1. Variation of CH Stretch Frequencies with CH4 Orientation in the CH4--F- Complex: Multiple Resonances as Vibrational Conical Intersections
Bishnu P Thapaliya, The University of Akron
ISMS,U of Illinois, Champaign/Urbana, June 20-24, 2016
F -
Na+
David S Perry

2. Spectroscopy of CH4--F-
IR Spectrum: Z. M. Loh et al., J Phys Chem A, 110 (2006) D. A. Wild, Z. M . Loh, E. J. Bieske, International Journal of Mass Spectrometry, 220 (2002) 273.
Theory: G. Czako, B. J. Braams, J. M. Bowman, J Phys Chem A, (2008) R. Wodraszka, J. Palma, U. Manthe, J Phys Chem A, (2012) J. Palma, U. Manthe, Chem Phys, 137 (2012)
CH4--X-: M.Geleijns, P. E. S. Wormer, Ad Van derAvoird, Chem Phys, 117 (2002) J. M. Loh et al., J Phys Chem A, 109 (2005) D. A. Wild et al., Chem Phys Lett., 332 (2000) 531.
Fig.1 IR Spectrum of CH4--F-

3. Reaction of CH4(ν1 vs ν3) on Ni(111) Surface
Symmetric CH stretch reaction – faster than asymmetric CH stretch .
Adiabatic evolution of CH4 vibration on approach to the surface.
1. Behavior of the CH stretch vibrations as a function of orientation of methane in complex.
2. Adiabatic behavior of the CH stretches vibration.
Fig. 3 Calculated transition state geometry for CH4 on metal surface, Ni (111)
Fig. 2 One-D potential energy diagram for methane activation on metal surface, Ni (111)
D.R. Killelea, A. L. Utz, PCCP, 15 (2013)
L.B.F. Juurlink, D.R. Killelea, A. L. Utz, Progress in Surface Science 84 (2009)

4. Vibrational Adiabaticity
Adiabatic separation – Fast and slow degrees of freedom solve the fast motion at each point in (ρ,γ) space solve the slow motion on the potential formed by fast states.
Vibrationally adiabatic approximation.
Vibrational conical intersections – Hamm and Stock - at least 2 “slow” coordinates Zeroth-order splitting and coupling both zero ρ γ
F -
Different level of theory is used to calculate the CH stretches vibration when methane unit is approaches to Fluoride surfaces
P. Hamm and G. Stock, Phys. Rev. Lett. 109, (2012).
P. Hamm and G. Stock, Mol. Phys. 111, 2046 (2013). [Fig. 8] at left

5. Ab Initio Calculations on CH4--X-, X=F, Na
CH4--F-and CH4--Na+
CH stretch vibrations - as a functions ρ and γ.
B3LYP/ G (3df,2pd), MP2(=Full)/ G(3df,2pd) CCSD(T)/aug-cc-pVTZ
All other degrees of freedom optimized .
Symmetrized ρ and γ coordinates. ρ γ
F -
Different level of theory is used to calculate the CH stretches vibration when methane unit is approaches to Fluoride surfaces

6. Ab Initio Results for CH4--F- ρ γ F - MP2(full)/6-311++G(3df,2pd) A'

7. Level and Basis set comparison for CH4--F- Symmetry- required CIs
B3LYP/
G(3df,2pd)
MP2(full)/
CCSD(T)/
aug-cc-pVTZ
Symmetry- required CIs
54.74
125.26
Symmetry-allowed CIs
21.25
32.25
79.60
110.16
158.49
18.56
29.24
83.32
110.25
156.98
22.24
34.35
83.00
103.45
167.15
Avoided crossing
99.77
100.06
96.21

8. Ab Initio Results for CH4--Na+
MP2(full)/ G(3df,2pd) A'
A'' A'

9. Comparison between CH4- -Na+ and CH4- -F- Symmetry-required CIs
MP2(full)/ G(3df,2pd)
CH4- -F-
Global minima
125.26
54.74
Symmetry-required CIs
Symmetry-allowed CIs
33.00
105.28
18.56
29.24
83.32
110.25
156.98
Avoided crossing
100.06

10. A Jahn-Teller treatment of CH4--F-ρ γ F-
A Jahn-Teller treatment of CH4--F-
Vibrationally adiabatic basis
FAST: 4 CH stretch fundamental vibrations (A1+T2)
SLOW: Orientation (ρ , γ) of CH4 relative to F- (e)
FAST Hamiltonian: fast K.E. plus the whole potential energy:
SLOW Hamiltonian: slow K.E.

11. T2⨂e Jahn-Teller problemρ γ F-
Tetrahedral symmetry
T2⨂e Jahn-Teller problem
a1 terms:
e terms: j = ε, ϑ
t2 terms: k = x, y, z
Tetrahedral harmonics
Fit paramters: {αi, εi, τi}.

12. Fit Result of Ab Initio dataρ γ F-
Fit Result of Ab Initio data
C3v
C3v
C2v
C2v
C2v
C3v
C3v
Rms=0.65 cm-1

13. Fit Result of Ab Initio data
Electronic Potential Energy
Symmetric CH Stretch Vibrations
Rms=0.73 cm-1
Rms=0.47 cm-1

14. ρ γ F-
Conclusions
F- (or Na+) removes degeneracy of T2 CH stretch vibrations ( > 70 cm-1).
68 vibrational conical intersections in 4π steradians.
12 narrowly avoided crossings
All fit by a T2⨂e Jahn-Teller Hamiltonian expanded in spherical harmonics.