workers (Refs. 59, 61, and 80) (rightmost column), but is consistent with the delocalized wave functions, large zero-point energies, and small interconversion barriers inferred from DMC studies of Bowman and co-workers (Refs. 45, 76, and 79).

Image of FIG. 10.
FIG. 10.

(a) DMC pair correlation function of as a function of . (b) Successive fits of the pair correlation function of to a sum of Legendre functions. Such behavior suggests good convergence for the POS model of by .


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Table I.

Particle-on-a-sphere (POS) Legendre coefficients for expansion of the and potentials in a pairwise-additive approximation

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Table II.

critical point geometries and energies for the full 15D and 10D pairwise fit potentials.

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Table III.

Zero-point energies of as a function of scale factor , calculated with (i) DMC/nonpairwise 10D potential, (ii) DMC/pairwise potential, and (iii) POS/pairwise potential.

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Table IV.

Lowest five converged levels of each symmetry/nonzero statistical weight for a potential scaled by . Energies are in with residual convergence error (in parentheses) estimated as energy decrease with respect to the next smaller basis set. By comparison with DMC results, the absolute energies for are converged and for and 0.01, respectively.

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Table V.

Expectation values of energy (in ) for a 1D X–H rotor in the pairwise potential corresponding to , demonstrating systematic convergence to the rigid-body diffusion Monte Carlo result (RBDMC) with increasing .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Large-amplitude quantum mechanics in polyatomic hydrides. II. A particle-on-a-sphere model for XHn(n=4,5)