Convergence behavior for a POS model of (, ) as a function of . The POS ground-state energy is within of DMC predictions (dotted lines) by .
POS convergence behavior for energies as a function of . The POS ground-state energy is compared against DMC predictions (dotted line).
(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.
Bending energies of as a function of the potential scale factor .
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.
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.
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.
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.
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).
(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 .
Particle-on-a-sphere (POS) Legendre coefficients for expansion of the and potentials in a pairwise-additive approximation
critical point geometries and energies for the full 15D and 10D pairwise fit potentials.
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.
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.
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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