1. International Symposium on Molecular Spectroscopy
63rd Meeting - - June 15-20, 2008
Shortcomings of a Reduced-Dimension Potential Surface: PIMC Simulation of Vibrational Shifts for CO2 in Hen Clusters Hui Li, Robert J. Le Roy, Nicholas Blinov, and Pierre-Nicholas Roy υ

2. Background
Spectroscopic studies of OCS, N2O, CO2 as dopant molecule embedded in small helium cluster
Microscopic understanding of macroscopic superfluidity, a collective bulk property and nanodroplets
J. Tang, Y. Xu, A. R. W. McKellar and W. Jager
Science 297, 2030 (2002)
J. P.Toennies and A. F. Vilesov, Angew. Chem, Int. Ed. 43, 2622 (2004)

3. Experiment
Observed discrete spectra, inertial constants and vibrational frequency shifts for CO2-HeN in region
J. Tang, A. R. M. McKellar F. Mezzacapo, and S. Moroni, Phys. Rev. Lett. 92, (2004)
J. Tang and A. R. M. McKellar, J. Chem. Phys. 121, 181 (2004)
A. R. M. McKellar, J. Chem. Phys. 128, (2008)

4. Theoretical Simulation
Simulating vibrational shift
1) Ʋ3 vibrational band of CO2 is perturbed by its
surroundings.
2) Influence of the surrounding He atoms is
determined by the total perturbing potential:
3) In first-order perturbation theory, the shift of
ground and first excited states are given by:
4) Band origin shifts is:
D. Eichenauer and R. J. Le Roy, Phys. Rev. Lett. 57, 2920 (1986)
D. Eichenauer and R. J. Le Roy, J. Chem. Phys. 88, 2898 (1988)

5. Potential Energy Surface
Previous 2-D PES
1) Adequate approximation for MW spectra of ground
state, but not for IR spectra involving vibrational
excitation of CO2 component
2) Most PES fit to an ESMMSV or HFD forms.
RMS residual cm-1.
1) Vibrational shift simulation needs a PES involving
vibrational stretching of the CO2 in the complex.
2) A new analytic 3-D MLR PES which explicitly
incorporates the Q3 asymmetric-stretch coordinate of
CO2 has been obtained.
3) Least-squares fit to 2832 points has a RMS
deviation of cm-1 using only 55 parameters.
4) However, Q1 normal mode coordinate was fixed
by ground-state (0,0,0) average C-O bond length r0
Recent 3-D PES
H. Li and R. J. Le Roy, Phys. Chem. Chem. Phys. DOI: /b800718g (2008)

6. 2-D MLR vibrationally averaged PES
Total wave function is a direct product
Vibrational wave function of CO2 obtained from
Vibrationally averaged He-CO2 potential is
For our 2-D MLR fitting, the RMS deviation is cm-1
and requires only 24 parameters

7. Path integral Monte Carlo
Hamiltonian for CO2 solvated in a He cluster
Canonical average of for any physical property can be evaluated as an matrix element of the density matrix
The vibrational band origin shift could be given by: or
D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995)
D. Marx and M. H. Muser, J. Phys.: Condens. Matter. 11, R117 (1999)
N. Blinov, X. G. Song, P.-N. Roy J. Chem. Phys. 128, (2004)
D. Eichenauer and R. J. Le Roy, J. Chem. Phys. 88, 2898 (1988)

8. Calculating the band origin shift
Ev=1=-17.94(3)
Ev=0=-18.07(5)
~100 times faster

9. Band origin shifts in CO2-Hen clusters
unmorphed ΔV
experiment

10. Band origin shifts in CO2-Hen clusters
morphed ΔV
experiment

11. Can we ignore the Q1 coordinate ?
Relationship between Q1 and Q3
Q1 is different for (0,0,0) and (0,0,1)
Calc.-Exp.(cm-1)
δ(Δv0)
RMS of 49 IR transitions
unmorph- MLR
0.0445
morphed-MLR
0.0142
0.0038
New-
MLR
0.0224
H. Li and R. J. Le Roy, Phys. Chem. Chem. Phys. DOI: /b800718g (2008)

12. Band origin shifts in CO2-Hen clusters
unmorphed ΔV
experiment

13. Compare calculate using different ΔV
experiment

14. Explaining the different behaviors

15. Explaining the different behaviors
experiment

16. Explaining the different behaviors

17. Explaining the different behaviors
experiment

18. Conclusions
Simulations on our new 2-D surfaces which depend on Q1 give excellent agreement with experimental shifts for n=1-40.
But … to obtain this good agreement, it was essential to take account of the associated change in the average value of Q1, which occurs because of anharmonic inter-mode coupling.
In generally, this implies that any attempt to provide a reduced-dimension treatment of interactions involving polyatomic mode must take account of degrees of freedom other than those of direct interest, if the average values of those coordinates change significantly on excitation of the mode of interest.

19. Acknowledgments
Prof. M. Nooijen and Prof. F. R. W. McCourt (University of Waterloo)
Dr. A. R. W. McKellar (NRC)
Research supported by the Natural Sciences and Engineering Research Council of Canada

20. unmorphed ΔV
experiment

21. Compare calculated ΔƲ0 using different ΔV
experiment

22. Can we ignore the Q1 coordinate ?
Relationship between Q1 and Q3
Calc.
Cac.-Exp.
Ʋ3 transition (cm-1)
68.73
27.43
6.74
δ(ΔƲ0) and RMS of IR transitions
unmorph- MLR
0.0445
morphed-MLR
0.0142
0.0038
New-MLR
0.0224
Q1 is different for (0,0,0) and (0,0,1)
H. Li and R. J. Le Roy, Phys. Chem. Chem. Phys. DOI: /b800718g (2008)