banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Blueshift and intramolecular tunneling of umbrella mode in clusters
Rent this article for


Image of FIG. 1.
FIG. 1.

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).

Image of FIG. 2.
FIG. 2.

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 “.”

Image of FIG. 3.
FIG. 3.

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).

Image of FIG. 4.
FIG. 4.

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.

Image of FIG. 5.
FIG. 5.

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.

Image of FIG. 6.
FIG. 6.

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.

Image of FIG. 7.
FIG. 7.

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.

Image of FIG. 8.
FIG. 8.

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).

Image of FIG. 9.
FIG. 9.

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.

Image of FIG. 10.
FIG. 10.

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


Generic image for table
Table I.

Correspondence between the umbrella angle (in deg) and the distance (in a.u.) taking into account the change of the distance (in a.u.).

Generic image for table
Table II.

Fit parameters for Eq. (5) ( in deg, in a.u.).

Generic image for table
Table III.

Parameter values used for the He-He and trial wave functions in a.u.

Generic image for table
Table IV.

Parameters (in a.u.) for the trial function and for the three projectors used in the POITSE calculations [cf. Eqs. (24) and (26).]

Generic image for table
Table V.

Experimental and theoretical (largest helium clusters) vibrational shifts (in ) and tunneling splittings reductions (in %). The results are obtained using the potential.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Blueshift and intramolecular tunneling of NH3 umbrella mode in Hen4 clusters