International Symposium on Molecular Spectroscopy

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Presentation transcript:

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

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)

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, 145503 (2004) J. Tang and A. R. M. McKellar, J. Chem. Phys. 121, 181 (2004) A. R. M. McKellar, J. Chem. Phys. 128, 044308 (2008)

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)

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 1.0-8.0 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 0.032 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:10.1039/b800718g (2008)

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 0.015 cm-1 and requires only 24 parameters

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, 044308 (2004) D. Eichenauer and R. J. Le Roy, J. Chem. Phys. 88, 2898 (1988)

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

Band origin shifts in CO2-Hen clusters unmorphed ΔV experiment

Band origin shifts in CO2-Hen clusters morphed ΔV experiment

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 -0.0299 0.0445 morphed-MLR 0.0142 0.0038 New- MLR -0.0019 0.0224 H. Li and R. J. Le Roy, Phys. Chem. Chem. Phys. DOI:10.1039/b800718g (2008)

Band origin shifts in CO2-Hen clusters unmorphed ΔV experiment

Compare calculate using different ΔV experiment

Explaining the different behaviors

Explaining the different behaviors experiment

Explaining the different behaviors

Explaining the different behaviors experiment

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.

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

unmorphed ΔV experiment

Compare calculated ΔƲ0 using different ΔV experiment

Can we ignore the Q1 coordinate ? Relationship between Q1 and Q3 Calc. Cac.-Exp. Ʋ3 transition (cm-1) 2417.87 68.73 2376.57 27.43 2355.88 6.74 0.390156 -0.000063 0.390031 0.002890 0.386954 -0.000187 δ(ΔƲ0) and RMS of IR transitions unmorph- MLR -0.0299 0.0445 morphed-MLR 0.0142 0.0038 New-MLR -0.0019 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:10.1039/b800718g (2008)