1. Tao Peng and Robert J. Le Roy
Quantitative Modelling of the Shifts and Splitting in the Infrared Spectra of SF6 in an Ar Matrix ‡
Tao Peng and Robert J. Le Roy
Guelph-Waterloo Centre for Graduate Work in Chemistry and Biochemistry, University of Waterloo
60th International Symposium on Molecular Spectroscopy, June 22, 2005
‡ Research supported by the Natural Sciences and Engineering Research Council of Canada

2. Introduction 15 (3N-6=15) vibrational modes
SF6: Octahedral molecule (Oh symmetry)
15 (3N-6=15) vibrational modes
normal mode: asymmetric stretching vibration triply degenerate

3. Introduction Frequency shifts and splitting
SF6 (gas phase): = 948 cm-1
SF6 in Ar matrix: unexpectedly large amount of structure, with 9-11 observed peaks
Monte Carlo simulation
Spectra Fitting
Experimental spectra for Ar/SF6=10,000; deposited at 10 K.
Lower : unannealed. Upper : annealed, 31K.1
1B. I. Swanson and L. H. Jones, J. Chem. Phys. 74, 3205 (1980)

4. Frequency Shifts (i=1-3) are the roots of
By 1st order perturbation theory:
(i=1-3) are the roots of

5. Instantaneous-dipole/induced-dipole (IDID) Mechanism
The SF6 molecule has no permanent dipole moment,
but when displaced from equilibrium, an instantaneous electric dipole moment arises …
Conclude: for any particular arrangement of perturbers, we can calculate the vibrational frequency shifts and splitting pattern.
Other models for the perturbation will give the same type of splitting patterns.

6. Vacancy Sites Site 1 Site 2 Site 3a Site3b
Yellow circles denote Ar atoms removed from FCC lattice to form vacancies for SF6.
Site Site Site 3a Site3b
Site 4a Site 4b Site 4c Site 5a

7. Flowchart of Simulation
Initial Configuration
Potential Calculation
MEQ: the maximum moves to equilibrate the system. In our simulation, the potential energy doesn’t decrease significantly after a relatively short run of ~1,000 moves/atom. Therefore, MEQ needn’t be very large.
MAV: the number of MC steps used to obtain the frequency shifts distribution. Tests considered between 30,000 moves/atom and 1,000,000 moves/atom.
Choose Particle
Move Particle
Ignore Trial Move
Potential Calculation No No
Random No. x
0 ≤ x ≤ 1
x ≤ e-ΔE/kT ?
ΔE ≤ 0 ? No
Yes No
Accept Move
Yes
MEQ ≤ moves ?
Yes
Calculate Shifts
MAV=moves ?
Yes
Results

8. Some Details of the Simulation
Ar atoms are initially in perfect FCC lattice positions. SF6 is initially at the center of the chosen vacancy site.
There are ~1,500 Ar atoms surrounding SF6.
SF6 is allowed to translate and rotate.
Inner Ar atoms are allowed to move during MC simulation. Outer ones are frozen in perfect FCC configuration. Convergence tests varied No. of moving atoms from ~55 to ~625.
The frequency shifts depend only upon the relative positions of Ar atoms and their distances from the center of mass of SF6.
The overall potential energy depends both on the orientation and the position of the SF6 molecule.
The overall potential energy is required for performing the MC simulation. It also helps determine the relative importance of the different possible lattice vacancy types.

9. Simulated Spectra
After the initial equilibration, frequency shifts are calculated at every move, i.e., every MC configuration gives us three sticks in the frequency shift axis.
After MAV ( ~108 ) moves, we count the No. of sticks within the same shift interval and obtain a distribution curve for this particular site.

10. Simulated Spectra
After the initial equilibration, frequency shifts are calculated at every move, i.e., every MC configuration gives us three sticks in the frequency shift axis.
After MAV ( ~108 ) moves, we count the No. of sticks within the same shift interval and obtain a distribution curve for this particular site.
The frequency shifts data were first fitted to a sum of Gaussians, using standard non-linear least-squares techniques.

11. No constraints Fix Peak Area Ratio 1:2
Peak Type Parameter Value Uncertainty
1 Gaussian position
width
height
2 Gaussian position
width
height
DSE=
Fix Peak Area Ratio 1:2
Peak Type Parameter Value Uncertainty
1 Gaussian position
width
height
2 Gaussian position
width
height
DSE=

13. Site 2 Presented a Problem
The expected area ratios of 1:1:1 or 1:2 or 2:1 or 3 are not found at first.
Two sub spectra were then obtained.

14. Results of Simulation

15. Because the calculated frequency shifts are smaller than experimental ones, the model clearly is not perfect. Some scaling correction will be necessary, such as
The total spectrum must be the linear combination of different sites:
A least-squares fit to the experimental spectrum was used to determine these parameters (A, B, p1 , p2a , p2b , … etc.).

16. Fit to the Experimental Spectrum
0.9597 B
-4.237
DSE
21.02
Site
Relative population 2a
0.46 2b
3.97 3a
7.25 3b
2.04
4a/b
0.63 4c
14.64 5a
4.37

17. Conclusion
Our fit shows that the observed spectrum is a linear combination of spectra for SF6 trapped in different types of lattice sites and the its peaks are assigned to different types of lattice sites.
Use of the IDID mechanism in a Monte Carlo averaging procedure successfully reproduces the experimental IR spectra for the vibrational band of SF6 in an Ar matrix.
The need for the ad hoc scaling and shifting of frequency shifts showing shortcomings of our frequency shift model should be addressed.
The effect of uncertainty in the Ar-SF6 potential function should be examined.

18. Thank You!

20. We sorted the frequency shifts into two groups based on the maximum peak separations, and we obtained the two plots:
The area ratios are found to be 2:1 and 1:2 , respectively, which is reasonable.