1. MODELING SPIN-ORBIT COUPLING IN THE HALOCARBENES
PHALGUN LOLUR1, RICHARD DAWES1, SILVER NYAMBO2, SCOTT REID2
1 Department of Chemistry, Missouri University of Science and Technology
2 Department of Chemistry, Marquette University
Friday, June 26,2015.

2. Outline Halocarbenes Spin-Orbit Coupling Methods
Results and Discussion
Conclusions
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3. Outline Halocarbenes Spin-Orbit Coupling Methods
Results and Discussion
Conclusions
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4. Halocarbenes
Carbenes – Two-coordinate carbon compounds that have two nonbonding electrons and no formal charge on carbon (R1R2C: )
Non-bonding electrons either spin-paired (singlet) or unpaired (triplet)
Halocarbenes have the general formula RXC: or X1X2C:
Reactivity of carbenes has been extensively studied as they are central to understanding reactive intermediate organic chemistry
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5. Singlet vs. Triplet Reactivity
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Skell, S.; Woodworth, R. C. J. Am. Chem. Soc., 1956, 78, 4496.

6. Schematic representations of the three lowest singlet (S0, S1 and S2) and lowest triplet (T1) state of a triatomic carbene XYC:
Which of the configurations (singlet vs. triplet) is lower in energy? What is the gap between them, and
how is it controlled by substituent-dependent steric and electronic affects?
Historically, theory and experiment have been coming together
H. F. Schaefer III, Science 231, 1100 (1986).
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7. Potential energy curves for four lowest states of :CHBr from an MRCI/cc-pVTZ calculation
These states form a Renner–Teller (RT) pair that is degenerate in the linear configuration (Figure 2), and the RT effect refers to the strong nonadiabatic interaction between these states that is maximal near the barrier to
linearity. The large change in bond angle also leads to axis-tilting and the appearance of forbidden sub-bands, which was recognized in the very first rotationally resolved spectra of the halocarbenes
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Kable et. al., International Reviews in Physical Chemistry, 2009, 28(3),

8. Outline Halocarbenes Spin-Orbit Coupling Methods
Results and Discussion
Conclusions
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9. Spin-orbit Coupling Responsible for the fine-structure of atomic lines
Interaction between μl and μs
Relativistic effect – gets bigger for heavier systems
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Michael Chapman & Carlos Sá de Melo. Nature 471, 41–42 (03 March 2011)

10. 2D plot of lowest 1A’, 1A” and 3A” states of CHCl
The two singlets are degenerate for collinear geometries (Theta = 180◦) forming a Renner-Teller pair.
The lowest 3A′′ triplet state (transparent) cuts through ground state singlet not far from the minimum and is lower than the singlets for collinear geometries.
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11. Outline Halocarbenes Spin-Orbit Coupling Methods
Results and Discussion
Conclusions
11/14/2018

12. Methods
MRCI-F12/VQZ-F12 and CCSD(T)-F12/VQZ-F12 methods were used to optimize the geometries
Peterson’s new PP F12-bases were used for Bromine and Iodine
Singlet-triplet gaps were predicted at the VnZ-F12 and VnZ-PP-F12 levels (n = 2-4).
Vibrational frequencies and mass-weighted normal mode displacements (i.e., ℓ-matrices) were computed with CCSD(T)-F12 and MRCI-F12 methods using the VQZ-F12 basis set.
Several DFT (B3LYP, M06, and M06-2X) and other post-Hartree-Fock (e.g., MP2) methods were tested for comparison.
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13. Building the Hamiltonian
Diagonal elements– The unperturbed anharmonic vibrational term energies of the singlet and triplet states in the absence of spin-orbit coupling were given by
Off-diagonal blocks – Spin-orbit coupling matrix elements
Model 1
Model 2
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14. Hamiltonian
Singlet vibrational term energies, given by the Dunham Expansion
SO Coupling Matrix Elements
Triplet vibrational term energies, given by the Dunham Expansion
SO Coupling Matrix Elements
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15. Methods Model 1 parameters: Model 2 parameters:
Calculated harmonic frequencies (6)
Anharmonic constants (12)
Spin-Orbit constant
Singlet-Triplet gap
Model 2 parameters:
Geometry dependence of spin-orbit
coupling is explored in this model
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16. Schematic diabatic one-dimensional picture of spin-orbit coupling in the halocarbenes~
(Model 1)
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Talk about parameters optimized and flexibilities for both models
For Model 2, the spin-orbit matrix elements were evaluated by full 3D integration over fitted geometry dependent spin-orbit coupling surfaces.

