Dependence of the three rotational constants of (in ) on the umbrella angle (in deg), shown together with the experimental gas phase average values and (Ref. 16, 17, and 26).
Cuts (in ) of the potential energy surface along the axis for and . The nitrogen atom is at , and when the molecule is not planar, the directions pointing toward and away from the H atoms are not identical. For , the potential is identical along and . Note that we have represented the cuts as a function of and indicated the direction towards the hydrogen atoms by “.”
Evolution of the blueshift of the umbrella mode, , in with the cluster size, as calculated from the first approximation (I) with vibrationally averaging over the umbrella mode of (open triangles) where this is represented by the double well potential . For comparison, we have also shown the values obtained within the second, adiabatic approximation described in Sec. III D using the same double well potential and including rotation (open circles).
Evolution of the tunneling splitting ratios and in % with the cluster size within the first approximation with the double well potential . The circles correspond to the ground state and the diamonds to the excited state.
The energy difference as a function of for . The line linking the triangles corresponds to a nonrotating ammonia molecule. The line connecting the open circles corresponds to a rotating molecule with the -dependent rotational constants, and the line with the asterisks corresponds to a rotating molecule having the experimental values. Note that the errors bars are smaller than the size of the symbols and that the stars and the open circles are nearly superimposed on this scale.
Evolution of the energy difference as a function of with cluster size , computed with a time step of and 2000 walkers in the ensemble. The error bars are smaller than the size of the symbols. For the smaller clusters, results with a time step of are not distinguishable on the scale of the figure.
Evolution of the blueshift (in ) with the cluster size using the second adiabatic approximation (II). Results obtained with the first double well potential are presented as open symbols and results obtained with as filled symbols.
Evolution of the tunneling splitting ratio , for the ground state (circles) and for the first excited vibrational state (diamonds) with cluster size , calculated with the second, adiabatic approximation (II). These results were obtained with a rotating molecule using both double well potentials (open symbols) and (filled symbols).
Renormalized POITSE correlation functions for cluster sizes ranging from to helium atoms as a function of imaginary time in a.u. The presented results correspond to an average over 4000–5000 decays using a time step of and an ensemble size of 2000 walkers. A magnification of the later time region is presented in the upper right corner with indication of the error bars for , 9, and 30.
Variation of the ratio between the correlation decays of Fig. 9 for various values and of the linear fit of the correlation decay for (i.e., ) as a function of the imaginary time. The left panel corresponds to computations made with an imaginary time step of , while the right panel corresponds to a time step of Similar results are obtained for the intermediate time step value of
Correspondence between the umbrella angle (in deg) and the distance (in a.u.) taking into account the change of the distance (in a.u.).
Fit parameters for Eq. (5) ( in deg, in a.u.).
Parameter values used for the He-He and trial wave functions in a.u.
Parameters (in a.u.) for the trial function and for the three projectors used in the POITSE calculations [cf. Eqs. (24) and (26).]
Experimental and theoretical (largest helium clusters) vibrational shifts (in ) and tunneling splittings reductions (in %). The results are obtained using the potential.
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