17. Contour plots showing the geometry dependence of spin-orbit coupling values in CH(D)I.
Coupling values (units of cm−1) vary slightly with the RC–I coordinate in
addition to the bend, but negligibly with the RC–H coordinate.
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18. Calculated Franck-Condon factors describing the overlap of the T1 origin with various S0 levels in CHI
(0,2,0)
Square of vibrational overlap
(0,3,0)
(0,1,0)
MRCI-F12/VQZ-F12
(0,4,0)
(0,0,0)
(1,2,0)
(1,1,0)
(1,3,0)
(1,0,0)
Wavenumber relative to triplet origin (cm-1)
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19. Outline Halocarbenes Spin-Orbit Coupling Methods
Results and Discussion
Conclusions
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20. Assignments of the observed energy levels for CHI
Energies are in cm−1. Levels in red are associated with the triplet state.
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21. Mean Average Deviation (MAD) Summary
Species
Model 1 MAD (cm-1)
Model 2 MAD (cm-1)
CHI
2.5
4.3
CDI
4.6
CHBr
3.4
5.7
CDBr
3.2
CHCl
2.1
2.0
CDCl
1.7
Our (Model 1) fit to 53 levels derived from SVL emission and SEP measurements yielded a MAD of 2.1 cm−1 in CHCl, which is a more than twofold improvement over a simple Dunham expansion fit to the observed singlet levels.
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22. Calculated and fit CHI and CDI vibrational frequencies in cm−1
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23. Calculated and fit CHBr and CDBr vibrational frequencies in cm−1
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24. Calculated and fit CHCl and CDCl vibrational frequencies in cm−1
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25. Calculated singlet-triplet gaps for CHI, CHBr and CHCl and comparison with both the models in cm-1
Model 1 ΔEST –
Method/Basis
VDZ-PP-F12
VTZ-PP-F12
VQZ-PP-F12
MRCI-F12
CCSD-F12
Model 2 ΔEST –
CHBr
Method/Basis
VDZ-PP-F12
VTZ-PP-F12
VQZ-PP-F12
MRCI-F12
CCSD-F12
Model 1 ΔEST –
Model 2 ΔEST –
CHCl
Method/Basis
VDZ-F12
VTZ-F12
VQZ-F12
MRCI-F12
CCSD-F12
Model 1 ΔEST –
Model 2 ΔEST –
Method/Basis
CVDZ-F12
CVTZ-F12
CVQZ-F12
(AE) MRCI-F12
(AE) CCSD-F12
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26. Energy level diagrams for CHBr in the 3700–4900 cm−1 region
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27. Correlation of derived CH(D)X spin-orbit coupling constants (model 1) with the experimental values of the corresponding halogen atoms
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28. Outline Halocarbenes Spin-Orbit Coupling Methods
Results and Discussion
Conclusions
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29. Conclusions Many new assignments were possible
Improved experimental values for the singlet-triplet gaps were calculated for comparison with theoretical predictions
Detailed information on derived spin-orbit coupling constants is provided
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30. Acknowledgements Dawes Research group: Richard Dawes Moumita Majumder
Steve Ndengue
Andrew Powell
Collaborators:
Scott Reid, Marquette
Silver Nyambo, Marquette
Department of Chemistry, Missouri S&T
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